Distributed MIMO single-carrier underwater acoustic communication combined channel estimation and symbol detection method

Abstract

The invention belongs to the field of distributed MIMO underwater acoustic communication, and discloses a distributed MIMO single-carrier underwater acoustic communication combined channel estimation and symbol detection method, which comprises the following steps of: constructing a system model; constructing a channel model; guiding a cost function; initializing parameters; updating parameters; estimating a symbol; estimating a channel tap; estimating a noise variance; estimating a first-order Markov coefficient; and estimating a channel noise variance. According to the method based on the subblocks, the problems of no cooperative arbitrary transmission, inter-channel interference and near-far effect in a distributed MIMO scene can be solved, and reliable distributed MIMO underwater acoustic communication under a slow time-varying underwater acoustic channel is realized by establishing a first-order Markov model of the channel.

Description

Technical Field

[0001] The present invention relates to the field of distributed MIMO underwater acoustic communication, and in particular to a distributed MIMO single-carrier underwater acoustic communication joint channel estimation and symbol detection method. Background Art

[0002] With the continued research and development of the ocean, the demand for high-speed underwater wireless networking communication technology is becoming increasingly urgent. Underwater acoustic communication has the advantage of propagating in the natural marine environment, allowing for longer distances. However, underwater acoustic communication technology also needs to achieve higher communication rates and adapt to more underwater application scenarios, such as multi-node networking. Distributed MIMO single-carrier underwater acoustic communication overcomes the limitation of each node taking turns communicating in networking, allowing multiple transmitting nodes to communicate with receiving nodes simultaneously, improving the throughput of inter-node networking and enhancing the timeliness of node communication.

[0003] In distributed MIMO underwater acoustic communications, multiple transmitting transducers are distributed across different nodes, each independently controlled by a different transmitter. Each transmitter is unaware of the data being transmitted by the others. The receiver receives and demodulates signals from multiple platforms via multiple hydrophones. Signals from the transmitting transducers to the receiving hydrophones experience varying large-scale and small-scale fading, resulting in near-far effects and varying slow time-varying channels. Furthermore, signals from different transmitting transducers collide at the receiver, resulting in varying staggered times and inter-channel interference.

[0004] Because of the different staggered times, traditional demodulation methods for traditional MIMO, such as RLS-DFE and MIMO-DFE, are no longer applicable to distributed MIMO scenarios. Therefore, a block-based processing approach can be used to segment the received signal into smaller sub-blocks and perform joint channel and symbol estimation within the sub-blocks. This paper proposes a joint channel estimation and symbol detection method for distributed MIMO single-carrier underwater acoustic communications from the perspective of maximum a posteriori probability estimation, and uses block coordinate descent to achieve optimized channel and symbol estimation, achieving better channel estimation and symbol detection performance in distributed MIMO slow time-varying environments. Summary of the Invention

[0005] The object of the present invention is to provide a distributed MIMO single-carrier underwater acoustic communication joint channel estimation and symbol detection method to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for joint channel estimation and symbol detection for distributed MIMO single-carrier underwater acoustic communication, the method comprising the following steps:

[0008] S1: Build a distributed MIMO single-carrier underwater acoustic communication system consisting of M transducers and N hydrophones;

[0009] S2: Construct a channel model. The channel between sub-blocks is represented by a first-order Markov model.

[0010] S3: Based on the distributed MIMO single-carrier underwater acoustic communication system and the channel model, the cost function of the distributed MIMO single-carrier underwater acoustic communication system is derived from the perspective of maximum a posteriori probability;

[0011] S4: Initialize the estimated value of the channel tap of the 0th sub-block in the channel model, the noise variance, the first-order Markov coefficient and the noise variance of the channel;

[0012] S5: In the kth sub-block, first keep the estimated values ​​of the channel taps, the estimated value of the noise variance, the estimated value of the first-order Markov coefficient, and the estimated value of the channel noise variance consistent with those of the k-1th sub-block;

[0013] Then the symbol of the kth sub-block is estimated to obtain its estimated value, and then the estimated value of the channel tap, the estimated value of the noise variance of the sub-block length, the estimated value of the first-order Markov coefficient, and the estimated value of the channel noise variance are successively updated;

[0014] S6: Iteratively repeat S5 using the block coordinate descent method until the number of iterations reaches the maximum number of iterations to finally achieve joint channel estimation and symbol detection.

