WO2012103843A2 - Method and device for using one multiplier to implement multiplication of complex numbers - Google Patents

Abstract

The present invention provides a method and a device for using one multiplier to implement multiplication of complex numbers. The method comprises: receiving a first complex number signal a+ci and a second complex number signal b+di, the first complex number signal and the second complex number signal being both digital communication signals; performing shift processing according to a first real part a and a first imaginary part c of the first complex number signal to acquire a first transformed value s, and performing shift processing according to a second real part b and a second imaginary part d of the second complex number signal to acquire a second transformed value t; according to the first transformed value s and the second transformed value t, performing calculation by using a multiplier to acquire a first reference value w1＝st; and acquiring the real part and the imaginary part of the product of the first complex number and the second complex number according to the first reference value w₁. The present invention further provides a corresponding device. The technical solutions of the present invention can overcome the disadvantage in the prior art that the utilization ratio of the multiplier is low.

Description

 Method and apparatus for implementing complex multiplication using a multiplier

 The present invention relates to digital signal processing techniques, and more particularly to a method and apparatus for implementing complex multiplication using a multiplier, which is in the field of communication technology. Background technique

 In the digital signal processing process in the field of communication technology, it is often necessary to multiply a large number of complex signals, and the above complex multiplication operations can be realized by a multiplier. For example, calculate the complex multiplication as follows:

 (a + ci) - (b + di) = (ab - cd ) -\- (ad + bc)i

According to the prior art scheme, four multipliers are required to calculate the values of ob, cd, ad, and be, respectively, and then calculate the values of ab - a and orf + b _C to obtain the final result.

 With the rapid development of computers and information technology, the amount of information that needs to be processed is increasing. When performing complex multiplication, a large number of multipliers are needed, and usually in data signal processing equipment, such as field programmable gate arrays. (Field - Programmable Gate Array, the following cartridge: FPGA), where the number of multipliers is limited, and a complex multiplication requires up to four multipliers. It can be seen that in the prior art, when complex multiplication is performed, there is a drawback that the multiplier is inefficiently utilized. Summary of the invention

 The present invention provides a method and apparatus for implementing complex multiplication using a multiplier for solving the drawbacks of low efficiency of multipliers existing in the prior art.

 The present invention provides a method for implementing complex multiplication using a multiplier, comprising: receiving a first complex signal α+α' and a second complex signal b+, the first complex signal and the second complex signal being communication digital signals ;

Performing a shift process according to the first real part of the first complex signal and the first imaginary part c to obtain a first transformed value S, and according to the second real part b and the second imaginary part d of the second complex signal Performing a shift process to obtain a second transformed value t; Calculating, by using the multiplier, the first reference value Mi = W according to the first transformed value S and the second transformed value ί;

 Obtaining a real part of a product of the first complex number and the second complex number according to the first reference value >, and an imaginary part of a product of the first complex number and the second complex number.

 The present invention also provides an apparatus for implementing complex multiplication by a multiplier, comprising: a first receiving module, configured to receive a first complex signal and a second complex signal b+^, the first complex signal and the second complex signal All are communication digital signals;

 a first acquiring module, configured to acquire a first transformed value S according to the first real part of the first complex signal and the first imaginary part c, and according to the second real part of the second complex signal b and the second imaginary part d are subjected to shift processing to obtain a second transformed value ί;

 a first calculating module, configured to calculate, according to the first transformed value S and the second transformed value ί, by using a multiplier to obtain a first reference value > H = w;

 a second acquiring module, configured to acquire, according to the first reference value >Η, a real part of a product of the first complex number and a second complex number, and an imaginary part of a product of the first complex number and the second complex number.

 A method and apparatus for implementing complex multiplication using a multiplier according to an embodiment of the present invention, by performing a complex multiplication, acquiring a first transformed value and a second transformed value according to a complex signal, and then performing calculation by using a multiplier to obtain a first reference value And further obtaining the real part -cd of the product of the first complex number and the second complex number according to the first reference value, and the imaginary part ^+bc of the product of the first complex number and the second complex number, the technical solution only needs to be The multiplier is used in calculating the first reference value, and only one multiplier is needed in the entire complex multiplication calculation process. Therefore, the technical solution of the present invention can effectively save the multiplier resources. DRAWINGS

 In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings to be used in the embodiments or the description of the prior art will be briefly described below, and obviously, the attached in the following description The drawings are some embodiments of the present invention, and other drawings may be obtained from those of ordinary skill in the art without departing from the scope of the invention.

 1 is a flow chart showing a method of implementing complex multiplication using a multiplier in an embodiment of the present invention;

2 is a schematic flow chart 1 of performing complex multiplication in a specific embodiment of the present invention; 3 is a schematic diagram 2 of a process for performing complex multiplication in a specific embodiment of the present invention;

 4 is a schematic diagram 3 of a process for performing complex multiplication in a specific embodiment of the present invention;

5 is a flow chart of another implementation of the complex multiplication calculation step shown in FIG. 3. FIG. 6 is a data structure diagram of a first reference value > 另一个 in another embodiment of the present invention; 7 is another embodiment of the present invention. + (2 ² "- ¹ ) data structure diagram

 8 is a schematic flow chart 4 of performing complex multiplication in a specific embodiment of the present invention

 9 is a schematic diagram of a process for performing complex multiplication in a specific embodiment of the present invention:

 10 is a schematic flow chart 6 of performing complex multiplication in a specific embodiment of the present invention

 11 is a schematic flow chart of performing complex multiplication in a specific embodiment of the present invention

 12 is a flow chart 8 of performing complex multiplication in a specific embodiment of the present invention; 13 is a schematic flowchart of performing complex multiplication in a specific embodiment of the present invention; 14 is a schematic flowchart of performing complex multiplication in a specific embodiment of the present invention.

 15 is a schematic flowchart 11 of the process of performing complex multiplication in a specific embodiment of the present invention; 16 is a schematic diagram of a process for performing complex multiplication in a specific embodiment of the present invention; 17 is a schematic flowchart of performing complex multiplication in a specific embodiment of the present invention. 18 is a schematic flow chart of performing complex multiplication in a specific embodiment of the present invention.

 19 is a schematic flowchart of performing complex multiplication in a specific embodiment of the present invention; FIG. 20 is a schematic flowchart of performing complex multiplication in a specific embodiment of the present invention.

 21 is a schematic flow chart of performing complex multiplication in a specific embodiment of the present invention.

 22 is a schematic flow chart of performing complex multiplication in a specific embodiment of the present invention

 23 is a schematic flowchart of performing complex multiplication in a specific embodiment of the present invention; FIG. 24 is a schematic flowchart of performing complex multiplication in a specific embodiment of the present invention.

 25 is a schematic flow chart of performing complex multiplication in a specific embodiment of the present invention. FIG. 26 is a schematic flowchart of performing complex multiplication in a specific embodiment of the present invention. FIG. 22 is a schematic flowchart of performing complex multiplication in a specific embodiment of the present invention. Twenty-three: 28 is a schematic structural diagram 1 of a device for implementing complex multiplication using a multiplier in the embodiment of the present invention;

 29 is a second schematic structural diagram of an apparatus for implementing complex multiplication using a multiplier according to an embodiment of the present invention;

30 is a structure of a device for implementing complex multiplication using a multiplier in an embodiment of the present invention Schematic three;

 Figure 31 is a fourth schematic diagram showing the structure of an apparatus for implementing complex multiplication using a multiplier in an embodiment of the present invention.

detailed description

 The technical solutions in the embodiments of the present invention are clearly and completely described in the following with reference to the accompanying drawings in the embodiments of the present invention. It is a partial embodiment of the invention, and not all of the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts are within the scope of the present invention.

 In the prior art, when performing multiplication calculation on a complex signal, it is required to use a large number of multipliers to cause a low utilization rate of the multiplier, and the present invention provides a technical solution in which a complex signal can be realized by using only one multiplier. multiplication.

 1 is a schematic flow chart of a method for implementing complex multiplication using a multiplier according to an embodiment of the present invention. As shown in FIG. 1, the method includes the following steps:

 Step 101: Receive a first complex signal α+d and a second complex signal b+^; wherein an absolute value of the first real part, the first imaginary part <^, the second real part b, and the second imaginary part d are less than or Equal to 2W - 1 , where is a positive integer, the first complex signal and the second complex signal are all communication digital signals; Step 102, according to the first real part of the first complex signal and the first imaginary part c The shift processing acquires the first transform value and performs shift processing according to the second real part b and the second imaginary part d of the second complex signal to obtain the second transform value ί;

 Step 103: Calculate, according to the first transformed value S and the second transformed value ί, by using a multiplier to obtain a first test value > H = W;

 Step 1 04: Acquire a real part of a product of the first complex number and a second complex number according to a first reference value >, and an imaginary part of a product of the first complex number and the second complex number.

The technical solution provided by the foregoing embodiment of the present invention, wherein when the complex multiplication is performed, the first transformed value and the second transformed value are obtained according to the complex signal, and then the first reference value is obtained by using a multiplier, and may further be based on the first The reference value obtains the real part of the product of the first complex number and the second complex number, and the imaginary part of the product of the first complex number and the second complex number. In the technical solution, only the multiplier is used in calculating the first reference value, and the whole complex multiplication is performed. Only one multiplication is needed in the calculation process The device can be implemented, and therefore, the technical solution of the present invention can effectively save multiplier resources. In the above embodiment of the present invention, the absolute values of the first real part, the first imaginary part c, and the second real part b and the second imaginary part d of the second complex signal are smaller than Or equal to 2"-1, where is a positive integer; and wherein the first transformed value s = a .2 ^2k ₊ c obtained according to the first complex signal, the second transformed value obtained according to the second complex signal i = ^ 2 ^M + ; and the first reference value >H = W = ^ · 2 ⁴ * + + fc) · 2 + .

In the above case, the second reference value may be further calculated according to the needs of the specific situation.

 In the embodiment of the present invention, for the first complex signal α+d and the second complex signal b+^, wherein the absolute values of the first real part, the first imaginary part 6, the second real part b, and the second imaginary part ^ Less than or equal to

2"-ι, ie |α|, Ι4Η, ≤ ^2Μ -ι, where is a positive integer. The absolute value is less than or equal to

The constraint of 2"-1 can be obtained for the first transformed value s = ^2 ² _{+ c} , and the second transformed value i = ^2 ² ₊ , whose absolute value is less than 2 - 1 , ie ^ - ¹ - ^^ ^ ¹ -^ ^ ¹ ^, Therefore, _s and ί are all signed integers of bits.

, 而由于 —2^k_¹+l<a,b,c,d<2^k_¹~L, 故可以得出： For the first reference value > Η, its value is taken as

, since -2 ^k _ ¹ +l<a,b,c,d<2 ^k _ ¹ ~L, it can be concluded that:

-(2" -l) < ab,ad,bc,cd < {l ^k ~ ^l -l)

-2(2 ^kl -if < ad + be <2(2 ^kl -if

 Thus the first equation is obtained:

0<_(2' ^c - ¹ _1) +(2 ² "-l)< cd + (2 ² ' ^c - ¹ _ 1) ≤ (2' ^c - ¹ _ 1) + (2 ² ' ^c - ¹ -l)< 2 ^2k - 1

0<_(2"_l) ² + (2 ² -\)< ab + (2 ² " _ 1) ≤ (2" - l) ² + (2 ² "-l)<2" -1

0<_2(2"_l) ² + (2 - ^l -\)< ad +bc + (2 ² "-l)< 2 (2 - ¹ - l) ² + (2 ² "-l)< 2 ² * -1 Second equation:

0 < _ (2 ^k - ¹ -l) ² + (2 ² " + 1) ≤ -cd + (2 - ¹ + 1) ≤ (2 ^k - ¹ - l) ² + (2 ² " + l) < twenty one

0 < _ (2 ^λ - ¹ -l) ² + (2 ² " + 1) ≤ -ab + (2 ² " + 1) ≤ (2 ^λ - ¹ -l) ² + (2 ² " + l) < twenty one

0< -2 (2 ^k - ¹ - I) ² + (2 ² " + l)< -(ad + (2 ² " + 1) ≤ 2 (2 ^λ - ¹ - l) ² + (2 ² " + l)<2" - 1 The right inequality of the last inequality in the above formula is due to ≥1, and the following equation is obtained according to the first equation above and the congruence property at =1, and the following congruence is obtained: _{= Mod (w 1 + (2} 2 "-l), 2 2λ) - (2 2" -ΐ)

 Where mod(a,b) represents an integer. The remainder obtained by dividing by the integer b (integer), and the remainder of the range is greater than or equal to 0 and less than or equal to b-1, ie. There is a unique decomposition: " = gb + mod(a,b), where is an integer.

