A Sparse Bayesian Learning Channel Estimation Method Based on Temporal Correlation and Approximate Message Passing

Abstract

The present invention provides a sparse Bayesian learning channel estimation method based on temporal correlation and approximate message passing, belonging to the technical field of underwater acoustic communication. In an underwater acoustic communication system based on single-carrier phase-shift keying modulation, to mitigate the error propagation in a single-carrier time-domain equalization system when the observation data is insufficient due to too short block length and the influence of error propagation on the sparse Bayesian learning channel estimation algorithm based on approximate message passing, a channel estimation algorithm based on temporal correlation is proposed. This algorithm uses a first-order autoregressive model to utilize the temporal correlation of the inter-block channels, thereby improving the performance of the AMP-SBL algorithm when the observation data is insufficient. The TC-AMP-SBL algorithm proposed by the present invention can obtain far better performance than the AMP-SBL algorithm at the same computational complexity as the AMP-SBL; the performance of the present invention exceeds that of the traditional SBL algorithm, and its computational complexity is much lower than that of the SBL algorithm. The present invention can significantly reduce the error propagation in the SC-TDE system when the observation data is insufficient.

Description

Technical Field

[0001] The present invention relates to the field of underwater acoustic communication. More precisely, it relates to a channel estimation algorithm that has the same computational complexity as the AMP-SBL algorithm, and whose performance far exceeds that of AMP-SBL and is better than that of the SBL algorithm. Background Art

[0002] The research on underwater acoustic communication equipment is of great significance to the national marine strategy. In actual single-carrier communication equipment (whether time-domain equalization or frequency-domain equalization), due to factors such as the computing power of the hardware platform, the size of the cache space, the real-time processing requirements (low node delay), and the strength of channel time-variation, a smaller block length is often required. However, insufficient observation data caused by too short a block length will seriously degrade the performance of channel estimation, thus causing catastrophic error propagation to the single-carrier time-domain algorithm that alternates between channel estimation and channel equalization. Therefore, reducing the degradation of channel estimation performance caused by a short block length is of great significance for the research and development of single-carrier communication equipment. To solve this problem, this paper proposes a channel estimation method that utilizes the temporal correlation of the inter-block channel. This method models the single-carrier time-domain equalization block channel estimation as a hidden Markov model, and then uses a first-order autoregressive model to capture the temporal correlation of the inter-block channel. On this basis, the inter-block information is transmitted into the SBL channel estimation process based on AMP to obtain the TC-AMP-SBL algorithm. This algorithm can significantly improve the performance of SBL and AMP-SBL channel estimation, while the computational complexity is much lower than that of the SBL algorithm.

[0003] Differences from TC-BP-SBL: (1) Similarities: Both TC-AMP-SBL and TC-BP-SBL use the temporal correlation of the channel between data blocks to improve the performance of channel estimation. (2) Differences: Based on TC-BP-SBL, TC-AMP-SBL generalizes the BP algorithm to the AMP algorithm, bringing two advantages. First, the TC-AMP-SBL algorithm has more robust performance under non-sparse observation matrix conditions. Second, the computational complexity of the TC-AMP-SBL algorithm is much lower than that of TC-BP-SBL, making it valuable for application in actual communication systems. Summary of the Invention

[0004] The purpose of the present invention is to provide a sparse Bayesian learning channel estimation method based on temporal correlation and approximate message passing.

[0005] The purpose of the present invention is achieved as follows: The steps are as follows:

[0006] (1) The passband acoustic signal collected by the hydrophone is demodulated after synchronization to obtain baseband symbols. The baseband symbols are evenly divided into B data blocks, and the symbols of the b-th block are yb = H b x b + w b , and b = [1, 2,..., B], where the received symbol is M is the length of the received symbol of the b-th block, m ∈ 1, 2,... M, and the baseband symbol transmitted by the transmitter is N b is y b The corresponding transmitted symbol length; the additive white Gaussian noise is H b is a cyclic convolution matrix;

[0007] (2) Inter-block interference cancellation; Before estimating the data channel of the b-th block IBI cancellation needs to be performed first

[0008]

[0009] Among them, the symbol estimated from the (b - 1)-th block data constitutes a cyclic convolution matrix

[0010]

[0011] (3) Inter-block prior message calculation;

[0012]

[0013] Among them,

[0014]

[0015] Among them, is the message passed from the variable node of the (b - 1)-th block to the relevant factor node, and β ∈ (-1, 1) represents the time correlation coefficient.

