CN103905355B - A kind of virtual time reversal underwater sound OFDM channel equalization methods - Google Patents
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Abstract
The present invention relates to a kind of virtual time reversal underwater sound OFDM channel equalization methods, it is characterised in that：Step 1：The detectable signal estimated for signal is added in transmitting terminal transmission signal；Step 2：Receiving terminal completes synchronizing process, extracts the detectable signal for receiving；According to the detectable signal for receiving, channel impulse response is estimated；Step 3：According to the channel impulse response estimated, anti-OFDM channel equalizations when completing virtual；Step 4：To the signal serioparallel exchange after equilibrium, Cyclic Prefix and cyclic suffix are gone, complete demodulating process.
Description
Technical Field
The invention relates to a virtual time reversal underwater sound OFDM channel equalization method.
Background
The underwater acoustic channel has the characteristics of limited bandwidth, serious multipath interference, space variation, time variation, frequency variation and the like, and particularly for a shallow sea underwater acoustic channel, the channel is very complicated under the influence of submarine topography and sound velocity distribution, the multi-path time delay of the channel often reaches hundreds of milliseconds, and serious interference is brought to underwater acoustic communication. OFDM (orthogonal frequency division multiplexing) has the advantages of high frequency band utilization rate, frequency selective fading resistance, simple equalization and the like, and is widely used in short-range high-speed underwater acoustic communication, but in order to overcome inter-symbol interference (ISI) and inter-carrier interference (ICI) caused by long multipath delay, a cyclic prefix larger than the maximum multipath delay length of a channel needs to be added, and a denser pilot frequency is inserted and an error correction code is added, which causes a serious reduction in the OFDM frequency band utilization rate, so how to reduce the interference of multipath channels to OFDM becomes one of the key problems in high-speed underwater acoustic communication.
The channel equalization technology is an effective method for overcoming interference caused by channel multipath, and a commonly used OFDM channel equalization method is a frequency domain channel equalization algorithm based on pilot frequency, and a known sequence is inserted into a time domain or a frequency domain, and a channel frequency response is estimated at a receiving end. The existing channel equalization algorithms, such as Least Square (LS), Minimum Mean Square Error (MMSE), etc., all need to add a cyclic prefix larger than the maximum multi-path delay of the channel to overcome ISI and ICI, and add a denser pilot frequency estimation channel, which severely limits the communication rate of OFDM.
Disclosure of Invention
The invention aims to provide a virtual time reversal underwater sound OFDM channel equalization method which can effectively shorten the length of a channel, reduce intersymbol interference caused by multiple paths and improve the utilization rate of an OFDM frequency band.
The technical scheme for realizing the aim of the invention is as follows:
a virtual time reversal underwater sound OFDM channel equalization method adds a cyclic prefix and a cyclic suffix which are larger than the maximum multi-path delay length of a channel in an OFDM symbol, and is characterized in that:
step 1: a detection signal for signal estimation is added into a transmitting signal of a transmitting terminal;
step 2: the receiving end completes the synchronization process and extracts the received detection signal; estimating channel impulse response according to the received detection signal;
and step 3: according to the estimated channel impulse response, completing virtual time reversal OFDM channel equalization;
and 4, step 4: and performing serial-parallel conversion on the equalized signals, and removing the cyclic prefix and the cyclic suffix to finish the demodulation process.
In step 1, a pseudo-random sequence is selected as a detection signal after OFDM modulation.
In step 2, according to the received detection signal, the amplitude, the time delay and the phase of the channel are estimated by using a matching tracking algorithm, and the channel impulse response is estimated.
In step 3, the estimated channel impulse response time is reversed and convolved with the received signal to complete the virtual time reversal OFDM channel equalization.
The invention has the following beneficial effects:
the invention adds the detecting signal for signal estimation into the transmitting signal of the transmitting terminal, the receiving terminal estimates the channel impulse response according to the received detecting signal, and completes the virtual time reversal OFDM channel equalization; by using the virtual time reversal channel equalization algorithm, the channel length can be effectively shortened, the receiving signal-to-noise ratio is improved, ISI and ICI caused by multi-path channels are reduced, the utilization rate of an OFDM frequency band is improved, and self-adaptive channel equalization is realized. The invention estimates the amplitude, the time delay and the phase of the channel by using the matching pursuit algorithm, has high estimation precision, can accurately estimate the channel impulse response and provides accurate channel information for the virtual time reversal channel.