Similarly, if the second reference value w ₂ =^^ is set, then it can be solved:

Ad +bc = mod (w ₂ + (2 ^2λ - ¹ - 1), 2 ^2λ ) - (2 ^2λ - ¹ - 1) Let the third reference value W _{3 =} ( ^W2 - ⁺ can be solved:

 2

Ab = mod (w ₂ + (2 ^2λ - ¹ - 1), 2 ^2k )- (2 ^2λ - ¹ - 1)

Specifically, when performing the complex complement calculation, the second reference value and the third reference value may be obtained according to the first reference value, and the product of the first imaginary part and the second imaginary part is further obtained according to the first reference value. When you can calculate it by the following method, if +^ ² ^ ¹ ^^. When the value of the lower bit of + (2 ² "- ¹ - 1) is obtained, the value of 2 ² " - 1 is subtracted from the value of α.

And by ιν _{1 +} (2 ^2ί: - ΐ ο, available:

- [w + (2 ^2λ - ¹ - 1)] = [-ab .2 ^2k - (ad + be)] .2 ^2k + ^-cd - (2 ^2λ - ¹ - 1)] > 0 , ie:

-[wj + (2 ² - ¹ - 1)] = [-ab · 2 ^2k - (ad + be) - 1] · 2 ^2k + [-c + (2 ² - ¹ + l)] >0

 Using the second equation, you can get:

O -cd + ^ ² "- ¹ +l)<2 ^2k -1

The non-negative number formed by the value of the lower bit of -[ ₊ ( ² -' -1)] is subtracted from the value of the opposite of the value of +1.

In addition, when the product of the first real part and the second imaginary part is obtained according to the second reference value w ₂ and the sum of the products of the first imaginary part and the second real part, the following may be specifically included, where ₂ + (2 ^2k - ¹ - 1) ≥ 0, obtain the non-negative number of the values of the low Ik bits of w ₂ + (2 ^2k - ¹ - 1) minus

The value of 2 ² " - 1 is the value of ad + bc.

And when _w2 + ( ²² wl) < 0, according to the second equation and the similar calculation described above, the non-negative number formed by the value of the lower bit of -[w ₂ + (2 ² "-l)] is subtracted + The opposite of the value of 1 is the value of ad+bc.

Obtaining the product of the first real part and the second real part according to the third reference value may specifically include the following content: First, when w ₃ +( ^22i: - ΐ^Ο, obtaining w ₃ +( ²² "-l The value of the lower bit is composed of a non-negative number minus the value of 2 ² " -1 is ^, when -Ι^Ο, according to the second For the equation and the similar calculation described above, the non-negative number formed by the value of the lower bit of -[^ + ( ² ^-1)] can be obtained by subtracting the value of 2 ² " + 1 from the opposite of the value of ab. The value of ab-cd can be obtained as the real part of the product of the first complex number and the second complex number.

Specifically, the calculation process of the above embodiment may be as shown in FIG. 2, FIG. 3 and FIG. 4, that is, first, in the first step, the values of ", c, b, d are input to the calculation in the form of complement code. In the device, where b is shifted to the left by 2 bits, and ^2 ² and ^2 ^{2 are obtained} , and further addition is performed to obtain a first transformed value s = ".2 ^M _{+ C} and a second transformed value i = fc .2 ^M ₊ , then use the multiplier to calculate to obtain the first reference value >H = st = ab-2 ^k + (ad + bc) - 2 ^2k + cd.

出参数 的值作为 的值。 进一步的， 可以计算

然后将 W₂进行向右移位处理， 得到 W₂=W₂/2。 在得到 上述的 w₂后， 可以再次利用 >¾执行上述步骤， 这次获得的参数 的值为 orf + be的值，并也可以进一步的计算 w₃ = w₂ - ,然后将 w₃进行向右移位处理， 得到 w₃=w₃/2 并进一步的， 将 ₃的值代入上述步骤， 其中得到的参数 的 值为 ab的值。 As shown in FIG. 3, in the second step, first inputting the above calculated >Η, and calculating the parameter VH+Z^-I, determining whether z<0 is established, if yes, taking the parameter 3⁄4=, and taking The parameter ν = _Μ [0: -1], the parameter is not true for the above formula, take the parameter v = z[0 : 2k-l] , the parameter

The value of the parameter is taken as the value. Further, it can be calculated

W _{2 is} then shifted to the right to obtain W ₂ = W ₂ /2. After obtaining the above w ₂ , the above steps can be performed again with >3⁄4, the value of the parameter obtained this time is the value of orf + be, and w ₃ = w ₂ - can be further calculated, and then w _{3 is} performed. The right shift process yields w ₃ = w ₃ /2 and further, the value of ₃ is substituted into the above step, wherein the value of the obtained parameter is the value of ab.

 After obtaining the values of ab and above, as shown in FIG. 4, in the third step, the real part r = b - of the product of the first complex number and the second complex number can be obtained by subtraction calculation, and the first complex number and the second The imaginary part of the product of the complex number i' = orf + bc.

 In the above complex calculation process, only one multiplier is needed, which can significantly reduce the number of multipliers used and avoid waste of resources compared to the prior art.

In addition, in the above embodiment, w ₂ +

(2^2i:- i-l^O和

(2 ^2i: - il^O and

In the case of +^ni^o, and considering the nature of the remainder, the above equations can be respectively added with the value ^·2, where is a positive integer, and ιν ₁₊ (2 ^2ί: - i -^ + . _≥0 ,

w ₂ + (2 ^2k - ¹ -l) + K _i -2 ^2k >0 , w ₃ +(2 ^2k - ¹ -l)+K _t -2 ^lk ≥0. At this time, according to the first reference value >H, the product cd of the first imaginary part and the second imaginary part is obtained, specifically, obtaining the low of ^ + (2 ^2k - ¹ -l) + K, · 2 ^2k

a non-negative number formed by the value of 2 bits minus a value of a value of 2 ² "-1; obtaining a product of the first real part and the second imaginary part according to the second reference value W ₂ , and the first imaginary part The sum of the products of the second real part, orf+b _C , is specifically obtained by taking the value of the lower 2k bits of w ₂ + (2 ² *- ¹ -l) + K _t · 2 ^2k Subtracting the value of 2 ¹ " - 1 from the value of ad + bc; obtaining the product ^ of the first real part and the second real part according to the third reference value W ₃ , specifically obtaining ^ + ^ Η - ^ + The value of the lower bit of ² is a non-negative number minus the value of 2 ² " - 1 is the value of ob.

For the above, the value of a single cartridge is such that the value is equal to 2" (there can be other values, only need to satisfy w _{1 +} (2 ² "_l) + i^2 ^2i: ≥ 0, ^ ₂ + (2 ^23⁄4 - ¹ -1)+^.-2 ^23⁄4 >0,

^+^^-^ + , · ² _≥Q can be), modify the calculation process shown in Figure 3 above, as shown in Figure 5, first input the above > Η, and further calculate the parameters

然后将 >¾进行向右 移位处理， 得到 w₂=w₂/2 在得到上述的 w₂后， 可以再次利用 >¾执行上述 步骤， 这次获得的参数 的值为 orf+b_c的值， 并也可以进一步的计算 w₃=w₂-x, 然后将 w₃进行向右移位处理， 得到 w₃=w₃/2 并进一步的， 将 w₃的值代入执行上述步骤， 其中得到的参数 的值为 Ob的值。 z = w ₁ +(2 ^2k - ¹ -l) + 2 ^6k , get the parameter v = _Z [0:2fc- 1] , and the parameter = _ν — 2 ² H+1, the value of the output parameter as the value, further Can be calculated

Then shift the processing to the right by >3⁄4 to obtain w ₂ =w ₂ /2. After obtaining the above w ₂ , the above steps can be performed again with >3⁄4, and the value of the parameter obtained this time is the value of orf+b _c And can further calculate w ₃ =w ₂ -x, then shift the w ₃ to the right to obtain w ₃ =w ₃ /2 and further, substituting the value of w ₃ into the above steps, wherein The value of the parameter is the value of Ob.

The embodiment of the present invention further provides another embodiment, that is, the above embodiment shows that: _(2- ¹ -if ≤ ab, ad, bc, cd ≤ (2 ^k - ¹ -if

-2(2" -l) ² ≤ad+bc≤ 2( 2- ¹ - 1) ²

 From the above two formulas can be obtained:

0<_(2- ¹ _1) ² +(2 ^3⁄4_1 ) < cd+{2 ^2k - ^l )≤{2 ^k - ¹ -if +{2 ^2k ~ ^l )≤ 2 ^2k -1 0<_(2- ¹ -l) ² +(2 - ≤"b+(2 - ≤(2- ¹ -l) ² +(2 ^3⁄4 - ¹ )<2 ^3⁄4 -1 0<- 2(2- ¹ -l) ² +{2 ^2k ~ ^l ) ≤ ad + bc + {2 ^2k - ^l ) ≤ 2 (2" -l) ² + {2 ^2k ~ ^l ) < 2 ^2k -1 From the congruence properties, the following congruence can be obtained:

Cd = mod(w _{1 +} (2 ^{2k l} ), 2 ^2λ )-(2 ² ") In addition, let _{W2 =} i^l, from which we can get: ad + bc = mod (w ₂ + (2 ^2λ - ¹ ), 2 ^2k ) - (2 ^2λ - ¹ )

Let (w ₂ — + bc)) , which gives you:

 2

^ = mod(w ₂ + (2 ^{M 1} ), 2 ^2k )-(2 ^2k - ¹ )

First consider the calculation of the product of the first imaginary part and the second imaginary part. The value of >Η can be represented as shown in Fig. 6, which includes from 0 to -1, a total of bits, Figure 6 is a signed integer, ^ is no The symbolic integer, W+^ ² — ¹ ) can be represented as shown in Fig. 7, where 1⁄4^ is a signed integer and w _t is an unsigned integer. In addition, the 0th to 2nd-2 bits of 1⁄4^ are the same as the 0th to 2-2th bits (numbered from low to high, and the lowest bit is 0), and the first of w _t - The 1 bit is opposite to the value of the -1 bit of >Η. Since >Η is an unsigned integer, you can get:

Mod(w ₁ + (2 ² "), 2 ^2k ) = w _L , ie crf ₌ w _£ _(2 ² ").

Wherein, signed integer, and ¼ ^ bits are 0 th to 2-2 and the first 0 to 2 - 2 of the same bit, and 2k _1 W _t of the first bit and cd 2k _1 The bits are reversed and thus are signed integers with the same bit representation. In addition, consider the calculation of >3⁄4, which is transformed by _W2 = ^l:

'cd + 2 ΗΊ + 2 )-w _L w _H .2 ^2k +w, Complement-based addition, you can get:

 in case

If 2k-1 bit (minimum

Bits are numbered starting from 0).

Where ν „ = _{W l} [6 k - l : 2 k ] , Μ : — 1: ] represents the value from the first to the 6th - 1st bit. In this embodiment, only the second reference value is required to obtain the second The reference value _W2 = i^^l, and the product cd of the first imaginary part and the second imaginary part is obtained according to the first reference value > ::

 Get the value of the signed integer (which may be negative, the same below) with the value of the lower bit;

 Then obtaining a product of the first real part and the second imaginary part according to the second reference value, and a sum of products of the first imaginary part and the second real part orf + :

 Obtain a signed integer with the value of M ^ bits to be the value of +bC, ie

Cd = w ₂ [2k-l:0] and where the value of the -1 bit of M| is 0, the value of W _{2 is} the value of the first -1st bit of M|; The value of the -1st bit has a value of 1, and the value of the first to sixth bits is added to 1.

Obtaining a product of the first real part and the second real part according to the second reference value: In the first 1 bit bit value is 0, the bit value acquired w to of _-12 constituted as a signed integer, at> ¾ -1 of bits is 0, Obtain a signed integer consisting of the value of the first to the -1st bit of >3⁄4 plus a 1 to get the signed integer ab

^ , [ w ₂ [Ul:2k], w ₂ [2k-l] = 0

The value of w, ie ¹ ^ = w ₂ [ ² 4^-l:2^] + l, w ₂ [2 - 1] = 1. °

 Wherein, when the value of the -1 bit of >H is 0, the value of the above is the value of the 6-1th bit of M|, and the value of the -1st bit of >H is 1, The value of the first to sixth 6-1 bits is incremented by one. Based on the above embodiment, the value that can be obtained is taken as the real part of the product of the first complex number and the second complex number.

