CN116599809A - OFDM signal peak-to-average ratio suppression method for underwater Internet of things - Google Patents
OFDM signal peak-to-average ratio suppression method for underwater Internet of things Download PDFInfo
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Abstract
The invention discloses an OFDM signal peak-to-average ratio suppression method of an underwater Internet of things, which mainly solves the problem of high peak-to-average ratio when an underwater OFDM system adopts high-order modulation and a large number of subcarriers to realize high-speed transmission. The scheme is as follows: modulating input data into an original frequency domain signal and performing inverse discrete Fourier transform on the original frequency domain signal to obtain an original time domain signal; calculating limiting noise by using the signal, primarily expanding the original frequency domain signal by the limiting noise, and carrying out expansion correction according to the reset expansion area; generating a phase factor sequence by using the chaotic sequence, and obtaining a time domain signal according to the phase factor sequence and the signal after expansion correction; the two sets of time domain signals are arbitrarily combined to generate a new time domain candidate signal, the peak-to-average ratio of all the time domain signals is calculated, and the smallest set is selected as a transmission signal. The invention reduces the peak-to-average ratio of the OFDM signal, can ensure that the error code loss is within an acceptable range, improves the overall performance of the OFDM system, and can be used for underwater Internet of things communication.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a peak-to-average ratio suppression method of an Orthogonal Frequency Division Multiplexing (OFDM) signal, which can be used for underwater Internet of things communication.
Background
In recent years, exploration of the ocean is more and more important, but the traditional underwater wireless communication mode based on sound waves and radio frequency is difficult to meet the increasing information transmission requirement, and the underwater wireless optical communication system based on blue-green light has become a hot spot of current research due to the advantages of high speed and low time delay. The underwater Internet of things is characterized in that intelligent wireless sensor areas are created, and data collected by the intelligent wireless sensor areas are transmitted at a high speed in real time through an underwater wireless optical communication system depending on equipment and a transmission unit which are served by the intelligent wireless sensor areas. OFDM modulation is widely used as an important means for improving the transmission rate, and high-capacity high-speed transmission requires OFDM to employ a high-order modulation scheme and a large number of subcarriers, which inevitably results in an excessively high peak-to-average ratio of the OFDM signal. And the peak-to-average power ratio signal will operate in the nonlinear region of the high power amplifier, thereby causing clipping distortion and deteriorating system performance.
The current method for inhibiting the peak-to-average ratio mainly comprises a distortion class clipping method, a probability class method and a constellation expansion method. The amplitude limiting method is characterized in that the amplitude limiting method is simple to realize and has good peak-to-average ratio inhibiting effect and lower complexity by carrying out distortion operation on a signal with high instantaneous peak power without changing the phase of the signal, but the amplitude limited signal has serious in-band distortion and out-of-band spectrum expansion, worsens the error rate performance of the system and is not suitable for a harsher underwater environment. The probability method processes signals by introducing phase weighting coefficients, and the method does not cause the error rate performance of the system to deteriorate, but does need to transmit a large amount of sideband information and carry out inverse processing operation at a receiving end, thereby not only increasing the complexity, but also reducing the frequency spectrum efficiency of the system. The constellation expansion is to map some data to a specific area instead of a specific point by changing the mapping mode, so as to achieve the effect of inhibiting the peak-to-average ratio. Therefore, the research on the OFDM signal peak-to-average ratio suppression method suitable for the underwater Internet of things has important guiding significance for promoting the development of the high-speed underwater wireless communication technology.
Liwei Yang et al in its published paper "OFDM-based algorithm for peak average power ratio suppressing in underwater wireless optical communications" (202220 th International Conference on Optical Communications andNetworks (ICOCN)) propose an improved selective mapping SLM algorithm that reduces the autocorrelation of data by generating random phase sequences using chaotic sequences, and only requires transmission of random phase sequence numbers, thereby reducing transmission of sideband information. The specific implementation steps are as follows: serial-parallel conversion of the mapped frequency domain transmission signals into multi-channel parallel data; then generating a plurality of groups of random phase sequences which are different and have the same length as the parallel data through the chaotic sequence, and multiplying the random phase sequences with the input data to obtain a plurality of groups of signals after dot multiplication; and finally, carrying out inverse discrete Fourier transform operation on the plurality of groups of signals to transform the signals into a time domain, calculating the peak-to-average ratio of the time domain signals at the moment, selecting a group with the minimum peak-to-average ratio as an output signal, and recording the serial number at the moment as sideband information for transmission. Although the method can reduce the transmission of the side information, the computation complexity is higher because a plurality of groups of alternative signals are generated by carrying out inverse discrete Fourier transform operation.
