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

Abstract

The invention relates to the technical field of underwater acoustic communication, in particular to a joint multi-branch equalization and polarization code decoding method oriented to underwater acoustic communication, compared with the prior art, multi-branch equalization and polarization code decoding are not mutually independent, but a loop is formed between the two modules, and soft information is exchanged between the two modules, so that the multi-branch equalization and polarization code decoding can be realized. The joint performance can be further improved, a simulation result verifies the effectiveness of loop iteration of the method, and compared with the performance of an existing algorithm, the advantages of the method are also explained.

Description

Technical field:

[0001] The present invention relates to the technical field of underwater acoustic communication, and more specifically to a joint multi-branch equalization and polarization code decoding method for underwater acoustic communication in which decoding modules are not independent of each other but form a loop, and soft information is continuously iterated and exchanged between two modules, thereby significantly improving the joint performance of equalization and decoding. Background technology:

[0002] Due to the complexity and variability of the underwater environment, the underwater acoustic channel has the characteristics of severe noise and time-varying multipath, which brings great challenges to the realization of the reliability of high-speed underwater acoustic communication. In addition to using equalization to eliminate inter-code interference, channel coding can be considered to further improve reliability. At present, the channel coding used for underwater acoustic communication mainly includes convolutional codes, Reed-Solomon (RS) codes, Bose-Chaudhuri-Hocquenghem codes, Low Density Parity Check (LDPC) codes, Repeat Accumulate (RA) codes and polarization codes, which have strong anti-interference performance. Compared with other codes, polarization codes are a kind of coding methods with excellent low bit error rate performance and concise and clear coding structure under short code length. Considering the long delay of the underwater acoustic channel, short code length is obviously more suitable for underwater acoustic communication. Therefore, short code length polarization code is a scheme with great potential advantages in underwater acoustic communication.

[0003] There are Monte Carlo method, density evolution method and other methods to construct polarization codes in underwater acoustic communication applications. However, these two methods are relatively complex. As for the decoding method, compared with the existing soft decoding methods such as Belief Propagation (BP) and SCAN, the soft list (SoftSC-List, SSCL) decoding method for additive white Gaussian noise channels proposed by L. Xiang et al. has better performance in iterative decoding than BP and SCAN methods, which can further improve the performance and is suitable for complex and changeable underwater acoustic environments.

[0004] Because the underwater acoustic channel has the characteristics of strong multipath, it is necessary to consider the elimination of inter-code interference before polarization code decoding. Considering the underwater sound wave propagation characteristics and fading problems, multiple hydrophones are usually arranged at the receiving end to better capture the energy of the acoustic signal, so the receiving end usually adopts multi-branch equalization. The underwater acoustic channel is complex and changeable. In order to obtain better performance, it is possible to consider the joint implementation of equalization and decoding. By forming a loop between the equalization and decoding modules and exchanging soft information through continuous iteration, the overall performance can be significantly improved, which is very helpful for further improving the reliability of underwater acoustic communication. However, in the existing joint equalization and decoding schemes for underwater acoustic communication, channel coding mainly uses convolutional codes, LDPC codes, etc. Studies have shown that polarization codes have more performance advantages under short code lengths. However, according to literature research, in the field of underwater acoustic communication research, there is currently no research on joint equalization and decoding algorithms based on polarization codes. Only schemes in which equalization and polarization code decoding are independent of each other have appeared, which cannot give full play to the potential advantages of equalization and polarization code decoding. Summary of the invention:

[0005] The present invention is different from the existing scheme in which equalization and polarization code decoding are independent of each other. It proposes an iterative loop between multi-branch equalization and polarization code decoding. By continuously exchanging soft information between the two modules, equalization and polarization code decoding are jointly realized, which can significantly improve the overall performance of the joint multi-branch equalization and polarization code decoding method for underwater acoustic communication.

