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OFDM_Benchmark_dev.m
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OFDM_Benchmark_dev.m
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%% Benchmarks for OFDM communication systems in AWGN and Rayleigh channel
% Author: Zhongyuan Zhao
% Date: 2021-03-10
% Link: https://github.com/zhongyuanzhao/dl_ofdm
% Cite this work:
% Zhongyuan Zhao, Mehmet C. Vuran, Fujuan Guo, and Stephen Scott, "Deep-Waveform:
% A Learned OFDM Receiver Based on Deep Complex-valued Convolutional Networks,"
% EESS.SP, vol abs/1810.07181, Mar. 2021, [Online] https://arxiv.org/abs/1810.07181
%
% Copyright (c) 2021: Zhongyuan Zhao
% Houston, Texas, United States
% <zhongyuan.zhao@huskers.unl.edu>
%% Usage: configurations are hard-coded
% see script_rayleigh.m for calling this function
% see inline configurations
function OFDM_Benchmark_dev(pilot_type, channel, longcp, eq_idx)
save_tx_data = 0;
N = 64; % FFT size, Number of total subcarriers
%% Step 1: Configurations
% mobile = ''; % uncomment this to disable mobility
mobile = '_mobile'; % uncomment this to enable mobility
mod_names = {'BPSK','QPSK','8QAM','16QAM'};
est_names = {'Perfect','LS-Spline','LS-Linear','LMMSE','LS-Quadeer',...
'LMMSE-Quadeer', 'ALMMSE','LMMSE-Uni-PDP', 'LMMSE-Exp-PDP', 'LMMSE-Fast'};
if longcp
mat_name = sprintf('BER_OFDM_%s_%s_%s_%d_Gray%s.mat',channel,est_names{eq_idx}, pilot_type, N, mobile);
csv_name = sprintf('BER_OFDM_%s_%s_%s_%d_Gray%s.csv',channel,est_names{eq_idx}, pilot_type, N, mobile);
fig_name = sprintf('BER_OFDM_%s_%s_%s_%d_Gray%s.fig',channel,est_names{eq_idx}, pilot_type, N, mobile);
png_name = sprintf('BER_OFDM_%s_%s_%s_%d_Gray%s.png',channel,est_names{eq_idx}, pilot_type, N, mobile);
else
mat_name = sprintf('BER_OFDM_%s_%s_%s_%d_Gray%s_shortcp.mat',channel,est_names{eq_idx}, pilot_type, N, mobile);
csv_name = sprintf('BER_OFDM_%s_%s_%s_%d_Gray%s_shortcp.csv',channel,est_names{eq_idx}, pilot_type, N, mobile);
fig_name = sprintf('BER_OFDM_%s_%s_%s_%d_Gray%s_shortcp.fig',channel,est_names{eq_idx}, pilot_type, N, mobile);
png_name = sprintf('BER_OFDM_%s_%s_%s_%d_Gray%s_shortcp.png',channel,est_names{eq_idx}, pilot_type, N, mobile);
end
if isfile(mat_name)
fprintf('%s already exist, skip \n', mat_name)
return;
else
fprintf('%s running \n', mat_name)
end
p = gcp('nocreate'); % If no pool, do not create new one.
if isempty(p)
poolsize = 0;
else
poolsize = p.NumWorkers;
end
% global n_cores;
% poolsize=n_cores;
% if save_tx_data
% mkdir('mat');
% end
% 1.1 OFDM parameters
if longcp
Ncp = round(N.*0.25); % Length of Cyclic prefix
cpstr = '';
else
Ncp = round(N.*0.07);
cpstr = '_shortcp';
end
if N == 64
Fs = 960000;
Np = 6; % No of pilot symbols
n_RB = 4;
elseif N==128
Fs = 1920000;
Np = 12; % No of pilot symbols
n_RB = 6;
elseif N==256
Fs = 3840000;
Np = 30; % No of pilot symbols
n_RB = 15;
elseif N==512
Fs = 7680000;
Np = 50; % No of pilot symbols
n_RB = 25;
elseif N==1024
Fs = 15360000;
Np = 100; % No of pilot symbols
n_RB = 50;
elseif N==1536
Fs = 23040000;
Np = 150; % No of pilot symbols
n_RB = 75;
elseif N==2048
Fs = 30720000;
Np = 300; % No of pilot symbols
n_RB = 150;
end
Np=n_RB*2;
Ts = 1/Fs; % Sampling period of channel
Fd = 70;
if strcmp(channel, 'AWGN') || strcmp(channel, 'Flat')
Fd = 0; % Max Doppler frequency shift
elseif strcmp(channel, 'EPA')
Fd = 5;
elseif strcmp(channel, 'EVA')
Fd = 70;
elseif strcmp(channel, 'ETU')
Fd = 70;