Drawings
FIG. 1 is a basic schematic diagram of VTRM technology;
FIG. 2 is a diagram of a transmitted signal frame structure;
FIG. 3 is a block diagram of a receiver implementation of a VTRM for OFDM channel equalization;
fig. 4 is a diagram illustrating the addition of a cyclic prefix and a cyclic suffix to an OFDM symbol.
Detailed Description
Step 1: according to the Virtual Time Reversal Mirror (VTRM) principle, a detection signal for signal estimation is added into a transmitting signal of a transmitting end;
as shown in fig. 1, the basic principle of the VTRM technique is to transmit a sounding signal before transmitting an information signal, estimate a channel impulse response according to the sounding signal, and convolve a time-reversed signal thereof with a received signal to obtain a virtual time-reversed signal.
According to the VTRM principle, a frame structure of a transmission signal is designed as shown in fig. 2, a frame header performs frame timing synchronization by using a Linear Frequency Modulation (LFM) signal, a single frequency pulse (CW) signal is added at the back for estimating a doppler factor, the doppler factor is eliminated at a receiving end, a detection signal is used for estimating channel impulse response, and finally an OFDM symbol is obtained. And a certain guard interval is reserved among the signals, and the guard interval is greater than the length of the maximum multi-path time delay of the channel.
Step 2: the receiving end completes the synchronization process and extracts the received detection signal; and estimating the amplitude, the time delay and the phase of the channel by using a matching tracking algorithm according to the received detection signal, and estimating the impulse response of the channel.
And step 3: according to the estimated channel impulse response, the convolved signals are synchronized again to complete virtual time reversal OFDM channel equalization;
and 4, step 4: and performing serial-parallel conversion on the equalized signals, and removing the cyclic prefix and the cyclic suffix to finish the demodulation process.
In specific implementation, as shown in fig. 3, after the received signal finds the initial position of the signal through the synchronization signal, the CW signal is extracted, the doppler compression factor is obtained through frequency measurement, and the received signal is subjected to variable sampling processing according to the doppler factor, so that the influence of doppler frequency offset on the signal is eliminated. And then extracting a detection signal from the signal after variable sampling, estimating channel impulse response, convolving the time reversal of the detection signal with a received signal to complete VTRM channel equalization, performing serial-parallel conversion on the equalized signal, removing a cyclic prefix and a cyclic suffix, performing FFT demodulation and constellation inverse mapping, and completing the OFDM demodulation process.
Among them, there is a key technology that affects the performance of VTRM for OFDM channel equalization, i.e. cyclic postfix should be added to OFDM symbol, and both cyclic postfix and cyclic prefix length should be greater than the maximum multi-path delay length of the time reversal channel. The cyclic suffix copies data from a number of previous OFDM symbol blocks to the following of the symbol blocks as shown in fig. 4.
Let the actual channel impulse response be h (t), and the estimated channel impulse response beDefining a virtual time-reversal channel impulse response asCan be considered as the channel through which the signal finally passes. Assuming that the direct sound amplitude is maximum, a discrete channel of length L can be represented as h = [ h (0) h (1).. h (L-1)]The time-reversal channel may be represented as h '= [ h' (1-L).. h '(-1) h' (0) h '(1).. h' (L-1)]The length of the channel is 2L-1, wherein h' (0) is the sound ray after the superposition of each path, the amplitude is maximum, and the back channel is a non-minimum phase channel when being seen, namely, a multipath component still exists before the sound ray with the maximum amplitude. If the sound ray with the maximum energy is used as the starting time in the synchronization, the ISI and the ICI caused by the multipath component after the sound ray with the maximum energy can be overcome by the cyclic prefix, and the ISI and the ICI caused by the multipath component after the sound ray with the maximum energy need to be overcome by the cyclic suffix.
