Joint multi-branch equalization and polar code decoding method for underwater acoustic communication

Abstract

This invention relates to the field of underwater acoustic communication technology, specifically a joint multi-branch equalization and polar code decoding method for underwater acoustic communication. Compared with existing technologies, the multi-branch equalization and polar code decoding are not independent of each other, but form a loop between the two modules. By exchanging soft information between the two modules, the joint performance can be further improved. Simulation results verify the effectiveness of the loop iteration of this invention. The performance comparison with existing algorithms also illustrates the advantages of the proposed invention.

Description

Technical fields:

[0001] This invention relates to the field of underwater acoustic communication technology, specifically to a joint multi-branch equalization and polar code decoding method for underwater acoustic communication. The decoding modules are not independent of each other, but form a loop. By continuously iterating and exchanging soft information between the two modules, the joint performance of equalization and decoding can be significantly improved. Background technology:

[0002] Due to the complex and variable underwater environment, underwater acoustic channels are characterized by severe noise and time-varying multipath propagation, posing a significant challenge to achieving reliable high-speed underwater acoustic communication. Besides using equalization to eliminate inter-symbol interference, channel coding can be considered to further improve reliability. Currently, channel coding methods used for underwater acoustic communication mainly include convolutional codes, Reed-Solomon (RS) codes, Bose-Chaudhuri-Hocquenghem codes, Low Density Parity Check (LDPC) codes, Repeat Accumulate (RA) codes, and polar codes, all of which offer strong anti-interference capabilities. Compared to other codes, polar codes offer advantages such as excellent low bit error rate performance and a concise and clear coding structure with short code lengths. Considering the long latency of underwater acoustic channels, short code lengths are clearly more suitable for underwater acoustic communication; therefore, short code length polar codes represent a highly promising solution for underwater acoustic communication.

[0003] Polar code encoding methods used in underwater acoustic communication include Monte Carlo methods and density evolution methods. However, both of these methods are highly complex. Regarding decoding methods, compared to existing soft decoding methods such as Belief Propagation (BP) and SCAN, the SoftSC-List (SSCL) decoding method proposed by L. Xiang et al., suitable for additive white Gaussian noise channels, outperforms BP and SCAN methods in iterative decoding, allowing for further performance improvements and making it suitable for complex and variable underwater acoustic environments.

[0004] Due to the strong multipath characteristics of underwater acoustic channels, inter-symbol interference must be eliminated before polar code decoding. Considering the propagation characteristics and fading issues of underwater sound waves, multiple hydrophones are usually deployed at the receiver to better capture the acoustic signal energy; therefore, multi-branch equalization is typically used at the receiver. Underwater acoustic channels are complex and variable. To achieve better performance, equalization and decoding can be implemented jointly. By forming a loop between the equalization and decoding modules and iteratively exchanging soft information, the overall performance can be significantly improved, which is very helpful for further improving the reliability of underwater acoustic communication. However, in existing joint equalization and decoding schemes for underwater acoustic communication, channel coding mainly uses convolutional codes, LDPC codes, etc. Research shows that polar codes have a performance advantage with short code lengths. However, according to literature review, there is currently no research on joint equalization and decoding algorithms based on polar codes in the field of underwater acoustic communication research. Only schemes where equalization and polar code decoding are independent have appeared, which cannot fully utilize the potential advantages of equalization and polar code decoding. Summary of the Invention:

[0005] Unlike existing schemes where equalization and polar code decoding are independent, this invention proposes a joint multi-branch equalization and polar code decoding method for underwater acoustic communication. This method forms an iterative loop between multi-branch equalization and polar code decoding, and achieves joint equalization and polar code decoding by continuously exchanging soft information between the two modules. This significantly improves the overall performance of the method.

