OFDM系统各种QAM调制阶数在多径信道下的误码性能仿真

本文考虑OFDM系统在多径信道下的误码性能 

代码

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

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

 

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

 

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

目前是假设信道估计是完美的，通常在现实的信号处理中需要在OFDM符号中插入导频，通过导频去估计信道，信道估计是受噪声影响的，此时误码性能如何变化。