• OFDM系统各种QAM调制阶数在多径信道下的误码性能仿真（暂存版本）

    本文考虑OFDM系统在多径信道下的误码性能 

    代码

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    clc;close all;clear
     
    %% Seting parameters
    EbN0_list = 20:2:40;
    Q_order_list = 2:2:10;
    loopNumber = 10000;
    fprintf('Qm\t EbN0 \t \t EsN0 \t \t SNR_Cal \t \t ser \t\t ser_theory\t\t\t ber\t\t nloop \t\t \n');
    for iQorder = 1 : length(Q_order_list)
    for iEbN0 = 1 : length(EbN0_list)
     
    %% Frame structure
    N_Frame = 1;
    N_Symbol = 1;
    N_RB = 106;
    N_SC_perRB = 12;
    N_SC = N_RB * N_SC_perRB;
    N_Ant = 1;
    N_fft_order = floor(log2(N_RB * N_SC_perRB));
    N_fft = 2^(N_fft_order+1);
    N_cp = N_fft/8;
    EbN0 = EbN0_list(iEbN0);
     
    %% Modulation
    Q_order = Q_order_list(iQorder);
    Qm = 2^Q_order;
    N_bit = N_Frame * N_Symbol * N_RB * N_SC_perRB * Q_order;
     
    %% Noise Calculation
    SNR =  EbN0 + 10 * log10(Q_order);
     
    %% Loop
    for iloop = 1 :loopNumber
    data_bit_in = randi([0 1], 1, N_bit);
    dataSymbolsIn = bi2de(reshape(data_bit_in, Q_order, N_bit/Q_order).', 'left-msb');
    dataMod = qammod(dataSymbolsIn, Qm,'UnitAveragePower', true);
     
    %% Show Constellation
    %scatterplotme(dataMod)
     
    %% Resource Mapping
    RE_Grid = zeros(N_RB * N_SC_perRB,N_Symbol * N_Frame);
    dataMod_tmp = reshape(dataMod,N_RB * N_SC_perRB,[]); %only data
    Power_Scale = 1;
    RE_Grid_all = Power_Scale * dataMod_tmp;
     
    %% IFFT add CP
    frame_mod_shift = ifftshift(RE_Grid_all);
    ifft_data = ifft(frame_mod_shift,N_fft)*sqrt(N_fft);
    %ifft_data = ifft(frame_mod_shift)*sqrt(1272);
    Tx_cd = [ifft_data(N_fft-N_cp+1:end,:);ifft_data];
    time_signal = reshape(Tx_cd,[],1);
     
    %% Channel
    power_RE = sum(sum(abs(RE_Grid_all).^2)) / N_RB / N_SC_perRB / N_Symbol / N_Frame;
    power_tp = sum(sum(abs(ifft_data).^2)) / N_RB / N_SC_perRB / N_Symbol / N_Frame;  %IFFT zero padding averages the true RE Power
    N0 = power_RE .* 10.^(-SNR / 10);
    white_noise_starand = 1/sqrt(2)*(randn(size(time_signal)) + 1j * randn(size(time_signal)));
    nTap = 2;
    taps = RayleighChanTaps(nTap);
    % taps = [0.9,0.1];
    time_signal_path = Multipath_channel(time_signal,taps);
    TransmittedSignal = time_signal_path + sqrt(N0) * white_noise_starand;
     
    %% Receive and Sys
    ReceivedSignal = TransmittedSignal;
    hF = fftshift(fft(taps,N_fft));
     
    %% FFT and Frame  
    frame_recieved_parallel = reshape(ReceivedSignal, N_fft + N_cp, []);
    frame_Received = frame_recieved_parallel(N_cp + 1:end,:);   
    frame_Grid_fft = fft(frame_Received,N_fft) / sqrt(N_fft);
    RE_Grid_all_fftshift = fftshift(frame_Grid_fft);
    RE_Grid_all_fftshift_eq = fftshift(diag(1./hF)*RE_Grid_all_fftshift);
    RE_Grid_all_Received = fftshift(RE_Grid_all_fftshift_eq(1:N_SC,:));
    % figure(1)
    % plot(abs(RE_Grid_all_fftshift(:,1)))
    % figure(2)
    % plot(abs(RE_Grid_all_fftshift_eq(:,1)))
    % figure(3)
    % plot(abs(abs(hF)))
    % figure(4)
    % plot(abs(abs(1./hF)))
     