[0006] This invention achieves its purpose through the following measures:

[0007] A joint multi-branch equalization and polar code decoding method for underwater acoustic communication is proposed. Consider an underwater acoustic communication system with a single transducer and multiple hydrophones. Assume the length of the transmitted bit data is K, denoted as vector u. A u A =[u1,u2,...,u K ] T , where u i ∈{0,1},i∈{1,2,...,K},u i The values ​​of h are independent of each other, and the values ​​of 0 and 1 are equally probable. Assume that there are M hydrophones at different water depths at the receiving end, let h j Let j∈{1,2,…,M} represent the underwater acoustic channel impulse response from the transmitter transducer to the receiver hydrophone. Then, the signal received by each hydrophone is expressed by the following formula.

[0008] Y j =r1 N / 2 *h j +n j (7), where j∈{1,2,…,M}, “*” represents convolution operation, n iThis represents the Gaussian white noise corresponding to hydrophone i, and then the following steps are performed:

[0009] Step 1: Multi-branch equalization processing: The received signals Y from each hydrophone i Let i∈[1,M], and let the tap coefficient vector of each branch feedforward filter be... Where D i Let N represent the i-th branch, k represent the k-th symbol currently being processed, and N represent the n-th branch. f N represents the length of the feedforward filter tap coefficient vector, and its value can be different. For simplicity, we assume that the length of the feedforward filter in all branches is N. f Corresponding to The signal vector is represented by the following formula: Among them, y i,l This indicates that the i-th branch receives signal Y. i The l-th value in

[0010] Then the output value of the i-th branch feedforward filter for

[0011] Where i∈{1,2,…,M}, the combined balanced processing of multiple branches can further improve the joint performance of merging and balancing, so this method is also adopted here. First, the total output of multiple branches is calculated, and its value can be obtained by the following formula.

[0012] Therefore, the total error of multi-branch merging is... in, Indicates corresponding to The expected value is obtained by considering that the tap coefficient vectors of each branch are not independent, but are jointly updated based on the total error. The update formula for the tap coefficient vectors of each branch using the multi-branch NLMS algorithm is as follows:

[0013]

[0014] Among them, g k =[g 1,k g 2,k ;…;g M,k ], “*” indicates conjugate operation, ò is a smaller number used to compensate the denominator, usually ò = 0.5, ξ represents the step size. In order to obtain better balance performance, ξ is adjusted in each iteration according to the formula ξ = ρξ0, 0 < ρ < 1, where ξ0 represents the initial value of the step size;

[0015] Step 2: Polar code decoding process;

[0016] Step 3: Feedback processing.

[0017] Step 2 of the present invention includes:

[0018] Step 2-1: After taking time k from 1 to N / 2, a series of values ​​are obtained. and The values ​​are then substituted into equations (13) and (14) to calculate the approximate expectations. and variance have:

[0019]

[0020] in, Indicates to A hard verdict;

[0021] Step 2-2: Calculate the conditional probability density function for the output estimate as follows:

[0022]

[0023] Based on this conditional probability density function (15), the value of the external log-likelihood ratio (LLRs) corresponding to the JMED-PC output can be obtained, as shown in the following formula. In the formula a i It is a set of symbols transmitted in the QPSK symbol set, and each symbol has a corresponding bit sequence {c i,j For QPSK modulation, j takes the value of 1 or 2, r k,j It is the j-th bit of the symbol transmitted at time k, where j takes the value of 1 or 2. The LLRs value corresponding to each bit can be obtained from equation (16).

[0024] Steps 2-3: The resulting log-likelihood ratio vector L ext =[L ext (r 1,1 ),L ext (r 1,2 ),...,L ext (r N / 2,1 ),L ext (r N / 2,2 )] T After deinterleaving, the input vector of the polar code decoding module can be obtained. Input this vector into the Soft-SCL decoding module to generate the soft information required for the feedback part.

