阅读说明：本技术 Uddf水声通信协作策略及多分支合并与均衡频域联合实现方法 (UDDF underwater acoustic communication cooperation strategy and multi-branch combination and balanced frequency domain combined implementation method ) 是由 刘志勇 谭周美 柯淼 于 2020-05-28 设计创作，主要内容包括：本发明涉及一种基于频域处理的水声协作通信系统,具体的说是一种UDDF水声通信协作策略及多分支合并与均衡频域联合实现方法,其中首先提出了一种异步水下解码和分布式频率转发的水声通信协作策略,在UDDF水声通信协作策略中,由于源节点和中继节点使用的载波频率不同,目的节点可在频域区分来自源节点和中继节点的信号,因而源节点和中继节点间的IDI,在理论上是可以消除的；而后,基于UDDF水声通信协作策略,提出了一种自适应多分支合并与均衡频域联合实现方法。(The invention relates to an underwater acoustic cooperative communication system based on frequency domain processing, in particular to an UDDF underwater acoustic communication cooperative strategy and a multi-branch combination and balanced frequency domain combined implementation method, wherein an underwater acoustic communication cooperative strategy of asynchronous underwater decoding and distributed frequency forwarding is firstly provided, in the UDDF underwater acoustic communication cooperative strategy, because the carrier frequencies used by a source node and a relay node are different, a target node can distinguish signals from the source node and the relay node in the frequency domain, and IDI between the source node and the relay node can be eliminated theoretically; and then, based on the UDDF underwater acoustic communication cooperation strategy, a self-adaptive multi-branch combination and balanced frequency domain combined implementation method is provided.)

1. A UDDF underwater acoustic communication cooperation strategy is applied to an asynchronous underwater acoustic cooperation communication system, the system consists of a source node S, a relay node R and a destination node D, each node works in a half-duplex mode and is provided with a single sending and receiving unit, all data packets received by the relay node and the destination node are supposed to be completely synchronous, and all the nodes are supposed to have the same average power constraint; assuming that the relay node is located between the source node and the destination node, the distances of S-D, S-R and R-D are respectively defined by l_SD、l_SRAnd l_RDIndicates that l should be satisfied_SD>l_SRAnd l_SD>l_RDCondition (1) assuming that_SRLess than l_RDThe underwater acoustic communication cooperation algorithm is characterized by comprising a broadcasting stage and a relay stage:

in the broadcasting stage, the data packet is broadcasted to the relay node and the destination node by the source node, and the signal continuously sent by the source node is represented as:

where d (j) represents rate-independent binary phase shift keying data, d (j) is { +1, -1}, A_jRepresenting the amplitude of the transmitted signal, T being the symbol duration; q (T) denotes raised cosine pulses, which are a real function and are limited in time interval to [0, T]And normalized, i.e.ω_cSRepresents the carrier angular frequency;

under the assumption of ideal carrier and synchronization, after passing through the carrier, the waveform shaping filter and the low-pass filter, the received baseband signal recovered by the relay node is given by:

wherein P is_SIs the transmit power of the source node, h_SR(t) denotes the underwater acoustic channel impulse response from the source node to the relay node, and x (t) may be represented by x (t) ═ F^-1{|Q(f)|²Is obtained by^-1{. denotes an inverse fourier transform, q (F) ═ F { q (t) }, F {. denotes a fourier transform, and n denotes a fourier transform_SR(t) represents a noise signal at the relay node; the corresponding baseband received signal at the destination node is represented as:

wherein h is_SD(t) denotes the underwater acoustic channel impulse response from the relay to the destination node, n_SD(t) represents a noise signal at the destination node;

in the relay stage, the received signal r is firstly received_SR(t) decoding and then using the decoded information bits other than ω_cSCarrier frequency ω of_cRModulated and immediately ready to generate a signal s_R(t) retransmission to destination node, s_R(t) is represented by the following formula:

whereinRepresenting decoded information bits, ω_cRIs the carrier angular frequency used for relay forwarding, for s_R(t), the baseband signal received by the destination node is as follows:

wherein P is_RRepresenting the transmission power of the relay node, n_RD(t) represents the noise signal at the destination node.