elseif strcmpi(channel, 'Custom')
Fd = 80;
end
if strcmpi(mobile, '')
Fd = 0;
end
Ndc = 2; % No of DC guard subcarriers
Ng = (N-Ndc-n_RB.*12)/2; % No of side guard subcarriers
% Ndata = N - Np - 2.*Ng - Ndc; % No of Data subcarriers per symbol
Frame_size = 7; % OFDM symbols per frame
Nframes = 20000; % Size of tested OFDM frames: set as 10^4 for smooth curve
M_set = [2, 4, 8, 16]; % Modulation orders
SNRs = -10:5:30; % Test SNR points
% 1.2 Vehicles for results
berofdm_all = zeros(5,length(SNRs));
berofdm_all(1,:) = SNRs;
serofdm_all = zeros(5,length(SNRs));
serofdm_all(1,:) = SNRs;
% 1.3 Calculate pilot locations
DC_sc = [N/2, N/2+1];
Effec_sc = [Ng+1:N-Ng];
Effec_sc = setdiff(Effec_sc, DC_sc);
% Pilot_sc = [5,12,19,26,34,41,48,55];
pilot_loc = [1:ceil(length(Effec_sc)/Np):length(Effec_sc)];
Pilot_sc = Effec_sc(pilot_loc);
guard_sc = [1:Ng,N-Ng+1:N];
Np = length(pilot_loc); % Recalculate Number of pilot
pilot_sc_frame = [];
guard_sc_frame = [];
DC_sc_frame = [];
pilot_gt = zeros(Np,Frame_size);
pilot_gf = zeros(Np,Frame_size);
for i_sym = 0:Frame_size-1
haspilot = 0;
if strcmpi(pilot_type, 'lte') % scattered LTE
if i_sym==0
pilot_sc_sym = Effec_sc([1:6:length(Effec_sc)]);
haspilot = 1;
elseif i_sym==4
pilot_sc_sym = Effec_sc([4:6:length(Effec_sc)]);
haspilot = 1;
end
elseif strcmpi(pilot_type, 'block')
if i_sym==0
pilot_sc_sym = Effect_sc([1:3:length(Effec_sc)]);
haspilot = 1;
end
elseif strcmpi(pilot_type, 'comb')
pilot_sc_sym = Effect_sc([1:6:length(Effec_sc)]);
haspilot = 1;
else % scattered legacy
pilot_sc_sym = Effec_sc(sort(mod((pilot_loc + i_sym*3)-1,length(Effec_sc))+1));
haspilot = 1;
end
if haspilot
pilot_gt(:,i_sym+1) = i_sym + 1;
pilot_gf(:,i_sym+1) = pilot_sc_sym;
pilot_sc_frame = [pilot_sc_frame, pilot_sc_sym+i_sym*N];
end
guard_sc_frame = [guard_sc_frame, guard_sc+i_sym*N];
DC_sc_frame = [DC_sc_frame, DC_sc+i_sym*N];
end
data_sc_frame = setdiff([1:Frame_size*N],guard_sc_frame);
data_sc_frame = setdiff(data_sc_frame, pilot_sc_frame);
data_sc_frame = setdiff(data_sc_frame, DC_sc_frame);
Ndata_frame = length(data_sc_frame);
pilot_gt = nonzeros(reshape(pilot_gt,Np*Frame_size,1));
pilot_gf = nonzeros(reshape(pilot_gf,Np*Frame_size,1));
[gt,gf] = meshgrid(1:Frame_size,1:N);
% 1.4 Channel
if ~strcmpi(channel, 'AWGN')
if strcmpi(channel, 'EPA')
tau = [0, 30, 70, 90, 110, 190, 410].*1e-9; % Path delays
pdb = [0.0, -1.0, -2.0, -3.0, -8.0, -17.2, -20.8]; % Avg path power gains
% eq_idx = 2; % LS-Spline
elseif strcmpi(channel, 'EVA')
tau = [0, 30, 150, 310, 370, 710, 1090, 1730, 2510].*1e-9; % Path delays
pdb = [0.0, -1.5, -1.4, -3.6, -0.6, -9.1, -7.0, -12.0, -16.9]; % Avg path power gains
% eq_idx = 2; % LS-Spline
elseif strcmpi(channel, 'ETU')
tau = [0, 50, 120, 200, 230, 500, 1600, 2300, 5000].*1e-9; % Path delays
pdb = [-1.0, -1.0, -1.0, 0.0, 0.0, 0.0, -3.0, -5.0, -7.0]; % Avg path power gains
% eq_idx = 2; % LS-Spline
elseif strcmpi(channel, 'Custom')
tau = [0, 70, 200, 230, 500, 1600, 2700, 3000].*1e-9; % Path delays
pdb = [0.0, -1.4, -1.4, -1.0, -3.0, -9.1, -15.0, -19.0]; % Avg path power gains
elseif strcmpi(channel, 'Flat')
tau = [0.0];
pdb = [0.0];
% eq_idx = 3; % LS-Linear
else
error('Unsupported Channel Estimator Option');
end
[Trms, Tmean] = rms_delay_spread(tau, pdb);
Trms = Trms./Ts;
Rhh_uni = mmse_pdp(length(tau), N, Trms, 1);
Rhh_exp = mmse_pdp(length(tau), N, Trms, 0);
% hdc = parallel.pool.Constant(h);
% chan = comm.RayleighChannel(...