[0006] The present invention is achieved by the following measures:

[0007] A joint multi-branch equalization and polarization code decoding method for underwater acoustic communication. Consider an underwater acoustic communication system with a single transducer and multiple hydrophones. Assume that the length of the transmitted bit data is K, 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 the probability of taking 0 and 1 is equal. Assume that there are M hydrophones at different water depths at the receiving end, let h j represents the impulse response of the underwater acoustic channel from the transmitter transducer to the receiver hydrophone, j∈{1,2,…,M}, 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}, “*” indicates convolution operation, and n irepresents the Gaussian white noise corresponding to hydrophone i, and the following steps are performed thereafter:

[0009] Step 1: Multi-branch equalization processing: The received signal Y of each hydrophone i ,i∈[1,M], let the tap coefficient vector of each branch feedforward filter be Where D i represents the i-th branch, k represents the k-th symbol currently being processed, and N f Represents the length of the tap coefficient vector of the feedforward filter, which can be different. For the convenience of implementation, the length of the feedforward filter of all branches is set to N. f . Corresponding to The signal vector is expressed as follows Among them, y i,l Indicates that the i-th branch receives the signal Y i The lth value in

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

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

[0012] It can be concluded that the total error of multi-branch merging is in, Indicates that it corresponds to The expected value of the tap coefficient vector of each branch is not independent of each other, but the tap coefficient vector of each branch is jointly updated based on the total error. According to the multi-branch NLMS algorithm, the update formula of the tap coefficient vector of each branch is as follows:

[0013]

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

[0015] Step 2: Polar code decoding processing;

[0016] Step 3: Feedback processing.

[0017] Step 2 of the present invention comprises:

[0018] Step 2-1: After changing the time k from 1 to N / 2, we get a series of and Then, these values ​​are substituted into equations (13) and (14) to calculate the approximate expectation and variance have:

[0019]

[0020] in, Express A hard verdict;

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

[0022]

[0023] According to 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 follows: Where a i It is a symbol in the QPSK symbol set, each symbol has a corresponding bit sequence {c i,j}(For QPSK modulation, j is 1 or 2, r k,j is the jth bit of the symbol sent at the kth time, and the value of j is 1 or 2. The LLRs value corresponding to each bit can be obtained from formula (16);

[0024] Step 2-3: Substitute the obtained 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 This vector is input into the Soft-SCL decoding module to generate the soft information required for the feedback part.

[0025] In step 3 of the present invention, the following steps are included:

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

[0027] Step 3-2: After interleaving, the interleaved LLRs value vector L can be obtained. a , and process it according to the following formula to get the signal after soft modulation

[0028] here and Respectively represent the symbol r k The corresponding first bit and second bit correspond to the value of LLRs, is 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 expressed as follows Feedback filterb k The length of the tap vector is same, The output of the feedback filter can be calculated as follows: The value calculated by formula (20) represents the interference of the previous symbol on the current symbol;

[0029] Step 3-3: From the decision feedback equalization, we can know that the total output expressed in formal (10) can be modified to be

[0030]

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

[0032]

[0033] Among them, i∈{1,2,…,M}.

[0034] Compared with the prior art, the multi-branch equalization and polar code decoding of the present invention are not independent of each other, but a loop is formed between the two modules. By exchanging soft information between the two modules, the joint performance can be further improved. The simulation results verify the effectiveness of the loop iteration of the present invention, and the advantages of the proposed invention are also explained by comparing the performance with the existing algorithms. Description of the drawings:

[0035] Attached Figure 1 W in the present invention N Schematic diagram of the basic channel model.

[0036] Attached Figure 2 It is a schematic diagram of the single-transmitter-multiple-receiver underwater acoustic communication system model in the present invention.

[0037] Attached Figure 3 It is the structural diagram of JMED-PC in the present invention.

[0038] Attached Figure 4 It is a schematic diagram of the structure of the SSCL decoder in the present invention.

[0039] Attached Figure 5 4 is a curve diagram 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] Attached Figure 6 3 is a curve diagram showing the effect of the number of iterations on the performance of JMED-PC in an embodiment of the present invention, where M=3.

[0041] Attached Figure 7 1 is a comparison result of bit error rate performance of different algorithms in the embodiment of the present invention, where M=2.

[0042] Attached Figure 8 1 is a comparison result of bit error rate performance of different algorithms in the embodiment of the present invention, where M=3.

