A channel equalization method for underwater acoustic communication based on joint message passing

Abstract

The present invention provides an underwater acoustic communication channel equalization method based on joint message passing, which belongs to the technical field of underwater acoustic communication. The present invention is implemented through the following technical scheme: the present invention is based on a single-carrier phase-shift keying modulation system, and is a two-layer iterative receiver structure based on approximate message passing and expected propagation joint message passing. In the inner iteration, the transmitted symbols are approximated as continuous Gaussian distribution random variables, and the approximate message passing algorithm is used for symbol estimation. In the outer iteration, the posterior probability estimation accuracy of the symbols is improved by expected propagation based on deterministic approximate variational inference, and this process utilizes the constraints of the discrete constellation diagram. The AMP‑EP equalization algorithm proposed in the present invention can greatly reduce the computational complexity of the linear minimum mean square error (LMMSE) equalizer. The AMP‑EP algorithm can utilize the constraints of the constellation diagram to improve the estimation accuracy of the posterior probability of the symbols.

Description

Technical Field

[0001] The present invention relates to the field of underwater acoustic communication, and more specifically, to an underwater acoustic communication channel equalization method capable of effectively improving symbol estimation accuracy and reducing computational complexity. Background Art

[0002] The maximum multipath delay in underwater acoustic communication channels is typically tens of milliseconds or even hundreds of milliseconds, meaning the coherence bandwidth can be as low as tens of Hz or even several Hz, which is typically far smaller than the bandwidth of underwater acoustic communication systems. Therefore, underwater acoustic communication is a typical ultra-wideband system. Multipath channels pose significant challenges to the performance and computational complexity of underwater acoustic communication receiver algorithms. Furthermore, underwater acoustic communication equipment must consider factors such as device size, battery life, and cost, so the computing power and power consumption it can provide for its built-in algorithms are very limited. Traditional symbol-by-symbol adaptive equalizers, while offering high performance, are not applicable to communication devices. Block-by-block channel estimation-based equalizers, which involve matrix inversion operations, also have high computational complexity. Consequently, channel equalization algorithms based on message passing and factor graphs have received extensive research. Against this backdrop, the present invention proposes a channel equalization algorithm based on joint message passing of AMP and EP. This algorithm not only reduces the computational complexity of the equalizer but also leverages information from the discrete constellation diagram by utilizing expectation propagation, improving equalizer performance without prior information provided by the channel decoder. Summary of the Invention

[0003] The purpose of the present invention is to provide an underwater acoustic communication channel equalization method based on joint message passing.

[0004] The object of the present invention is achieved in that the steps are as follows:

[0005] (1) The passband acoustic signal collected by the hydrophone is synchronized and demodulated to obtain the baseband symbol. The baseband symbol is evenly divided into B data blocks. The symbol of the bth block is y b =H b x b +w b , and b=[1,2,...,B], where the received symbol is M is the length of the b-th block of received symbols, m∈1,2,...M, and the baseband symbols transmitted by the transmitter are N b y b The corresponding transmission symbol length. Additive Gaussian white noise is H b is the circular convolution matrix.

[0006] (2) Inter-block interference elimination; when estimating the b-th block data channel Before that, IBI elimination must be performed

[0007]

[0008] Among them, the symbol of the b-1th block data estimate Constructing a circular convolution matrix

[0009]

[0010] (3) Channel estimation. Use known pilot sequences or estimated symbols Construct the measurement matrix X b After inter-block interference elimination and X b Get the estimated channel

[0011] (4) AMP-EP inner iteration: calculation of the mean and variance of the messages at the likelihood factor nodes;

[0012] According to the approximate message passing algorithm, the likelihood factor node The variance and mean of the message are

[0013]

[0014]

[0015] Among them, t represents the number of inner iterations of the current AMP-EP algorithm, H b,m,n Represented by the estimated channel The measurement matrix H b The element in the mth row and nth column of m represents the noise power, and η b,n Represents the marginal probability distribution at the variable node The mean and variance of

[0016] (5) AMP-EP inner iteration: variable node x b,n Calculation of the mean and variance of the messages;

[0017] According to the approximate message passing algorithm, the variance and mean of all messages from the likelihood factor nodes aggregated at the variable node are

[0018]

[0019]

[0020] (6) AMP-EP inner iteration: variable node x b,n Calculation of marginal posterior probabilities at ;

[0021] Estimated symbol x b,n The marginal posterior probability of

[0022]

[0023] in, Indicates a slave mapping node Prior information transmitted.