[0015] Furthermore, the S1 includes: M transducers distributed on M different transmitting nodes, each of which is independently controlled, and each transmitter cannot know the transmission data of other transmitters; N hydrophones are distributed on the same receiving end to receive and demodulate signals from multiple transmitting nodes; M different transmitting nodes have similar speeds and are at arbitrary distances from the receiving end, and the M transducers send data at arbitrary times.

[0016] Furthermore, the estimated value of the channel tap of the 0th sub-block initialized in S4 includes:

[0017] S4.1: Construct a Toeplitz matrix of the training symbols of the data transmitted by the mth transducer;

[0018] S4.2: intercepting the portion of the m-th transducer training symbol vector corresponding to the n-th hydrophone received data;

[0019] S4.3: The channel tap estimate for the 0th sub-block between the mth transducer and the nth hydrophone is expressed using the least squares method, i.e., the pseudo-inverse of the Toeplitz matrix of the training symbols of the data transmitted by the mth transducer is multiplied by the portion of the training symbol vector for the mth transducer corresponding to the data received by the nth hydrophone.

[0020] Furthermore, the S5 specifically includes:

[0021] S5.1: In the kth sub-block, first keep the estimated values ​​of the channel taps, the estimated values ​​of the noise variance, and the estimated values ​​of the first-order Markov coefficients consistent with those of the k-1th sub-block;

[0022] S5.2: Estimating a symbol of the kth sub-block to obtain an estimated value thereof, comprising: estimating, in the kth sub-block, the symbol of the kth sub-block based on a received signal, an estimated value of a channel tap, an estimated value of a noise variance, and a variance of the symbol to obtain an estimated value thereof;

[0023] S5.3: Updating the estimated value of the channel tap includes: in the kth sub-block, updating the estimated value of the channel according to the received signal, the estimated value of the symbol, the estimated value of the noise variance, the estimated value of the first-order Markov coefficient, and the estimated value of the channel noise variance;

[0024] S5.4: Updating the estimated value of the noise variance includes: in the kth sub-block, updating the estimated value of the noise variance based on the received signal, the estimated value of the symbol, the estimated value of the channel tap, and the sub-block length;

[0025] S5.5: Updating the estimated value of the first-order Markov coefficient includes: in the kth sub-block, updating the estimated value of the first-order Markov coefficient based on the estimated value of the channel tap of the current kth sub-block and the estimated value of the channel tap of the k-1th sub-block;

[0026] S5.6: Updating the channel noise variance estimate includes: in the kth sub-block, updating the channel noise variance estimate based on the estimated value of the current kth sub-block channel tap, the estimated value of the k-1th sub-block channel tap, the estimated value of the k-1th sub-block first-order Markov coefficient, and the channel length.

[0027] Furthermore, the S5.2 specifically includes: according to the cost function of the kth sub-block, setting the partial derivative of the cost function on the sign of the kth sub-block to zero, so as to obtain the estimated value of the sign of the kth sub-block.

[0028] Furthermore, the S5.3 specifically includes: according to the cost function of the kth sub-block, setting the partial derivative of the cost function on the channel of the kth sub-block to zero, and obtaining an estimated value of the channel tap of the kth sub-block.

[0029] Furthermore, the S5.4 specifically includes: according to the cost function of the kth sub-block, setting the partial derivative of the cost function on the noise variance of the kth sub-block to zero, obtaining the noise variance estimate of the kth sub-block, and the result is the square of the 2-norm of the received signal residual divided by the length of the sub-block.

[0030] Furthermore, the S5.5 includes: according to the cost function of the kth sub-block, setting the partial derivative of the cost function on the first-order Markov coefficient of the kth sub-block to zero, obtaining the first-order Markov coefficient estimate of the kth sub-block, the result of which is the conjugate transpose of the k-1th sub-block channel tap estimate multiplied by the k-1th sub-block channel tap estimate, and then divided by the square of the 2-norm of the k-1th sub-block channel tap estimate.

[0031] Furthermore, the S5.6 specifically includes: according to the cost function of the kth sub-block, setting the partial derivative of the cost function on the channel noise variance of the kth sub-block to zero, obtaining the channel noise variance estimate of the kth sub-block, and the result is the square of the 2-norm of the channel residual of the kth sub-block divided by the length of the channel.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1) This invention uses a sub-block-based approach to overcome the problems of uncoordinated arbitrary transmission, inter-channel interference, and near-far effect in distributed MIMO scenarios. It also establishes a first-order Markov model of the channel to achieve reliable distributed MIMO underwater acoustic communication in slowly time-varying underwater acoustic channels.