% 'SampleRate',Fs, ...
% 'PathDelays',tau, ...
% 'AveragePathGains',pdb, ...
% 'NormalizePathGains',true, ...
% 'MaximumDopplerShift',0, ...
% 'RandomStream','Global stream', ...
% 'PathGainsOutputPort',true);
end
Lmst=32;
lsnr20 = 10.^(20/10);
%% Step 2: Test Loops
snr = SNRs;
betas = [1,1,17/9,17/9];
% EsNo= EbNo + 10*log10((N-2.*Np)/N)+ 10*log10(N/(N+Ncp)); % symbol to noise ratio
% snr= EsNo - 10*log10(N/(N+Ncp));
if ~strcmp(channel,'AWGN')
modulations = [1];
else
modulations = [1,2,3,4];
end
for m_ary = modulations
beta = betas(m_ary);
M = M_set(m_ary); % No of symbols for PSK modulation
const = qammod([0:M-1],M,'gray'); % Get constellation
berofdm = zeros(1,length(snr));
serofdm = zeros(1,length(snr));
% Step 2.1 Transmitter
tic
matname_tx = sprintf('TX_all_%s_%s_FFT%d%s.mat',mod_names{m_ary}, channel, N, cpstr);
% if isfile(matname_tx)
% load(matname_tx);
% else
% 2.1.1 Random bits generation
% D = round((M-1)*rand(Ndata*Frame_size,Nframes));
D = round((M-1)*rand(Ndata_frame,Nframes));
% D_test = reshape(D, Ndata, Frame_size*Nframes);
D_gray = D; % gray2bin(D_test,'qam',M);
txbits = de2bi(D_gray(:)); % transmitted bits
% 2.1.2 Modulation
if M == 8
Dmod = qammod(D,M,'gray');
else
Dmod = qammod(D,M,'gray');
end
% 2.1.3 Framing
Data = zeros(N*Frame_size,Nframes); % Guard sc Insertion
Data(data_sc_frame,:) = Dmod; % Data sc Insertion
txamp = max(abs(Dmod(:)));
pilot_signal = txamp.*sqrt(1/2).*(1+1i); % Norm pilot power to peak constellation power
Data(pilot_sc_frame,:)= pilot_signal; % Pilot sc Insertion
Data = reshape(Data, N, Frame_size*Nframes);
% 2.1.4 To Time-domain OFDM symbol
IFFT_Data = (N/sqrt(N-2*Np))*ifft(Data,N);
TxCy = [IFFT_Data((N-Ncp+1):N,:); IFFT_Data]; % Add Cyclic prefix
[r, c] = size(TxCy);
Tx_Data = TxCy;
% 2.1.5 Clip PAPR to 8 (9dB)
Tx_Amp = abs(Tx_Data);
Tx_Power = Tx_Amp.^2;
Power_PAPR8 = 8.*mean(Tx_Power,1);
Clip_loc = Tx_Power > Power_PAPR8;
Clip_Data = Tx_Data./Tx_Amp;
Clip_Data = sqrt(Power_PAPR8).*Clip_Data;
Tx_Data(Clip_loc) = Clip_Data(Clip_loc);
% Step 2.2 Wireless Channel
Tx_Pow_Freq = mean2(abs(Tx_Data).^2);
Tx_Data = reshape(Tx_Data, r*Frame_size,[]);
totalFrames = c/Frame_size;
% 2.2.1 Rayleigh Fading
if ~strcmp(channel,'AWGN')
G = zeros(N*Frame_size, Nframes);
% totalFrames = c/Frame_size;
Ch_Data = zeros(size(Tx_Data));
slice_idx = [1:ceil(Nframes./poolsize):Nframes];
slice_size = diff([slice_idx, Nframes+1]);
Ch_Data_sliced = mat2cell(Ch_Data, [r*Frame_size], slice_size);
Tx_Data_sliced = mat2cell(Tx_Data, [r*Frame_size], slice_size);
G_sliced = mat2cell(G, [N*Frame_size], slice_size);
parfor ip=1:poolsize
h = rayleighchan(Ts, Fd, tau, pdb);
% h.MaxDopplerShift = 0;
h.StoreHistory = 0;