[0024] (7) Judgment: If t≤T a , then repeat steps (4)-(6). Otherwise, execute the subsequent steps. Where t represents the number of inner layer iterations of the AMP-EP algorithm, T a Indicates the maximum number of inner layer iterations of the AMP-EP algorithm.

[0025] (8) AMP-EP outer iteration: variable node x b,n Passed to the mapping factor node Calculation of messages;

[0026] According to the expected propagation criterion, we have

[0027]

[0028] Where Proj[·] represents the projection operation and C represents the normalization factor.

[0029] (9) AMP-EP outer iteration: connecting to mapping factor nodes Passed to variable node x b,n Calculation of messages;

[0030] According to the expected propagation criterion, we have

[0031]

[0032] in, Represents the prior information passed from the bit variable node.

[0033] (10) Judgment: If t e ≤T e , then return to step (4) to continue. Otherwise, end the iteration and output the marginal posterior probability distribution The mean and variance η b,n ,in That is the baseband symbol information transmitted by the transmitting transducer. e Indicates the current outer iteration number of the AMP-EP algorithm, T e Indicates the maximum number of outer iterations of the AMP-EP algorithm

[0034] Compared with the prior art, the present invention has the following advantages: the proposed AMP-EP equalization algorithm can significantly reduce the computational complexity of the linear minimum mean square error (LMMSE) equalizer. The AMP-EP algorithm can improve the estimation accuracy of the symbol posterior probability by utilizing the constraints of the off-constellation diagram. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Flowchart of underwater acoustic communication channel equalization technology based on AMP-EP;

[0036] Figure 2 Test location and experimental arrangement;

[0037] Figure 3 Performance comparison of balancing algorithms. DETAILED DESCRIPTION

[0038] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0039] 1. Specific implementation:

[0040] (1) System construction: In a single-input single-output underwater acoustic communication system, the baseband signal obtained by sampling and demodulating the acoustic signal collected by the receiving hydrophone is

[0041]

[0042] Among them, w m Indicates that the mean value collected at time t is 0 and the variance is σ m The additive Gaussian white noise of Express the above formula in matrix form

[0043] y=Hx+w, (11)

[0044] in,

[0045]

[0046] (2) Data block division: In order to cope with the influence of time-varying channels, the entire frame signal is divided into several blocks for processing. The b-th block of received data without inter-block interference is expressed as

[0047] y b =H b x b +w b , (13)

[0048] Where b = [1, 2, ..., B] represents the block index, and

[0049]

[0050] Where M = Nb +L-1 represents the length of each received data block, and N b Indicates that y b The corresponding x b Length, H b The definition of is similar to that of H.

[0051] (3) Inter-block interference elimination; using Estimated In use Estimated Channel Before that, IBI elimination must be performed

[0052]

[0053] in, for The circular convolution matrix X b-1 part of

[0054]

[0055] It should be noted that when processing the b+1th block of data, according to formula (24) and The former is used for channel 's update, while the latter is updated with the Used for Estimates.