In this embodiment, the specific calculation process may be as shown in FIG. 8. First, the calculated >Η is input into the computing device, and the obtained values of the Qth to the -1st bit are used as complements and output. It is judged whether the value of the -1st bit of the Η is 0, and if so, the second reference value is w ₂ =>H[6fc-l:2^], otherwise, the second reference value is W ₂ =>H [6 — 1: ] +1.

否则， i^=w₂[4 — 1:2^+1。 对于 orf+bc, 其值取 o =w₂[2^- 1:0]。 After obtaining the second reference value, determining whether the value of the -1st bit of the second reference value w ₂ is 0, and if so,

Otherwise, i^=w ₂ [4 — 1:2^+1. For orf+bc, its value is o = w ₂ [2^- 1:0].

 In the specific calculation process, appropriate adjustment can also be made, that is, as shown in FIG. 9, it is no longer judged whether the value of the -1 bit of >Η is 0, but directly

1: ]的 值增加 1。 进一步的， 也不需要判断 w₂的第 -1比特位的值是否为 0, 而 是直接使 =w₂[ - 1: ] +w₂ [ - 1], 这样在 w₂的第 -1比特位为 0时，相当 于 i^=w₂[4 — 1: ],而在 w₂的第 -1比特位为 1时，相当于 i^=w₂[4 — 1: ]的 值增加 1。 w ₂ =Μ|[6λ:-1:2λ:]+>3⁄4[2^-1], so that when the 2k-i bit is 0, it is equivalent

The value of 1: is increased by 1. Further, it is not necessary to determine whether the value of the -1st bit of w ₂ is 0, but directly make =w ₂ [ - 1: ] +w ₂ [ - 1], such that the -1 bit of w ₂ When the bit is 0, it is equivalent to i^=w ₂ [4 - 1: ], and when the -1 bit of w ₂ is 1, the value equivalent to i^=w ₂ [4 - 1: ] is increased by 1. .

 In the above embodiment of the present invention, for the case where the values of the first real part, the first imaginary part (the second real part b, and the second imaginary part d are greater than or equal to 0), due to the particularity of the non-negative integer, the computer implements It will be more simple, and the range of numbers can have a larger range of values.

The range is 0 ≤ a, b, _c , d ≤ . Since each of the above values is an integer, it can be obtained:

≤ a, b, c, d ≤ 2 ^k -l

At this time, the first transformed value s = a.2 ² _{+ C} , and the second transformed value t = b.2 +d , which can be obtained: 0 < s,t <(2 ^k -l)-2 ^2k +2 ^k -l<2 ^3k -I

 And the above S and ί are all unsigned integers of bits.

Calculate the first reference value to get: 1⁄4i = st = ab-2 ^k +{ad+bc)-2 ^2k +cd

2 ^2k -I

0<ab,ad,bc,cd <<2 ^2k -1

 2 .

0<ad + bc <2-^—^- = 2 ^2k -1

 2

 The congruence can be obtained by using the congruence property:

Cd = mod( _Wl , 2 ^2k ), and the second reference value _W2= i^l can be obtained by the same reason: ad + bc = mod(^w ₂ , ^M ) Let the third reference value W ₃ be obtained:

Ab = mod(w ₃ , 2 ^2k )

Since the above calculation process and the calculation result are both non-negative integers, the above operations of subtraction, remainder, and division by 2 ^2k can be performed, and the value can be taken as the value of the 0th to 2 - 1th bits of M. a non-negative integer; the value of +bc is a non-negative integer consisting of the value of the -1st bit of M, that is, a non-negative integer formed by the value of the intermediate bit, which is taken as the product of the first complex number and the second complex number. An imaginary part; a non-negative integer consisting of the value of ob to the first to the -1 bit of Η, that is, a non-negative integer consisting of the value of the last Ik bit, and then a value that can be obtained as the first complex sum The real part of the product of the second complex number.

The calculation process of this embodiment may be as shown in FIG. 10, first inputting the first real part first imaginary part ^ the second real part b and the second imaginary part, and further shifting the first real part β, right Shifting a bit, and filling the lower one of the bits into the first imaginary part c, that is, obtaining the first transformed value S = · 2 ₊ c, and shifting the second real part b, and shifting the right side by two The bit, and the lower bit is padded as the second imaginary part d, that is, the second transformed value i = 2 ² ₊ d is obtained. Then multiplying the first transformed value and the second transformed value by using a multiplier

W _l =st = ab-2 ^4k +(ad+ be) - 2 ^2k + cd , on the basis of which, a value of 0 to -1 bit may be taken as a non-negative integer, orf+bc The value is a non-negative integer consisting of the value of the first to -1 bit of Mi, and the value of ib is a non-negative integer consisting of the value of the first 6-1 bit of >Η. The real and imaginary parts of the complex multiplication result orf+bc are obtained by using the definition of complex multiplication. In the above embodiment of the present invention, when the values of the first real part, the first imaginary part ^the second real part, and the second imaginary part 6? are all greater than or equal to 0, and the value range is larger,

0 ≤ a, b, c, d ≤ 2 ^k -l, where is a positive integer, that is, ^/^^ are all unsigned integers of bits, using the following transform values. The first transformed value s = α · 2 ⁺¹ + c , and the second transformed value = · 2 ⁺¹ + ί / , which yields:

0<s,t<(2 ^k -l)- 2 ^2k+1 +2 ^k -l< 2 ^3k+1 - 1

 And the above S and ί are both unsigned integers of +1 bits.

Calculate the first reference value to get: ν^ΐ = ίώ· 2 ^4k+2 +(ad+bc) · 2 ^M+1 +cd

, 因此可得： due to

, so you can get:

0≤ab,ad,bc,cd≤(2 ^k -if =2 ^2k +1- Ϋ ⁺ <2 ^2k _l

0≤ad+bc<2-(2 ^2k -l)<2 ^2k+1 -l The congruence can be obtained by using the congruence property:

Cd = mod( _Wl , 2 ^2k ), and the second reference value _W2= i!^l can be obtained by the same reason: ad+bc = mod(w ₂ , 2 ^2k+1 ) Let the third reference value _W3= zi^ , you can get: ab = mod(w ₃ , 2 ^2k )

Since the above calculation process and the calculation result are both non-negative integers, the above operations of subtraction, remainder, and division by 2 ^a can be performed, and specifically, the values of bits 0 to -1 of >Η can be obtained. A non-negative integer is a value of cd; a non-negative integer constituting a value of the 2nd to +1th bits of >H is obtained as the imaginary part of the product of the first complex number and the second complex number, that is, obtaining +b _c ; The imaginary part ob of the product of the first complex number and the second complex number; the further imaginable value is used as the first complex number and the second The real part of the product of the complex number;

在此基础上， 可以取 的值为The calculation process of this embodiment may be as shown in FIG. 11, first inputting the first real part, the first imaginary part ^, the second real part b and the second imaginary part, and will further move the first real part Bit processing, shifting left by +1 bit, and filling the lower one of the bits into the first imaginary part C, that is, obtaining the first transformed value s = .2 ^M+1 _{+ c} , and the second real part b Perform shift processing, shift left by +1 bit, and fill the lower bit into the second imaginary part d, that is, obtain the second transform The value ί = · 2- ⁺¹ + d. Then multiplying the first transformed value and the second transformed value by using a multiplier

On this basis, the value that can be taken

>The non-negative integer consisting of the values of bits 0 to 2-1 of Η, the value of +bc is the non-negative integer of the value of the +1st to +1th bits of M, and the value of ob is the third of M. +2 to the non-negative integer formed by the value of the bit, and the retrieved value is taken as the real part of the product of the first complex number and the second complex number.

With the above embodiment for both the real and imaginary parts of the two complex signals being unsigned integers, it is possible to construct a complex multiplication using a multiplier with fewer bits. In the embodiment of the present invention, for the first complex signal α+α′ and the second complex signal b+, wherein the first real part fl, the first imaginary part c, the second real part b of the second complex signal, and the second virtual The part d is a bit signed integer and their absolute values are all less than or equal to 2 -ι, that is, |4|φμ|≤2^_ι, where _≥0 .

 First calculate b ' = -b, c ' = -c, = - d , these values can be calculated by calculating the opposite number. For computer complement, you can do this by inverting and adding 1.

 The product of the first complex signal α + ά and the second complex signal b + di is calculated in 16 cases below, and the multipliers in the method of the above embodiment are respectively used.

 In the first case, "≥0, c≥0, fc≥0, d≥. For this case, refer to the embodiment shown in Fig. 11 above. For details, see Fig. 12, according to the first real part", first The imaginary part, the second real part b and the second imaginary part d of the second complex signal, obtain the first transformed value by using the shift method

s = a - 2 ^{2k + l} + c and the second transformed value t = b - 2 ^{2k + l} + d , and then using the multiplier to obtain the first reference value M = W = ab' ²⁴ + (oi + bc) ' ^{2 +1} + a , and the product of the first complex signal α+α' and the second complex signal +·, X + , x = ab-cd , y = d + c, can be obtained according to the method of the embodiment shown in FIG.

_{+ c}'， 所述根据第二复数 信号获取的第二变换值^ = ^2 ⁺¹ + ^ , 其中^为 的相反数， b'为 b的相反 数， c'为 c的相反数， 为 d的相反数， 然后使用乘法器得到第一参考值 ¼ =st=a'b'-2^4k+2 Ha'd'+b'c')-!²^¹ +c'd' ,进一步的根据第一参考值 >Η可以获取 所述第一复数和第二复数的乘积 + , x = a'b' - c'd' , y = a'd'+b'c' _: In the second case, where the values of the first real part, the first imaginary part (7, the second real part ^ and the second imaginary part d of the second complex signal are less than 0, ^ a < 0, c < 0, b < 0, d < 0, and when the absolute value thereof is less than 2 -1, where is a non-negative integer; as shown in FIG. 13, the first transform obtained according to the first complex signal can be obtained by shift processing Value is s =

_{+ c} ', the second transformed value obtained according to the second complex signal ^ = ^2 ⁺¹ + ^ , where ^ is the opposite, b' is the opposite of b, and c' is the opposite of c, The opposite of d, then use the multiplier to get the first reference value 1⁄4 = st=a'b'-2 ^4k+2 Ha'd'+b'c')-! ² ^ ¹ +c'd' , further Obtaining the product of the first complex number and the second complex number +, x = a'b' - c'd' , y = a'd' + b'c' according to the first reference value > _::

Obtaining a value of a non-negative integer consisting of the values of bits 0 to -1 of >Η; The obtained non-negative integer of the value of the 2k+1th to the +1st bit is used as the imaginary part of the product of the first complex number and the second complex number, that is, y = ^ + ;

 A non-negative integer consisting of the value of the 3⁄4+2 bit of M is obtained as the value of ob; the value of ab_cd is obtained as the real part of the product of the first complex number and the second complex number, that is, 5 x = ab - cd.

In the third case, wherein the absolute value of the first real part, the first imaginary part ^, the second real part of the second complex signal, and the second imaginary part d are both less than 2 - 1, 3_a ≥ 0, c < 0, b> 0, d <0 ^, where is a non-negative integer; as shown in FIG. 14, the first transform value obtained according to the first complex signal can be obtained by shift processing s = _Ω · 2 ^M+1 ₊ c ', the second transform ¹⁰ value obtained according to the second complex signal ί = · 2 ^{Μ +1} _{+ ί} Τ, where c' is the opposite of c, ^ is the opposite of d, and then using the multiplier to obtain the a reference value _Wl = st = ab - 4 ^{4k + 2} + (ad ' + bc ') - 2 ^{2k + 1} + c 'd', further according to the first reference value > Η can obtain the first complex number and the first The product of the two complex numbers x- , _{x = ab} — _c ' _d ,, y = ad '-\- be''

 Obtaining a value of the non-negative integer consisting of the values of bits 0 to -1 of >Η;

¹⁵ obtaining a non-negative integer consisting of the values of the +1st to +1th bits of >Η, obtaining the inverse of the non-negative integer as the imaginary part of the product of the first complex number and the second complex number, ie y = - ( + be ) , the inverse of y is calculated as the imaginary part of the product of the first complex number and the second complex number.

