A Sparse Bayesian Time-Varying Channel Estimation Method Based on Temporal Correlation and Belief Propagation

Abstract

This invention provides a sparse Bayesian time-varying channel estimation method based on time correlation and confidence propagation. In a single-carrier phase-shift keying (PSK) modulation system, to reduce the impact of error propagation during block data processing in time-varying channel environments on the confidence propagation-based sparse Bayesian learning channel estimation algorithm, a time correlation-based channel estimation algorithm is proposed. This algorithm models channel estimation in block data processing as a hidden Markov model and utilizes a first-order autoregressive model to capture the time correlation of the channel between data blocks, thereby improving the algorithm's stability in the presence of error propagation. The proposed algorithm achieves almost the same performance as traditional methods with the same computational complexity; it reduces the impact of error propagation during block data processing in time-varying channel environments on the stability of the BP-SBL channel estimation algorithm; and the proposed TC-BP-SBL can be easily extended to other message passing systems.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic communication, and more specifically, to a channel estimation algorithm that has the same computational complexity as the BP-SBL algorithm, but achieves performance far exceeding that of BP-SBL, and possesses the same performance and stability as the SBL algorithm. Background Technology

[0002] With the development of the national maritime strategy, the ocean, with its abundant underwater resources and maritime navigation, has gradually become a focus of attention. Underwater acoustic communication technology is widely used in underwater resource exploration, marine environmental monitoring, data acquisition, and early warning systems. Therefore, the research and development of underwater acoustic communication technology is of great significance in the process of ocean development.

[0003] Research on underwater communication technology has revealed that underwater acoustic channels possess rich multipath delay structures, and these delays can exceed 100ms for long-distance data transmission. Furthermore, because the speed of sound is much slower than that of electromagnetic waves, underwater acoustic communication is relatively slow, requiring significantly more time to transmit the same amount of data. During data transmission, the time-varying nature of the channel severely impacts the decoding process. Block data processing is an effective method for addressing time-varying channels, assuming the channel remains constant throughout the duration of each data block. On the other hand, while traditional SBL channel estimation algorithms can effectively recover sparse underwater acoustic channels, their high computational complexity makes them unsuitable for large-scale systems. The proposed low-complexity BP-SBL algorithm based on message passing is sensitive to time-varying channels, exhibiting a sharp performance drop during block data processing. Therefore, developing high-performance BP-SBL channel estimation algorithms is a crucial area requiring breakthroughs. Summary of the Invention

[0004] The purpose of this invention is to provide a sparse Bayesian time-varying channel estimation method based on time correlation and confidence propagation.

[0005] The objective of this invention is achieved as follows: The steps are as follows:

[0006] (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, and the symbol of the b-th 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 received symbol, m∈1,2,...M, and the baseband symbol transmitted by the transmitter is... N b For y bThe corresponding transmitted symbol length. Additive white Gaussian noise is... H b It is a circular convolution matrix.

[0007] (2) Inter-block interference cancellation; in estimating the data channel of the b-th block First, IBI elimination needs to be performed.

[0008]

[0009] The sign of the estimated data in the (b-1)th block is... Construct a circular convolution matrix

[0010]

[0011] (3) Calculation of prior information between blocks;

[0012]

[0013] in, For variable node h b-1,l Passed to factor node g b The news Let β be a function of the first-order autoregressive model, where β∈(-1,1) represents the time correlation coefficient.

[0014] (4) Intra-block message: Calculation of message from variable node to likelihood factor node;

[0015]

[0016] in, To remove f b,m The message passed from the likelihood factor node to the variable node after the outermost likelihood factor node, k∈S(h b,l )\m means removing f b,m All external variables and node h b,l Connected likelihood factor nodes f b,k The index.

[0017] (5) Intra-block message: Likelihood factor node → Variable node message calculation;

[0018]

[0019] in, X follows a Gaussian likelihood distribution. b,m,l Indicates by x b The observation matrix X constituted b The element in the m-th row and l-th column.

[0020] (6) Calculate the message from the variable node to the related factor node;

[0021]

[0022] The probability distribution of messages passed from variable nodes to related factor nodes is approximately equal to the marginal probability distribution at the variable node.

[0023] (7) Update the prior and noise power;

[0024]

[0025]

[0026] (8) BP iteration; if the number of iterations j < J, where J is the preset maximum number of iterations, then repeat steps (3)-(7). Otherwise, output... Where, μ b,l This is the estimated channel result.