[0056] (4) Channel estimation. Use known pilot sequences or estimated symbols Construct the measurement matrix X b After inter-block interference elimination and X b Get the estimated channel

[0057] (5) AMP-EP inner iteration: calculation of the mean and variance of the message at the likelihood factor node;

[0058] Assume that the estimated symbol is a continuous Gaussian random variable and meets the large system assumption. Therefore, according to the approximate message passing algorithm, the likelihood factor node The mean and variance of

[0059]

[0060]

[0061] Among them, t represents the number of inner iterations of the current AMP-EP algorithm, H b,m,n Represented by the estimated channel The measurement matrix Hb The element in the mth row and nth column of m represents the noise power, and η b,n Represents the marginal probability distribution at the variable node The mean and variance of

[0062] (6) AMP-EP inner iteration: variable node x b,n Calculation of the mean and variance of the messages;

[0063] According to the approximate message passing algorithm, the variance and mean of all messages from the likelihood factor nodes aggregated at the variable node are

[0064]

[0065]

[0066] (7) AMP-EP inner iteration: variable node x b,n Calculation of marginal posterior probabilities at ;

[0067] Estimated symbol x b,n The marginal posterior probability of

[0068]

[0069] in, Indicates a slave mapping node Prior information transmitted.

[0070] (8) Judgment: If t≤T a , then repeat steps (4)-(6). Otherwise, execute the subsequent steps. Where t represents the number of inner layer iterations of the AMP-EP algorithm, T a Indicates the maximum number of inner layer iterations of the AMP-EP algorithm.

[0071] (9) AMP-EP outer iteration: variable node x b,n Passed to the mapping factor node Calculation of messages;

[0072] According to the expected propagation criterion, we have

[0073]

[0074] Where Proj[·] represents the projection operation and C represents the normalization factor.

[0075] (10) AMP-EP outer iteration: connect mapping factor node Passed to variable node x b,nCalculation of messages;

[0076] According to the expected propagation criterion, we have

[0077]

[0078] in, Represents the prior information passed from the bit variable node.

[0079] (11) Judgment: If t e ≤T e , then return to step (4) to continue. Otherwise, end the iteration and output the marginal posterior probability distribution The mean and variance η b,n Where t e Indicates the current outer iteration number of the AMP-EP algorithm, T e Indicates the maximum number of outer iterations of the AMP-EP algorithm

[0080] 2. Experimental research

[0081] Test conditions:

[0082] The proposed receiver algorithm is verified using experimental data collected during China's 11th Arctic scientific expedition in August 2020. Figure 2 As shown, the test was conducted in high-latitude waters within 85° North Latitude. The water depth was approximately 2690 m and the test site was covered by approximately 50 cm of ice. The receiving array was located at position R1 and remained unchanged. The transmitting position T1 was 225 m away from the receiving array. The transmitted data was a single-carrier phase-shift keying (PSK) modulated signal with a system sampling rate of 48 kHz, a carrier frequency of 4 kHz, and a root-raised cosine filter roll-off factor of 1. The transmitted symbol period was 1 ms, resulting in a bandwidth of 2 kHz.

[0083] Technical effect: Figure 3 The data processing results of several channel equalization algorithms are presented, and we can draw three conclusions: First, the AMP and LMMSE equalization algorithms have almost exactly the same performance, because the AMP and LMMSE used are both based on Bayesian theory and therefore have the same performance. Second, we can clearly see that the proposed AMP-EP algorithm can significantly improve the performance of symbol estimation, and its performance improves with the increase in the number of EP iterations. The bit error rate of the AMP-EP algorithm after 10 iterations is an order of magnitude lower than that of the AMP and LMMSE algorithms. Third, the computational complexity of LMMSE equalization is The computational complexity of the AMP-EP equalization algorithm is T e (32T a M+19T a+29·2 Q +31). When the block length is greater than 200, the computational complexity of the AMP-EP equalization algorithm after 2 iterations is much lower than that of the LMMSE algorithm.