 Obtaining the value of the non-negative integer formed by the value of the 3⁄4+2 to the bit ob; obtaining the real value of the product of the first complex number and the second complex number as the real part of the product of the first complex number and the second complex number, that is, A

^ ^w x-ab-cd ₀

In the fourth case, wherein the absolute values of the first real part, the first virtual part ί, the second real part b of the second complex signal, and the second imaginary part d are all less than 2 -l, ^-a < 0, c ≥ 0, b < 0, d > 0 ^ ^ where is a non-negative integer; as shown in FIG. 15, the first transform value obtained according to the first complex signal can be obtained by shift processing, S = ₊ c, The second variable ²⁵ obtained according to the second complex signal is i = 2 ^M+1 ₊ d , where c' is the opposite of c, ^ is the opposite of d, and then the first reference value M is obtained using a multiplier =W = a'b'.2 ⁴ + (a'i +b' _C 2 ⁺¹ +o , further according to the first reference value > Η can obtain the product x- of the first complex number and the second complex number, _{x = a} ' _b '_ _cd , y two a, d + b, c ·

 Obtaining a value of the non-negative integer consisting of the values of bits 0 to -1 of >H;

³⁰ acquires> non-negative integer value of the bit to +1 +1 Η constituted to obtain the non-negative integer opposite of the first plurality and a second plurality of the product of the imaginary unit, i.e., y = - + be) , The opposite of y is calculated as the imaginary part of the product of the first complex number and the second complex number.

 The obtained value of the 3⁄4+2 to the bit constitutes a non-negative integer as the value of ob; the value of ab_cd is obtained as the real part of the product of the first complex number and the second complex number, i.e., x-ab-cd.

In the fifth case, wherein the absolute values of the first real part, the first imaginary part, the second real part of the second complex signal, and the second imaginary part d are all less than 2 -l, 3_a ≥ 0, c ≥ 0, b < 0, d < 0 ^, where is a non-negative integer; as shown in FIG. 16, the first transform value obtained according to the first complex signal can be obtained by shift processing S = · 2 ² w _{+ c} The second transformed value i = 2 ^{2 +1} _{+ i} r obtained according to the second complex signal, where is the opposite of b, ^ is the opposite of d, and then the first reference value is obtained using a multiplier 1⁄4i = 2 ^{4 2} +(W+ 'c).2 ⁺¹ +of, further obtaining the product of the first complex number and the second complex number according to the first reference value > - -X - _{x = ab} ' - _cd , , y = Ad -\- bc ·

Obtaining a non-negative integer consisting of the values of bits 0 to 2 -1 of >Η is a value of _ _cd ; obtaining a non-negative integer consisting of values of +1 to +1 bits of >H, obtaining the non-negative The inverse of the integer is the imaginary part of the product of the first complex number and the second complex number, ie y = -iad +bc), and the inverse of y is calculated as the imaginary part of the product of the first complex number and the second complex number;

The obtained non-negative integer of the value of the 3⁄4+2 to the bit is the value of - _ab ; the opposite of the value of = (-ab) - (-cd) is obtained as the product of the first complex number and the second complex number The real part.

In the sixth case, the absolute values of the second real part ^ and the second imaginary part d of the first real part, the first imaginary part ^, the second complex signal are all less than 2 - 1, and "<0 , c<0, fc≥0, when d≥0, where is a non-negative integer; as shown in FIG. 17, the first transform value obtained according to the first complex signal can be obtained by shift processing S = '· 2 ² w ₊ c ' , the second transformed value obtained according to the second complex signal i = ^2 ^M+1 + , where ^ is the opposite, C ' is the opposite of C, and then the first reference is obtained using the multiplier The value ^^ ^^^+^^+^^^^+^ further obtains the product of the first complex number and the second complex number -x- according to the first reference value > ,, _{x = a} ' _b _ _c ' _d , y = a ¹ d -- be ¹ '

Obtaining a non-negative integer consisting of the values of bits 0 to 2-1 of >H is a value of _ _cd ; obtaining a non-negative integer consisting of values of +1 to +1 bits of >H, obtaining the non-negative The inverse of the integer is the imaginary part of the product of the first complex number and the second complex number, ie y = ~(ad + be) , and the inverse of the y is calculated as the imaginary part of the product of the first complex number and the second complex number . The obtained non-negative integer consisting of the value of the 3⁄4+2 to the bit is the value of - _ab ; the opposite of the value of = (-ab) - {-cd) is obtained as the product of the first complex number and the second complex number The real part.

In the seventh case, the absolute values of the second real part ^ and the second imaginary part d of the first real part, the first imaginary part ^, the second complex signal are all less than 2 - 1 , and "≥ 0 , c < 0, fc < 0, d ≥ 0, where is a non-negative integer; as shown in FIG. 18, the first transform value obtained according to the first complex signal can be obtained by shift processing s = ^2 ^{M+ 1} _{+ c} ' , the second transformed value obtained according to the second complex signal i = 2 ^M+1 ₊ d , where c' is the opposite of C, is the opposite of b, and then the first reference is obtained using a multiplier The value >H=W = ab'.2 ^{4i: +2} + (a + b ). 2 ⁺¹ + cW , further the product of the first complex number and the second complex number can be obtained according to the first reference value > - - x+ , _{x = ab} '- _c ' _d , y = ad + b ¹ c ¹ '

Obtaining a non-negative integer consisting of the values of bits 0 to 2-1 of >H is a value of _ _cd ; a non-negative integer of values obtained by the obtained +1st bit is used as the first complex number and the second complex number The imaginary part of the product, ie y = ^ + ;

The obtained non-negative integer of the value of the 3⁄4+2 to the bit is the value of - _ab ; the opposite of the value of = (-ab) - (-cd) is obtained as the product of the first complex number and the second complex number The real part.

, 进一步的根据第一参考 值 >Η可以获取所述第一复数和第二复数的乘积 -x+ , _{x = a}'_b-_cd， , y = a ' d '-\- be ' In the eighth case, where the absolute value of the first real part, the first imaginary part (7, the second real part ^ and the second imaginary part d of the second complex signal are both less than 2 - 1 , and " 0, c ≥ 0, fc ≥ 0, where d < 0, where is a non-negative integer; as shown in FIG. 19, the first transform value obtained according to the first complex signal can be obtained by shift processing S = 2 ^{2k+ l} ₊ c, the second transformed value ί = ^2 ^{2 +1} _{+ ί} Γ obtained according to the second complex signal, where ^ is the opposite of ", the opposite of d, and then using the multiplier to obtain the first reference value

Further, according to the first reference value > Η, the product of the first complex number and the second complex number -x+, _{x = a} ' _b - _cd , , y = a ' d '-\- be '

Obtaining a non-negative integer consisting of the values of bits 0 to 2-1 of >H is a value of _ _cd ; a non-negative integer of values obtained by the obtained +1st bit is used as the first complex number and the second complex number The imaginary part of the product, ie y = ^ + ;

The obtained non-negative integer of the value of the 3⁄4+2 to the bit is the value of - _ab ; the opposite of the value of = (-ab) - (-cd) is obtained as the product of the first complex number and the second complex number The real part. In the ninth case, the absolute values of the second real part ^ and the second imaginary part d of the first real part, the first imaginary part ^, the second complex signal are all less than 2 - 1, and "≥0 , c≥0, fc≥0, where d <0, where is a non-negative integer; as shown in FIG. 20, the first transform value obtained according to the first complex signal can be obtained by shift processing S = · 22w ₊ c The second transformed value +fe obtained according to the second complex signal, where is the inverse of d, and then using the multiplier to obtain the first reference value

_Wi =st=ad'-2 ^4k+2 +(ab+cd')-2 ^2k+1 +bc , further obtaining the product y of the first complex number and the second complex number according to the first reference value>Η Ab ₊ cd^ x ad'- be:

Obtaining a non-negative integer consisting of the values of bits 0 to 2k-1 of >Η is the value of _bc ;

The obtained non-negative integer consisting of the value of the +1st bit is used as the real part of the product of the first complex number and the second complex number, that is, y = ^- obtains the value of the 3⁄4+2 to the bit of M The non-negative integer is the value of _ad; the opposite of the value of =(- _ad ) - (be) is obtained as the imaginary part of the product of the first complex number and the second complex number.

In the tenth case, wherein the absolute values of the first real part, the first imaginary part ^, the second real part b of the second complex signal, and the second imaginary part d are all less than 2 - 1, and "≥0 , c≥0, fc≥0, where d <0, where is a non-negative integer; as shown in FIG. 21, the first transform value obtained according to the first complex signal can be obtained by shift processing S = c '· 2 ^Μ+1 ₊ , the second transformed value obtained from the second complex signal i = fe.2 ^M+1 ₊ , where C ' is the inverse of c, and then the first reference value is obtained using a multiplier

1⁄4i = st=bc'- 2 ^4k+2 +(ab+c'd) · 2 ^2k+l +ad , further obtaining the product _{y of} the first complex number and the second complex number according to the first reference value M| _{= ab + cd} ', x = bc'-ad:

 Obtaining a value of the non-negative integer consisting of the values of bits 0 to 2 -1 of >Η is ^;

 The obtained non-negative integer of the value of the +1st bit is taken as the real part of the product of the first complex and the second complex, that is, y = ^ - ^;

The obtained non-negative integer consisting of the value of the 3⁄4+2 to the bit is the value of - _bc ; the opposite of the value of the obtained = - _bc) _ _ad) is taken as the imaginary part of the product of the first complex number and the second complex number .

_{+ c}, 所述根据第二复数信号获取的第二变 换值 i = d.2 ⁺¹ ₊fe'， 其中 b'为 b的相反数， 然后使用乘法器得到第一参考值 w_l=st=ad- 2^4k+2 +(ab'+cd) · 2^2k+1 +b'c , 进一步的根据第一参考值 >H可以获取所 述第一复数和第二复数的乘积 + _{y = ab}'_+cd , x = ad-b'c : In the eleventh case, wherein the absolute values of the first real part, the first virtual part ί, the second real part of the second complex signal, and the second imaginary part d are all less than 2 - 1, Ha>0 , c≥0, b<0, d >0^, where is a non-negative integer; as shown in FIG. 22, the first transform value obtained according to the first complex signal can be obtained by shift processing s =

_{+ c} , the second transformed value i = d.2 ⁺¹ ₊ fe' obtained according to the second complex signal, where b' is the opposite of b, and then the first reference value is obtained using a multiplier w _l =st=ad- 2 ^4k+2 +(ab'+cd) · 2 ^2k+1 +b'c , further obtaining the product of the first complex number and the second complex number according to the first reference value >H + _{y = ab} ' _+cd , x = ad-b'c :

 Obtaining a value of the non-negative integer consisting of the values of bits 0 to 2 -1 of >Η;

Obtaining a non-negative integer consisting of the values of the +1st to +1st bits, obtaining the opposite of the non-negative integer as the real part of the product of the first complex number and the second complex number, ie, _y = - _ab + _cd Calculate the inverse of y as the real part of the product of the first complex and the second complex.

The value of the non-negative integer formed by the value of the 3⁄4+2 to the bit of >Η is the value of ^; the value of == {-be is obtained as the imaginary part of the product of the first complex number and the second complex number. In the twelfth case, where the absolute value of the first real part, the first imaginary part (:, the second real part ^ and the second imaginary part d of the second complex signal are less than 2 - 1, Ha < 0, c> 0, b ≥ 0, d > 0 ^, where is a non-negative integer; as shown in FIG. 23, the first transform value obtained according to the first complex signal can be obtained by shift processing = 2 ^{Μ + 1} _{+ Ω} ', the second transformed value i = fe.2 ^M+1 ₊ obtained according to the second complex signal, wherein α' is the opposite of ", and then using the multiplier to obtain the first reference value w _x = st =ad− 2 ^4k+2 + (ab ^f +cd) · 2 ^2k+1 +b'c , further obtaining the product of the first complex number and the second complex number according to the first reference value >H - y + _y = a'b ₊ cd ' x bc_a'd

Obtaining a non-negative integer consisting of the values of bits 0 to 2 -1 of >Η is a value of _{_ad} ; obtaining a non-negative integer consisting of values of bits +1 to +1 of M, obtaining the non-negative integer The opposite number is the real part of the product of the first complex number and the second complex number, i.e., _y = - _ab + _cd , and the inverse of y is calculated as the real part of the product of the first complex number and the second complex number.