[0034] 2) The present invention derives the cost function from the perspective of maximum a posteriori probability estimation and uses the block coordinate descent method to realize iterative estimation between symbols, channels, and hyperparameters in sub-blocks, so as to achieve better channel estimation and symbol detection performance in a distributed MIMO slow time-varying environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flow chart of the present invention.

[0036] Figure 2 is the real channel tap generated by simulation Schematic diagram of .

[0037] Figure 3 is the result of the 0th sub-block channel tap estimation .

[0038] Figure 4 This is a flow chart of S6.

[0039] Figure 5 is the first-order Markov coefficient estimate in each sub-block 's curve graph.

[0040] Figure 6 1 and 2 are the demodulation constellation diagrams and bit error rates of the method of the present invention, wherein (a) is the demodulation constellation diagram and bit error rate of Tx1, and (b) is the demodulation constellation diagram and bit error rate of Tx2. DETAILED DESCRIPTION

[0041] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0042] like Figure 1 As shown, a distributed MIMO single-carrier underwater acoustic communication joint channel estimation and symbol detection method includes the following steps:

[0043] S1: Construct a system model: Construct a distributed MIMO single-carrier underwater acoustic communication system, which includes M transducers and N hydrophones. The M transducers are distributed on M different transmitting nodes, each of which is independently controlled. Each transmitter cannot know the transmission data of other transmitters. The N hydrophones are distributed on the same receiving end and receive and demodulate the signals from multiple transmitting nodes. The speeds of the M different transmitting nodes are roughly the same, and the distance from the receiving end is arbitrary. The M transducers can send data at any time. In this embodiment, let M=2, N=2. For convenience of representation, define Txm and Rxn as the mth transducer and nth hydrophone respectively. Assume that the data x sent by Txm is m for:

[0044]

[0045] The superscript T means transposition. Indicates t m ×1-dimensional zero vector, parameter t m Denotes the time delay of each transducer transmission. Without loss of generality, let t1<...<t M , and t1=0, x m,p Represents the training symbol vector sent by Txm, x m,d Represents the information symbol vector sent by Txm. The data has zero mean and variance is In this embodiment, the delay transmission time is t1=0, t2=1000, and the training symbol length is L p is 511, the length of the symbol is L d 3840. The data received by Rxn is y n for:

[0046]

[0047] Among them, w n represents zero mean and variance is Complex Gaussian noise, H m,n is the channel convolution matrix between Txm and Rxn, which is composed of the channel tap h between Txm and Rxn m,n Defined as:

[0048]

[0049] in, It is an operation to construct a diagonal matrix by extracting the elements in the matrix. In this embodiment, the channel tap h generated by simulation is m,n As shown in Figure 2, the channel tap length L ch is 15.

[0050] Then receive data Divide into sub-blocks, assuming the sub-block length is L sb , the overlap length between sub-blocks is L ovlp , then the received signals of the k sub-blocks of Rxn for:

[0051]

[0052] in is the channel convolution matrix of the kth sub-block between Txm and Rxn, is the data sent by the kth sub-block corresponding to Txm, The zero mean and variance of the k sub-blocks received by Rxn are Complex Gaussian noise, N sb is the number of sub-blocks, specifically:

[0053]

[0054]

[0055]

[0056]

[0057] in Indicates that Rxn receives signal y n The i-th element of Data x sent by Txm m The i-th element of Indicates that Rxn receives complex Gaussian noise w n The i-th element of are the channel taps of Txm and Rxn at the kth block, and is the i-th element of the channel tap of the k-th sub-block of Txm and Rxn, N sb is the number of sub-blocks. In this embodiment, the sub-block length L is set sb is 40, and the overlap length between sub-blocks is L ovlp is 15, so the number of sub-blocks N sb It is 215.

[0058] S2: Construct channel model: To cope with the slow time-varying characteristics of underwater acoustic communication channels, the channels between sub-blocks are represented by a first-order Markov model, namely:

[0059]

[0060] in is the first-order Markov coefficient of the k-th block of Txm and Rxn, and For the adjacent and The channel taps of the sub-blocks, represents zero mean and variance is The complex Gaussian noise is used to model the random noise component in the channel state transition.