2. The UDDF underwater acoustic communication cooperation strategy-based multi-branch combination and equalization frequency domain joint implementation method as claimed in claim 1, wherein r is paired with symbol interval T_SD(t) and r_RD(t) sampling, corresponding to r_SD(t) and r_RD(t) using a for each discrete received signal_SD(n) and a_RD(n) indicates that the input block data of each branch consists of 2M sample values including M previous samples and M current samples, according to the overlap-and-store method, consisting of a_i(n) the signal vector is formed as follows

Where i ∈ { SD, RD }, [ a ]_i(nM),…,a_i(nM+M-1)]Representing the nth data block, M being the length of the block, the total signal vector is given by:

a(n)＝[a_SD(n)；a_RD(n)] (7)，

where a (n) is a 4M × 1 vector;

calculating the frequency domain signal vector form of a (n) by using 4M point fast Fourier transform, and obtaining the following formula

A(n)＝diag{FFT[a(n)]} (8)

Where A (n) denotes a 4M × 4M diagonal matrix, diag is an operator used to compute the diagonal matrix. The corresponding frequency domain tap weight vector can be calculated by

Where W (n) is the frequency domain 4M × 1 weight vector, w_i(n) is the time domain M1 weight vector, i ∈ { SD, RD }, 0_M×1Represents an M × 1 null vector, and therefore, the frequency domain output vector is given by:

Y(n)＝A(n)W(n) (10)

2M time domain outputs are represented as

y(n)＝[q_out(M+1:2M)；q_out(3M+1:4M)] (11)

Wherein q is_out(n) ═ IFFT { y (n) }, which represents an inverse fast fourier transform, retaining only elements from M +1 to 2M and from 3M +1 to 4M +1, since q is_out(M +1:2M) and q_Out(3M +1:4M) represents the same transmission information d (n), so the total output vector of the detection method is represented by q_out(M +1:2M) and q_OutThe sum of (3M +1:4M) gives:

y_total(n)＝q_out(M+1:2M)+q_out(3M+1:4M) (12)

wherein y is_total(n) is a time domain M × 1 vector, and for the nth data block, the total error vector is calculated by the following formula:

3. the method of claim 2, wherein the frequency-domain weight vector is selected with a minimum mean square error according to a minimum mean square error criterion:

the realization of MSE minimization is simplified by adopting an iterative process of a random algorithm, the total error vector is used for adaptively adjusting the frequency domain weight vector, and in order to update the weight vectors of the SD and RD branches, the frequency domain error vector is calculated by the following formula:

in order to solve the problem of gradient noise amplification caused by large element value in A (n), a normalization method similar to that in a time domain normalization least mean square algorithm is adopted, and corresponding to each weight in the weight vector, a normalization coefficient is calculated as follows

Wherein A is_ii(n) represents the elements of the ith row and ith column on the diagonal of matrix A (n), λ is a constant, λ>0, λ is used to overcome A_ii(n) difficulty in numerical calculation when instantaneous is small; for convenience of representation, 4M normalized coefficients are represented in a matrix form

G(n)＝diag{[g₁,g₂,…,g_4M]} (17)

The block gradient estimate is given by:

wherein p (n) ═ IFFT [ G (n) A^H(n)E(n)]The adaptive frequency domain joint multi-branch merging equalization algorithm can be expressed as

Where μ denotes a step size parameter.

4. The method as claimed in claim 2, wherein for the assumption that the channel is not changed during the transmission of a data packet, a short data packet is used, which consists of training sequences and data symbols, the number of symbols of the training sequences for smooth observation of weight vector adjustment is limited, and for ensuring the convergence of (19), the training sequences in the data packet are repeatedly reused to update the weight vectors until the weight vectors converge to a stable state, and for each repeated update using the same training sequences, the weight vectors are initialized by the weights updated last time.

The technical field is as follows:

the invention relates to an underwater acoustic cooperative communication system based on frequency domain processing, in particular to an UDDF underwater acoustic communication cooperative strategy and a multi-branch merging and balanced frequency domain combined implementation method which can enable a target node to distinguish signals from a source node and a relay node in frequency so as to eliminate IDI between the source node and the relay node.

Background art:

the Underwater Acoustic Channel (UAC) is one of the most complex wireless channels to date. Signal transmission in UAC has the characteristics of long propagation delay, limited bandwidth and large multipath delay spread, which presents challenges to the realization of reliable underwater acoustic communication links.