进一 步的根据第一参考值 >Η可以获取所述第一复数和第二复数的乘积 -y + x , a'b + e'd¹ ' x a d bc： The obtained non-negative integer consisting of the value of the 3⁄4+2 bit is the value of _bc ; the value of = _bc) _ _ _ad) is obtained as the imaginary part of the product of the first complex number and the second complex number. In the thirteenth case, the absolute values of the second real part ^ and the second imaginary part d of the first real part, the first imaginary part ^, the second complex signal are all less than 2 - 1, 3_a <0 , c< 0, b> 0, d < 0 ^, where is a non-negative integer; as shown in FIG. 24, the first transform value obtained according to the first complex signal can be obtained by shift processing S = 2 ² w _{+ c} ' , the second transformed value obtained according to the second complex signal i = d'.2 ^M+1 ₊ fc , ^ is the opposite of ", C' is the opposite of c, ^ is the opposite of d, Then use the multiplier to get the first reference value

Further, according to the first reference value > Η, a product of the first complex number and the second complex number -y + x , a'b + e'd ¹ ' xad bc:

Obtaining the value of the 0th to -1st bits of ^ to form a non-negative integer of the value of _; Obtaining a non-negative integer consisting of the values of the +1 to 4 l bits of >H, obtaining the opposite of the non-negative integer as the real part of the product of the first complex number and the second complex number, ie _y = - _ab + _cd , calculating the opposite of y as the real part of the product of the first complex number and the second complex number.

The value of the non-negative integer formed by the value of the 3⁄4+2 to the bit of >Η is the value of ^; the value of == ₎₎ _ _bc) is taken as the imaginary part of the product of the first complex number and the second complex number. In the fourteenth case, wherein the absolute values of the first real part, the first imaginary part ^, the second real part of the second complex signal, and the second imaginary part d are all less than 2 - 1 , Ha ≥ 0 , c < 0, b < 0, d < 0 ^, where is a non-negative integer; as shown in FIG. 25, the first transform value obtained according to the first complex signal can be obtained by shift processing S = c '· 2 ^Μ+1 ₊ , the second transformed value obtained according to the second complex signal i = 2 ^Μ+1 _{+ ί} τ , where b' is the opposite of b, c' is the opposite of c, and ^ is the opposite of d a number, and then using a multiplier to obtain a first reference value ν Η = = · 2 ^{4 2} + (^' + ^β Γ) · 2 ⁺¹ + ί 3⁄4 Γ, further according to the first reference value > Η can obtain the first complex sum Product of the second complex number

~y ^{+ xl} y = _a b'+c'd' , x = b'c'-ad'- Get the value of the 0th to 2 -1 bits of >H to form a non-negative integer of the value of _ _ad ; Obtaining a non-negative integer consisting of the values of the +1st to +1th bits of >H, obtaining the opposite of the non-negative integer as the real part of the product of the first complex number and the second complex number, ie _y = - _ab + _cd , calculating the opposite of y as the real part of the product of the first complex number and the second complex number.

The non-negative integer formed by the value of the 3⁄4+2 to the bit of W is obtained as the value of _bc ; the value of = _bc) _ _ _ad) is obtained as the imaginary part of the product of the first complex number and the second complex number. In the fifteenth case, wherein the absolute values of the first real part, the first imaginary part ^, the second real part of the second complex signal, and the second imaginary part d are all less than 2 - 1 , 3_a < 0 , c < 0, b < 0, d > 0 ^, where is a non-negative integer; as shown in FIG. 26, the first transform value obtained according to the first complex signal can be obtained by shift processing S = '· 2 ² w ₊ c ' , the second transformed value i = d .2 ⁺¹ + fc' obtained according to the second complex signal, wherein α' is the opposite of ", b' is the opposite of b, c' is C The opposite number, then use the multiplier to get the first reference value

1⁄4 = st = a'd-2 ^4k+2 + (a'b'+c'd) · 2 ^2k+l +b'c', further obtaining the first complex number and the first according to the first reference value The product of the two complex numbers _{y = a} ' _b ' _{+ c} ' _d , _x = a'd-b'c':

The non-negative integer formed by the values of the 0th to 2k-1th bits is the value of _bc ;

The obtained non-negative integer consisting of the value of the +1st bit is taken as the real part of the product of the first complex number and the second complex number, ie y = ^- Obtaining a non-negative integer consisting of the value of the 3⁄4+2 to the bit of >H is the value of _ad; obtaining the opposite of the value of =(- _ad ) - (be) as the first complex number and the second complex number The imaginary part of the product.

进一 步的根据第一参考值 >Η可以获取所述第一复数和第二复数的乘积 + 的 实部 _y = w_+Ci , 以及所述第一复数和第二复数的乘积的虚部 c = b'_c-_a'^ : 获取 >Η的第 0到 2 -1比特位的值构成的非负整数为 ^的值； In the sixteenth case, wherein the absolute value of the first real part, the first imaginary part (:, the second real part b of the second complex signal, and the second imaginary part d are both less than 2 - 1, Ha ≥ 0, c < 0, b < 0, d < 0 ^, where is a positive integer; as shown in FIG. 27, the first transform value obtained according to the first complex signal can be obtained by shift processing s = _c '· 2 ^Μ+1 ₊ , the second transformed value obtained from the second complex signal i = 2 ^{2 +1} _{+ i} r , where b' is the opposite of b, c' is the opposite of c, 'the opposite of d Number, then use the multiplier to get the first reference value

Further, according to the first reference value > Η, a real part _y = w _{+ Ci} of the product of the first complex number and the second complex number, and an imaginary part of the product of the first complex number and the second complex number c = b ' _c - _a '^ : Get the value of the 0 to 2 -1 bits of >Η to form a non-negative integer of ^;

 The obtained non-negative integer of the value of the +1st bit is taken as the real part of the product of the first complex and the second complex, that is, y = ^ - ^;

Obtaining a non-negative integer consisting of the value of the 3⁄4+2 to the bit of >Η is the value of _-bc ; obtaining the opposite of the value of = _{_bc) _ad)} as the product of the first complex number and the second complex number The imaginary part.

In this embodiment, unlike the first transform value and the second transform value in the first embodiment, for the same range, Η, ^{≤ 2} * - ¹ , the first complex signal α+α and the second complex number are calculated. The product of the signal b+, the first embodiment requires the use of a +3 bit multiplier, this embodiment requires the use of a + 1 bit multiplier, but requires additional different cases of judgment and the calculation of the opposite number, that is, the complement is taken Reverse and add 1 operation.

The present invention also provides an apparatus for implementing complex multiplication using a multiplier, and FIG. 28 is a schematic structural diagram 1 of an apparatus for implementing complex multiplication using a multiplier according to an embodiment of the present invention. As shown in FIG. 28, the apparatus includes a first reception. The module 11, the first obtaining module 12, the first calculating module 13 and the second obtaining module 14, wherein the first receiving module 11 is configured to receive the first complex signal α+d and the second complex signal b+di, the first The first plurality of signals and the second plurality of signals are communication digital signals; the first obtaining module 12 is configured to obtain a first transformed value S according to the first real part of the first complex signal and the first imaginary part c performing shift processing. And performing a shift process according to the second real part b and the second imaginary part d of the second complex signal to obtain a second transform value ί; the first calculating module 13 is configured to The first transform value and the second transform value are calculated by using a multiplier to obtain a first reference value>H=W; the second obtaining module 14 is configured to acquire the first reference value according to the first reference value>Η The real part of the product of the complex number and the second complex number, and the imaginary part of the product of the first complex number and the second complex number.

 The technical solution provided by the foregoing embodiment of the present invention, wherein, when performing complex multiplication, the first obtaining module acquires the first transformed value and the second transformed value according to the complex signal, and then the first calculating module uses the multiplier to perform calculation to obtain the first reference value. And further obtaining, according to the first reference value, a real part of the product of the first complex number and the second complex number, and an imaginary part ad+bc of the product of the first complex number and the second complex number, where only the first calculation is needed in the technical solution The module uses a multiplier when calculating the first reference value, and only one multiplier is needed in the entire complex multiplication calculation process. Therefore, the technical solution of the present invention can effectively save the multiplier resources.

In the above embodiment of the present invention, the first real part of the first complex signal received by the first receiving module 11 and the first imaginary part c, and the second real part b and the second of the second complex signal The absolute value of the imaginary part d is less than or equal to 2" -1 , where is a positive integer; the first transformation value obtained by the first acquisition module 12 according to the first complex signal S = _Ω · 2 ₊ c , according to the The second transformed value obtained by the second complex signal = ^2 ₊ the first reference value calculated by the first calculating module 13 is _Wi = W = ^ · 2 ⁴ + + fc) · 2 ^2k + cd.

Specifically, the second obtaining module 14 may include different functional modules, such as the first reference value acquiring unit 141 and the first coefficient acquiring unit 142, as shown in FIG. 29, corresponding to the foregoing method embodiments. And the first reference value obtaining unit 141 is configured to acquire the second reference value w ₂ =fc^1 and the third reference value according to the first reference value>Η

( ^w 2-i ^ad+bc )). The first coefficient acquisition unit 142 is configured to: acquire 2 according to the first reference value

O时，获取 w₂ + (^2M- Li)的低 比特位 的值构成的非负数减去 2²" -1的值作为所述第一复数和第二复数的乘积 的虚部， 在 w₂

Q时， 获取 -[ν _{2 +} (² - ' -Ι)]的低 比特位的值构成 的非负数减去 2²"+l的值的相反数作为所述第一复数和第二复数的乘积 的虚部； 以及根据所述第三参考值 W₃获取第一实部和第二实部的乘积 ob, 即在 w₃ + (2²*-¹ - 1)≥ 0时， 获取 w₃ + (2²*-¹ - 1)的低 2k比特位的值构成的非负数减 去 2 - Li的值为 ab的值， 在 H¾+(2 - i-l^Q时， 获取- [w_{3 +} (2^M- 1)]的低 比 特位的值构成的非负数减去 2²" + 1的值的相反数为 ob的值； 取 ab_cd的 值作为所述第一复数和第二复数的乘积的实部。 Take the product of the first imaginary part and the second imaginary part, that is, when +(2 ^23⁄4 - ¹ -1) ≥ 0, obtain the non-negative number of values of the lower 2k bits of + (2 ^23⁄4 - ¹ -1) To the value of 2 ² " - 1 value, when + (2 ² *- ¹ -1) < 0, obtain the non-negative number of values of the lower 2k bits of + [2 ^2k - ¹ - 1)] The inverse of the value of 2 ² " + 1 is the value of ^; the product of the first real part and the second imaginary part is obtained according to the second reference value > 3⁄4, and the product of the first imaginary part and the second real part And the imaginary part of the product of the first complex number and the second complex number, ie, at w ₂

At time O, the non-negative number formed by the value of the low bit of w ₂ + ( ^2M - Li) is subtracted from the value of 2 ² " -1 as the imaginary part of the product of the first complex number and the second complex number, at w ₂

For Q, the value of the low bit of -[ν _{2 +} ( ² - ' -Ι)] is obtained. The non-negative number minus the inverse of the value of 2 ² "+l as the imaginary part of the product of the first complex number and the second complex number; and the first real part and the second real part are obtained according to the third reference value W ₃ The product ob of the part, that is, when w ₃ + (2 ² *- ¹ - 1) ≥ 0, obtain the non-negative number of the value of the lower 2k bits of w ₃ + (2 ² *- ¹ - 1) minus 2 - The value of Li is the value of ab. In H3⁄4+(2 - il^Q, get the non-negative number of the value of the low bit of [w _{3 +} (2 ^M - 1)] minus 2 ² " + 1 The opposite of the value is the value of ob; the value of ab_cd is taken as the real part of the product of the first complex number and the second complex number.

Alternatively, as shown in FIG. 30, the second acquiring module 14 includes a first reference value acquiring unit 141 and a second coefficient acquiring unit 143, where the first reference value acquiring unit 141 is configured to use the first reference value>Η Obtaining a second reference value w ₂ =fc^1 and a third reference value ( ^w 2-i ^ad+bc )). The second coefficient obtaining unit 143 is configured to: acquire according to the first reference value

2

Taking the product cd of the first imaginary part and the second imaginary part, that is, obtaining a non-negative number of values of the lower 2k bits of + (2 ^2k - ¹ -l) + K _t · 2 ^2k minus 2 ² "-1 Value of the value, where is a positive integer, and

以及根据所述第三参考值获取第一 实部和第二实部的乘积 ob, 即获取 Η¾+(²²"-1) + ··^2Μ的低 比特位的值构 成的非负数减去 2²"-1的值为 ab的值， 其中 为正整数， 且 w ₁ +(2 ^3⁄4 - ¹ -l) ₊ ^..2 ^3⁄4 >0; obtaining a product of the first real part and the second imaginary part according to the second reference value, and the first imaginary part and the second real part The sum of the products + b _C as the imaginary part of the product of the first complex number and the second complex number, that is, the value of the low Ik bit of + (2 ² *- ¹ -l) + K _t · 2 ^2k a non-negative number minus the value of 2 ² " -1 as the imaginary part of the product of the first complex number and the second complex number, where is a positive integer, and

And obtaining a product ob of the first real part and the second real part according to the third reference value, that is, obtaining a non-negative number formed by the value of the low bit of the Η3⁄4+( ²² "-1)+·· ^2Μ minus 2 ² "The value of -1 is the value of ab, where is a positive integer, and

w _{3 +} (2 ^2k - ^l -l) + K 2 ^2k > Q - The value of ab - is obtained as the real part of the product of the first complex number and the second complex number.

