1. Basic principles of underwater channel modeling

Underwater communication channel modeling is a key technique for understanding and predicting the characteristics of signal propagation in underwater environments. During the modeling process, in-depth research is required on the physical characteristics of the underwater environment, signal propagation mechanisms, and statistical characteristics of the received signals.

1.1. Basic principles of underwater communication channel modeling

The main goal of underwater communication channel modeling is to describe the attenuation, scattering, absorption and other characteristics of signals when propagating in water. These characteristics are mainly affected by the physical characteristics of the water body, such as water depth, flow rate, temperature, salinity, etc. In addition, the frequency, waveform, power and other characteristics of the signal also need to be considered.

1.2. Mathematical formulas for underwater communication channel modeling

The main mathematical formulas for modeling underwater communication channels usually include propagation loss formulas, multipath effect models, and channel impulse response models. The propagation loss formula is mainly used to describe the energy attenuation of signals during propagation. A commonly used propagation loss formula is:

L(d) = L(0) + 10nlog(d) + Xσ

Among them, L(d) is the propagation loss at distance d, L(0) is the propagation loss at the reference distance (usually 1m), n is the attenuation coefficient, and Xσ is a random variable of Gaussian distribution, used to describe random multiple diameter effect.

The multipath effect model describes the propagation of signals through multiple paths due to reflection, scattering and refraction of various objects and organisms in the water. The multipath effect causes changes in the amplitude and phase of the received signal, thereby affecting communication quality. The channel impulse response model describes the response of the received signal in the time domain. It can be viewed as a superposition of multiple impulse responses, each corresponding to a specific multipath path. Modeling of channel impulse response usually requires specialized measurement equipment and techniques.

1.3. LMS-based underwater communication channel modeling

The LMS (Least Mean Square) algorithm is an adaptive filtering algorithm that can be used for underwater communication channel modeling. The basic principle is to automatically adjust the coefficients of the filter through an iterative process to minimize the sum of squared errors. The basic principle of the LMS algorithm is to use the error between the input signal and the expected signal to adjust the coefficients of the filter. The specific formula is as follows:

μ(n) = μ0 + Σ[ω(k) * x(nk) * e(nk)] (1)

Among them, μ(n) is the coefficient vector of the filter, μ0 is the initial coefficient vector, ω(k) is the step parameter, x(nk) is the input signal vector, and e(nk) is the error between the expected signal and the actual signal.

The implementation steps of underwater communication channel modeling based on LMS are as follows:

Initialize filter coefficients. Typically, the initial coefficients of the filter can be set to zero or set based on some prior information.
For each time step, the error between the filter output and the desired signal is calculated.
The errors are weighted and averaged to obtain the average error.
Based on the average error, the coefficients of the filter are updated. This step is achieved through an iterative process.
Use the updated filter for signal processing at the next time step. Repeat steps 2-5 until the preset number of iterations or convergence conditions are reached.

1.4. Underwater communication channel modeling based on neural network

Neural network is a computing model that simulates the connection of neurons in the human brain and has powerful nonlinear mapping capabilities and self-learning capabilities. In underwater communication channel modeling, neural networks can be used to describe the complex mechanisms of signal propagation. Neural network is a computing model that simulates the connection of neurons in the human brain. It can learn and approximate complex nonlinear mapping relationships. In neural network-based underwater communication channel modeling, we can use neural networks to learn and approximate the characteristics of underwater communication channels.
The basic principle of neural network is to approximate a nonlinear mapping relationship through learning and training, thereby mapping the input signal to the desired output signal. In the modeling of underwater communication channels based on neural networks, we can regard the underwater communication channel as a nonlinear system and use neural networks to approximate its characteristics. Steps The implementation steps of underwater communication channel modeling based on neural network are as follows:

(1) Determine the topology of the neural network, including the number of nodes in the input layer, hidden layer and output layer.
(2) Initialize the parameter vector θ of the neural network.
(3) Receive the input signal x(n) of the underwater communication channel and send it to the neural network.
(4) Calculate the output signal y^(n) based on the input signal x(n) and the mapping function f of the neural network.
(5) Calculate the error e(n) between the expected signal y^(n) and the actual signal y(n).
(6) Update the parameter vector θ of the neural network according to the error e(n) and the gradient descent algorithm.
(7) Repeat steps (3) ~ (6) until the set number of iterations is reached or the error reaches the acceptable range.

Underwater communication channel modeling based on neural networks needs to consider issues such as the construction and annotation of data sets, the efficiency and stability of model training, and the evaluation of model performance. At the same time, due to the complexity and uncertainty of the underwater communication environment, the neural network may need to be trained and adjusted multiple times to achieve ideal performance.
Underwater communication channel modeling is a key technology for efficient communication of underwater equipment such as underwater robots and underwater detectors. By establishing appropriate mathematical models, the signal propagation characteristics of the underwater environment can be better understood and predicted, thereby optimizing the performance of the communication system. LMS and neural network are two commonly used modeling methods, each with its own characteristics and scope of application. In practical applications, appropriate modeling methods need to be selected based on specific problems and data characteristics.

2. MATLAB core program

for channelNumber = 1:10
    channelNumber
    x1 =x_all(channelNumber,:)'>0.5; %第n个通道的输入通道数据
    d1 = y_all(channelNumber,:)'>0.5; %将通道与输入卷积
    x2 =x2_all(channelNumber,:)'>0.5; %第n个通道的输入通道数据
    d2 = y2_all(channelNumber,:)'>0.5; %将通道与输入卷积
    
    lms=dsp.LMSFilter(filter_order,'StepSize',0.01,'WeightsOutputPort',true);
    [~,e,w1]=lms(double(x1),double(d1)); %LMS滤波器权重
    [~,e,w2]=lms(double(x2),double(d2)); %LMS滤波器权重
    
    lms_filter1=w1./w1(1); %估计均衡器系数
    lms_filter2=w1./w1(1); %估计均衡器系数
    
    dataOut1=(filter(1,lms_filter1,d1))>0.5; %信息比特通过均衡器
    dataOut2=(filter(1,lms_filter2,d2))>0.5; %信息比特通过均衡器
    LmsBerEst1(channelNumber)=biterr(x1,dataOut1)/length(x1); %信道BER
    LmsBerEst2(channelNumber)=biterr(x2,dataOut2)/length(x2); %信道BER
    
    %Levinson Durbin
    [a1 ~]=levinson(autocorr(d1,filter_order),filter_order-1);
    [a2 ~]=levinson(autocorr(d1,filter_order),filter_order-1);
    b1=a1;
    b2=a2;
    dataOut1=(filter(b1,1,d1))>0.5; %信息比特通过均衡器
    dataOut2=(filter(b2,1,d2))>0.5; %信息比特通过均衡器
    LevBerEst1(channelNumber)=biterr(x1,dataOut1)/length(x1);  
    LevBerEst2(channelNumber)=biterr(x2,dataOut2)/length(x2);  
end
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Underwater channel modeling and matlab simulation based on LMS adaptive filtering algorithm