Yuzhuo Liu et al in its published paper "Novel ACE Scheme for PAPR Reduction of High Broadband OFDM Systems" (2019IEEE 19th International Conference on Communication Technology (ICCT)) propose a predistortion constellation extension ACE algorithm, implemented as follows: performing inverse discrete Fourier transform operation on the mapped frequency domain data to convert the frequency domain data into a time domain signal, performing amplitude limiting processing on the time domain signal, calculating amplitude limiting noise by the amplitude limited signal and the original time domain signal, and performing Fourier transform on the amplitude limiting noise to obtain frequency domain amplitude limiting noise; expanding the original frequency domain signal; then correcting the spread signal according to the set constellation point expandable region, and performing inverse discrete Fourier transform operation on the corrected frequency domain signal to transform the frequency domain signal into a time domain; the peak-to-average ratio of the time domain signal is calculated, and a group with the smallest peak-to-average ratio is selected as the output signal. Although the method does not need to transmit sideband information and expands internal constellation points, when high-order modulation and a large number of subcarriers are adopted, the peak-to-average ratio inhibition performance of the method is poor.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides an OFDM signal peak-to-average ratio suppression method for the underwater Internet of things, so that the OFDM signal peak-to-average ratio suppression performance is improved, the complexity of a system is reduced, and the OFDM signal peak-to-average ratio suppression requirement of the underwater Internet of things is met.
The key technology of the invention is as follows: redefining an expansion mode of constellation points, expanding both inner and outer constellation points, and increasing the expansion number of constellation points; generating a random phase factor sequence by adopting a chaotic sequence, and multiplying the frequency domain signal after expansion with the random phase factor sequence; any two different sets of time-domain candidate signals are combined using the linear nature of the inverse discrete fourier transform to produce a new candidate signal. The implementation steps comprise the following steps:
in order to achieve the above purpose, the technical scheme adopted by the invention comprises the following steps:
(1) Modulating a binary bit stream of a system transmitting end into an original frequency domain OFDM signal X;
(2) Up-sampling the original frequency domain signal X to obtain an up-sampled frequency domain signal X ', and performing inverse discrete Fourier transform on the X' to obtain an up-sampled time domain signal U;
(3) Performing amplitude limiting operation on the time domain signal U, calculating time domain amplitude limiting noise, performing Fourier transformation on the time domain amplitude limiting noise to obtain frequency domain amplitude limiting noise C clip ；
(4) From the frequency-domain clipping noise C clip The original OFDM signal X is subjected to preliminary expansion, and the preliminary expansion signal is corrected according to a set expansion area:
(4a) From C clip The signal X is subjected to preliminary expansion to obtain a preliminary expansion frequency domain signal；
(4b) Dividing the constellation point expandable region into an inner part and an outer part, wherein the outer part comprises a two-dimensional square expansion region E square And a one-dimensional linear expansion region E line The inner expansion area is a two-dimensional circular expansion area E round ；
(4c) For each preliminary spread frequency domain signalCorresponding two-dimensional square extension area E square Is corrected to obtain corrected spread frequency domain signal Y i ：
wherein ,representing the real part of the i < th > preliminary spread frequency domain signal, < >>Representing the imaginary part, X, of the i < th > preliminary spread frequency domain signal i Representing the i-th original frequency domain signal, i is more than 0 and less than N-1,O max =max (Real (X)) and Q max =max (Imag (X)) represents the real and imaginary maxima, respectively, of the constellation point of the selected modulation scheme;
(4d) For each preliminary spread frequency domain signalCorresponding one-dimensional linear expansion area E line Is corrected to obtain corrected spread frequency domain signal Y r ：
wherein ,Xr Representing the r original frequency domain signal, wherein r is more than 0 and less than N-1;
(4e) For each preliminary spread frequency domain signalCorresponding two-dimensional circular shapeExtension area E round Is corrected to obtain corrected spread frequency domain signal Y l ：
Wherein delta represents the maximum distortion amount, X l Representing the first original frequency domain signal,phase representing the first frequency-domain clipping noise, < >>Representing imaginary units, wherein l is more than 0 and less than N-1;
(4f) With spread correction of each frequency-domain signal Y i 、Y r and Yl Forming all corrected frequency domain signals Y;
(5) Generating M groups of random phase factor sequences P with the length of N by adopting a chaotic sequence;
(6) Multiplying the corrected frequency domain signal Y with the random phase factor sequence P to obtain a frequency domain signal after dot multiplication
(7) Frequency domain signal after dot multiplicationPerforming inverse discrete fourier transform operation to obtain a time domain signal d, and generating a new time domain alternative signal s by utilizing the linear property of inverse discrete fourier transform:
s z,k ＝cosθ·d g,k +j·sinθ·d h,k
wherein ,sz,k Represents the kth data, d, in the z-th set of new time-domain candidate signals g,k Represents the kth data, d, in the g-th set of time domain signals h,k Represents the kth data in the h time domain signal, wherein z is not less than 1 and not more than M (M-1)/2, g is not less than 1 and not more than M, h is not less than 1 and not more than M, g is not less than h, and 0 < theta < pi/2；
(8) And forming all time domain signals f by using the time domain signal d and the new time domain alternative signal s, calculating the peak-to-average power ratio of the time domain signals f, and selecting a group with the minimum peak-to-average power ratio as an output signal.