Next, how to overcome ISI and ICI with cyclic postfix is analyzed, and let the p-th OFDM symbol of current demodulation be rpThe corresponding transmitted signal is denoted spThe former and latter OFDM symbols are denoted as sp-1、sp+1If the cyclic prefix and cyclic suffix are not added, the received signal can be represented as a signal after passing through a channel with an impulse response h
Wherein r isp、sp、sp-1、sp+1And npIs an N × 1-dimensional column vector,andis an N × N-dimensional matrix which can be expressed as
As can be seen from equation (1), the first termFor the desired signal, the second termAnd item IIIIntersymbol interference, n, caused for a preceding symbol and a following symbolpIs a noise term. Wherein the interference termCan be overcome by adding cyclic prefix, and interference itemA cyclic suffix needs to be added for overcoming. If a cyclic prefix and a cyclic suffix larger than the channel length L are added, the received signal can be expressed as a received signal without the cyclic prefix and the cyclic suffix
Wherein,is a circulant matrix which can be expressed as
It can be seen that after the cyclic prefix and suffix are removed, the linear convolution of the original transmitted signal in the time domain and the channel impulse response is changed to a circular convolution. As can be seen from equation (5), the output of the current symbol block is only related to the input of the current symbol block, and is independent of the previous and subsequent symbol blocks, i.e. ISI caused by the previous and subsequent symbols and ICI caused by multipath are eliminated by the cyclic prefix and cyclic postfix.
The key of VTRM channel equalization is channel estimation, the invention adopts Matching Pursuit (MP) algorithm to estimate the channel impulse response, compared with the common method of signal copy correlation channel estimation, the estimation precision is high, and can estimate out the channel phase information, the following introduces the specific implementation process of MP algorithm.
Linear models commonly used in view of sparsity
y=Ax+v (7)
Wherein, x ∈ RMFor the sparse signal to be estimated, y ∈ RNTo observe the vector, v ∈ RNIs a Gaussian noise vector, A ∈ RN ×MAnd N is<M, A may be represented as
A=[a1,a2,...,aM](8)
Wherein, ai∈RNI =1, 2.. said, M, commonly referred to as a dictionary or atomic pool, aiAre atoms in a dictionary. The basic idea of the MP algorithm is that in each iteration process, atoms which are most matched with signals are found from a dictionary to construct sparse approximation, then signal residual errors are solved, atoms which are most matched with the signal residual errors are continuously selected from the rest atoms, and after multiple iterations, sparse signals can be reconstructed by observing vectors and the selected atoms. The MP algorithm does not require atoms in the dictionary to be orthogonal, but requires a two-norm ai||2=1。
Let the residual after the p-th iteration be rpIs initialized to r0=y，The matching atoms selected from the dictionary areEach time the atom in the remaining atom pool with the smallest inner product with the residual signal is selected, i.e. the atom with the smallest inner product with the residual signal
Wherein, Ip-1∈{s1,s2,...,sp-1Is the set of matching atom indices chosen for the first p-1 iterations,
estimating the elements of the signal x in the p-th iterationCan be expressed as
The residual signal can be expressed as
When residual signal | | | rp||2<The iteration terminates, given a residual threshold, as a quantity related to the input signal-to-noise ratio. Based on the above analysis, the specific steps for summarizing the MP algorithm are as follows:
1. initialization: setting a residual threshold, r0=y
2. Selecting matched atoms:
3. obtaining an estimated signal component:
4. residual error:
5. p < th >1 iteration
6. Matching from the remaining atom pool:
7. signal component estimated for the p-th iteration:
8. residual of p-th iteration:
in order to estimate the channel impulse response using the MP algorithm, a sparse signal model is first constructed, considering the probe signal x (n) passing through the channel with the channel impulse response h (n), and the received signal y (n) can be expressed as
Wherein,representing convolution, and Fourier transform is performed on both sides of equation (12) at the same time, which can be expressed as
Y=XH+V (13)
Wherein Y and X are Fourier transforms of Y (n) and X (n), respectively, H is a channel frequency response matrix, is a Fourier transform of a channel impulse response, and can be expressed as
The formula (14) is introduced into the formula (13), and can be expressed as
Wherein,is a diagonal matrix of X, and h can be expressed as
h=[h(0),h(1),...,h(L)]T(16)
Wherein, the [ alpha ], [ beta ]]TDenotes transpose, F is Fourier transform matrix, and can be expressed as
As can be seen from the above derivation, equation (15) is consistent with the representation of sparse signals, Y can be represented as an observation matrix,which may be represented as a dictionary, since X and Y are frequency domain representations of the transmitted and received sounding signals, which are complex matrices, the complex gain and delay of the channel can be estimated by the MP algorithm. In this case, the detection signal should be a signal with good autocorrelation in the frequency domain, and the invention selects a pseudo-random sequence as the detection signal after OFDM modulation.