Alternatively, as shown in FIG. 31, the second obtaining module 14 includes a second reference value obtaining unit 144 and a third coefficient acquiring unit 145, where the second reference value acquiring unit 144 is configured to acquire the first reference value>Η according to the first reference value The second reference value _W2 =i^^l; the third coefficient obtaining unit 145 is configured to obtain, according to the first reference value>Η, a product αί of the first imaginary part and the second imaginary part, that is, a value of obtaining a low bit a value of a signed integer; obtaining a product of the first real part and the second imaginary part according to the second reference value w ₂ , and a sum of products of the first imaginary part and the second real part orf+bc as the The imaginary part of the product of a complex number and the second complex number, that is, the value of the value of >3⁄4 low Ik bits The integer number is the imaginary part of the product of the first complex number and the second complex number, and wherein the value of the 2k _1 bit of > Η is 0, the value of w ₂ is equal to the first to the -1st bit of ^ Value; the value of the 2 - 1 bit of > Η is 1, the value of w ₂ is equal to the value of the first to the -1st bit of > 加上 plus 1; the first is obtained according to the second reference value w ₂ The product ab of the real part and the second real part, that is, when the value of the 2k _1 bit of w ₂ is Q, the obtained value of the first -1st bit constitutes a signed integer whose value is ob, at >3⁄4 a bit value of 0, ^2-1, bit 1 bit value of the acquired configuration coupled with a signed integer unsigned integer value obtained ob; and wherein said value> ¾ in > The value of the 2nd - 1st bit of Η is equal to the value of the first to the -1st bit of >Η, the value of the 2nd - 1st bit of >Η is 1, and the value of >3⁄4 is equal to >Η The value of the first to the -1st bit is incremented by 1; the value of ab- is obtained as the real part of the product of the first complex number and the second complex number.

In another embodiment, the first real part of the first complex signal received by the first receiving module 11, the first imaginary part, the second real part b of the second complex signal, and the second imaginary part d The value of each of the values is greater than or equal to the integer of Q, the first transforming value obtained by the first acquiring module 12 according to the first complex signal S = · 2 _{+ c} , and the second transformed value obtained according to the second complex signal = b- ₊ d , and the first reference value calculated by the first calculating module 13

w _l = st = ab - 2 ^k + (ad + be) - 2 ^2k + cd , where is a positive integer; and the second acquisition module 14 is specifically used to obtain the non-values of the 0 to -1 bits of >Η a value of a negative integer, a non-negative integer formed by the values of the 2nd to 1st bits obtained as the imaginary part of the product of the first complex number and the second complex number, and the value of the first to -1 bit of >Η is obtained. The constructed non-negative integer is a value; the value of ab - is obtained as the real part of the product of the first complex number and the second complex number.

_{+ c}, 根据第二复数信号获取的第二变换值 t = b-2^ ₊ d , 第一计算模块 13计算得到的第一参考值 As shown in FIG. 28, the apparatus for implementing complex multiplication using a multiplier, the first real part of the first complex signal received by the first receiving module 11, the first imaginary part, and the second complex signal The values of the second real part b and the second imaginary part d are all integers greater than or equal to 0, and are less than or equal to 2 -1, where are non-negative integers; and the first obtaining module 12 obtains according to the first complex signal. First transformed value s =

_{+ c} , the second transformed value t = b-2^ ₊ d obtained according to the second complex signal, the first reference value calculated by the first calculating module 13

1⁄4 = st=ab-2 ^4k+2 + (ad+bc)-2 ^2k+l + cd; The second obtaining module 14 is specifically configured to obtain a non-value of the 0th to the -1th bits of >Η a value of a negative integer; a non-negative integer formed by the value of the +1st to +1th bits of M as the imaginary part of the product of the first complex number and the second complex number; the value of the obtained +2 to the bit The non-negative integer formed is the value of ob; obtained a value as the real part of the product of the first complex number and the second complex number;

Alternatively, the values of the first real part a, the first imaginary part (the second real part b, and the second imaginary part d of the second complex signal) of the first complex signal received by the first receiving module 11 are When it is less than 0, and its absolute value is less than 2 -1, where is a non-negative integer; the first transform value obtained by the first acquiring module 12 according to the first complex signal is s = 22w _{+ c} ', The second transformed value obtained by the two complex signals t = b ¹ - 2 ^2k+1 + where 'the opposite number, 'b is the opposite of b, c ' is the opposite of c, ^ is the opposite of d, The first reference value calculated by the first calculation module 13 is >H=W=i^'.2 ^{4 +2} +(a'6 +/ c').2 ⁺¹ +c'6 ; The module 14 is specifically configured to obtain a value of a non-negative integer formed by values of bits 0 to -1 of >Η; a non-negative integer formed by the value of the obtained first to +1 bits as the first complex number and the first The imaginary part of the product of the two complex numbers; the value of the non-negative integer formed by the value of the +2 to the bit of Mi is the value of ab; the value of ab-cd is obtained as the real part of the product of the first complex number and the second complex number ;

Alternatively, the absolute values of the first real part of the first complex signal received by the first receiving module 11, the first real part, the second real part b of the second complex signal, and the second imaginary part d are both It is less than 2 ^k -1, 3_a > 0, c < 0, b > 0, d < 0 ^, where is a non-negative integer; the first transform value obtained by the first obtaining module 12 according to the first complex signal is S = ₊ c', the second transformed value ί = ·2 ^Μ+1 _{+ ί 获取} obtained according to the second complex signal, wherein c' is the opposite of c, which is the inverse of d, the first calculating module 13 calculated first reference value

_Wi = st = ab - 2 ^{4k + 2} + (ad '+bc ') - 2 ^{2k + l} + c'd'; The second obtaining module 14 is specifically configured to acquire bits 0 to -1 of >H a non-negative integer constituting a value of ^; a non-negative integer constituting a value of +1 to +1 bit of >Η, obtaining an inverse of the non-negative integer as the first complex number The imaginary part of the product of the two complex numbers; the value of the non-negative integer formed by the value of the 3⁄4+2 to the bit of >Η is the value of ab; the value of ab-cd is obtained as the product of the first complex number and the second complex number Real;

 Or the first real part of the first complex signal received by the first receiving module 11

", the first imaginary part ^ the absolute value of the second real part b and the second imaginary part d of the second complex signal are less than 2 ^k -l, -^a < 0, c ≥ 0, b < 0, d ≥ 0 ^, where is a non-negative integer; the first transform value obtained by the first acquiring module 12 according to the first complex signal is S = '· ₊ c, and the second transform value obtained according to the second complex signal is i = 2 ^M+1 + d , where ^ is the opposite of ", the opposite of b, the first reference value calculated by the first calculation module 13

_Wi =st=a'b'-2 ^4k+2 +(a'd+b'c)-2 ^2k+l +cd; The second obtaining module 14 is specifically configured to acquire >H a non-negative integer consisting of the values of bits 0 to -1 is a value of ^; obtaining a non-negative integer consisting of the value of the first to the +1st bits of >Η, obtaining the opposite of the non-negative integer as the The imaginary part of the product of the first complex number and the second complex number; the value of the non-negative integer formed by the value of +2 to the bit of >Η is the value of _ab ; the obtained value is the product of the first complex number and the second complex number Real part

Or, the absolute value of the first real part, the first imaginary part, the second real part b, and the second imaginary part d of the first complex signal received by the first receiving module 11 All are smaller than 2 ^k -1, 3_a ≥ 0, c ≥ 0, b < 0, d < 0 ^ , where is a non-negative integer; the first transform value obtained by the first acquiring module 12 according to the first complex signal is S = · _{+ c} , the second transformed value i = 2 ^M+1 _{+ i} r obtained according to the second complex signal, wherein is the opposite of b, ^ is the inverse of d, the first calculating module 13 calculates The obtained first reference value

1⁄4 = st = ab' - 2 ^{4k + 2} + (ad' + b'c) - 2 ^{2k + l} + cd '; The second obtaining module 14 is specifically configured to acquire bits 0 to -1 of >H The non-negative integer formed by the value of the value; the non-negative integer formed by the value of the obtained +1st bit, and the inverse of the non-negative integer is obtained as the virtual product of the product of the first complex number and the second complex number Obtaining a value of a non-negative integer consisting of a value of +2 to a bit of >Η; obtaining an inverse of the value of (_ -(_^) as a product of the product of the first complex number and the second complex number unit;

_{+ C}'， 所述根据第二复数 信号获取的第二变换值 i = fe.2^{2 +1} + , 其中 ^为"的相反数， c'为 C的相反 数， 所述第一计算模块 13计算得到的第一参考值 Or the absolute value of the first real part α, the first imaginary part ^, the second real part b and the second imaginary part d of the second complex signal received by the first receiving module 11 All are less than 2 ^k -l, 3_a < 0, c < 0, b > 0, d > 0 ^ , where is a non-negative integer; the first transform value obtained by the first obtaining module 12 according to the first complex signal is s =

_{+ C} ', the second transformed value i = fe.2 ^{2 +1} + obtained according to the second complex signal, wherein ^ is the opposite of ", c' is the opposite of C, the first calculating module 13 Calculated first reference value

w _l = st = a'b-2 ^{4k + 2} + (a'd + bc') - 2 ^{2k + l} + c'd; the second acquisition module 14 is specifically used to obtain the 0th - 1st bit a non-negative integer formed by the value of the bit; a non-negative integer formed by the obtained value of the +1st bit, and an inverse of the non-negative integer as the product of the first complex and the second complex An imaginary part; obtaining a value of a non-negative integer consisting of a value of +2 to a bit of >Η; obtaining an inverse of a value of (_^)-(_^) as the first complex number and the second plural number The real part of the product;

Or the absolute value of the first real part a, the first imaginary part ^, the second real part b and the second imaginary part d of the second complex signal received by the first receiving module 11 Less than 2^-1, Ha≥0, c<0, b<0, d>0^, where is a non-negative integer; the first transform value obtained by the first acquiring module 12 according to the first complex signal is S= ₊ c', the second transformed value i = ^2 ^M+1 +d obtained according to the second complex signal, wherein C' is the opposite of c, which is the inverse of b, the first calculating module 13 calculates The first reference value obtained

w _l =st=ab'-2 ^4k+2 +(ad+b'c')-2 ^2k+l +c'd; The second obtaining module 14 is specifically configured to acquire 0th to -1 of M| The value of the bit constitutes a value of a non-negative integer; the obtained non-negative integer of the value of the +1 to 4k+1 bit is the imaginary part of the product of the first complex number and the second complex number; The value of the 3⁄4+2 to the value of the bit constitutes a non-negative integer; the opposite of the value of = ₍ _ _ab ) _ ₍ . _cd) is obtained as the real part of the product of the first complex and the second complex ;

 Or the first real part of the first complex signal received by the first receiving module 11

", the first imaginary part ^, the absolute value of the second real part b and the second imaginary part d of the second complex signal are both smaller than

其中 为非负整数； 所述第一获取模块 12 根据第一复数信号获取的第一变换值为 S = '· ₊ c， 所述根据第二复数信 号获取的第二变换值 ί = ·2 ⁺¹ _{+ ί}τ,其中 ^为"的相反数， _d '为 d的相反数， 所述第一计算模块 13计算得到的第一参考值 2 ^k -l, JLa<0,c≥0,b≥0,d

The first transform value obtained by the first acquiring module 12 according to the first complex signal is S = '· ₊ c, and the second transform value obtained according to the second complex signal is ί = · 2 ^{+ 1} _{+ ί} τ, where ^ is the opposite of ", _d ' is the opposite of d, the first reference value calculated by the first calculation module 13