[0025] Step 3 of this invention includes the following steps:

[0026] Step 3-1: SSCL decoder input is After processing by the Log-SCL, BP, and LLR-flip modules, the output LLRS value of the SSCL decoder for this turbo iteration can be obtained. This value is the feedback soft information in the turbo iteration, denoted as the vector formed by the soft information. It can be expressed as the following formula in, This represents the output LLRs value of the j-th bit corresponding to the i-th symbol in the l-th turbo iteration;

[0027] Step 3-2: For By performing interleaving, we can obtain the interleaved LLRs value vector L. a The signal after soft modulation can be obtained by processing it according to the following formula.

[0028] here and Representing the symbol r k The first and second bits correspond to the values ​​of LLRs. This is the input to the feedback filter; here, we assume the symbol length of the feedback is N. b Then this signal vector can be represented as follows Feedback filter b k The length of the tap vector and same, The output of the feedback filter can be calculated using the following formula. The value calculated by equation (20) represents the interference of the previous symbol on the current symbol;

[0029] Step 3-3: From the decision feedback equilibrium, we know that the total output of the modifiable formal (10) is

[0030]

[0031] Thus, a closed loop is constructed between the multi-branch equalization and polar code decoding modules. Turbo iteration can be used to improve the joint performance of the multi-branch equalization and polar code decoding. The total error of the multi-branch decision feedback equalization can also be corrected as follows: Based on the total error of equation (22), the correction formulas for the tap coefficient vectors of multiple feedforward filters and the update formulas for the tap coefficient vectors of feedback filters can be expressed as equations (23) and (24), respectively.

[0032]

[0033] Where i∈{1,2,…,M}.

[0034] Compared with existing technologies, the multi-branch equalization and polar code decoding in this invention are not independent of each other, but form a loop between the two modules. By exchanging soft information between the two modules, the joint performance can be further improved. Simulation results verify the effectiveness of the loop iteration of this invention. The performance comparison with existing algorithms also illustrates the advantages of the proposed invention. Attached image description:

[0035] Appendix Figure 1 W is in this invention N A schematic diagram of the basic model of a channel.

[0036] Appendix Figure 2 This is a schematic diagram of the single-transmitter, multi-receiver underwater acoustic communication system model in this invention.

[0037] Appendix Figure 3 This is a structural diagram of the JMED-PC in this invention.

[0038] Appendix Figure 4 This is a schematic diagram of the SSCL decoder structure in this invention.

[0039] Appendix Figure 5 This is a graph showing the effect of the number of iterations on the performance of JMED-PC in an embodiment of the present invention, where M = 2.

[0040] Appendix Figure 6 This is a graph showing the effect of the number of iterations on the performance of JMED-PC in this embodiment of the invention, where M=3.

[0041] Appendix Figure 7 This is a comparison of the bit error rate performance of different algorithms in the embodiments of the present invention, where M=2.

[0042] Appendix Figure 8 This is a comparison of the bit error rate performance of different algorithms in the embodiments of the present invention, where M=3.

[0043] Appendix Figure 9 This is a comparison of bit error rate performance under different numbers of hydrophones in the embodiments of the present invention. Detailed implementation method:

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] The channel polarization phenomenon involved in this invention was discovered through rigorous derivation in 2009. It refers to the phenomenon where, given N binary discrete memoryless channels (B-DMC), through channel combining and channel splitting, N independent channels W can be polarized. N Correlation forms a synthetic channel W N Then, the channel is split into N sub-channels. And if N→∞, sub-channel Channel capacity One part tends towards 0, while another part tends towards 1. For B-DMC channels, the Shannon channel capacity limit is 1, meaning that some channels can reach the Shannon limit. This phenomenon of channel polarization is called channel polarization. The method of transmitting information using polar codes is to select K noise-free channels (K also represents the length of the original information to be transmitted) and NK pure noise channels from N synthetic channels as N→∞ to transmit information. This is the basic principle of polar code information transmission.