Compared with the prior art, the invention has the following advantages:
firstly, the invention redefines the constellation expansion mode by adopting the method of combining the predistortion ACE algorithm and the SLM algorithm, expands the points inside and outside the constellation, increases the expansion number of the constellation points, and then combines the SLM algorithm to further improve the peak-to-average ratio inhibition performance, thereby overcoming the problem that the prior peak-to-average ratio inhibition method has poor inhibition performance on high-order modulation and a large number of subcarriers under the condition of ensuring the unchanged error code performance of a receiving end, and improving the inhibition performance of the peak-to-average ratio.
Secondly, the method adopts the chaos sequence to generate the random phase factor sequence, and only needs to send specific sequence numbers after determining the random phase factor sequence, thereby reducing the transmission of side information and overcoming the problem of lower frequency spectrum utilization rate caused by excessive side information transmission in the prior art;
thirdly, the invention generates a new alternative signal by combining any two groups of different time domain alternative signals, and can reduce the times of inverse discrete Fourier transform when the same alternative signal is used, thereby overcoming the problem of higher complexity caused by performing inverse discrete Fourier transform operation for a plurality of times in the prior art, ensuring the peak-to-average ratio inhibition performance and reducing the complexity of a system.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
fig. 2 is a schematic diagram of a first quadrant constellation point scalable region in accordance with the present invention;
FIG. 3 is a schematic diagram of a constellation point expansion scheme of a two-dimensional square region in the present invention;
fig. 4 is a schematic diagram of a constellation point expansion mode of a one-dimensional straight line region in the present invention;
FIG. 5 is a schematic diagram of a constellation point expansion scheme of a two-dimensional circular region in the present invention;
FIG. 6 is a graph comparing the peak-to-average ratio suppression performance of the present invention with the prior art;
fig. 7 is a graph comparing bit error rate performance of the present invention with that of the prior art.
Detailed Description
Embodiments and effects of the present invention are described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the implementation steps of the present invention are as follows:
and step 1, modulating a binary bit stream of a system transmitting end into an original frequency domain OFDM signal X.
Quadrature amplitude modulation is carried out on a binary bit stream of a system transmitting end, and an original frequency domain signal X is obtained:
X＝[X 0 ,X 1 ,···,X k ,···,X N-1 ]
wherein ,Xk Represents the kth data in the original frequency domain signal, k=0, 1, ·, N-1, N is the number of subcarriers contained in the OFDM symbol, quadrature amplitude modulation adopted is 256qam, n=512.
Step 2, up-sampling the original frequency domain signal X to obtain an up-sampled time domain signal U.
2.1 Inserting (J-1) X N zeros in the middle of the original frequency domain signal to obtain an up-sampled frequency domain signal X':
wherein ,Xk Represents the kth data, X ', in the original frequency domain signal' n Represents the nth data in the up-sampled frequency domain signal, J represents the up-sampling factor and, j=4, n=0, 1, JN-1;
2.2 X 'for up-sampled frequency domain signal' n Performing inverse discrete fourier transform to obtain an up-sampled time domain signal U:
U＝[U 0 ,U 1 ,···,U n ,···,U JN-1 ]
wherein ,Un Representation upsamplingThe nth data in the post-time domain signal.
Step 3, performing amplitude limiting operation on the time domain signal U to obtain frequency domain amplitude limiting noise C clip 。
3.1 Calculating clipping threshold A clip ：
wherein ,CR Represents the clipping rate, C R ＝4.68，Representing the average power of the up-sampled time domain signal U;
3.2 According to the clipping threshold A clip Performing amplitude limiting operation on the up-sampled time domain signal U pair to obtain an amplitude-limited time domain signal
wherein ,the nth data in the limited time domain signal is represented by the following formula:
in the formula ,θn For the up-sampled time domain signal U n Is used for the phase of the (c) signal,representing imaginary units, wherein |·| is modulo arithmetic;
3.3 According to the limited time domain signalAnd up-sampling time domain signal time domain U to calculate time domain limiting noise c clip ：
c clip ＝[c clip,0 ,c clip,1 ,···,c clip,n ,···,c clip,JN-1 ]
wherein ,representing the nth data in the limited noise signal;
3.4 Time-slicing noise c) clip Performing discrete Fourier transform and downsampling to obtain frequency domain limiting noise C clip ：
C clip ＝[C clip,0 ,C clip,1 ,···,C clip,k ,···,C clip,N-1 ]
wherein ,Cclip,k Representing the kth data in the frequency-domain limited noise signal.