[0016] (4) Intra-block message: the mean and variance of the message at the likelihood factor node;

[0017] At the likelihood factor node, the variance and mean of the message are respectively

[0018]

[0019] Among them, t represents the number of iterations of the AMP algorithm, μ b,l and v b,l represent the mean and variance of the marginal probability distribution at the variable node in the previous iteration. The complex number X b,m,l represents the element in the m-th row and l-th column of the observation matrix X b constituted by

[0020] (5) In-block message: mean and variance of the message at the variable node;

[0021]

[0022] where σ m represents the noise power of the received signal.

[0023] (6) Mean and variance of the message from the variable node to the relevant factor node;

[0024] Calculate the message passed from the variable node to the relevant factor node as

[0025]

[0026] where,

[0027]

[0028] (7) Marginal probability distribution at the variable node;

[0029] The probability distribution of the message passed from the variable node to the relevant factor node is equal to the marginal probability distribution at the variable node. So, the mean and variance of the marginal probability distribution at the variable node are

[0030]

[0031] (8) Update the hyperprior and the noise power;

[0032] γ b,l = |μ b,l | 2 + v b,l , (10)

[0033]

[0034] (9) AMP iteration; if the number of iterations t < T m , where T m is the preset maximum number of iterations, then repeat steps (3)-(9). Otherwise, output μ b,l and v b,l as the final channel estimation result.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows: This algorithm utilizes a first-order autoregressive model to exploit the temporal correlation of the inter-block channels, thereby improving the performance of the AMP-SBL algorithm when the observed data is insufficient. The advantages of the present invention are: (1) The proposed TC-AMP-SBL algorithm can achieve far better performance than the AMP-SBL algorithm at the same computational complexity as AMP-SBL; (2) The performance of the proposed TC-AMP-SBL method exceeds that of the traditional SBL algorithm, and its computational complexity is much lower than that of the SBL algorithm. (3) The proposed TC-AMP-SBL algorithm can significantly reduce the error propagation in the SC-TDE system when the observed data is insufficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flowchart of a sparse Bayesian learning channel estimation method based on temporal correlation and approximate message passing;

[0037] Figure 2 is a contour plot of the bit error rate results of data simulation;

[0038] Figure 3 is a graph showing the variation of the computational complexity with the length of the observed data and the length of the channel. DETAILED DESCRIPTION OF THE INVENTION

[0039] The present invention will be further described in detail below in conjunction with the drawings and the detailed implementation manners.

[0040] 1. Specific implementation:

[0041] (1) System setup; In a single-input single-output underwater acoustic communication system, the baseband signal obtained after sampling and demodulating the acoustic signal collected by the receiving hydrophone is

[0042]

[0043] where, w m represents the additive white Gaussian noise with a mean of 0 and a variance of σ m at time t, that is Express the above formula in matrix form

[0044] y = Hx + w, (13)

[0045] where,

[0046]

[0047] (2) Data block division; To cope with the influence of the time-varying channel, the entire frame of signal is divided into several blocks for processing. Then the received data of the b-th block without inter-block interference is expressed as

[0048] y b = Hb x b +w b , (15)

[0049] where \(b = [1, 2, \cdots, B]\) represents the block index, and

[0050]

[0051] where \(M = N\) b +L - 1 represents the length of the received data for each block, and N b represents the length of x b corresponding to y b , and the definition of H b is similar to that of H.

[0052] (3) Inter - block interference cancellation; Using estimated to obtain Before estimating the channel using , IBI cancellation needs to be performed first

[0053]

[0054] where is a part of the circular convolution matrix X b-1 formed by, that is

[0055]

[0056] It should be noted that when processing the \((b + 1)\) - th block of data, according to formula (25), and are obtained successively. The former is used for updating the channel , and the latter and the updated are used for estimation.