[0061] S3: Based on the distributed MIMO single-carrier underwater acoustic communication system and the channel model, derive the cost function J of the distributed MIMO single-carrier underwater acoustic communication system from the perspective of maximum a posteriori probability. S3 includes the following sub-steps:

[0062] S3.1: Due to the overlap between sub-blocks L ovlp symbols, so some symbols in the current sub-block can be accurately estimated in the previous sub-block, so in the current k-th sub-block, the m-th user's to-be-estimated symbol The front L g symbols It can be regarded as known, and the unknown part is the post-L u symbols , L g and L u Meet L g +L u =L sb +L ch -1, so:

[0063]

[0064] S3.2: Reconstruct the system model of the kth sub-block as:

[0065]

[0066] in, yes 1st to L g List, yes L g to L g +L u List.

[0067] When in the kth sub-block, the symbol Known channel taps When is unknown, the system model of the kth sub-block can be rewritten as:

[0068]

[0069] in, is the symbol convolution matrix of Txm in the kth sub-block, expressed as:

[0070]

[0071] Among them, v is the median number, .

[0072] S3.3: According to the system model and channel model, the kth sub-block The maximum posterior probability p k for:

[0073]

[0074] Where e is a natural constant.

[0075] S3.4: Take the natural logarithm and the inverse of the posterior probability to obtain the k-th sub-block cost function J k for:

[0076]

[0077] S4: Initialization: Initialize the channel tap estimation of the 0th sub-block , noise variance , the first-order Markov coefficient and the noise variance of the channel In this embodiment, initialization , , Initialize the channel tap estimate for the 0th sub-block The following sub-steps are included:

[0078] S4.1: Construct the Toeplitz matrix X of the training symbols of the data sent by Txm m,p for:

[0079]

[0080] in, Represents the training symbol vector X m,p The i-th element of .

[0081] S4.2: Intercept Rxn received data y n The corresponding Txm training symbol vector X m,p The part is:

[0082]

[0083] S4.3: The estimated channel taps for the 0th sub-block between the mth transducer and the nth hydrophone can be expressed using the least squares method, i.e., the pseudo-inverse of the Toeplitz matrix of the training symbols of the data transmitted by the mth transducer is multiplied by the portion of the training symbol vector of the mth transducer corresponding to the data received by the nth hydrophone. for:

[0084]

[0085] The superscript H means conjugate transpose, and the superscript -1 means matrix inversion. In this embodiment, the channel tap estimation result of the 0th sub-block is As shown in Figure 3.

[0086] S5: In the kth sub-block, first keep the estimated value of the channel, the estimated value of the noise variance, the estimated value of the first-order Markov coefficient, and the estimated value of the channel noise variance consistent with those of the k-1th sub-block;

[0087] Then the symbol of the kth sub-block Make an estimate and get its estimated value Then, the channel estimate, the noise variance estimate of the sub-block length, the first-order Markov coefficient estimate, and the channel noise variance estimate are updated successively. Specifically,

[0088] S5.1: In the kth sub-block, first keep the estimated value of the channel, the estimated value of the noise variance, and the estimated value of the first-order Markov coefficient consistent with the k-1th sub-block, that is, update , , , ,in is the channel estimation result of the kth sub-block, is the channel tap estimation result of the k-1th sub-block, are the first-order Markov coefficients of the k-1th block of Txm and Rxn.

[0089] S5.2: In the kth sub-block, according to the received signal , the estimated value of the channel tap , the estimated value of the noise variance , the variance of the sign Pair Symbols Make an estimate and get its estimated value Specifically, the cost function J of the kth sub-block is k , define the variable , so that J k right Taking the partial derivative and setting it to zero, we get Estimated value of :

[0090]

[0091] in, , , yes L g to L g +L u List, Defined as:

[0092]

[0093] Therefore, combined with the known , you can get the estimated value for .

[0094] S5.3: In the kth sub-block, according to the received signal , the estimated value of the symbol , the estimated value of the noise variance , the first-order Markov coefficient estimate and the channel noise variance estimate Estimates of channel taps Update. Specifically, according to the cost function J of the kth sub-block k ,definition , so that J k right Taking the partial derivative and setting it to zero, we get Estimated value of :

[0095]

[0096] in, , , The symbol estimated by the kth sub-block Composition, expressed as:

[0097]

[0098] Among them, v is the median number, .