Step 4, limiting noise C according to the frequency domain clip And performing preliminary expansion on the original OFDM signal X, and correcting the preliminary expansion signal according to the set expansion area.
The original OFDM signal X corresponds to the standard constellation point of the quadrature amplitude modulation, the dispersion range of the constellation point after clipping is smaller, and the noise C needs to be clipped through the frequency domain clip And the spreading factor performs preliminary spreading on the frequency domain signal to increase nonlinear distortion caused by amplitude limiting, so that constellation points are more dispersed, and a preliminary spread frequency domain signal, namely, dispersed constellation points after distortion is obtained. And the expansion area of the constellation point is redefined, and the preliminary expansion frequency domain signals of the inner area and the outer area are corrected to increase the expansion number of the constellation point and improve the peak-to-average ratio inhibition performance, and the method is concretely realized as follows:
4.1 From frequency domain limiting noise C clip The signal X is subjected to preliminary expansion to obtain a preliminary expansion frequency domain signal
wherein ,represents the kth data in the preliminary spread frequency domain signal, G represents the spreading factor, and the values of this example are 10 and 15;
4.2 Dividing the area:
referring to fig. 2, the step is to divide the constellation point expandable region into an inner and an outer portions, and the outer portion includes a two-dimensional square expandable region E square And a one-dimensional linear expansion region E line The inner expansion area is a two-dimensional circular expansion area E round ；
4.3 For each preliminary spread frequency domain signalCorresponding two-dimensional square extension area E square Is subjected to expansion correction:
referring to fig. 3, this step extends the frequency domain signal initially according to several different scenarios as followsAnd (3) correcting:
when the frequency domain signal is preliminarily spreadLocated in a two-dimensional square extension E square In the inner case, no correction is made, as shown in fig. 3 (a);
when the frequency domain signal is preliminarily spreadIs larger than the real part of the original frequency domain signal, but initially spreads the frequency domain signal +>When the imaginary part of (a) is smaller than the imaginary part of the original frequency domain signal,preliminary spreading of the frequency-domain signal +.>Is corrected to the original frequency domain signal X i As shown in fig. 3 (b);
when the frequency domain signal is preliminarily spreadWhen both the real part and the imaginary part of the original frequency domain signal are smaller than the real part and the imaginary part of the original frequency domain signal, the original frequency domain signal is primarily spread +>Corrected to original frequency domain signal X i As shown in fig. 3 (c).
Expanding corrected frequency domain signal Y i The following formula is shown:
wherein ,representing the real part of the i < th > preliminary spread frequency domain signal, < >>Representing the imaginary part, X, of the i < th > preliminary spread frequency domain signal i Representing the i-th original frequency domain signal, i is more than 0 and less than N-1,O max =max (Real (X)) and Q max =max (Imag (X)) represents the real and imaginary maxima, respectively, of the constellation point of the selected modulation scheme;
4.4 For each preliminary spread frequency domain signalCorresponding one-dimensional linear expansion area E line Is corrected by the constellation point signal:
referring to fig. 4, this step extends the frequency domain signal initially according to several different scenarios as followsAnd (3) correcting:
when the frequency domain signal is preliminarily spreadLocated in a one-dimensional linear expansion region E line In the above, no correction is performed, as shown in fig. 4 (a);
when the frequency domain signal is preliminarily spreadIs greater than or equal to the original frequency domain signal X r When the real part and the imaginary part of (a) are the frequency domain signal is preliminarily extended +.>Is corrected to the original frequency domain signal X r As shown in fig. 4 (b);
when the frequency domain signal is preliminarily spreadIs greater than or equal to the real part of the original frequency domain signal X r Is the real part of (a), but initially spreads the frequency domain signal +>Is smaller than the original frequency domain signal X r Will initially spread the frequency domain signal +.>Corrected to original frequency domain signal X r As shown in fig. 4 (c).