[0057] (4) Calculation of inter - block prior messages; We model the process of channel estimation using the temporal correlation between individual data blocks as a hidden Markov model. Define the message passed from variable node h b-1 to the relevant factor node g b as

[0058]

[0059] Use a first - order autoregressive model to capture the correlation of the time - varying channel, that is

[0060]

[0061] And when \(b = 1\),

[0062]

[0063] Among them, β ∈ (-1, 1) represents the time - related coefficient. Therefore, the message passed from the correlation factor node to the variable node is

[0064]

[0065] Among them, represents the message passed from the (b - 1)-th variable node to the correlation factor node, defined as

[0066]

[0067] (5) Intra - block message: Variable node → Likelihood factor node message calculation;

[0068] First, define the variable node h b,l and the likelihood factor node The messages passed between them are respectively

[0069]

[0070] Therefore, the message passed from the variable node to the factor node is expressed as

[0071]

[0072] where k ∈ S(h b,l ) \ m represents all the indices of the likelihood factor nodes f b,m connected to the variable node h b,l except for f b,k . According to the convolution criterion of the Gaussian distribution, the above formula gives

[0073]

[0074] (6) Intra - block message: Likelihood factor node → Variable node message calculation;

[0075] The known Gaussian likelihood distribution is

[0076]

[0077] According to belief propagation, the message passed from the likelihood factor node to the variable node h b,l is

[0078]

[0079] where, X b,m,l represents the element in the m - th row and l - th column of the observation matrix X b constituted by x b . According to the convolution criterion of the Gaussian distribution, we get

[0080]

[0081] (7) Approximation of inter-block messages

[0082] We define

[0083]

[0084] According to the expectation propagation approximation method, approximate the messages passed between variable nodes and likelihood factor nodes. The message at the likelihood factor node is obtained as

[0085]

[0086] The message at the variable node is

[0087]

[0088] where t represents the number of iterations.

[0089] (8) Variable node → related factor node message calculation; Since the messages passed from the (b + 1)-th related factor node to the b-th variable node are assumed to be uniform distributions, the probability distribution of the message passed from the variable node to the related factor node is approximately equal to the marginal probability distribution at the variable node, which is

[0090]

[0091] According to the multiplication rule of Gaussian distributions, we get

[0092]

[0093] According to the hidden Markov model, the mean and variance of the marginal probability distribution at the variable node are respectively

[0094]

[0095] (9) Update hyper-prior and noise power; In each message passing iteration, update the hyper-prior and noise power

[0096] γ b,l =|μ b,l | 2 +v b,l , (36)

[0097]

[0098] (10) AMP iteration; If the number of iterations t < T m , where T mis the preset maximum number of iterations, then steps (4), (7), (8) and (9) are repeated. Otherwise, output and as the final channel estimation result.

[0099] 2. Simulation study

[0100] Simulation conditions:

[0101] Baseband simulation using a time-varying multipath channel is used to verify and compare the performance of the proposed TC-AMP-SBL algorithm. In the simulation, a QPSK single-carrier symbol with a length of N = 5000 is used as the transmitted symbol sequence, where the first 500 and the last 500 symbols are training sequences, and the middle 4000 symbols are information sequences. A sparse ISI channel is randomly set as the 70 ms multipath delay channel for simulation. Additive white Gaussian noise is superimposed on the positions of non-zero coefficients in the convolutional channel matrix formed by h to simulate the time-variability of the channel. The symbols passing through the time-varying channel are then passed through an additive white Gaussian noise channel to obtain the received symbols.

[0102] The received data is block-divided. The starting point of the block is 100, and the block length is 200, where L′ is the channel length set during channel estimation. A total of 22 data blocks are divided, that is, 1 training sequence data block at each end and 20 information sequence data blocks in the middle. The first 500 symbols of the symbol sequence are known training sequences, which can be used for initial channel estimation. During the processing of the block data, the channel state information of each data block comes from the result estimated by the previous data block. Starting from the second data block, IBI cancellation is performed before channel estimation and channel equalization. In this paper, the performances of three channel estimation algorithms, namely TC-AMP-SBL, TC-BP-SBL and SBL, are compared, and the equalizer algorithm is the minimum mean square error equalizer.