[0099] S5.4: In the kth sub-block, according to the received signal , the estimated value of the symbol , the estimated value of the channel tap and sub-block length Estimate of the noise variance Update. Specifically, according to the cost function J of the kth sub-block k , so that J k right Taking the partial derivative and setting it to zero, we get Estimated value of :

[0100]

[0101] S5.5: In the kth sub-block, according to the estimated value of the channel tap of the current kth sub-block and the estimated value of the k-1th sub-block channel tap Estimates of the first-order Markov coefficients Update. Specifically, according to the cost function J of the kth sub-block k , so that J k right Taking the partial derivative and setting it to zero, we get Estimated value of for:

[0102]

[0103] S5.6: In the kth sub-block, according to the estimated value of the current kth sub-block channel tap , the estimated value of the k-1th sub-block channel tap , the first-order Markov coefficient estimate and the channel tap length L ch Estimation of channel noise variance Update. Specifically, according to the cost function J of the kth sub-block k , so that J k right Taking the partial derivative and setting it to zero, we get Estimated value of :

[0104]

[0105] S6: Iteratively repeat S5.1-S5.6 using block coordinate descent, as Figure 4 As shown, until the number of iterations reaches the maximum number of iterations N iter Finally, joint channel estimation and symbol detection are realized. In this embodiment, let N iter =5, the first-order Markov coefficient of each sub-block k is Figure 5 shown.

[0106] In this embodiment, the distributed MIMO underwater acoustic communication signal is demodulated, and a distributed MIMO single-carrier underwater acoustic communication joint channel estimation and symbol detection method of the present invention is used to demodulate the constellation diagram and bit error rate. Figure 6 As shown in the figure, the coding bit error rate of Tx1 is 0.23%, and the coding bit error rate of Tx2 is 0.17%. After decoding, both achieve zero bit error rate.

[0107] The present invention proposes a distributed MIMO single-carrier underwater acoustic communication joint channel estimation and symbol detection method, which uses a sub-block-based algorithm to achieve better channel estimation and symbol detection performance in a distributed MIMO slow time-varying environment.

[0108] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for joint channel estimation and symbol detection in distributed MIMO single-carrier underwater acoustic communication, characterized in that: The method comprises the following steps: S1: Build a distributed MIMO single-carrier underwater acoustic communication system consisting of M transducers and N hydrophones; S2: Construct a channel model. The channel between sub-blocks is represented by a first-order Markov model. S3: Based on the distributed MIMO single-carrier underwater acoustic communication system and the channel model, the cost function of the distributed MIMO single-carrier underwater acoustic communication system is derived from the perspective of maximum a posteriori probability; S4: Initialize the estimated value of the channel tap of the 0th sub-block in the channel model, the noise variance, the first-order Markov coefficient and the noise variance of the channel; S5: In the kth sub-block, first keep the estimated values ​​of the channel taps, the estimated value of the noise variance, the estimated value of the first-order Markov coefficient, and the estimated value of the channel noise variance consistent with those of the k-1th sub-block; Then the symbol of the kth sub-block is estimated to obtain its estimated value, and then the estimated value of the channel tap, the estimated value of the noise variance of the sub-block length, the estimated value of the first-order Markov coefficient, and the estimated value of the channel noise variance are successively updated; S6: Iteratively repeat S5 using the block coordinate descent method until the number of iterations reaches the maximum number of iterations to finally achieve joint channel estimation and symbol detection.

2. The method for joint channel estimation and symbol detection for distributed MIMO single-carrier underwater acoustic communication according to claim 1, characterized in that: The S1 includes: M transducers distributed on M different transmitting nodes, each of which is independently controlled, and each transmitter cannot know the transmission data of other transmitters; N hydrophones distributed on the same receiving end receive and demodulate signals from multiple transmitting nodes; M different transmitting nodes have similar speeds and are at any distance from the receiving end, and the M transducers can send data at any time.