[0046] The channel combining process involves generating a combined channel W from N independent B-DMC channels recursively. N The channel splitting process involves combining these N composite channels W. N Split into N distinct associated sub-channels Then information transmission takes place, which is relevant to the entire encoding process. In the formula, U represents the set of original input information bits, X represents the set of encoded bits, and U, X∈{0,1}, satisfying N=2 n Let n≥0, where N represents the information length after polar coding. Let x and y be the single-bit channel signals before and after transmission through the channel, respectively, and x∈X, y∈Y, where Y is the set of output signals. During channel transmission, there exists a transition probability W(y|x), where Y and W(y|x) vary depending on the channel. Assume there are two independent W values ​​of length N / 2. N / 2 Channel synthesis into W N Channel, has And s 2i =u 2i , 1≤i≤N / 2. R N This represents a flipped matrix, similar to the "flipping" in shuffling cards. It is a permutation operation that can transform (s1, s2, ..., s...) into a matrix. N The substitution was performed as (s1, s3, ..., s). N-1 ,s2,s4,...,s N This forms two Ws. N / 2 The input part of the structure, such as Figure 1 As shown, where {v i} represents the intermediate bit term, indicating (s1, s2, ..., s N After being flipped, it is input into W. N / 2 For the channel bits, when i takes values ​​from 1 to N, the corresponding value of vi is (s1, s3, ..., s). N-1 ,s2,s4,...,s N ).

[0047] From the underlying raw channel W N After splitting the sub-channel The overall mapping at the input of (representing the N associated sub-channels after synthesis and splitting) The process is a linear mapping process. This represents information bits of length N. This represents the information bits after polarization coding, and this process can be represented by a transformation matrix G. N To describe, that is In the formula G N Let W represent a generating matrix of length N, and W represent a generating matrix of length N. N and W N Relative to the output signal The transition probabilities of the two channels are:

[0048]

[0049] The formula satisfies And for any N=2 n For n≥0, there is a generating matrix G. N for

[0050]

[0051] Where R N The permutation matrix representing bit flipping, and Let represent the Kronecker product, and the Nth degree Kronecker product of the F matrix is ​​represented as . The Kronecker product of two matrices is calculated as follows:

[0052]

[0053] where A=[A ij ] and B = [B ij ] represent two m×n matrices respectively.

[0054] Will After expansion, the encoded code elements It can be represented as follows:

[0055]

[0056] In the formula, the channel index set is denoted as A, G N (A) represents G, which is the row corresponding to the information bit set A. N Submatrix, A c Let u represent the complement of set A in {1,…,N}. A Represents information bits, Represents frozen bits. This represents modulo-2 addition.

[0057] Before polar coding, the information bit u needs to be determined. A Position and frozen bits The position is considered here. The Reed-Muller (RM) construction method is used to solve this. The Reed-Muller (RM) construction is a low-complexity explicit construction method that does not require known channel state information for implementation. One heuristic for selecting A is to use a fractional function p:{1,...,N}→R, and to select A as the set of exponents i, 1≤i≤N, where p(i) is among the largest K fractions in the list p(1),...,p(N). The fractional function of RM is:

[0058] p(i)=w(i-1) (5)

[0059] Where w(i-1) is the number of accumulated "1"s in binary format when the value is i-1, 0≤i-1≤N-1, and i represents the i-th channel after synthesis. For example, w(12)=2, because 12 has a binary representation of 1100, which is the sum of two binary "1" values. Since this rule is used to generate RM codes, this function is called the RM fractional function. Thus, different w(i-1) values ​​can be sorted, i∈{1,…,N}, and then the first K channels are selected as index channels A according to the value, thereby determining the information bit u. A and frozen bits The position indicates the completion of the RM construction. Compared to the PW construction method in 5G NR channels, this construction method has lower complexity, a simpler structure, and better performance. Therefore, this invention considers the RM construction method in underwater acoustic channels, mainly due to its advantages of low complexity and fast index set construction.