In order to improve the reliability of the underwater acoustic communication link, cooperative communication techniques that have emerged in recent years have created opportunities to solve this problem. In cooperative communication, a signal of a source node is transmitted to a target node with the help of a relay node. Thus, the destination node receives a plurality of signals from the direct path and the relay path. The combination of multiple signals will affect the performance of cooperative communication to some extent. In the research of underwater acoustic cooperative communication, the existing schemes mostly adopt Equal Gain Combining (EGC) and Maximum Ratio Combining (MRC). MRC may achieve better performance than EGC, but it needs to assume that Channel State Information (CSI) between nodes is known. For practical underwater acoustic channels, CSI is difficult to obtain. In view of the long and variable propagation delay in UAC, asynchronous Underwater amplify-and-forward (UAF) and Underwater decode-and-forward (UDF) have been proposed in the prior art, which assume that Inter-symbol interference (ISI) and Inter-packet interference (IDI) do not exist in the received signals from the source node and the relay node. For both cooperation modes, the relay node forwards the received signal from the source node to the destination node immediately after processing the received signal, rather than waiting for the next time slot to forward again, as in the case of Amplify-and-forward (AF) and Decode-and-forward (DF) in terrestrial wireless communication. However, due to varying propagation delays of UAC and large multipath delay spread, the presence of IDI and ISI is inevitable. To eliminate ISI, time-domain or frequency-domain equalization has been used in underwater acoustic communications. The underwater acoustic channel multipath delay spread time is longer, and the time domain equalization needs a longer tap length to obtain better performance, thereby leading to high implementation complexity. Frequency-domain equalization (FDE) can effectively reduce implementation complexity. However, in the prior art, the research is directed to a non-cooperative communication system, which means that no relay participates in the transmission of information. To our knowledge, frequency domain equalization research oriented to underwater acoustic cooperative communication is still lacking.

The invention content is as follows:

aiming at the defects and shortcomings in the prior art, the invention provides an Underwater acoustic communication cooperation algorithm of asynchronous Underwater decoding and distributed-frequency forwarding (UDDF), wherein in the UDDF Underwater acoustic communication cooperation algorithm, because the carrier frequencies used by a source node and a relay node are different, a target node can distinguish signals from the source node and the relay node in a frequency domain, and IDI between the source node and the relay node can be eliminated theoretically; then, based on the UDDF underwater acoustic communication cooperation algorithm, a Frequency domain joint multi-branch combining and equalization detector (FD-JMCED) is provided.

The invention is achieved by the following measures:

a UDDF underwater acoustic communication cooperation strategy is applied to an asynchronous underwater acoustic cooperation communication system, the system consists of a source node S, a relay node R and a destination node D, each node works in a half-duplex mode and is provided with a single sending and receiving unit, all data packets received by the relay node and the destination node are supposed to be completely synchronous, and in addition, all the nodes are supposed to have the same average power constraint; assuming that the relay node is located between the source node and the destination node, the distances of S-D, S-R and R-D are respectively defined by l_SD、l_SRAnd l_RDIndicates that l should be satisfied_SD>l_SRAnd l_SD>l_RDIn order to prevent the problem of erroneous transmission of the relay node as much as possible, assume that_SRLess than l_RDSuch that the S-R channel has a sufficient instantaneous signal-to-noise ratio; the underwater acoustic communication cooperation algorithm is characterized by comprising a broadcasting stage and a relay stage:

in the broadcasting stage, the data packet is broadcasted to the relay node and the destination node by the source node, and the signal continuously transmitted by the source node is represented as

Wherein d (j) represents equal-rate uncorrelated Binary phase-shift keying (BPSK) data, d (j) is { +1, -1}, A_jRepresenting the amplitude of the transmitted signal, T being the symbol duration, q (T) representing a raised cosine pulse which is a real function, limited in time interval to [0, T]And normalized, i.e.ω_cSRepresents the carrier angular frequency;

under the assumption of ideal carrier and synchronization, the received baseband signal recovered by the relay node after passing through the subcarrier, the waveform shaping filter and the low-pass filter is given by

Wherein P is_SIs the transmit power of the source node, h_SR(t) denotes the underwater acoustic channel impulse response from the source node to the relay node, and x (t) may be represented by x (t) ═ F^-1{|Q(f)|²Is obtained by^-1{. denotes an inverse fourier transform, q (F) ═ F { q (t) }, F {. denotes a fourier transform, and n denotes a fourier transform_SR(t) represents a noise signal at the relay node;

the corresponding baseband received signal at the destination node may be expressed as