Claims (1)
1. A virtual time reversal underwater sound OFDM channel equalization method is characterized in that:
step 1: according to the Virtual Time Reversal Mirror (VTRM) principle, a detection signal for signal estimation is added into a transmitting signal of a transmitting end;
before transmitting an information signal, a detection signal is sent, channel impulse response is estimated according to the detection signal, and then the time reversal signal is convoluted with a receiving signal to obtain a signal after virtual time reversal;
the method comprises the steps that a frame head of a transmitting signal adopts Linear Frequency Modulation (LFM) signals to carry out frame timing synchronization, a single-frequency pulse (CW) signal is added at the back of the frame head to estimate a Doppler factor, the receiving end is used for eliminating the influence of Doppler frequency offset, then a detection signal is used for estimating channel impulse response, and finally an OFDM symbol is obtained, a certain protection interval is reserved among all signals, and the protection interval is larger than the length of the maximum multi-path time delay of a channel;
step 2: the receiving end completes the synchronization process and extracts the received detection signal; estimating the amplitude, time delay and phase of a channel by using a matching tracking algorithm according to the received detection signal, and estimating channel impulse response;
and step 3: according to the estimated channel impulse response, the convolved signals are synchronized again to complete virtual time reversal OFDM channel equalization;
and 4, step 4: performing serial-parallel conversion on the equalized signals, removing cyclic prefix and cyclic suffix to complete the demodulation process,
after a received signal finds a signal initial position through a synchronous signal, a CW signal is extracted, a Doppler compression factor is obtained through frequency measurement, variable sampling processing is carried out on the received signal according to the Doppler factor, the influence of Doppler frequency offset on the signal is eliminated, then a detection signal is extracted from the variable sampled signal, channel impulse response is estimated, the time reversal of the channel impulse response is convoluted with the received signal, VTRM channel equalization is completed, the equalized signal is subjected to serial-parallel conversion, a cyclic prefix and a cyclic suffix are removed, FFT demodulation and constellation inverse mapping are carried out, and an OFDM demodulation process is completed;
wherein, a key technology influences the performance of the VTRM for OFDM channel equalization, namely, a cyclic postfix is added in an OFDM symbol, the length of the cyclic postfix and the length of the cyclic prefix are both larger than the maximum multi-path delay length of a time reversal channel, the cyclic postfix copies a plurality of data in front of an OFDM symbol block to the back of the symbol block,
let the actual channel impulse response be h (t), and the estimated channel impulse response beDefining a virtual time-reversal channel impulse response asThe channel through which the signal finally passes; a discrete channel of length L, given maximum direct sound amplitude, is denoted h ═ h (0) h (1)]The time-reversal channel is denoted as h '═ h' (1-L.. h '(-1) h' (0) h '(1).. h' (L-1)]The length of the channel is 2L-1, where h' (0) is the sound ray after superposition of each path, the amplitude is maximum, and it can be seen that the time reversal channel is a non-minimum phase channel, that is, there is a multipath component before the sound ray with the maximum amplitude, if the sound ray with the maximum energy is used as the starting time in synchronization, ISI and ICI caused by the multipath component after the sound ray with the maximum energy are overcome by a cyclic prefix, and ISI and ICI caused by the multipath component after the sound ray with the maximum energy are overcome by a cyclic suffix, which specifically includes:
let the current demodulated p-th OFDM symbol be rpThe corresponding transmitted signal is denoted spThe former and latter OFDM symbols are denoted as sp-1、sp+1If the cyclic prefix and the cyclic suffix are not added, after the signal passes through a channel with impulse response h, the received signal is expressed as
Wherein r isp、sp、sp-1、sp+1And npIs an N × 1-dimensional column vector,andis an N × N-dimensional matrix respectively represented as