_Wl =st=a'b-2 ^4k+2 +(a'd'+bc)- 2 ^2k+l +cd'; The second obtaining module 14 is specifically configured to acquire bits 0 to -1 of >H The value of the bit constitutes a value of a non-negative integer; the obtained non-negative integer of the value of the 4k+1 bit is the imaginary part of the product of the first complex and the second complex; obtaining the 3⁄4 of the > +2 to the value of the bit constitutes a non-negative integer; the opposite of the value of ₍ _ _ab _ _ _cd ) is obtained as the real part of the product of the first complex and the second complex; or The first real part a of the first complex signal received by the first receiving module 11 a. The absolute value of the second real part b and the second real part b of the second complex signal are less than 2 ^k - l, 3_a>0, c>0, b>0, d<0^, where is a non-negative integer; the first transform value obtained by the first obtaining module 12 according to the first complex signal is S = · _{+ c} , The second transformed value d ^{2 1} ^ obtained according to the second complex signal, where ^ is the inverse of d, and the first reference value calculated by the first calculating module 13 is 1⁄4i = st=ad'-2 ^{4k+ 2 + (b + cd ')} - 2 2k + l + bc; the second acquisition module 14 for acquiring specific A value of a non-negative integer formed by a value of 0 to -1 bit; a non-negative integer formed by the value of the obtained first to +1 bit as a real part of a product of the first complex number and the second complex number; The non-negative integer formed by the value of the 3⁄4+2 to the bit of H is the value of -ad; the opposite of the value of (-^)-^) is obtained as the first complex number and the second The imaginary part of the product of the complex number;

 Or the first real part of the first complex signal received by the first receiving module 11

", the first imaginary part ^, the absolute value of the second real part b and the second imaginary part d of the second complex signal are both smaller than

2*-1, J_«>0, c<0,fe>0, d>0H†, where is a non-negative integer; the first transform value obtained by the first obtaining module 12 according to the first complex signal is S= c '· ₊ , the second transformed value i^^^ + obtained according to the second complex signal, where C ' is the opposite of C, and the first reference value calculated by the first calculating module 13 > Η = =^·'·2 ^{4 2} +(^+^6 ·2 ⁺¹ +^; the non-negative integer formed by the value of the 0th to 2 - 1 bits specifically used by the second obtaining module 14 is ^ a value of a non-negative integer formed by the value of the first to the +1st bits of >H as the real part of the product of the first complex number and the second complex number; the obtained value of the 3⁄4+2 to the bit is non-formed The negative integer is the value of - _bc ; the opposite of the value of - _bc ) _ _ad) is taken as the imaginary part of the product of the first complex number and the second complex number;

Or the absolute value of the first real part, the first imaginary part C, the second real part b and the second imaginary part d of the second complex signal received by the first receiving module 11 All are less than 2^-1, J_«>0, c>0, fe<0, d>0H†, where is a non-negative integer; the first transform value obtained by the first acquiring module 12 according to the first complex signal is S = · ₊ c , the second transformed value i = d .2 ⁺¹ ₊ fc' obtained according to the second complex signal, where b' is the opposite of b, and the first calculating module 13 calculates A reference value 1⁄4i = st = ad-2 ^{4k + 2} + (ab' + cd) - 2 ^{2k + l} + b'c; the second acquisition module 14 is specifically used to obtain 0 to 2 -1 of >3⁄4 non-negative integer value composed of bits of the value of _BC _; non-negative integer Get> value of the bit to +1 Η constituting acquires the first plurality of non-negative integer and the opposite of a The real part of the product of the two complex numbers; the value of the non-negative integer formed by the value of the first bit of >Η is the value of ^; the value of (^)_(_^^ is obtained as the first complex number and the second plural number The imaginary part of the product;

Alternatively, the absolute values of the first real part of the first complex signal received by the first receiving module 11, the first real part, the second real part b of the second complex signal, and the second imaginary part d are both If the value is less than 2 ^k -1 , JLa < 0, c ≥ 0, b ≥ 0, d ≥ 0 ^, where is a non-negative integer; the first transform value obtained by the first acquiring module 12 according to the first complex signal is S = c · ₊ α· , the second transformed value i = 2 ² w ₊ obtained according to the second complex signal, wherein ^ is the opposite number, the first reference value calculated by the first calculating module 13 is 1⁄4i = st =ad-2 ^4k+2 + ( b'+cd) - 2 ^{2k + l} + b'c; the second acquisition module 14 is specifically configured to obtain a non-negative value of the 0th to 2 - 1th bit values The integer is the value of _ _ad ; the non-negative integer formed by the value of the first to the +1th bit of >Η is obtained, and the non-negative integer is obtained. The opposite of the integer is taken as the real part of the product of the first complex number and the second complex number; the value of the non-negative integer formed by the value of the +2 to the bit of >Η is obtained; the value of _(_^ ^ is obtained) An imaginary part of the product of the first complex number and the second complex number;

_{+ C}'， 所述根据第二复数 信号获取的第二变换值^ = ^2^{2 +1} , 其中^为"的相反数， c'为 C的相反 数， 为 d的相反数, 所述第一计算模块 13计算得到的第一参考值 Alternatively, the absolute values of the first real part of the first complex signal received by the first receiving module 11, the first real part, the second real part b of the second complex signal, and the second imaginary part d are both Less than 2 ^k -l, 3_a < 0, c < 0, b > 0, d < 0 ^ , where is a non-negative integer; the first transform value obtained by the first obtaining module 12 according to the first complex signal is s =

_{+ C} ', the second transformed value obtained according to the second complex signal ^ = ^2 ^{2 +1} , where ^ is the opposite of ", c' is the opposite of C, is the opposite of d, the a first reference value calculated by a calculation module 13

W _l =si=a'd'-2 ^4k+2 +(a'b+c'd')-2 ^2k+1 +bc'; the second obtaining module 14 is specifically configured to obtain the 0th of >H A non-negative integer consisting of a value of -1 bit is a value of _^; a non-negative integer consisting of the obtained value of the +1st bit is obtained, and an inverse of the non-negative integer is obtained as the first complex sum The real part of the product of the second complex number; the value of the non-negative integer formed by the value of the 3⁄4+2 to the bit of >Η is the value of ^; the value of (^) _ ( _-bc) is obtained as the first complex sum The imaginary part of the product of the second complex number;

 Alternatively, the absolute value of the first real part, the first imaginary part c, the second real part b and the second imaginary part d of the first complex signal received by the first receiving module 11 Less than

2 ^k -l, J_«>0, c<0, fe<0, d<0H†, where is a non-negative integer; the first transform value obtained by the first obtaining module 12 according to the first complex signal is S = c '· ₊ , the second transformed value i = 2 ^{2 +1} _{+ i} r obtained according to the second complex signal, where b' is the opposite of b, c' is the opposite of c, d, is d The first reference value calculated by the first calculating module 13

w _l =st=b'c'-2 ^4k+2 +(ab'+c'd')- 2 ^2k+l +ad'; the second obtaining module 14 is specifically configured to obtain the 0th of >H a value of a non-negative integer formed by a value of -1 bit; a non-negative integer formed by the value of the first to the +1st bit of >Η, obtaining the opposite of the non-negative integer as the first complex number The real part of the product of the two complex numbers; the non-negative integer consisting of the value of the 3⁄4+2 to the bit of >Η is the value of be; the value of φ_α) is obtained as the product of the first complex number and the second complex number Imaginary part

_{+ C}'， 所述根据第二复数 信号获取的第二变换值 i = d.2 ⁺¹W, 其中 α'为。的相反数， b'为 b的相反 数， c'为 c的相反数， 所述第一计算模块 13计算得到的第一参考值 Alternatively, the absolute value of the first real part, the first imaginary part c, the second real part b and the second imaginary part d of the first complex signal received by the first receiving module 11 All are smaller than 2 ^k -1, 3_a < 0, c < 0, b < 0, d > 0 ^ , where is a non-negative integer; the first transform value obtained by the first acquiring module 12 according to the first complex signal is s =

_{+ C} ', according to the second plural The second transformed value of the signal acquisition is i = d.2 ⁺¹ W, where α' is . The opposite of the number, b' is the opposite of b, c' is the opposite of c, the first reference value calculated by the first calculating module 13

W _l =st = a'd-2 ^4k+2 +(a'b'+c'd)-2 ^2k+1 +b'c'; the second obtaining module 14 is specifically used to obtain the 0th to a value of a non-negative integer formed by a value of 1 bit; a non-negative integer formed by the value of the +1st to 4k+1 bits obtained as a real part of a product of the first complex number and the second complex number; a value of a non-negative integer formed by the value of the 3⁄4+2 to the bit; obtaining an inverse of the value of _{_ad} , _ _{bc) as the imaginary part of the product of the first complex number and the second complex number; The absolute value of the first real part, the first imaginary part, the second real part b, and the second imaginary part d of the first complex signal received by the first receiving module 11 is less than 2 -1, J ≥ 0, c < 0, fc < 0, where d < 0, where is a non-negative integer; the first transform value obtained by the first obtaining module 12 according to the first complex signal is s = c'- 2^ ₊ a , the second transformed value i = feW _{+ i} r obtained according to the second complex signal, where b' is the opposite of b, c' is the opposite of c, and ^ is the opposite of d, The first reference value calculated by the first calculation module 13 is _l lst=b=c'-2 ^4k+2 +(ab'+c'd')-2 ^2k+l +ad'; the second obtaining module 14 is specifically configured to obtain a value of the non-negative integer formed by the value of the 0th to the -1th bits of >H, and obtain the value of the first 4k+l bit of >Η The non-negative integer formed by the value of the bit is the real part of the product of the first complex number and the second complex number; the value of the non-negative integer consisting of the value of the 3⁄4+2 to the bit of >Η is obtained as the value of _; _bc) _ _ad) opposite of the first plurality and a second plurality of the product of the imaginary part of the value. A person skilled in the art can understand that all or part of the steps of implementing the above method embodiments may be completed by using hardware related to program instructions, and the foregoing program may be stored in a computer readable storage medium, and the program is executed when executed. The foregoing storage medium includes: ROM, RAM, magnetic disk or optical disk, and the like, which can store various program codes. Finally, the above embodiments are only used to illustrate the technical solution of the present invention. The invention is described in detail with reference to the foregoing embodiments, and those of ordinary skill in the art should understand that the technical solutions described in the foregoing embodiments may be modified or some of the techniques may be The features are equivalent to those of the embodiments of the present invention.

Claims

Claim  A method for implementing complex multiplication using a multiplier, comprising: receiving a first complex signal α+α' and a second complex signal b+, wherein the first complex signal and the second complex signal are both communicating Digital signal; Performing a shift process according to the first real part of the first complex signal and the first imaginary part c to obtain a first transformed value ⁵ , and according to the second real part b and the second imaginary part d of the second complex signal Performing a shift process to obtain a second transformed value ί;  Determining, by using the multiplier, the first reference value >H=W according to the first transformed value s and the second transformed value ί;  Obtaining a real part of a product of the first complex number and the second complex number according to the first reference value >, and an imaginary part of a product of the first complex number and the second complex number. 2. The method for implementing complex multiplication using a multiplier according to claim 1, wherein: the first real part of the first complex signal and the first imaginary part c, and the second complex signal The absolute values of the second real part b and the second imaginary part d are both less than or equal to 2" -1 , where is a positive integer; the first transformed value s = ^ 2 ² _{+ c} obtained according to the first complex signal The second transformed value t = b. ₊ d ' obtained according to the second complex signal, and the first reference value w _l = st = ab - 2 ^4k + (ad + be) - 2 ^2k + cd.  3. The method for implementing complex multiplication using a multiplier according to claim 2, wherein the real part of the product of the first complex number and the second complex number is obtained according to the first reference value > ,, and The imaginary part of the product of the first complex number and the second complex number includes: Obtaining a second reference value w ₂ = ί ^ 1 and a third reference value according to the first reference value > Η ( ₂ - (ad + bc)) =- - _t ; obtaining the product cd of the first imaginary part and the second imaginary part according to the first reference value >Η: When W + (2 ² *- ¹ - 1) ≥ 0, the value of the lower 2k bits of + (2 ² *- ¹ - 1) is obtained by subtracting the value of 2 ² - ¹ - 1 value; When W + (2 ² *- ¹ - 1) < 0, the value of the lower 2k bits of - + (2 ² *- ¹ - 1)] is obtained by subtracting the value of 2 ² " + 1 The opposite number is the value of cd; Obtaining, according to the second reference value W ₂ , a product of the first real part and the second imaginary part, and a sum of products of the first imaginary part and the second real part being a virtual product of the product of the first complex number and the second complex number Department: When _W2 + ( ₂ 2" - 1) ≥ 0, the value of the low Ik bit of w ₂ + (2 ^M - ¹ - 1) is obtained by subtracting the value of 2 ² " -1 from the value of 2 ² " -1 ad + bc a value of the imaginary part of the product of the first complex number and the second complex number; When w ₂ + (2 ² - ¹ _ 1) < 0, obtain the value of the lower 2k bits of the -[w ₂ + (2 ² " - 1)] non-negative number minus the value of 2 ² " +1 The opposite number is the value of orf+bc as the imaginary part of the product of the first complex number and the second complex number; Obtaining a product ab of the first real part and the second real part according to the third reference value W ₃ : When w ₃ + (2 ² *- ¹ - 1) ≥ 0, the non-negative number formed by the value of the low Ik bit of w ₃ + (2 ² *- ¹ - 1) is subtracted by 2 ² - ¹ -1 a value of ab; When w ₃ + (2 ² *- ¹ - 1) < 0, obtain the opposite of the value of the lower 7k bits of - [ w ₃ + ( - ¹ - 1)] minus the value of + 1 Is the value of ab;  The value of ab_cd is obtained as the real part of the product of the first complex number and the second complex number.  4. The method for implementing complex multiplication using a multiplier according to claim 2, wherein the real part of the product of the first complex number and the second complex number is obtained according to the first reference value > ,, and The imaginary part of the product of a complex number and the second complex number includes:

Obtaining a product cd of the first imaginary part and the second imaginary part according to the first reference value Μ|: obtaining a non-negative number formed by a value of a low 2k bit of + (2 ² *- ¹ -1) + ^· 2 ^2k Subtract the value of the value of 2 ² " - 1 , where is a positive integer, and w + (2 ² - L^ + ^^ O; Obtaining, by the second reference value W ₂ , a product of the first real part and the second imaginary part, and a sum of products of the first imaginary part and the second real part + bc as a product of the first complex number and the second complex number The imaginary part: Obtaining a non-negative number formed by the value of the lower 2k bits of w ₂ + (2 ^2k - ¹ -l) + K, · 2 ^2k minus the value of 2 ^2ί - 1 as the product of the first complex number and the second complex number An imaginary part, where is a positive integer, and w ₂ + (2 ^2k - ¹ -l) + K 2 ^2k >0; Obtaining the product ab of the first real part and the second real part according to the third reference value ⁄4: obtaining a non-negative number formed by the value of the low Ik bit of u' ₃ + (2 ^2k - ¹ -l) + · 2 ^2k Subtract - 1 The value is "the value of b, where is a positive integer, and w ₃ + (2 ^M - i - +

O ;  The value of ab-cd is masked as the real part of the product of the first complex number and the second complex number.  5. The method for implementing complex multiplication using a multiplier according to claim 2, wherein the real part of the product of the first complex number and the second complex number is obtained according to the first reference value > ,, and The imaginary part of the product of the first complex number and the second complex number includes: Obtaining a second reference value w ₂ =fc^ according to the first reference value>Η; obtaining a product cd of the first imaginary part and the second imaginary part according to the first reference value>Η:  Get >low the value of the bit to form a signed integer whose value is cd; Obtaining, according to the second reference value w ₂ , a product of the first real part and the second imaginary part, and a sum of products of the first imaginary part and the second real part, ad +bc, as the first complex number and the second complex number The imaginary part of the product:  Obtaining a signed integer consisting of a value of >3⁄4 low bits as the imaginary part of the product of the first complex number and the second complex number, and wherein a value of >3⁄4 when the value of the -1st bit of >Η is 0 The value of the first to the -1st bit equal to >Η; the value of the -1st bit of >Η is 1, and the value of the first to the -1st bit of >Η is equal to 1; Obtaining a product ob of the first real part and the second real part according to the second reference value w ₂ : In _ί 2K and w ₂ of the bit is 0, to obtain the value of 1 bit of the _2-bit signed integer w is composed of, in the w ₂ - 1 bit when the bit is 0 And obtaining a signed integer consisting of the value of the Ik to -1 bit of w ₂ plus a value obtained by adding a signed integer; wherein the value of the w _{2 is} at the value of the -1 bit of M| The value of the first to the -1st bit equal to 0, the value of the -1 bit of >H is 1, and the value of w ₂ is equal to the value of the first -1st bit of M| plus 1;  The value of ab-cd is masked as the real part of the product of the first complex number and the second complex number.  6. The method for implementing complex multiplication using a multiplier according to claim 1, wherein values of the first real part, the first imaginary part ^, the second real part b, and the second imaginary part d are When the integer is ^^, the 2 obtained according to the first complex signal a first transformed value S = · 2 ₊ c , the second transformed value obtained according to the second complex signal t = b - 2 ^2k + d ; and the first reference value

Among them Positive integer  Obtaining a real part of a product of the first complex number and the second complex number according to the first reference value >Η, and an imaginary part of a product of the first complex number and the second complex number includes:  Obtaining a value of the non-negative integer consisting of the values of bits 0 to -1 of >Η;  Obtaining a non-negative integer consisting of the value of the first to the -1 bits of >Η as the imaginary part of the product of the first complex number and the second complex number; Obtaining a non-negative integer consisting of the value of the first _ι bit of w _x is the value of ob;  The value of ab-cd is taken as the real part of the product of the first complex number and the second complex number.  A device for implementing complex multiplication using a multiplier, comprising: a first receiving module, configured to receive a first complex signal α+d and a second complex signal b+^, the first complex signal and The second plurality of signals are all communication digital signals;  a first acquiring module, configured to acquire a first transformed value s according to a first real part of the first complex signal and a first virtual part c, and a second real part according to the second complex signal b and the second imaginary part d are subjected to shift processing to obtain a second transformed value ί; a first calculating module, configured to calculate, by using the multiplier, the first reference value>H=w according to the first transformed value _S and the second transformed value ί;  a second acquiring module, configured to acquire, according to the first reference value >Η, a real part of a product of the first complex number and a second complex number, and an imaginary part of a product of the first complex number and the second complex number. 8. The apparatus for implementing complex multiplication using a multiplier according to claim 7, wherein the first real part of the first complex signal received by the first receiving module and the first imaginary part c, and The absolute value of the second real part b and the second imaginary part d of the second complex signal are both less than or equal to 2" - 1 , where is a positive integer; the first acquiring module obtains the first according to the first complex signal a transform value S = · 2 ₊ c , the second transform value obtained from the second complex signal t = b . 2 ; the first reference value calculated by the first calculation module M^^ ^ +^+k +d  9. The apparatus for implementing complex multiplication using a multiplier according to claim 8, wherein the second obtaining module comprises: a first reference value obtaining unit, configured to acquire a second reference value w ₂ = ^l and a third reference value _W3 = ~^; ^) according to the first reference value > a first coefficient acquiring unit, configured to acquire a product of the first imaginary part and the second imaginary part according to the first reference value>Η, that is, when w _{1 +} ( ^2M − ι^ο, obtain w _{1 +} ( ² - Li The value of the low-bit value consists of a non-negative number minus the value of 2^ -1, at +( ^223⁄4 - ii O, get - a non-negative number formed by the value of the lower 2k bits of [v, + (2 ² *- ¹ - 1)] minus the value of the opposite of the value of 2 ² " + 1; according to the second reference value W ₂ acquiring the product of the first real part and the second imaginary part, and the sum of the product of the first imaginary part and the second real part + bc as the imaginary part of the product of the first complex number and the second complex number, ie, at w ₂ + ( ²² "-l) ≥ 0, obtain the non-negative number formed by the value of the low bit of w ₂ + ( - il) minus the value of 2 ² " - 1 as the product of the first complex number and the second complex number The imaginary part, when w ₂ + (2 ² "- ¹ - 1) < 0, obtains the non-negative number of the value of the low Ik bit of [w ₂ + ( - ¹ - 1)] minus + i An inverse of the value as an imaginary part of the product of the first complex number and the second complex number; obtaining a product ab of the first real part and the second real part according to the third reference value W ₃ , that is, at w ₃ + ( ²² When Hl) ≥ 0, the value of the low bit of + ( ² *- ¹ - 1) is obtained by subtracting the value of 2 ² " - 1 from the value of ob. In H3⁄4 + ( ² -, get - The value of the low-bit value of [νν _{3 +} ( ^22λ - ' -1)] is subtracted from the value of 2^ +1 by the value of ob; The value of ab-αί is taken as the real part of the product of the first complex number and the second complex number.  10. The apparatus for implementing complex multiplication using a multiplier according to claim 8, wherein the second obtaining module comprises: a first reference value acquiring unit, configured to acquire a second reference value according to the first reference value>Η

a second coefficient acquiring unit, configured to acquire a product cd of the first imaginary part and the second imaginary part according to the first reference value>Η, that is, obtain W + (2 ² *- ¹ -l) + K _t · 2 ^2k The value of the low Ik bit constitutes a non-negative number minus the value of the value of 2 - i, where is a positive integer, and +(2 ² - i -^ + ^^O; obtains the first reference value according to the second reference value a product of a real part and a second imaginary part, and a sum of products of the first imaginary part and the second real part orf+bc as the imaginary part of the product of the first complex number and the second complex number, that is, obtaining w ₂ + ( - ¹ -l) + K _t · 2 ^2k The value of the low 2k bit constitutes a non-negative number minus the value of 2 ² " - 1 as the imaginary part of the product of the first complex number and the second complex number, where is positive Integer, and w ₂ + (2 ^2k - ¹ -l) + K 2 ^2k >0; and obtaining a product ab of the first real part and the second real part according to the third reference value, that is, obtaining w ₃ + (2 ² *- ¹ -l) + K _t · 2 ^2k The value of the low 2k bit is a non-negative number minus the value of 2 - i is the value of ob, where is a positive integer, and w ₃ +(2 ^M - i- + ^ ^O ; The value of ob is taken as the real part of the product of the first complex number and the second complex number.  11. The apparatus for implementing complex multiplication using a multiplier according to claim 8, wherein the second obtaining module comprises: a value obtaining unit, configured to acquire a second reference value according to the first reference value>Η

a third coefficient acquiring unit, configured to acquire, according to the first reference value>Η, a product of a first imaginary part and a second imaginary part, that is, a value obtained by acquiring a value of a lower-lower bit; The second reference value w ₂ obtains a product of the first real part and the second imaginary part, and a sum of products of the first imaginary part and the second real part + bc as an imaginary part of the product of the first complex number and the second complex number , that is, a signed integer consisting of a value of >3⁄4 low bits is obtained as the imaginary part of the product of the first complex number and the second complex number, and wherein the value of the 2k _1 bit of >Η is 0, w ₂ The value of the value is equal to the value of the first to the -1st bit; the value of the -1st bit is 1, and the value of w ₂ is equal to the value of the first to -1st bit of M| plus 1; The second reference value w ₂ obtains the product ab of the first real part and the second real part, that is, when the value of the 2k _1th bit is 0, the value of the 2nd to -1st bits of the w ₂ is obtained. unsigned integer value of ab, 1 bit when the first bit is 0, to obtain the value of 1 bit of the _2-bit signed integer w configuration plus 1 obtained as a signed integer; , The value w ₂ in> -1 bit value of 0 is equal to Η> Η value of the first bit to -1, the value of> -1 bits of Η 1, The value of w ₂ is equal to the value of the first to the -1st bit of >Η plus 1; the value of - is obtained as the real part of the product of the first complex number and the second complex number.  12. The apparatus for implementing complex multiplication using a multiplier according to claim 7, wherein: the first real part of the first complex signal received by the first receiving module, the first imaginary part c, the first The values of the second real part b and the second imaginary part d of the two complex signals are all integers greater than or equal to 0, and the first acquiring module obtains the first transformed value according to the first complex signal. s = a - 2 ^2t ₊ c , the second transformed value i = ^ 2 ^M ₊ obtained according to the second complex signal, and the first reference value calculated by the first calculating module

+aii , where is a positive integer; The second acquisition module is configured to non-negative integer value acquired ^Wl cd value of 0 to -1 bits constituting acquires nonnegative integer value of 1 bit to ^2-bit configuration as W Place The product of said first complex and the second complex number imaginary unit, acquires the value of non-negative integer value composed of bits 1 bit to ^1; a value obtained as a product of the first plurality and second plurality of Real.