Wherein h is_SD(t) denotes the underwater acoustic channel impulse response from the relay to the destination node, n_SD(t) represents a noise signal at the destination node;

in the relay stage, the received signal r is firstly received_SR(t) decoding, and then using the decoded information bits other than ω_cSCarrier frequency ω of_cRModulated and immediately ready to generate a signal s_R(t) retransmission to the destination programPoint, s_R(t) can be represented by the following formula

WhereinRepresenting decoded information bits, ω_cRIs the carrier angular frequency used for relay forwarding, for s_R(t), the baseband signal received by the destination node may be represented in a form similar to equation (3)

Wherein P is_RRepresenting the transmission power of the relay node, n_RD(t) represents the noise signal at the destination node. The principle of the UDDF underwater acoustic communication cooperative algorithm provided by the invention is that the carrier frequencies used by the forwarding of the source node and the relay node are different, and in addition, a band-limited waveform is used so as to eliminate the use of different carrier frequencies (omega) in the frequency domain_cSAnd ω_cR) The overlapping of the received signals, from the view point of the destination node, the signals received from the source node and the relay node work in different frequency bands, and the received signals from the source node and the relay node can be distinguished and extracted according to the different frequency bands, so that the IDI can be removed to a certain extent through band-pass filtering; further, since signals from the source node or the relay node can be distinguished by different frequency bands, the distance requirements between the source node, the relay node and the destination node are not as strict as UDF, and there are corresponding limitations for avoiding ISI and IDI; in the present invention, even if the signals received from the source node and the relay node completely overlap, the desired signal can be extracted, and thus, the end-to-end delay can be further reduced.

The invention also provides a multi-branch combination and balanced frequency domain joint realization method based on the UDDF underwater acoustic communication cooperation strategy, which is characterized in that a symbol interval T is used for r_SD(t) and r_RD(t) sampling, corresponding to r_SD(t) and r_RD(t) using a for each discrete received signal_SD(n) and a_RD(n) indicates that the input block data of each branch consists of 2M sample values including M previous samples and M current samples, according to the overlap-and-store method, consisting of a_i(n) the signal vector is formed as followsWhere i ∈ { SD, RD }, [ a ]_i(nM),…,a_i(nM+M-1)]Representing the nth data block, M being the length of the block, the total signal vector may be given by:

a(n)＝[a_SD(n)；a_RD(n)](7) wherein a (n) is a 4M × 1 vector;

the frequency domain signal vector form of a (n) is calculated by using 4M point Fast Fourier Transform (FFT), which can be obtained by the following formula

A(n)＝diag{FFT[a(n)]} (8)

Where A (n) denotes a 4M × 4M diagonal matrix, diag is an operator used to compute the diagonal matrix. The corresponding frequency domain tap weight vector can be calculated by

Where W (n) is the frequency domain 4M × 1 weight vector, w_i(n) is the time domain M1 weight vector, i ∈ { SD, RD }, 0_M×1Represents an M × 1 null vector, and therefore, the frequency domain output vector is given by:

Y(n)＝A(n)W(n) (10)

the 2M time domain outputs may be represented as

y(n)＝[q_out(M+1:2M)；q_out(3M+1:4M)] (11)

Wherein q is_out(n) ═ IFFT { y (n) }, which represents an Inverse Fast Fourier Transform (IFFT), retaining only elements from M +1 to 2M and from 3M +1 to 4M +1, since q is the inverse of the IFFT, and so on_out(M +1:2M) and q_Out(3M +1:4M) represents the same transmitted information d (n), so the overall output of the detection methodVector is composed of q_out(M +1:2M) and q_OutThe sum of (3M +1:4M) gives

y_total(n)＝q_out(M+1:2M)+q_out(3M+1:4M) (12)

Wherein y is_total(n) is a time domain M × 1 vector, and for the nth data block, the total error vector can be calculated by the following formula:

the purpose of the detection method of the invention is to recover the information bits sent by the source node, so that the frequency domain weight vectors are selected with a minimum Mean Square Error (MSE) according to the Minimum Mean Square Error (MMSE) criterion

The implementation of MSE minimization can be simplified by adopting an iterative process of a random algorithm, the total error vector is used for adaptively adjusting the frequency domain weight vector, and in order to update the weight vectors of the SD and RD branches, the frequency domain error vector is calculated by the following formula:

in order to solve the problem of gradient noise amplification caused by large element values in A (n), a normalization method similar to that in a time domain Normalized Least Mean Square (NLMS) algorithm is adopted, and corresponding to each weight in the weight vector, a normalization coefficient is calculated as follows