Expanding corrected frequency domain signal Y r The following formula is shown:
wherein Real (Y r ) Representing the real part of the r-th expansion corrected frequency domain signal, imag (Y r ) Representing the imaginary part of the r-th extended modified frequency domain signal,representing the real part of the r-th preliminary spread frequency domain signal, a ∈>Representing the imaginary part, X, of the r-th preliminary spread frequency domain signal r Representing the r original frequency domain signal, wherein r is more than 0 and less than N-1;
4.5 For each preliminary spread frequency domain signalCorresponding two-dimensional circular extension area E round Is corrected by the constellation point signal:
referring to fig. 5, this step extends the frequency domain signal initially according to several different scenarios as followsAnd (3) correcting:
when the frequency domain signal is preliminarily spreadLocated in a two-dimensional circular extension area E round When the internal part is not corrected, as shown in fig. 5 (a);
when the frequency domain signal is preliminarily spreadLocated in a two-dimensional circular extension area E round Externally, the frequency domain signal is primarily spread +.>Corrected to two-dimensional circular extension E round In, as shown in FIG. 5 (b)。
Expanding corrected frequency domain signal Y l The following formula is shown:
wherein, delta represents the maximum distortion, the value of delta is 0.01,represents the first preliminary spread frequency domain signal, X l Representing the first original frequency domain signal, +.>Representing the phase of the first frequency domain clipping noise, wherein l is more than 0 and less than N-1;
4.6 Corrected frequency domain signal Y with expansion in two-dimensional square expansion area i Extended modified frequency domain signal Y in one-dimensional linear extension region r And an extended modified frequency domain signal Y in a two-dimensional circular extension region l And forming the frequency domain signal Y after all the expansion correction.
And 5, generating M groups of random phase factor sequences P with the length of N by adopting a chaotic sequence.
The traditional phase factor sequence P is generated by randomly generating a group of numbers, all phase factor information needs to be transmitted, so that the frequency spectrum efficiency of the system is lower, the example adopts a mode of generating a random phase factor sequence by a chaotic sequence, after the random phase factor sequence is determined, only specific number numbers need to be transmitted, the transmission of side information is reduced, and the frequency spectrum efficiency of the system is improved, and the method is concretely realized as follows:
5.1 Using a chaotic sequence to generate a random number x:
x＝[x 1 ,x 2 ,···,x a ,x a+1 ···,x N ]
wherein ,xa+1 ＝μ·x a ·(1-x a ) Represents the value of the a+1st chaotic sequence, mu represents the fractal parameter, a=0, 1, ··, N-1 is a group of the components, in this example, μ=4, when a=0,setting an initial value x of a chaotic sequence 0 ＝0.0019；
5.2 Binary quantization of the random number x) to obtain a selection signal B:
B＝[B 0 ,B 1 ,···,B b ,···,B N-1 ]
wherein ,representing the result after the b-th binary quantization, b=0, 1, ··, N-1;
5.3 Selecting a phase factor by the selection signal B, resulting in a first set of random phase factor sequences T:
T＝[T 0 ,T 1 ,···,T k ,···,T N-1 ]
wherein ,a kth value representing a first set of random phase factor sequences,
5.4 Cyclically shifting the first set of random phase factor sequences T by lambda bits to produce the remaining M-1 set of random phase factor sequences W:
W＝[W 1 ,W 2 ,···,W λ ,···,W M-1 ]
wherein ,Wλ ＝[T λ ,···,T N-1 ,T 0 ,T 1 ,···,T λ-1 ]Represents a lambda group random phase factor sequence, lambda=1, 2, ··, M-1, M represents the group number of all random phase factor sequences P, and the value of M is 2 or 4;
5.5 A first set of random phase factor sequences T and the remaining M-1 set of random phase factor sequences W constitute the complete phase factor sequence P.
And 6, generating a new time-domain alternative signal s by utilizing the linear property of the inverse discrete Fourier transform.
According to the linear property of inverse discrete Fourier transform, the method combines any two groups of different time domain alternative signals to generate a new alternative signal s so as to reduce the times of inverse discrete Fourier transform when the same alternative signal is used, so that the method can reduce the complexity of a system while ensuring the peak-to-average ratio inhibition performance, and the implementation steps are as follows:
6.1 Multiplying the frequency domain signal Y after expansion correction with the random phase factor sequence P to obtain a frequency domain signal after dot multiplication
wherein ,kth data, X, representing an mth set of point multiplied signals k Represents the kth data, P, in the original frequency domain signal m,k K data representing the M-th group of random phase factor sequences, wherein M is more than or equal to 1 and less than or equal to M;
6.2 Frequency domain signal after dot multiplicationPerforming inverse discrete fourier transform operation to obtain a time domain signal d, and generating a new time domain alternative signal s by utilizing the linear property of inverse discrete fourier transform:
s z,k ＝cosθ·d g,k +j·sinθ·d h,k
wherein ,sz,k Represents the kth data, d, in the z-th set of new time-domain candidate signals g,k Represents the kth data, d, in the g-th set of time domain signals h,k Representing kth data in the h time domain signal, wherein z is not less than 1 and not more than M (M-1)/2, g is not less than 1 and not more than M, h is not less than 1 and not more than M, g is not less than h, and θ=pi/4;
and 7, calculating a time domain signal peak-to-average power ratio F according to the time domain signal d and the new time domain alternative signal s.