According to the formula (1), item oneFor the desired signal, the second termAnd item IIIIntersymbol interference, n, caused for a preceding symbol and a following symbolpIs a noise term; wherein the interference termOvercome by adding cyclic prefix, and interference itemA cyclic suffix is added for overcoming the defect, and if a cyclic prefix and a cyclic suffix which are larger than the channel length L are added, the received signal is expressed as the cyclic prefix and the cyclic suffix are removed
Wherein,is a circulant matrix expressed as
After the cyclic prefix and suffix are removed, the linear convolution of the original sending signal and the channel impulse response in the time domain is changed into circular convolution; according to equation (5), the output of the current symbol block is only related to the input of the current symbol block and is not related to the previous and next symbol blocks, i.e. the ISI caused by the previous and next symbols and the ICI caused by multipath are eliminated by the cyclic prefix and cyclic postfix;
estimating channel impulse response by using a Matching Pursuit (MP) algorithm, wherein the MP algorithm specifically comprises the following steps:
linear models commonly used in view of sparsity
y＝Ax+v (7)
Wherein, x ∈ RMFor the sparse signal to be estimated, y ∈ RNTo observe the vector, v ∈ RNIs a Gaussian noise vector, A ∈ RN×MAnd N < M, A is represented by
A＝[a1,a2,...,aM](8)
Wherein, ai∈RN1, 2., M, called a dictionary or atom pool, aiIs an atom in a dictionary; the MP algorithm does not require atoms in the dictionary to be orthogonal, but requires a two-norm ai||2＝1；
Let the residual after the p-th iteration be rpIs initialized to r0Y, the matching atom selected from the dictionary isEach time the atom in the remaining atom pool with the smallest inner product with the residual signal is selected, i.e. the atom with the smallest inner product with the residual signal
Wherein, Ip-1∈{s1,s2,...,sp-1Is front p-1The p-th iteration estimates the elements of signal xIs shown as
The residual signal is represented as
When residual signal | | | rp||2If < then, the iteration terminates, for a given residual threshold, a quantity related to the input signal-to-noise ratio; the MP algorithm comprises the following specific steps:
1. initialization: setting a residual threshold, r0＝y
2. Selecting matched atoms:
3. obtaining an estimated signal component:
4. residual error:
5. p < 1 for the p-th iteration
6. Matching from the remaining atom pool:
7. signal component estimated for the p-th iteration:
8. residual of p-th iteration:
in order to estimate the channel impulse response using the MP algorithm, a sparse signal model is first constructed, considering the channel where the probe signal x (n) passes through the channel with the channel impulse response h (n), and the received signal y (n) is expressed as
Wherein,representing convolution, and Fourier transform is simultaneously performed on two sides of the formula (12) as shown in
Y＝XH+V (13)
Wherein Y and X are Fourier transforms of Y (n) and X (n), respectively, and H is a channel frequency response matrix, which is a Fourier transform of a channel impulse response, expressed as
The formula (14) is introduced into the formula (13) shown in
Wherein,is a diagonal matrix of X, and h is represented by
h＝[h(0),h(1),...,h(L)]T(16)
Wherein, the [ alpha ], [ beta ]]TRepresenting transpose, F is a Fourier transform matrix, represented as
Equation (15) is in accordance with the representation of the sparse signal, Y is represented as an observation matrix,denoted as a dictionary, since X and Y are transmit andthe frequency domain representation of the received probe signal is a complex matrix.
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| CN106712781A (en) * | 2016-12-08 | 2017-05-24 | 浙江大学 | In-band full duplex underwater acoustic communication apparatus capable of suppressing interference from digital domain and analog domain |
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| CN107454024A (en) * | 2017-07-24 | 2017-12-08 | 哈尔滨工程大学 | A kind of underwater sound OFDM MFSK channel equalization methods based on Virtual time reversal mirror |
| CN107862289A (en) * | 2017-11-10 | 2018-03-30 | 哈尔滨工程大学 | The FPGA implementation method of anti-passive Direction Finding Algorithm when virtual |
| CN108169560A (en) * | 2017-12-21 | 2018-06-15 | 哈尔滨工程大学 | A kind of segmentation Sine-Fitting decomposition method |
| CN109617662B (en) * | 2019-01-04 | 2020-05-12 | 浙江大学 | Joint resource optimization method based on underwater sound OFDM-NOMA system downlink |
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