Wherein A is_ii(n) represents the elements of the ith row and ith column on the diagonal of matrix A (n), λ is a constant, λ>0, λ is used to overcome A_ii(n) instantNumerical calculation is difficult when the time is small; for convenience of representation, 4M normalized coefficients are represented in a matrix form

G(n)＝diag{[g₁,g₂,…,g_4M]} (17)

Thus, the block gradient estimate is given by:

wherein p (n) ═ IFFT [ G (n) A^H(n)E(n)]. With these definitions, the adaptive frequency domain joint multi-branch combining equalization algorithm can be expressed as

Where μ denotes a step size parameter.

In order to meet the assumption that the channel is unchanged during the transmission of a data packet, the invention adopts a short data packet which consists of training sequences and data symbols, the number of the symbols of the steady observation training sequences for adjusting the weight vector is limited, in order to ensure the convergence of the proposed adaptive algorithm (19), the training sequences in the data packet are repeatedly reused to update the weight vector until the weight vector converges to a steady state, and for each repeated update using the same training sequence, the weight vector is initialized by the weight value after the last update; in addition, the multi-branch combination does not need to assume that the CSI between nodes is known, but is obtained based on iterative updating of the proposed adaptive algorithm, so that the algorithm is more suitable for the actual underwater acoustic communication system.

Description of the drawings:

FIG. 1 is a schematic diagram of a frequency-joint multi-branch merging equalization detection method according to the present invention.

Fig. 2 is a graph of error rate performance in embodiment 1 of the present invention.

Fig. 3 is a graph showing convergence performance in example 1 of the present invention.

The specific implementation mode is as follows:

the invention is further described below with reference to the accompanying drawings and examples.

The invention firstly provides an asynchronous Underwater decoding and distributed-frequency forwarding (UDDF) mode, in the UDDF, because the carrier frequencies used by a source node and a relay node are different, a target node can distinguish signals from the source node and the relay node in a frequency domain, and therefore IDI between the source node and the relay node can be eliminated theoretically. Then, aiming at the UDDF cooperation mode, a Frequency domain joint multi-branch combining and equalization detector (FD-JMCED) is provided, the combination of the received signals from the source node and the relay node can be obtained based on the proposed adaptive algorithm, the algorithm does not need to assume that CSI between links is known, and the algorithm also jointly realizes equalization while combining.

The invention is applied to an asynchronous underwater acoustic cooperative communication system, which consists of a source node S, an UDDF relay node R and a destination node D, wherein each node works in a half-duplex mode and is provided with a single sending and receiving unit. It is assumed that all packets received by the relay node and the destination node are completely synchronized. Further, it is also assumed that all nodes have the same average power constraint.

In the proposed UDDF model, assuming that the relay node is located between the source node and the destination node, the distances S-D, S-R and R-D are defined by l, respectively_SD、l_SRAnd l_RDIndicates that l should be satisfied_SD>l_SRAnd l_SD>l_RDThe conditions of (1). To prevent the problem of erroneous transmission of the relay node as much as possible, assume l_SRLess than l_RDSo that the S-R channel has a sufficient instantaneous Signal-to-noise ratio (SNR). In the cooperative transmission process, the implementation of the UDDF mode requires two phases, namely a broadcast phase and a relay phase, wherein in the broadcast phase: the data packet is broadcasted to the relay node and the destination node by the source node, and the signal continuously transmitted by the source node can be represented as

Wherein d (j) represents equal-rate uncorrelated Binary phase-shift keying (BPSK) data, d (j) is { +1, -1}, A_jRepresenting the amplitude of the transmitted signal, T being the symbol duration, q (T) representing a raised cosine pulse which is a real function, limited in time interval to [0, T]And normalized, i.e.ω_cSRepresenting the carrier angular frequency.

Under the assumption of ideal carrier and synchronization, the received baseband signal recovered by the relay node after passing through the subcarrier, the waveform shaping filter and the low-pass filter is given by

Wherein P is_SIs the transmit power of the source node, h_SR(t) denotes the underwater acoustic channel impulse response from the source node to the relay node, and x (t) may be represented by x (t) ═ F^-1{|Q(f)|²Is obtained by^-1{. denotes an inverse fourier transform, q (F) ═ F { q (t) }, F {. denotes a fourier transform, and n denotes a fourier transform_SR(t) represents a noise signal at the relay node.

