平坦瑞利衰落下的QPSK性能仿真

痛定思痛。 2023-01-21 04:26 12阅读 0赞

这里先把代码附上，原理过两天补上来

%%%    Main    %%%
    clc
    clear 
    close all
    
    M = 4;                     %QPSK
    A = 1;                     %信号幅度
    Rs = 1000;                 %码元速率:1000 baud
    Rb = Rs * log2(M);         %比特速率:2000 bps
    fc = 2*Rb;                 %载波频率:4000 Hz
    
    Ts = 1/Rs;                 %码元宽度
    Tb = 1/Rb;                 %比特持续期
    Tc = 1/fc;                 %载波周期宽度
    sampling_point = 20;       %在一个比特持续期内采样20个点
    ts = Tb/sampling_point;    %采样间隔(一个比特持续期是Tb,在一个周期内抽样20个点)
    fs = 1/ts;                 %抽样频率: 4000Hz
    frame_length = 5;          %一帧发送5个符号(10bit)
    
    t_frame = 0:ts:(frame_length*log2(M)*Tb-ts);    %一帧持续的时间
    t_symbol = 0:ts:(log2(M)*Tb-ts);                %一个码元的持续时间
    
    %--------------------------------仿真-------------------------------------%
    snr_dB = 0:1:10;                                  %在0-10dB下测试瑞利衰落下的QPSK性能
    for k = 1:length(snr_dB)
        frame_num = 0;
        error_bit = 0;
        
        while error_bit < 10^5/(snr_dB(k).^2+1)       %根据不同的SNR决定仿真到需要多少error_bit, SNR大,error_bit就小一些
            s = round(rand(1, frame_length*log2(M))); %产生一帧的原始比特数据(10个)
            
            st = QPSK_modulation(s, fc, t_symbol);
            
            snr = 10^(snr_dB(k) / 10);             %功率比值
            Eb = (1/2)*(A^2)*Tb;                   %比特能量
            n0 = Eb/snr;                           %噪声功率谱密度
            delta = sqrt(n0*(fs/2));
            noise = delta * randn(1, length(st));
            
            %产生瑞利信道衰减系数
            %注:假设信道在相干时间内传输一帧的数据,这样一来在同一帧内的数据将经历
            %相同的信道衰减系数,而不同帧间的信道衰减系数独立随机变化
            h = sqrt(1/2) * (randn(1,1) + j*randn(1,1));
            
            r_QPSK = h.*st + noise;
            
            %开始相干检测+相干解调
            %注:在本次仿真中,假设我们可以精确地获得信号的衰减系数h
            Xc1 = conj(h).* r_QPSK.*cos(2*pi*fc*t_frame) ./ abs(h).^2;
            Xs1 = conj(h).* r_QPSK.*(-sin(2*pi*fc*t_frame)) ./ abs(h).^2;
    
            %接下来对一个码元宽度内积分,一个码元宽度应该包括80个采样点
            Xc2 = reshape(Xc1, sampling_point*log2(M), []);
            Xs2 = reshape(Xs1, sampling_point*log2(M), []);
    
            Xc = sum(Xc2) * ts;
            Xs = sum(Xs2) * ts;
    
            %积分完了之后就到了判决
            decis = [];
            for m = 1:frame_length
                if(Xc(m) > 0 && Xs(m) > 0)
                    decis = [decis 1 1];
                elseif (Xc(m) > 0 && Xs(m) < 0)
                    decis = [decis 1 0];
                elseif (Xc(m) < 0 && Xs(m) > 0)
                    decis = [decis 0 1]; 
                elseif (Xc(m) < 0 && Xs(m) < 0)
                    decis = [decis 0 0];
                end
            end
    
            %本帧内误比特数统计(一帧)
            temp_bit = sum(xor(s, decis));
            
            %计算多帧里面的错误比特总数 
            error_bit = error_bit + temp_bit;
            
            %如果错误比特数没有足够多,那么就再取一些帧进行解码
            frame_num = frame_num + 1;   
        end
        
        %计算误比特率
        Pb(k) = error_bit / frame_length / frame_num;
    end
    
    figure;
    semilogy(snr_dB, Pb, 'ro-'); hold on; grid on;
    xlabel('E_b/n_0(dB)');
    ylabel('P_e');
    title('瑞利衰落下QPSK系统性能分析');

%% QPSK调制 %%
    function [st] = QPSK_modulation(s, fc, t_symbol)
        %s:原始二进制序列
        %fc:载波频率
        %t_symbol:一个符号的持续时间
    
        %下面进行符号映射(注意:在映射的同时也完成了增加采样点的操作)
        st = [];
        for i = 1:2:length(s)
            if s(i:i+1) == [1 1]
                st = [st cos(2*pi*fc*t_symbol + pi/4)];
            elseif s(i:i+1) == [0 1]
                st = [st cos(2*pi*fc*t_symbol + 3*pi/4)];
            elseif s(i:i+1) == [0 0]
                st = [st cos(2*pi*fc*t_symbol + 5*pi/4)];
            elseif s(i:i+1) == [1 0]
                st = [st cos(2*pi*fc*t_symbol + 7*pi/4)];
            end
        end
    
    end

仿真结果：  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NDU4NjQ3Mw_size_16_color_FFFFFF_t_70_pic_center]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NDU4NjQ3Mw_size_16_color_FFFFFF_t_70_pic_center]: /images/20221021/13ec60d2f3634a3d9f367eec90a8ca7b.png