[0027] Compared with existing technologies, the beneficial effects of this invention are: the proposed TC-BP-SBL algorithm can achieve almost the same performance as traditional SBL with the same computational complexity as BP-SBL. Therefore, it can reduce the impact of error propagation during block data processing in time-varying channel environments on the stability of the BP-SBL channel estimation algorithm. Furthermore, the proposed TC-BP-SBL can be easily extended to other message passing systems. Attached Figure Description

[0028] Figure 1 This is a flowchart of the belief propagation sparse Bayesian time-varying channel estimation method based on time correlation;

[0029] Figure 2 It is a contour plot of the bit error rate results from data simulation. Detailed Implementation

[0030] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0031] 1. Specific implementation:

[0032] (1) System Setup; In a single-input single-output underwater acoustic communication system, the baseband signal obtained after sampling and demodulation of the acoustic signal collected by the receiving hydrophone is...

[0033]

[0034] Among them, w t This indicates that the mean of the samples collected at time t is 0 and the variance is 0. Additive white Gaussian noise, i.e. Express the above equation in matrix form.

[0035] y = Hx + w, (10)

[0036] in,

[0037]

[0038] (2) Data Blocking; To cope with the effects of time-varying channels, the entire frame signal is divided into several blocks for processing. The data received without inter-block interference in the b-th block is represented as follows:

[0039] y b =H b x b +w b (12)

[0040] Where b = [1, 2, ..., B] represents the block index, and

[0041]

[0042] Where M = N b +L-1 represents the length of each block of received data, while N b Indicates with y b Corresponding x b The length.

[0043] (3) Inter-block interference elimination; utilizing Estimated In use Channel estimation First, IBI elimination needs to be performed.

[0044]

[0045] in, for The circular convolution matrix X is formed b-1 Part of, namely

[0046]

[0047] It should be noted that when processing the (b+1)th data block, the data is obtained sequentially according to formula (6). and The former is used for channels The update, and the latter with the update For The estimate.

[0048] (4) Inter-block prior message calculation; We model the process of channel estimation using time correlation between data blocks as a Hidden Markov Model. Assume the message passed from the variable node to the relevant factor node is...

[0049]

[0050] A first-order autoregressive model is used to capture the correlation of time-varying channels, i.e.

[0051]

[0052] Furthermore, when b = 1,

[0053]

[0054] Where β∈(-1,1) represents the time correlation coefficient. Therefore, the message passed from the correlation factor node to the variable node is...

[0055]

[0056] (5) Intra-block message: Calculation of message from variable node to likelihood factor node; Let the message passed from the likelihood factor node to the variable node be...

[0057]

[0058] Therefore, the message passed from the variable node to the factor node is:

[0059]

[0060] in, To remove f b,m The message passed from the likelihood factor node to the variable node after the outermost likelihood factor node, k∈S(h b,l )\m means removing f b,m All external variables and node h b,l Connected likelihood factor nodes f b,k The index.

[0061] (6) Intra-block message: Likelihood factor node → Variable node message calculation; Given the Gaussian likelihood distribution is...

[0062]

[0063] According to confidence propagation, the message passed from the likelihood factor node to the variable node is...

[0064]

[0065] Among them, X b,m,l Indicates by x b The observation matrix X constituted b The element in the m-th row and l-th column.

[0066] (7) Message calculation from variable node to related factor node; since the message from the (b+1)th related factor node to the bth variable node is assumed to be uniformly distributed, the probability distribution of the message from the variable node to the related factor node is approximately equal to the marginal probability distribution at the variable node.

[0067]

[0068] (8) Update the prior and noise power; in each BP iteration, update the prior and noise power.

[0069]

[0070]

[0071] (9) BP iteration; if the number of iterations j < J, where J is the preset maximum number of iterations, then repeat steps (4)-(8). Otherwise, output... This serves as the final channel estimation result.

[0072] 2. Simulation Research

[0073] Simulation conditions:

[0074] Baseband simulations using a time-varying multipath channel were used to verify and compare the performance of the proposed TC-BP-SBL algorithm. In the simulation, a QPSK single-carrier symbol sequence of length N = 5000 was used as the transmitted symbol sequence, with the first and last 500 symbols being the training sequence and the middle 4000 symbols being the information sequence. A sparse ISI channel was randomly set to h = [1, 0, 6, 0, 7, 0]. 10 [0.5,08,0.3,09,0.1] T That is, the channel length L = 41. Additive white Gaussian noise is superimposed at the non-zero coefficient positions in the convolutional channel matrix formed by h to simulate the time-varying nature of the channel. The symbols that have passed through the time-varying channel are then passed through the white Gaussian noise channel to obtain the received symbols.