The corresponding baseband received signal at the destination node may be expressed as

Wherein h is_SD(t) denotes the underwater acoustic channel impulse response from the relay to the destination node, n_SD(t) represents the noise signal at the destination node.

For UDDF relaying, the received signal r is first received_SRAnd (t) decoding. Then, the decoded information bits are used with a value different from ω_cSCarrier frequency ω of_cRIs modulated and immediately generatedSignal s of_R(t) retransmission to destination node, s_R(t) can be represented by the following formula

WhereinRepresenting decoded information bits, ω_cRIs the carrier angular frequency used by the relay. For s_R(t), the baseband signal received by the destination node may be represented in a form similar to equation (3)

Wherein P is_RRepresenting the transmission power of the relay node, n_RD(t) represents the noise signal at the destination node.

The principle of UDDF is that the source node and the relay node forward using different carrier frequencies. In addition, band-limited waveforms are used to eliminate the use of different carrier frequencies (ω) in the frequency domain_cSAnd ω_cR) The superposition of the received signals. From the destination node's perspective, the signals received from the source node and the relay node operate in different frequency bands. The received signals from the source node and the relay node can be distinguished and extracted according to the difference of frequency bands, so that the IDI can be removed to some extent by band-pass filtering. Further, since signals from the source node or the relay node can be distinguished by different frequency bands, the distance requirements between the source node, the relay node and the destination node are not as strict as UDF, which has corresponding limitations to avoid ISI and IDI. In the proposed UDDF, even if the signals received from the source node and the relay node completely overlap, the desired signal can be extracted, and thus the end-to-end delay can be further reduced.

The invention also provides an FD-JMCED detection method based on the UDDF underwater acoustic communication cooperation algorithm, a schematic block diagram of the detection method is shown in figure 1, and the detection method is different from a traditional detector (single-branch Frequency domain equalization detector) in point-to-point communication, wherein the branch number in the FD-JMCED is more than 1, and in order to obtain better diversity gain, the input signals of two branches are processed in a combined manner.

At symbol intervals T to r_SD(t) and r_RD(t) after sampling, corresponds to r_SD(t) and r_RDThe discrete received signals of (t) may be respectively represented by a_SD(n) and a_RDAnd (n) represents. In FD-JMCED, the input block data of each branch consists of 2M sample values including M previous samples and M current samples, a, according to the overlap-save method_i(n) the signal vector is formed as follows

Where i ∈ { SD, RD }, [ a ]_i(nM),…,a_i(nM+M-1)]Representing the nth data block and M is the length of the block. For joint processing of the received signals of the two branches, the total signal vector can be given by:

a(n)＝[a_SD(n)；a_RD(n)](7) where a (n) is a 4M 1 vector.

Using a 4M-point Fast Fourier Transform (FFT) to compute a (n) frequency domain signal vector form, a (n) diag { FFT [ a (n) ] (8) can be derived from the following equation, where a (n) represents a 4M × 4M diagonal matrix and diag is the operator used to compute the diagonal matrix;

the corresponding frequency domain tap weight vector can be calculated by

Where W (n) is the frequency domain 4M × 1 weight vector, w_i(n) is the time domain M x 1 weight vector, i ∈{SD,RD}，0_M×1Represents an M × 1 null vector, and therefore, the frequency domain output vector of FD-JMCED can be given by:

Y(n)＝A(n)W(n) (10)

the 2M time domain outputs of FD-JMCED can be expressed as

y(n)＝[q_out(M+1:2M)；q_out(3M+1:4M)] (11)

Wherein q is_out(n) ═ IFFT { y (n) }, which denotes an Inverse Fast Fourier Transform (IFFT). Only elements from M +1 to 2M and from 3M +1 to 4M +1 are retained. Because q is_out(M +1:2M) and q_Out(3M +1:4M) represents the same transmitted information d (n), so the total output vector of the detector can be represented by q_out(M +1:2M) and q_OutThe sum of (3M +1:4M) gives

y_total(n)＝q_out(M+1:2M)+q_out(3M+1:4M) (12)

Wherein y is_total(n) is a time domain M × 1 vector. For the nth data block, the total error vector can be calculated by the following formula:

the purpose of the detector is to recover the information bits sent by the source node. Thus, the frequency domain weight vectors are selected to minimize Mean Square Error (MSE) according to a Minimum Mean Square Error (MMSE) criterion