[0043] Attached Fig. 9 1 is a comparison result of the bit error rate performance under different numbers of hydrophones in the embodiment of the present invention. Specific implementation method:

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

[0045] The channel polarization phenomenon involved in the present invention was discovered through rigorous deduction in 2009. It refers to the fact that given N binary discrete memoryless channels (B-DMC), N independent channels W can be merged and split into two channels by channel merging and channel splitting. N Associate to form a composite channel W N After that, it is split into N sub-channels through channel splitting And if N→∞, the subchannel Channel capacity One part tends to 0, while the other part tends to 1. For the B-DMC channel, its Shannon channel capacity limit is 1, that is, a part of the channel can reach the Shannon limit. This channel polarization phenomenon is the channel polarization phenomenon. The way to transmit information using polar codes is to select K noise-free channels (K also represents the length of the original information to be sent) and NK pure noise channels from N synthetic channels to transmit information when N→∞, which is the basic principle of polar code information transmission.

[0046] The channel merging process is to generate a synthetic channel W by recursively combining N independent B-DMC channels. N , and the channel splitting process is to synthesize these N associated channels W N Split into N different associated sub-channels Then the information is transmitted. For the whole encoding process, Where U represents the original input information bit set, X represents the encoded bit set, and U, X∈{0,1}, satisfying N=2 n ,n≥0, N also represents the information length after polarization coding. Let x, y be the single-bit channel signals before and after channel transmission, and x∈X, y∈Y, Y is the output signal set, and there is a transition probability W(y|x) during channel transmission, where Y and W(y|x) vary with different channels. Assume there are two independent W with length N / 2 N / 2 The channel is synthesized into W N Channel, yes And s 2i =u 2i , 1≤i≤N / 2. N Represents a flip matrix, which is similar to the "flip" in shuffling cards. It is a permutation operation that can transform (s1, s2, ..., s N ) is replaced by (s1,s3,...,s N-1 ,s2,s4,...,s N ), thus forming two W N / 2 The input part of the structure, such as Figure 1 As shown, where {vi} is the middle bit item, indicating (s1,s2,...,s N ) is flipped and input to W N / 2 The bits of the channel, when i is 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 To the split subchannel The overall mapping of the input end of (representing the N associated sub-channels after synthesis and splitting) The process is a linear mapping process. represents information bits of length N, represents the information bit after polarization coding, and this process can be represented by a transformation matrix G N Describe, that is Where G N represents a generator matrix of length N, and about W N and W N Relative to the output signal The transition probability of the two channels is:

[0048]

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

[0050]

[0051] Where R N represents the permutation matrix of bit flipping, and represents the Kronecker product, and the N-th Kronecker product of the F matrix is ​​expressed 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 unit It can be expressed as follows:

[0055]

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

[0057] Before polarization coding, it is necessary to determine the information bit u A Position and freeze bits Here we consider using the RM construction method to solve it. The Reed-Muller (RM) construction is a low-complexity explicit construction method, and its implementation does not require known channel state information. One heuristic method for selecting A is to use a score function p:{1,...,N}→R, and select A as the set of index i, 1≤i≤N, p(i) is among the largest K scores in the list p(1),...,p(N), and the score function of RM is:

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

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

[0060] The present invention contemplates an underwater acoustic communication system having a single transducer, multiple hydrophones, such as Figure 2 As shown, assuming that the length of the transmitted bit data is K, it can be written as vector u A ,u A =[u1,u2,...,u K ] T , where ui ∈{0,1},i∈{1,2,...,K},u i The values ​​of are independent of each other, and the probability of taking 0 and 1 is equal. Then, according to the RM construction rule, K bit index channels are selected from the N synthetic channels, thereby determining the channel index sets A and A in formula (4): c , thus determining u A and According to formula (4), the information bits after polarization coding can be obtained. Here, it is assumed that the values ​​of the bits selected in the frozen bit set are uniformly set to "0". Represents the information bit after encoding, where the position with a value of 0 represents the frozen bit. After that, we enter the interleaving module, where we mainly use block interleaving, with an interleaving depth of P (number of columns) and an interleaving width of Z (number of rows). The bits in the Z×P matrix are written in row order and read out in column order to obtain the interleaved sequence

[0061]

[0062] in, Represents the bit information ranked at the i-th position after interleaving.