[0103] Technical effects: Figure 2 is the contour plot of the simulation bit error rate results. It can be seen from the figure that when the signal-to-noise ratio is relatively high or the time-variability of the channel is relatively weak, the performance ranking of the three algorithms is TC-AMP-SBL > TC-BP-SBL > SBL. The performances of TC-AMP-SBL and TC-BP-SBL based on time correlation are about 2 dB better than that of the SBL algorithm.

[0104] Figure 3 is the analysis result of the computational complexity. It can be seen that the computational complexity of the proposed TC-AMP-SBL is much lower than that of the TC-BP-SBL and SBL algorithms under various conditions of the observed data length. When the channel length is 100, the computational complexity of TC-AMP-SBL is about two orders of magnitude lower than that of the TC-BP-SBL and SBL algorithms.

[0105] In summary, the proposed TC-AMP-SBL channel estimation method not only has better performance, but also has much lower computational complexity than traditional algorithms.

[0106] In summary, the purpose of the present invention is to provide a sparse Bayesian learning channel estimation method based on time correlation and approximate message passing, belonging to the field of underwater acoustic communication technology. The present invention is realized through the following technical solutions: in an underwater acoustic communication system based on single-carrier phase shift keying modulation, in order to reduce the error propagation of the single-carrier time-domain equalization (SC-TDE) system when the observation data is insufficient due to too short block length, and the influence of the error propagation on the approximate message passing (AMP)-based sparse Bayesian learning (SBL) channel estimation (AMP-SBL) algorithm, we propose a time-correlation-based AMP-SBL channel estimation (TC-AMP-SBL) algorithm.

Claims

1. A sparse Bayesian learning channel estimation method based on time correlation and approximate message passing, characterized in that The steps are as follows: (1) The passband acoustic signal collected by the hydrophone is demodulated after synchronization to obtain baseband symbols. The baseband symbols are evenly divided into B data blocks, and the b-th block of symbols 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 received symbol, m ∈ 1, 2,... M, and the baseband symbol transmitted by the transmitter is N b is for y b corresponding transmitted symbol length; the additive white Gaussian noise is H b is a cyclic convolution matrix; (2) Eliminate the interference between blocks; Before estimating the b-th data channel perform IBI cancellation: Among them, the symbol estimated from the (b - 1)-th block of data forms a cyclic convolution matrix (3) Calculate the prior message between blocks; Among them, is the message passed from the (b - 1)-th variable node to the relevant factor node, and β ∈ (-1, 1) represents the time correlation coefficient; (4) Intra-block message: the mean and variance of the message at the likelihood factor node; At the likelihood factor node, the variance and mean of the message are respectively: where t represents the number of iterations of the AMP algorithm, and μ b,l and v b,l represent the mean and variance of the marginal probability distribution at the variable nodes in the previous iteration; the complex number X b,m,l represents the element in the m-th row and l-th column of the observation matrix X b formed by (5) Intra-block message: the mean and variance of the message at the variable node; Among them, σ m represents the noise power of the received signal; (6) The mean and variance of the message from the variable node to the relevant factor node; Calculate the message passed from the variable node to the relevant factor node as: Among them, (7) Obtain the marginal probability distribution at the variable node; The probability distribution of the message passed from the variable node to the relevant factor node is equal to the marginal probability distribution at the variable node; the mean and variance of the marginal probability distribution at the variable node are: (8) Update the hyperprior and the noise power as: γ b,l = |μ b,l | 2 + v b,l , (9) AMP iteration; if the number of iterations t < T m , where T m is the preset maximum number of iterations, then repeat steps (3)-(8); otherwise, output μ b,l as the final channel estimation result.

2. A computer device / equipment / system, comprising a memory, a processor, and a computer program stored on the memory, characterized in that: The processor executes the computer program to implement the steps of the method described in claim 1.

3. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that: When the computer program / instructions are executed by the processor, the steps of the method described in claim 1 are implemented.

4. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by the processor, the steps of the method described in claim 1 are implemented.

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