[0060] This invention considers an underwater acoustic communication system having a single transducer and multiple hydrophones, such as... Figure 2 As shown, assuming the length of the transmitted bit data is K, it can be written as a vector u. A u A =[u1,u2,...,u K ] T , where u i ∈{0,1},i∈{1,2,...,K},u i The values ​​of are independent of each other, and taking 0 and 1 is equally probable. Then, according to the RM construction rule, K bit index channels are selected from N synthetic channels, thereby determining the channel index set A and A in equation (4). c Thus determining u A and According to formula (4), the polar-coded information bits can be obtained. Here, it is assumed that the selected bits in the frozen bit set are uniformly set to "0". This represents the encoded information bits, where the positions with a value of 0 indicate frozen bits. Next, we enter the interleaving module, which mainly uses block interleaving. The interleaving depth is P (number of columns), and the interleaving width is Z (number of rows). The bits are written row-wise and read column-wise in a Z×P matrix to obtain the interleaved sequence.

[0061]

[0062] in, This represents the bit information in the i-th position after interleaving.

[0063] Then, the interleaved sequence When performing QPSK modulation, since two bits are mapped to one symbol, the resulting mapped sequence length is N / 2. Let the QPSK modulated signal be denoted as . r i Let represent the i-th modulation symbol. Assume... Figure 2 In the model shown, the receiving end has M hydrophones at different water depths, let h j Let j∈{1,2,…,M} represent the underwater acoustic channel impulse response from the transmitter transducer to the receiver hydrophone. Then, the signal received by each hydrophone can be expressed by the following formula.

[0064]

[0065] Where j∈{1,2,…,M}, “⊙” represents convolution operation, and n i This represents the Gaussian white noise corresponding to hydrophone i.

[0066] The structure diagram of the JMED-PC algorithm proposed in this invention is as follows: Figure 3 As shown, this algorithm will directly process the signal Y received by the receiver. i The system, i∈[1,M], mainly consists of three parts: multi-branch equalization, polar code decoding module, and feedback processing module. These will be introduced separately below.

[0067] The received signal Y of each hydrophone can be obtained from the system model. i Let i∈[1,M], and let the tap coefficient vector of each branch feedforward filter be... Where D i Let N represent the i-th branch, k represent the k-th symbol currently being processed, and N represent the n-th branch. fN represents the length of the feedforward filter tap coefficient vector, and its value can be different. For simplicity, we assume that the length of the feedforward filter in all branches is N. f Corresponding to The signal vector can be represented by the following formula:

[0068]

[0069] Among them, y i,l This indicates that the i-th branch receives signal Y. i The l-th value in.

[0070] Then the output value of the i-th branch feedforward filter for

[0071]

[0072] Where i∈{1,2,…,M}, the combined balanced processing of multiple branches can further improve the joint performance of merging and balancing, so this method is also adopted here. First, the total output of multiple branches is calculated, and its value can be obtained by the following formula.

[0073]

[0074] Therefore, the total error of multi-branch merging can be derived as follows:

[0075]

[0076] in, Indicates corresponding to The expected value. The tap coefficient vectors of each branch are not independent, but are jointly updated based on the total error. The update formula for the tap coefficient vectors of each branch using the multi-branch NLMS algorithm is as follows:

[0077]

[0078] Among them, g k =[g 1,k g 2,k ;…;g M,k The asterisk (*) indicates the conjugate operation, ò is a smaller number used to compensate for the denominator, typically ò = 0.5, and ξ represents the step size. To achieve better balance performance, ξ is adjusted in each iteration according to the formula ξ = ρξ0, 0 < ρ < 1, where ξ0 represents the initial value of the step size.

[0079] By taking values ​​from 1 to N / 2 for time k, we can obtain a series of... and The values ​​are then substituted into equations (13) and (14) to calculate the approximate expectations. and variance have:

[0080]

[0081]

[0082] in, Indicates to A firm verdict.