7.1 A time domain signal f) is composed of a time domain signal d and a new time domain candidate signal s:
f＝[d 1 ,d 2 ,···,d m ,···,d M ,s 1 ,s 2 ,···,s z ,···,s M·(M-1)/2 ]
wherein ,dm Representing the m-th set of time domain signals, s z Representing a new time-domain candidate signal of the z-th group;
7.2 Calculating the average power value alpha of the total time domain signal f):
calculating a v-th set of time domain signals f v Is a mean power value alpha of (a) v ：
wherein ,fv,k The kth data of the v-th time domain signal is represented, v is not less than 1 and not more than M+M (M-1)/2,
the average power value of each group is calculated by using the formula, and the average power value alpha of all groups is obtained:
α＝[α 0 ,α 1 ,···,α v ,···,α M+M·(M-1)/2 ]；
7.3 Calculating the maximum power value beta of the total time domain signal f:
β＝[β 0 ,β 1 ,···,β v ,···,β M+M·(M-1)/2 ]
wherein ,βv ＝max(|f v | 2 ) Representing a v-th group of time domain signals f v Is a maximum power value of (a);
7.4 Calculating the peak-to-average power ratio F of all the time domain signals F according to the average power value alpha and the maximum power value beta of the time domain signals F:
wherein ,representing the peak-to-average power ratio of the v-th set of time domain signals;
7.5 Selecting a time domain signal corresponding to the minimum value in the peak-to-average power ratio F as a transmitting signal.
The technical effects of the present invention will be further described with reference to the following simulation experiments.
1. Simulation experiment conditions:
the simulation adopts simulation software of AMD Ruilong R74800H, main frequency of 2.90GHz, memory of 16.0GB, 64-bit operating system and Microsoft windows professional edition MATLAB 2020 b. The modulation mode is 256QAM quadrature amplitude modulation, the number of subcarriers N is set to 512, the up-sampling multiple J is set to 4, the clipping rate CR is set to 4.68dB, the spreading factor G is set to 15, and the number of packets M is set to 2 and 4.
2. Simulation content and result analysis:
under the simulation condition, the invention sets the spreading factor to 15, the grouping number to 4, the spreading factor to 15 in the prior predistortion constellation spreading method, the grouping number to 4 in the prior selection mapping method, and the three methods are used for respectively carrying out peak-to-average ratio suppression on the original OFDM signals, and the obtained peak-to-average ratio suppression gain is shown in figure 6.
As can be seen from the simulation results of FIG. 6, the value of the function at the complementary cumulative distribution is 10 -4 When the pre-distortion constellation expansion method is used, the existing pre-distortion constellation expansion method can only obtain the peak-to-average ratio suppression gain of 2dB, the existing selection mapping method can also only obtain the peak-to-average ratio suppression gain of 2.5dB, and the peak-to-average ratio suppression gain of 3dB can be obtained.
Simulation 2, under the simulation conditions, the invention sets the expansion factor to 15, and the grouping number to 2 and 4; the existing predistortion constellation expansion method sets the expansion factor to 15, and the two methods are used for respectively carrying out peak-to-average ratio inhibition on the original OFDM signal, so that the obtained bit error rate performance is shown in figure 7.
As can be seen from the results of FIG. 7, the present invention has a spreading factor of 15 and an identical bit error rate, i.e., 10, as compared with the existing predistortion constellation -3 The signal-to-noise ratio loss is the same for both methods. It can also be seen that the present invention has a spreading factor of 15, which is differentThe number of packets of 2 or 4 does not affect the change of the error rate of the system. Therefore, compared with the existing predistortion constellation extension method, the method does not cause the error rate deterioration of the system.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the invention, but any modifications, equivalents, improvements, etc. within the principles of the present invention should be included in the scope of the present invention.