[0063] Then, the interleaved sequence QPSK modulation is performed. Since two bits are mapped to one symbol, the length of the sequence after mapping is N / 2. The signal after QPSK modulation is recorded as r i represents the i-th modulation symbol. Assume Figure 2 In the model shown, there are M hydrophones at different water depths at the receiving end. Let h j represents the impulse response of the underwater acoustic channel from the transmitting transducer to the receiving hydrophone, j∈{1,2,…,M}, then the signal received by each hydrophone can be expressed as follows:

[0064]

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

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

[0067] The received signal Y of each hydrophone can be obtained from the system model: i ,i∈[1,M], let the tap coefficient vector of each branch feedforward filter be Where D i represents the i-th branch, k represents the k-th symbol currently being processed, and N f Represents the length of the tap coefficient vector of the feedforward filter, which can be different. For the convenience of implementation, the length of the feedforward filter of all branches is set to N. f . Corresponding to The signal vector can be expressed as follows

[0068]

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

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

[0071]

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

[0073]

[0074] It can be concluded that the total error of multi-branch merging is

[0075]

[0076] in, Indicates that it corresponds to The tap coefficient vectors of each branch are not independent of each other, but are jointly updated based on the total error. According to the multi-branch NLMS algorithm, the update formula of the tap coefficient vector of each branch is as follows:

[0077]

[0078] Among them, g k =[g 1,k ; g 2,k ;…;g M,k], "*" indicates the conjugate operation, ò is a smaller number used to compensate the denominator, generally ò=0.5, ξ indicates the step size. In order to obtain better equalization performance, ξ is adjusted in each iteration according to the formula ξ=ρξ0, 0<ρ<1, where ξ0 indicates the initial value of the step size.

[0079] After changing the time k from 1 to N / 2, we can get a series of and Then, these values ​​are substituted into equations (13) and (14) to calculate the approximate expectation and variance have:

[0080]

[0081]

[0082] in, Express A hard verdict.

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

[0084]

[0085] According to 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 follows:

[0086]

[0087] Where a i It is a symbol in the QPSK symbol set, each symbol has a corresponding bit sequence {c i,j}(For QPSK modulation, j is 1 or 2), r k,j is the jth bit of the symbol sent at the kth time (the value of j is 1 or 2). The LLRs value corresponding to each bit can be obtained from equation (16).

[0088] Then, the obtained 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 This vector is input into the Soft-SCL decoding module to generate the soft information required for the feedback part.

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

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

[0091]

[0092] in, express Figure 3 The output LLRs value of the jth bit corresponding to the ith symbol in the lth turbo iteration is shown in FIG. After interleaving, the interleaved LLRs value vector L can be obtained. a , and process it according to the following formula to get the signal after soft modulation

[0093]

[0094] here and Respectively represent the symbol r k The corresponding first and second bits correspond to the values ​​of the 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 expressed as follows

[0095]

[0096] Feedback filter b k The length of the tap vector is same, The output of the feedback filter can be calculated as follows:

[0097]

[0098] The value calculated by equation (20) represents the interference of the previous symbol on the current symbol. From the decision feedback equalization, we can know that the total output expressed by equation (10) can be modified to be

[0099]

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

[0101]

[0102] According to the total error of formula (22), the correction formula of the tap coefficient vector of multiple feedforward filters and the update formula of the tap coefficient vector of feedback filters can be expressed as formula (23) and (24) respectively.

[0103]

[0104]

[0105] Among them, i∈{1,2,…,M}.

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

[0107] Table 1

[0108]

[0109]

[0110] Example:

[0111] In order 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 transmitter transducer depth was set to 80m, and three hydrophones were set at the receiving end in the simulation, with 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] Firstly, the influence of the number of iterations on the performance of JMED-PC was verified through simulation. Figure 5 and Figure 6 The bit error rate curves of JMED-PC with the number of iterations are given when the number of hydrophones M is 2 and 3. When M is 2, the hydroacoustic channels corresponding to the hydrophone depths of 10m and 15m are used. When M is 3, the hydroacoustic channels corresponding to the depths of 10m, 15m and 20m are used. Figure 5 and Figure 6It can be seen that as the number of iterations increases, the bit error rate performance of JMED-PC will improve accordingly. This is because the number of iterations is an important parameter that affects the performance of JMED-PC. By exchanging soft information between the equalization and decoding modules for iteration, the joint performance of equalization and decoding can be further improved. However, when the number of iterations increases further, the performance gain of JMED-PC becomes smaller. Considering that the implementation complexity will increase with the number of iterations, here we consider selecting the number of iterations at which the bit error rate performance is no longer significantly improved as a better number of iterations. Figure 5 and Figure 6 It can be seen that the value of the number of iterations IT that meets the compromise is 5. Therefore, in the subsequent simulations, the number of iterations of the JMED-PC algorithm will also be set to 5.