The implementation of MSE minimization may be simplified by an iterative process employing a random algorithm. The total error vector may be used to adaptively adjust the frequency domain weight vector. To update the weight vectors for the SD and RD branches, the frequency domain error vector may be calculated by:

to solve the problem of gradient noise amplification caused when the element value in a (n) is large, a normalization method similar to that in the time domain Normalized Least Mean Square (NLMS) algorithm is used. The normalization coefficient is calculated for each weight in the weight vector as follows

Wherein A is_ii(n) represents the elements of the ith row and ith column on the diagonal of matrix A (n), λ is a constant, λ>0, λ is used to overcome A_ii(n) numerical calculation when the instantaneous is small is difficult. For convenience of representation, 4M normalized coefficients may be represented in a matrix form

G(n)＝diag{[g₁,g₂,…,g_4M]} (17)

Thus, the block gradient estimate may be given by:

wherein p (n) ═ IFFT [ G (n) A^H(n)E(n)]. With these definitions, the adaptive frequency domain joint multi-branch combining equalization algorithm can be expressed as

Where μ denotes a step size parameter.

To satisfy the assumption that the channel is unchanged during the transmission of one packet, we use a short packet, which consists of a training sequence and data symbols. The number of stationary observation training sequence symbols used for weight vector adjustment is limited. In order to ensure the convergence of the proposed adaptive algorithm (19), the training sequences in the data packets are repeatedly reused to update the weight vectors until the weight vectors converge to a steady state. For each repeated update using the same training sequence, the weight vectors are initialized with the weights that were updated last time. In addition, it should be noted that multi-branch combining does not need to assume that the CSI between nodes is known, but results from iterative updating based on the proposed adaptive algorithm. Therefore, the algorithm is more suitable for the actual underwater acoustic communication system.

Example 1:

in this example, a Monte Carlo simulation was built based on the hydroacoustic channel model. In this model, the carrier frequencies of the source node and the relay node are set to 10kHz and 20kHz, respectively. The water depth is set to be 80m, and the source node, the relay node and the destination node are respectively located at positions 50m, 30m and 20m away from the sea surface. Assume that the distances S-D, S-R and R-D are 1000m, 350m and 700m, respectively. We also assume that the hydroacoustic channel is semi-stationary, meaning that during the transmission of one packet the channel remains unchanged, but for the next packet the channel will change. In the simulations, BPSK modulation was used. The weight vector lengths for both the S-D and R-D branches are set to 32. μ and λ are set to 0.15 and 0.5, respectively. The data frame consists of K sets of training sequences and data symbols, and in each data packet, the length of the training sequence is set to 256 and the length of the data symbol is also set to 256. The number of repetitions of the training sequence was set to 4. The data packets in the data frames are transmitted continuously, so we assume that the signals received from the source node and the relay node are completely overlapping.

In FIG. 2, we examined the Bit Error Rate (BER) performance of the proposed FD-JMCED and existing methods, with the horizontal axis representing the signal-to-noise ratio (SNR) SNR of the S-D branch_SD. In the simulation, it is assumed that the condition SNR is satisfied_RD＝SNR_SD+1. FD-SMCED refers to an equalization detector similar to that in a single branch that will update the weight vector for each branch independently and then combine the outputs of the S-D and R-D branches by equal gain combining. It can be seen from fig. 2 that FD-SMCED can achieve better BER performance than FD-SBED. This is because the equalized outputs of the S-D and R-D branches are combined in EGC mode, which achieves a certain diversity gain. Furthermore, it can be seen from fig. 2 that the proposed FD-JMCED achieves comparable gain compared to FD-SMCED. This is because in FD-JMCED, the weight vectors of the S-D and R-D branches are jointly obtained from the total error in (13),better combining gain can be obtained.

FIG. 3 shows the convergence properties of FD-JMCED and FD-SBED. Since the training sequence in each packet is reused 4 times in the simulation, the length of the horizontal axis is 1024. As can be seen from FIG. 3, similar convergence rates were achieved for FD-JMCED and FD-SBED, but better steady state mean square error performance was obtained for FD-JMCED. This result is consistent with the comparison of BER performance in fig. 2, since the steady state MSE performance is an important parameter affecting equalization performance.

The simulation result verifies the effectiveness of the method and shows that the method has advantages compared with the prior method.