    %% Demodulation
    RE_PreDeMod = reshape(RE_Grid_all_Received,[],1);
    dataSymbolsOut = qamdemod(RE_PreDeMod, Qm,'UnitAveragePower', true);
    data_bit_out = reshape((de2bi(dataSymbolsOut, 'left-msb')).',1,[]);
    power_RE_receid = sum(sum(abs(RE_PreDeMod).^2)) / N_RB / N_SC_perRB / N_Symbol / N_Frame;
    snr_all(iQorder,iEbN0,iloop) = 10*log10(power_RE/(power_RE_receid - power_RE));
     
    %% Result: Ser and Ber
    %Ser
    sym_err = length(find(dataSymbolsOut - dataSymbolsIn));
    ser_all(iQorder,iEbN0,iloop) = sym_err / length(dataSymbolsOut);
    %Ber
    bit_error = sum(abs(data_bit_out - data_bit_in));
    ber_all(iQorder,iEbN0,iloop) = bit_error / length(data_bit_out);
    end
    sers = mean(ser_all,3);
    snrs = mean(snr_all,3);
    bers = mean(ber_all,3);
    sers_theory(iQorder,iEbN0) = QAM_SER_Theory(Qm,EbN0);
     
        fprintf('%dQAM\t%f\t %f\t %f\t %e\t\t%e\t\t%e\t\t%d\t\n', Qm, EbN0, SNR,snrs(iQorder,iEbN0),sers(iQorder,iEbN0),sers_theory(iQorder,iEbN0),bers(iQorder,iEbN0),loopNumber);
        end
    end
     
    figure(1)
    semilogy(EbN0_list, bers(1,:), 'k--+');
    hold on
    grid on
    semilogy(EbN0_list, bers(2,:), 'r--o');
    semilogy(EbN0_list, bers(3,:), 'b--x');
    semilogy(EbN0_list, bers(4,:), 'g--s');
    xlabel('Eb/N0,dB');
    ylabel('BER');
    title('BER VERS SNR');
    legend('QPSK','16QAM','256QAM','1024QAM');
     
     
    figure(2)
    semilogy(EbN0_list, sers(1,:), 'k--+');
    hold on
    grid on
    semilogy(EbN0_list, sers(2,:), 'r--o');
    semilogy(EbN0_list, sers(3,:), 'b--x');
    semilogy(EbN0_list, sers(4,:), 'g--s');
    xlabel('Eb/N0,dB');
    ylabel('SER');
    title('SER VERS SNR');
    %SML =  simulation, THR = theory
    legend('QPSK','16QAM','256QAML','1024QAM');

     用到的信道与过信道代码

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    function taps = RayleighChanTaps(nTap)
      taps= 1/sqrt(2)*1/sqrt(nTap)*(randn(nTap,1) + 1j*randn(nTap,1));
       
    end

     

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    function taps = ExponentialChanTaps(SampRateMHz, delaySprdNsec)
    sampTimeNsec = 1000 / SampRateMHz;
     
    if delaySprdNsec == 0
        Kmax = 0;
        vark = 1;
    else
        Kmax = ceil(10 * delaySprdNsec/sampTimeNsec);
        var0 = 1 - exp(- sampTimeNsec /delaySprdNsec);
        k = (0:Kmax)';
        vark = var0 * exp( -k *sampTimeNsec/delaySprdNsec);
    end
        stdDevReOrIm = sqrt(vark/2);
        taps = stdDevReOrIm .*(randn(Kmax +1,1) + 1j*randn(Kmax+1,1));
    end

     

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    function yt = Multipath_channel(xt,taps)
        ht = taps;
        xht = conv(ht,xt);
        %yt = xht(end - length(xt)+1:end);
        yt = xht(1:length(xt));
    end

     仿真结果

    瑞利信道下的仿真结果，设置抽头系数为2，仿真次数设置1000次曲线才会平滑。

    在瑞利信道和白噪声下的仿真结果对比

    一个感兴趣的点是固定信噪比时误码性能随多径的数量是如何变化的，先保证最大时延扩展没有超过CP的长度。该实验结果仅设置了100次，看起来曲线不是很光滑。在完美已知信道抽头系数的情况下，多径的数量不会影响解调性能。

     

    结论分析

    瑞利信道下的误码率曲线近似为直线，（很奇怪，难以理解）

    反思

     

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  • 原文地址：https://www.cnblogs.com/TensorLearning/p/18043051