[0083] Then, the conditional probability density function for the output estimate is calculated as follows:

[0084]

[0085] Based on this conditional probability density function (15), the value of the external log-likelihood ratio (LLRs) corresponding to the JMED-PC output can be obtained, as shown in the following formula.

[0086]

[0087] In the formula a i It is a set of symbols transmitted in the QPSK symbol set, and each symbol has a corresponding bit sequence {c i,j (For QPSK modulation, j takes the value 1 or 2), r k,j It is the j-th bit of the symbol transmitted at time k (j takes the value 1 or 2). The LLRs value corresponding to each bit can be obtained from equation (16).

[0088] Then, the resulting log-likelihood ratio vector L ext =[L ext (r 1,1 ),L ext (r 1,2 ),...,L ext (r N / 2,1 ),L ext (r N / 2,2 )] T After deinterleaving, the input vector of the polar code decoding module can be obtained. Input this vector into the Soft-SCL decoding module to generate the soft information required for the feedback part.

[0089] SSCL decoder structure as follows Figure 4 As shown, its input is Depend on Figure 4 As can be seen, after processing by the Log-SCL, BP and LLR-flip modules, the output LLRS value of the SSCL decoder for this turbo iteration can be obtained. This value is the feedback soft information in the turbo iteration.

[0090] The vector formed by the soft information in the feedback is It can be expressed as the following formula

[0091]

[0092] in, express Figure 3 The output LLRs value of the j-th bit corresponding to the i-th symbol in the l-th turbo iteration is shown. Then, for... By performing interleaving, we can obtain the interleaved LLRs value vector L. a The signal after soft modulation can be obtained by processing it according to the following formula.

[0093]

[0094] here and Representing the symbol r k The first and second bits correspond to the values ​​of LLRs. for Figure 3 The input of the feedback filter, where the symbol length of the feedback is assumed to be N. b Then this signal vector can be represented as follows

[0095]

[0096] Feedback filter b k The length of the tap vector and same, The output of the feedback filter can be calculated using the following formula.

[0097]

[0098] The value calculated by equation (20) represents the interference of the previous symbol on the current symbol. According to the decision feedback equilibrium, the total output represented by the modifiable equation (10) is...

[0099]

[0100] Thus, a closed loop is constructed between the multi-branch equalization and polar code decoding modules, and turbo iteration can be used to improve the joint performance of the multi-branch equalization and polar code decoding. The total error of the multi-branch decision feedback equalization can also be corrected as follows:

[0101]

[0102] Based on the total error of equation (22), the correction formulas for the tap coefficient vectors of multiple feedforward filters and the update formulas for the tap coefficient vectors of feedback filters can be expressed as equations (23) and (24), respectively.

[0103]

[0104]

[0105] Where i∈{1,2,…,M}.

[0106] In summary, the implementation process of the JMED-PC algorithm proposed in this invention is shown in Table 1.

[0107] Table 1

[0108]

[0109]

[0110] Example:

[0111] To verify the effectiveness and advantages of the proposed algorithm, a Monte Carlo simulation was constructed based on a statistical underwater acoustic channel. In the generation of the channel impulse response, the water depth was set to 100m, the transducer depth at the transmitting end was 80m, and the receiving end was equipped with three hydrophones at depths of 10m, 15m, and 20m, respectively. Other relevant parameters used in the simulation are shown in Table 2.