[0115] Figure 7 and Figure 8 The bit error rate performance comparison of different algorithms when M is 2 and 3 is given. The PCD algorithm in the figure indicates that only the SSCL decoding algorithm is used to process the signal received by each hydrophone, without using equalization, and then the outputs of each branch decoder are combined with equal gain; SMED-PC indicates that the multi-branch equalization and polar code decoding modules are separated and independent of each other, and no iterative loop is formed. Figure 7 and Figure 8 It can be seen that the proposed JMED-PC and SMED-PC can 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. In addition, from Figure 7 and Figure 8 It can also be seen that the proposed JMED-PC algorithm can achieve better bit error rate performance compared with 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 the joint performance can be further improved through iteration. Fig. 9 The performance comparison of the JMED-PC algorithm with different numbers of hydrophones is given. As can be seen from the figure, the bit error rate performance of the JMED-PC algorithm when M is 3 is better than that when M is 2. This is because as the number of hydrophones at the receiving end increases, more signal energy can be captured, thereby achieving better diversity gain.

[0116] Considering the need to further improve the reliability of underwater acoustic communication links in complex and changeable underwater acoustic environments, the present invention proposes a joint multi-branch equalization and decoding algorithm based on polarization codes. In this algorithm, multi-branch equalization and polarization code decoding are not independent of each other, but a loop is formed between the two modules. By exchanging soft information between the two modules, the joint performance can be further improved. The simulation results verify the effectiveness of the loop iteration of the proposed JMED-PC algorithm. The advantages of the proposed JMED-PC algorithm are also demonstrated by comparing the performance with that of existing algorithms.

Claims

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

2. The method for joint multi-branch equalization and polarization code decoding for underwater acoustic communication according to claim 1, characterized in that: Step 2 includes: Step 2-1: After changing the time k from 1 to N / 2, we get a series of and Then, these values ​​are substituted into equations (13) and (14) to calculate the approximate expectation and variance have: in, Express A hard verdict; Step 2-2: Calculate the conditional probability density function for the output estimate: According to 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 follows: Where a i It is a symbol in the QPSK symbol set, each symbol has a corresponding bit sequence {c i,j }(For QPSK modulation, j is 1 or 2, r k,j is the jth bit of the symbol sent at the kth time, and the value of j is 1 or 2. The LLRs value corresponding to each bit can be obtained from formula (16); Step 2-3: Substitute the obtained 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 This vector is input into the Soft-SCL decoding module to generate the soft information required for the feedback part.

3. The method for joint multi-branch equalization and polarization code decoding 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 being processed by the Log-SCL, BP and LLR-flip modules, the output LLRS value of the SSCL decoder of this turbo iteration can be obtained. This value is the feedback soft information in the turbo iteration. The vector composed of the soft information is recorded as It can be expressed as the following formula in, represents the output LLRs value of the jth bit corresponding to the i-th symbol in the l-th turbo iteration; Step 3-2: After interleaving, the interleaved LLRs value vector L can be obtained. a , and process it according to the following formula to get the signal after soft modulation here and Respectively represent the symbol r k The corresponding first bit and second bit correspond to the value of LLRs, is 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 expressed as follows Feedback filter b k The length of the tap vector is same, The output of the feedback filter can be calculated as follows: The value calculated by formula (20) represents the interference of the previous symbol on the current symbol; Step 3-3: From the decision feedback equalization, we can know that the total output expressed in formal (10) can be modified to be Thus, a closed loop between the multi-branch equalization and polar code decoding modules is constructed. Turbo iteration can be used to improve the joint performance of multi-branch equalization and polar code decoding. The total error of multi-branch decision feedback equalization can also be corrected as follows: According to the total error of formula (22), the correction formula of the tap coefficient vector of multiple feedforward filters and the update formula of the tap coefficient vector of feedback filters can be expressed as formula (23) and (24) respectively. Among them, i∈{1,2,…,M}.

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