[0084] In summary, the present invention discloses an underwater acoustic communication channel equalization method based on joint message passing, which belongs to the field of underwater acoustic communication technology. The present invention is implemented by the following technical scheme: the present invention is based on a single-carrier phase-shift keying modulation system and is a two-layer iterative receiver structure based on approximate message passing (AMP) and expected propagation (EP) joint message passing (AMP-EP). In the inner iteration, the transmitted symbols are approximated as continuous Gaussian distribution random variables, and the approximate message passing (AMP) algorithm is used for symbol estimation. In the outer iteration, the posterior probability estimation accuracy of the symbols is improved by expected propagation based on deterministic approximate variational inference, and this process utilizes the constraints of the discrete constellation diagram. The advantages of the present invention are that (1) the proposed AMP-EP equalization algorithm can greatly reduce the computational complexity of the linear minimum mean square error (LMMSE) equalizer. (2) The AMP-EP algorithm can utilize the constraints of the discrete constellation diagram to improve the estimation accuracy of the posterior probability of the symbols.

Claims

1. A method for underwater acoustic communication channel equalization based on joint message passing, characterized in that: Here are the steps: Step 1: The passband acoustic signal collected by the hydrophone is synchronized and demodulated to obtain the baseband symbol, which is evenly divided into B data blocks. The symbol of block b is y b =H b x b +w b , and b=[1,2,…,B], where the received symbol is M is the length of the b-th block of received symbols, m∈1,2,...M, and the baseband symbols transmitted by the transmitter are N b y b The corresponding transmission symbol length; additive white Gaussian noise is H b is the circular convolution matrix; Step 2: Eliminate inter-block interference; Step 3: Channel estimation, using pilot sequence or estimated symbols Construct the measurement matrix X b ; According to the inter-block interference elimination and X b Get the estimated channel Step 4: AMP-EP inner iteration: calculation of the mean and variance of the message at the likelihood factor node; Step 5: AMP-EP inner iteration: variable node x b,n Calculation of the mean and variance of the messages; Step 6: AMP-EP inner iteration: variable node x b,n Calculation of marginal posterior probabilities at ; Step 7: Judgment: If t≤T a , then repeat steps (4)-(6); otherwise, execute the subsequent steps; where t represents the number of inner layer iterations of the AMP-EP algorithm, T a Indicates the maximum number of inner layer iterations of the AMP-EP algorithm; Step 8: AMP-EP outer iteration: variable node x b,n Passed to the mapping factor node Calculation of messages; According to the expected propagation criterion, we have Where Proj[·] represents the projection operation and C represents the normalization factor; is the likelihood factor node; Step 9: AMP-EP outer iteration: connect mapping factor node Passed to variable node x b,n Calculation of messages; According to the expected propagation criterion, we have in, Represents the prior information passed from the bit variable node; Step 10: Judgment: If t e ≤T e , then return to step (4) to continue execution; otherwise, end the iteration and output the marginal posterior probability distribution The mean and variance η b,n ,in That is the baseband symbol information transmitted by the transmitting transducer; t e Indicates the current outer iteration number of the AMP-EP algorithm, T e Indicates the maximum number of outer iterations of the AMP-EP algorithm.

2. The underwater acoustic communication channel equalization method based on joint message passing according to claim 1 is characterized in that: Step 2 specifically includes: estimating the b-th block data channel Before, perform IBI elimination: Among them, the symbol of the b-1th block data estimate Constructing the circular convolution matrix 3. The underwater acoustic communication channel equalization method based on joint message passing according to claim 2, characterized in that: Step 4 is as follows: According to the approximate message passing algorithm, the likelihood factor node The variance and mean of the messages at are: Among them, t represents the number of inner iterations of the current AMP-EP algorithm, H b,m,n Represented by the estimated channel The measurement matrix H b The element in the mth row and nth column of m represents the noise power, and η b,n Represents the marginal probability distribution at the variable node The mean and variance of 4. The underwater acoustic communication channel equalization method based on joint message passing according to claim 3 is characterized by: Step 5 is as follows: According to the approximate message passing algorithm, the variance and mean of all messages from the likelihood factor node aggregated at the variable node are:

5. The underwater acoustic communication channel equalization method based on joint message passing according to claim 4 is characterized in that: Step 6 is as follows: Estimate the symbol x b,n The marginal posterior probability of in, Represents a slave mapping node Prior information transmitted.

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