[0075] The received data is divided into blocks, starting at a point of 100 and with a block length of 450, where L′ is the channel length set during channel estimation. A total of 12 data blocks are formed: one training sequence block at the beginning and end, and 10 information sequence blocks in the middle. The first 500 symbols of the symbol sequence are the known training sequence, sufficient for initial channel estimation. During block data processing, the channel state information for each data block comes from the estimation result of the previous data block. Starting from the second data block, IBI cancellation is performed before channel estimation and channel equalization. This paper compares the performance of three channel estimation algorithms: TC-BL-SBL, BP-SBL, and SBL. All equalizer algorithms use LMMSE equalization.

[0076] Technical effects of the present invention: Figure 2 To illustrate the simulation results using contour plots, we limited the observation range to a bit error rate (BER) of <0.1%. As shown in the plot, when the signal-to-noise ratio (SNR) is high or the channel time-varying nature is weak, the performance ranking of the three algorithms is SBL > TC-BP-SBL > BP-SBL, with very small performance differences. At the contour line with BER = 0.010, the performance difference among the three algorithms is less than 0.5 dB. However, as the SNR decreases or the channel time-varying nature increases, the performance of BP-SBL drops sharply. In contrast, the proposed TC-BP-SBL algorithm consistently maintains performance comparable to SBL. At the contour line with BER = 0.100, the performance difference between BP-SBL and both TC-BP-SBL is the smallest, approximately 2.5 dB.

[0077] The purpose of this invention is to provide a sparse Bayesian time-varying channel estimation method based on time correlation and confidence propagation. This invention discloses a sparse Bayesian time-varying channel estimation method based on time correlation and confidence propagation, belonging to the field of underwater acoustic communication technology. This invention is achieved through the following technical solution: In a single-carrier phase-shift keying modulation (PSK) system, to reduce the impact of error propagation during block data processing in a time-varying channel environment on the BP-SBL (BP-SBL) channel estimation algorithm based on confidence propagation (BP), a time-correlation-based BP-SBL channel estimation algorithm (TC-BP-SBL) is proposed. This algorithm models the channel estimation in block data processing as a hidden Markov model and uses a first-order autoregressive model to capture the time correlation of the channel between data blocks, thereby improving the stability of the BP-SBL algorithm in the presence of error propagation. The advantages of this invention are: (1) the proposed TC-BP-SBL algorithm can achieve almost the same performance as the traditional SBL with the same computational complexity as BP-SBL; (2) it can reduce the impact of error propagation during block data processing in time-varying channel environments on the stability of the BP-SBL channel estimation algorithm; and (3) the proposed TC-BP-SBL can be easily extended to other message passing systems.

Claims

1. A sparse Bayesian time-varying channel estimation method based on time correlation and confidence propagation, characterized in that, The steps are as follows: Step 1: The passband acoustic signal acquired by the hydrophone is synchronized and demodulated to obtain the baseband symbol. The baseband symbol is then evenly divided into B data blocks, with the b-th block being 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 For y b The corresponding transmitted symbol length, additive white Gaussian noise is H b It is a circular convolution matrix; Step 2: Eliminate inter-block interference; Estimating the b-th data channel Before proceeding, perform IBI elimination: The sign of the estimated data in the (b-1)th block is... Constructing a circular convolution matrix: Step 3: Calculate inter-block prior information: in, For variable node h b-1,l Passed to factor node g b The news For a first-order autoregressive model, β∈(-1,1) represents the time correlation coefficient; Step 4: Intra-block messages: Calculate variable node → Likelihood factor node message; Where: k∈S(h b,l )\m means removing f b,m All external variables and node h b,l Connected likelihood factor nodes f b,k index, To remove f b,m The message passed from the likelihood factor node to the variable node after the outermost step; Step 5: Intra-block messages: Calculate the likelihood factor node → variable node message; in: X follows a Gaussian likelihood distribution. b,m,l Indicates by x b The observation matrix X constituted b The element in the m-th row and l-th column of the array; Step 6: Calculate the variable node → related factor node message; The probability distribution of messages passed from variable nodes to related factor nodes is approximately equal to the marginal probability distribution at the variable node. Step 7: Update the prior and noise power as follows: Step 8: BP iteration; if the number of iterations j < J, where J is the preset maximum number of iterations, then repeat steps (3)-(7); otherwise, output... Where, μ b,l This is the estimated channel result.

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