Claims (8)
1. An OFDM signal peak-to-average ratio suppression method of an underwater Internet of things is characterized by comprising the following steps:
(1) Modulating a binary bit stream of a system transmitting end into an original frequency domain OFDM signal X;
(2) Up-sampling the original frequency domain signal X to obtain an up-sampled frequency domain signal X ', and performing inverse discrete Fourier transform on the X' to obtain an up-sampled time domain signal U;
(3) Performing amplitude limiting operation on the time domain signal U, calculating time domain amplitude limiting noise, performing Fourier transformation on the time domain amplitude limiting noise to obtain frequency domain amplitude limiting noise C clip ；
(4) From the frequency-domain clipping noise C clip The original OFDM signal X is subjected to preliminary expansion, and the preliminary expansion signal is corrected according to a set expansion area:
(4a) From C clip The signal X is subjected to preliminary expansion to obtain a preliminary expansion frequency domain signal
(4b) Dividing the constellation point expandable region into an inner part and an outer part, wherein the outer part comprises a two-dimensional square expansion region E square And a one-dimensional linear expansion region E line The inner expansion area is a two-dimensional circular expansion area E round ；
(4c) For each preliminary spread frequency domain signalCorresponding two-dimensional square expansionExhibition area E square Is corrected by the constellation point signal to obtain a frequency domain signal Y after expansion correction i ：
wherein ,representing the real part of the i < th > preliminary spread frequency domain signal, < >>Representing the imaginary part, X, of the i < th > preliminary spread frequency domain signal i Representing the i-th original frequency domain signal, i is more than 0 and less than N-1,O max =max (Real (X)) and Q max =max (Imag (X)) represents the real and imaginary maxima, respectively, of the constellation point of the selected modulation scheme;
(4d) For each preliminary spread frequency domain signalCorresponding one-dimensional linear expansion area E line Is corrected by the constellation point signal to obtain a frequency domain signal Y after expansion correction r ：
wherein ,Xr Representing the r original frequency domain signal, wherein r is more than 0 and less than N-1;
(4e) For each preliminary spread frequency domain signalCorresponding two-dimensionCircular extension E round Is corrected by the constellation point signal to obtain a frequency domain signal Y after expansion correction l ：
Wherein delta represents the maximum distortion amount, X l Representing the first original frequency domain signal,phase representing the first frequency-domain clipping noise, < >>Representing imaginary units, wherein l is more than 0 and less than N-1;
(4f) With spread correction of each frequency-domain signal Y i 、Y r and Yl Forming all corrected frequency domain signals Y;
(5) Generating M groups of random phase factor sequences P with the length of N by adopting a chaotic sequence;
(6) Multiplying the corrected frequency domain signal Y with the random phase factor sequence P to obtain a frequency domain signal after dot multiplication
(7) Frequency domain signal after dot multiplicationPerforming inverse discrete fourier transform operation to obtain a time domain signal d, and generating a new time domain alternative signal s by utilizing the linear property of inverse discrete fourier transform:
s z,k ＝cosθ·d g,k +j·sinθ·d h,k
wherein ,sz,k Represents the kth data, d, in the z-th set of new time-domain candidate signals g,k Represents the kth data, d, in the g-th set of time domain signals h,k Representing the kth data in the h time domain signal, 1.ltoreq.z≤M·(M-1)/2，1≤g≤M，1≤h≤M，g≠h，0＜θ＜π/2；
(8) And forming all time domain signals f by using the time domain signal d and the new time domain alternative signal s, calculating the peak-to-average power ratio of the time domain signals f, and selecting a group with the minimum peak-to-average power ratio as an output signal.
2. The method of claim 1, wherein the original frequency domain OFDM signal X generated in step (1) is represented as follows:
X＝[X 0 ,X 1 ,···,X k ,···,X N-1 ]
wherein ,Xk Represents the kth data in the original frequency domain signal, k=0, 1, and N-1, N is the number of subcarriers contained in the OFDM symbol.
3. The method of claim 1, wherein the up-sampled time domain signal U obtained in step (2) is implemented as follows:
(2a) Inserting (J-1) X N zeros in the middle of the original frequency domain signal to obtain an up-sampled frequency domain signal X':
wherein ,Xk Represents the kth data in the original frequency domain signal, k=0, 1, ··, N-1, X' n Represents the nth data in the up-sampled frequency domain signal, J represents the up-sampling factor, J is greater than or equal to 4, n=0, 1, JN-1, N is the number of subcarriers contained in OFDM symbol;
(2b) For X' n Performing inverse discrete fourier transform to obtain an up-sampled time domain signal U:
U＝[U 0 ,U 1 ,···,U n ,···,U JN-1 ]
wherein ,Un Representing the nth data in the up-sampled time domain signal.