[0112] Table 2 Simulation-related parameters

[0113]

[0114] First, the impact of the number of iterations on the performance of JMED-PC was verified through simulation. Figure 5 and Figure 6 The bit error rate (BER) curves of JMED-PC as a function of iteration number are presented for hydrophones M=2 and M=3, respectively. When M=2, the underwater acoustic channels corresponding to hydrophone depths of 10m and 15m are used; when M=3, the underwater acoustic channels corresponding to depths of 10m, 15m, and 20m are used. Figure 5 and Figure 6 It can be seen that the bit error rate performance of JMED-PC improves with the increase of the number of iterations. This is because the number of iterations is a crucial parameter affecting JMED-PC performance; by exchanging soft information between the equalization and decoding modules during iteration, the joint performance of equalization and decoding can be further improved. However, as the number of iterations increases further, the performance gain of JMED-PC diminishes. Considering that the implementation complexity increases with the number of iterations, we consider selecting the number of iterations where the bit error rate performance no longer shows significant improvement as a more optimal number of iterations. Figure 5 and Figure 6 It can be seen that the iteration number IT that satisfies this compromise is 5. Therefore, in subsequent simulations, the number of iterations for the JMED-PC algorithm will also be set to 5.

[0115] Figure 7 and Figure 8 The bit error rate performance of different algorithms is compared when M is 2 and 3. In the figure, the PCD algorithm represents the use of only the SSCL decoding algorithm to process the signal received by each hydrophone, without equalization, and then the outputs of each branch decoder are combined with equal gain; SMED-PC represents the separation of the multi-branch equalization and polar code decoding modules, which are independent of each other and do not form an iterative loop. Figure 7 and Figure 8 It can be seen that the proposed JMED-PC and SMED-PC achieve better bit error rate performance than PCD. This is because both JMED-PC and SMED-PC use multi-branch equalization, which can eliminate the influence of inter-symbol interference to a certain extent. Furthermore, from... Figure 7 and Figure 8 It can also be seen that the proposed JMED-PC algorithm achieves better bit error rate performance compared to the SMED-PC algorithm. This is because in the JMED-PC algorithm, the multi-branch equalization and polar code decoding modules are jointly implemented, and their joint performance can be further improved through iteration. Figure 9 The performance comparison of the JMED-PC algorithm with different numbers of hydrophones is presented. As can be seen from the figure, the bit error rate performance of the JMED-PC algorithm is better when M is 3 than when M is 2. This is because as the number of hydrophones at the receiver increases, more signal energy can be captured, thus achieving better diversity gain.

[0116] To further improve the reliability of underwater acoustic communication links in complex and variable underwater acoustic environments, this invention proposes a joint multi-branch equalization and decoding algorithm based on polar codes. In this algorithm, multi-branch equalization and polar code decoding are not independent but form a loop between these two modules. By exchanging soft information between the two modules, the joint performance can be further improved. Simulation results verify the effectiveness of the loop iteration in the proposed JMED-PC algorithm. Performance comparison with existing algorithms also demonstrates the advantages of the proposed JMED-PC algorithm.

Claims

1. A joint multi-branch equalization and polar code decoding method for underwater acoustic communication, characterized in that, Consider an underwater acoustic communication system with a single transducer and multiple hydrophones. Assume the length of the transmitted bit data is K, written as a vector. Where u i ∈{0,1},i∈{1,2,...,K},u i The values ​​of h are independent of each other, and the values ​​of 0 and 1 are equally probable. Assume that there are M hydrophones at different water depths at the receiving end, let h j Let j∈{1,2,…,M} represent the underwater acoustic channel impulse response from the transmitter transducer to the receiver hydrophone. Then, the signal received by each hydrophone is expressed by the following formula. Where j∈{1,2,…,M}, "*" represents convolution operation, and n i This represents the Gaussian white noise corresponding to hydrophone i, and then the following steps are performed: Step 1: Multi-branch equalization processing: The received signals Y from each hydrophone i Let i∈[1,M], and let the tap coefficient vector of each branch feedforward filter be... Where D i Let N represent the i-th branch, k represent the k-th symbol currently being processed, and N represent the n-th branch. f Let N represent the length of the feedforward filter tap coefficient vector, and let the length of the feedforward filter in all branches be N. f Corresponding to The signal vector is represented by the following formula. Among them, y i,l This indicates that the i-th branch receives signal Y. i The l-th value in Then the output value of the i-th branch feedforward filter for Where i∈{1,2,…,M}, the combined balanced processing of multiple branches can further improve the joint performance of merging and balancing. Therefore, this method is also adopted here. First, the total output of multiple branches is calculated, and its value is obtained by the following formula. Therefore, the total error of multi-branch merging is... in, Indicates corresponding to The expected value is obtained by considering that the tap coefficient vectors of each branch are not independent, but are jointly updated based on the total error. The update formula for the tap coefficient vectors of each branch using the multi-branch NLMS algorithm is as follows: Among them, g k =[g 1,k g 2,k ;…;g M,k ], "*" indicates conjugate operation, ∈ is a number used to compensate the denominator, ∈ = 0.5, ξ represents the step size. In order to obtain better balance performance, ξ is adjusted in each iteration according to the formula ξ = ρξ0, 0 < ρ < 1, where ξ0 represents the initial value of the step size; Step 2: Polar code decoding process; Step 3: Feedback processing.