3. The method for joint channel estimation and symbol detection for distributed MIMO single-carrier underwater acoustic communication according to claim 1, characterized in that: The estimated value of the channel tap for initializing the 0th sub-block in S4 includes: S4.1: Construct a Toeplitz matrix of the training symbols of the data transmitted by the mth transducer; S4.2: intercepting the portion of the m-th transducer training symbol vector corresponding to the n-th hydrophone received data; S4.3: The channel tap estimate for the 0th sub-block between the mth transducer and the nth hydrophone is expressed using the least squares method, i.e., the pseudo-inverse of the Toeplitz matrix of the training symbols of the data transmitted by the mth transducer is multiplied by the portion of the training symbol vector for the mth transducer corresponding to the data received by the nth hydrophone.

4. The method for joint channel estimation and symbol detection for distributed MIMO single-carrier underwater acoustic communication according to claim 1, characterized in that: The S5 specifically includes: S5.1: In the kth sub-block, first keep the estimated values ​​of the channel taps, the estimated values ​​of the noise variance, and the estimated values ​​of the first-order Markov coefficients consistent with those of the k-1th sub-block; S5.2: Estimating a symbol of the kth sub-block to obtain an estimated value thereof, comprising: estimating, in the kth sub-block, the symbol of the kth sub-block based on a received signal, an estimated value of a channel tap, an estimated value of a noise variance, and a variance of the symbol to obtain an estimated value thereof; S5.3: Updating the estimated value of the channel tap includes: in the kth sub-block, updating the estimated value of the channel according to the received signal, the estimated value of the symbol, the estimated value of the noise variance, the estimated value of the first-order Markov coefficient, and the estimated value of the channel noise variance; S5.4: Updating the estimated value of the noise variance includes: in the kth sub-block, updating the estimated value of the noise variance based on the received signal, the estimated value of the symbol, the estimated value of the channel tap, and the sub-block length; S5.5: Updating the estimated value of the first-order Markov coefficient includes: in the kth sub-block, updating the estimated value of the first-order Markov coefficient based on the estimated value of the channel tap of the current kth sub-block and the estimated value of the channel tap of the k-1th sub-block; S5.6: Updating the channel noise variance estimate includes: in the kth sub-block, updating the channel noise variance estimate based on the estimated value of the current kth sub-block channel tap, the estimated value of the k-1th sub-block channel tap, the estimated value of the k-1th sub-block first-order Markov coefficient, and the channel length.

5. The method for joint channel estimation and symbol detection for distributed MIMO single-carrier underwater acoustic communication according to claim 4, characterized in that: The S5.2 specifically includes: according to the cost function of the kth sub-block, setting the partial derivative of the cost function on the sign of the kth sub-block to zero, and obtaining the estimated value of the sign of the kth sub-block.

6. The method for joint channel estimation and symbol detection for distributed MIMO single-carrier underwater acoustic communication according to claim 4, characterized in that: The S5.3 specifically includes: according to the cost function of the kth sub-block, setting the partial derivative of the cost function on the channel of the kth sub-block to zero, and obtaining an estimated value of the channel tap of the kth sub-block.

7. The method for joint channel estimation and symbol detection for distributed MIMO single-carrier underwater acoustic communication according to claim 4, characterized in that: The S5.4 specifically includes: according to the cost function of the kth sub-block, setting the partial derivative of the cost function on the noise variance of the kth sub-block to zero, obtaining the noise variance estimate of the kth sub-block, and the result is the square of the 2-norm of the received signal residual divided by the length of the sub-block.

8. The method for joint channel estimation and symbol detection for distributed MIMO single-carrier underwater acoustic communication according to claim 4, characterized in that: The S5.5 includes: according to the cost function of the kth sub-block, setting the partial derivative of the cost function on the first-order Markov coefficient of the kth sub-block to zero, obtaining the first-order Markov coefficient estimate of the kth sub-block, and the result is the conjugate transpose of the channel tap estimate of the k-1th sub-block multiplied by the channel tap estimate of the kth sub-block, and then divided by the square of the 2-norm of the channel tap estimate of the k-1th sub-block.

9. The method for joint channel estimation and symbol detection for distributed MIMO single-carrier underwater acoustic communication according to claim 4, characterized in that: The S5.6 specifically includes: according to the cost function of the kth sub-block, setting the partial derivative of the cost function on the channel noise variance of the kth sub-block to zero, obtaining the channel noise variance estimate of the kth sub-block, and the result is the square of the 2-norm of the channel residual of the kth sub-block divided by the length of the channel.

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