4. The method according to claim 1,characterized in that the frequency domain clipping noise C is generated in the step (3) clip The implementation is as follows:
(3a) Calculating limiting threshold A clip ：
wherein ,CR Representing the clipping rate and,representing the average power of the up-sampled time domain signal U, U n N=0, 1, JN-1, J represents an upsampling factor, J is greater than or equal to 4, and n is the number of subcarriers included in the OFDM symbol;
(3b) According to the limiting threshold A clip Performing amplitude limiting operation on the up-sampled time domain signal U pair to obtain an amplitude-limited time domain signal
wherein ,represents the nth data, θ, in the limited time domain signal n For the up-sampled time domain signal U n Is the modulo operation;
(3c) From limited time domain signalsAnd up-sampling time domain signal time domain U to calculate time domain limiting noise c clip ：
c clip ＝[c clip,0 ,c clip,1 ,···,c clip,n ,···,c clip,JN-1 ]
wherein ,representing the nth data in the limited noise signal;
(3d) For time-domain clipping noise c clip Performing discrete Fourier transform and downsampling to obtain frequency domain limiting noise C clip ：
C clip ＝[C clip,0 ,C clip,1 ,···,C clip,k ,···,C clip,N-1 ]
wherein ,Cclip,k Representing the kth data in the frequency-domain limited noise signal.
5. The method of claim 1, wherein the preliminary spread frequency domain signal generated in step (4 a)The expression is as follows:
wherein ,represents kth data in the preliminary spread frequency domain signal, G represents a spreading factor, k=0, 1, ··, N-1, N is the number of sub-carriers contained in OFDM symbol, C clip,k Representing the kth data in the frequency-domain clipping noise.
6. The method of claim 1, wherein the generation of the random phase factor sequence P in step (5) is accomplished by:
(5a) The random number x is generated by adopting a chaotic sequence:
x＝[x 1 ,x 2 ,···,x a ,x a+1 ···,x N ]
wherein ,xa+1 ＝μ·x a ·(1-x a ) The value of the (a+1) th chaotic sequence is represented, mu represents a fractal parameter, 3.566 mu is not less than 4, a=0, 1, N-1, N is the number of subcarriers contained in an OFDM symbol;
(5b) Binary quantization is carried out on the random number x to obtain a selection signal B:
B＝[B 0 ,B 1 ,···,B b ,···,B N-1 ]
wherein ,representing the result after the b-th binary quantization, b=0, 1, ··, N-1;
(5c) Selecting the phase factors by the selection signal B, resulting in a first set of random phase factor sequences T:
T＝[T 0 ,T 1 ,···,T k ,···,T N-1 ]
wherein ,the kth value, which represents the first set of random phase factor sequences, "> and />Conform to [0,2 pi ]]Is uniformly distributed, k=0, 1, N-1;
(5d) The first set of random phase factor sequences T are cyclically shifted by lambda bits to produce the remaining M-1 set of random phase factor sequences W:
W＝[W 1 ,W 2 ,···,W λ ,···,W M-1 ]
wherein ,Wλ ＝[T λ ,···,T N-1 ,T 0 ,T 1 ,···,T λ-1 ]Represents a lambda group random phase factor sequence, lambda=1, 2, ··, M-1, M represents the group number of the whole random phase factor sequence P;
(5f) The entire phase factor sequence P is composed of the first set of random phase factor sequences T and the remaining M-1 set of random phase factor sequences W.
7. The method of claim 1, wherein the point multiplied signal is obtained in step (6)The expression is as follows:
wherein ,kth data, X, representing an mth set of point multiplied signals k Represents the kth data, P, in the original frequency domain signal m,k Kth data, representing the mth set of random phase factor sequences, 1.ltoreq.m, k=0, 1, ··, N-1, M represents the group number of the whole random phase factor sequence P, N is the number of sub-carriers contained in the OFDM symbol.
8. The method of claim 1, wherein the peak-to-average power ratio of the total time domain signal f is calculated in step (8) as follows:
(8a) Calculating the average power value alpha of all time domain signals f:
α＝[α 0 ,α 1 ,···,α v ,···,α M+M·(M-1)/2 ]
wherein ,representing a v-th group of time domain signals f v Average power value f of (f) v,k The kth data of the v-th group time domain signal is represented, N is the number of subcarriers contained in an OFDM symbol, v is more than or equal to 1 and less than or equal to M+M (M-1)/2, k is more than or equal to 0,1, N-1, M represents the group number of all random phase factor sequences P;
(8b) Calculating the maximum power value beta of all time domain signals f:
β＝[β 0 ,β 1 ,···,β v ,···,β M+M·(M-1)/2 ]
wherein ,βv ＝max(|f v | 2 ) Representing a v-th group of time domain signals f v Is a maximum power value of (a);
(8c) The peak-to-average power ratio F of the whole time domain signal F is calculated according to the average power value alpha and the maximum power value beta of the time domain signal F:
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