2. The joint multi-branch equalization and polar code decoding method for underwater acoustic communication according to claim 1, characterized in that, Step 2 includes: Step 2-1: After taking time k from 1 to N / 2, a series of values ​​are obtained. and The values ​​are then substituted into equations (13) and (14) to calculate the approximate expectation. and variance have: in, Indicates to A hard verdict; Step 2-2: Calculate the conditional probability density function for the output estimate as follows: Based on this conditional probability density function (15), the value of the external log-likelihood ratio LLRs corresponding to the JMED-PC output is obtained, as shown in the following equation. In the formula a i It is a set of symbols transmitted in the QPSK symbol set, and each symbol has a corresponding bit sequence {c i,j For QPSK modulation, j takes the value of 1 or 2, and r k,j Then, it is the j-th bit of the symbol transmitted at time k, where j takes the value of 1 or 2. The LLRs value corresponding to each bit is obtained from equation (16). Steps 2-3: The resulting log-likelihood ratio vector L ext =[L ext (r 1,1 ),L ext (r 1,2 ),...,L ext (r N / 2,1 ),L ext (r N / 2,2 )] T After deinterleaving, the input vector of the polar code decoding module is obtained. Input this vector into the Soft-SCL decoding module to generate the soft information required for the feedback part.

3. The joint multi-branch equalization and polar code decoding method for underwater acoustic communication according to claim 1, characterized in that, Step 3 includes the following steps: Step 3-1: SSCL decoder input is After processing by the Log-SCL, BP, and LLR-flip modules, the output LLRS value of the SSCL decoder for this turbo iteration is obtained. This value is the feedback soft information in the turbo iteration, denoted as the vector formed by the soft information. Expressed as the following formula in, This represents the output LLRs value of the j-th bit corresponding to the i-th symbol in the l-th turbo iteration; Step 3-2: For Perform interleaving to obtain the interleaved LLRs value vector L. a The signal is processed according to the following formula to obtain the soft-modulated signal. here and Representing the symbol r k The first and second bits correspond to the values ​​of LLRs. This is the input to the feedback filter; here, we assume the symbol length of the feedback is N. b The signal vector is then represented as follows: Feedback filter b k The length of the tap vector and same, The output of the feedback filter is then calculated using the following formula. The value calculated by equation (20) represents the interference of the previous symbol on the current symbol; Step 3-3: From the decision feedback equilibrium, we know that the total output represented by the modified form (10) is Thus, a closed loop is constructed between the multi-branch equalization and polar code decoding modules. Turbo iteration is used to improve the joint performance of multi-branch equalization and polar code decoding. The total error of multi-branch decision feedback equalization is also corrected to the following formula. Based on the total error of equation (22), the correction formulas for the tap coefficient vectors of multiple feedforward filters and the update formulas for the tap coefficient vectors of feedback filters are expressed as equations (23) and (24), respectively. Where i∈{1,2,…,M}.

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