h.StorePathGains = 1;
h.ResetBeforeFiltering = 1; % reset the filter after each call
[tmp, sliceFrames] = size(Tx_Data_sliced{ip});
for j = 1:sliceFrames % Channel response updated per frame
Ch_Data_sliced{ip}(:,j) = filter(h,Tx_Data_sliced{ip}(:,j).'); % Pass through Rayleigh channel
a = h.PathGains;
AM = h.channelFilter.alphaMatrix;
% release(chan);
% rng(slice_idx(ip)+j);
% [Rx_symbol, a] = chan(Tx_Data_sliced{ip}(:,j));
% Ch_Data_sliced{ip}(:,j) = Rx_symbol;
% % a = h.PathGains;
% chaninfo = info(chan);
% AM = chaninfo.ChannelFilterCoefficients;
% g = a(1,:)*AM;
g = a*AM; % Channel coefficients
Gfr = fft(g.',N); % DFT of channel coefficients
if h.MaxDopplerShift == 0
G_sliced{ip}(:,j) = repmat(Gfr(:), Frame_size, 1); % Slow Fading, Repeat Channel Coefficients
else
G3d = reshape(Gfr, N, [], Frame_size);
G2d = mean(G3d, 2);
G_sliced{ip}(:,j) = G2d(:);
end
end
end
Ch_Data = cell2mat(Ch_Data_sliced);
G = cell2mat(G_sliced);
else
Ch_Data = Tx_Data;
G = ones(N*Frame_size, Nframes);
end
GN = G(1:N,:);
% Long term channel covariance matrix for fast LMMSE
GNs = reshape(G, N, [], Frame_size*Nframes);
Rhhlt = (GNs*GNs')./(Frame_size*Nframes);
% parsave(matname_tx, D, D_gray, txbits, Dmod, Data, txamp,...
% pilot_signal, IFFT_Data, TxCy, r, c, Tx_Data, Tx_Amp,...
% Tx_Power, Power_PAPR8, Clip_loc, Clip_Data, Tx_Pow_Freq,...
% totalFrames, G, Ch_Data);
% end
toc
for i = 1:length(snr)
tic
% create filter object inside parfor to avoid error
lsnr = 10.^(snr(i)/10);
% 2.2.2 Add AWGN noise
y = awgn(Ch_Data,snr(i),'measured');
y1 = reshape(y,r,[]);
% Step 2.3: OFDM Receiver
% 2.3.1 Remove cyclic prefix
Rx = y1(Ncp+1:r,:);
% 2.3.2 Transform to Frequency-Domain
Rx_Freq = (sqrt(N-2*Np)/N)*fft(Rx,N,1);
Xe_Freq = zeros(N*Frame_size,Nframes);
% long term LMMSE matrix for fast ALMMSE
Wfast = Rhhlt*inv(Rhhlt+(beta/lsnr)*eye(N));
if ~strcmp(channel,'AWGN')
Rx_Freq = reshape(Rx_Freq,N*Frame_size,[]);
Hhat = Rx_Freq(pilot_sc_frame,:)./pilot_signal;
if eq_idx == 1
Gls = G;
else
Gls = zeros(N*Frame_size,Nframes);
parfor j = 1:Nframes
Hhat_fr = Hhat(:,j);
if eq_idx == 2
% Spline Interpolation for scattered 2D pilot
Glsfr = griddata(pilot_gf,pilot_gt,Hhat_fr,gf,gt,'v4');
elseif eq_idx == 3
% Linear Interpolation for scattered 2D pilot
fex = scatteredInterpolant(pilot_gf,pilot_gt,Hhat_fr);
Glsfr = fex(gf,gt);
elseif eq_idx == 4
% ideal LMMSE Estimator
H = G(:,j);
H = reshape(H, N, Frame_size);
HhatLS = griddata(pilot_gf,pilot_gt,Hhat_fr,gf,gt,'v4');
Glsfr = zeros(N, Frame_size);
for ii = 1: Frame_size
Rhh = H(:,ii)*H(:,ii)';
W = Rhh*inv(Rhh+(beta/lsnr)*eye(N));
Glsfr(:,ii) = W*HhatLS(:,ii);
end
elseif eq_idx == 7
% Approximate LMMSE Estimator
HhatLS = griddata(pilot_gf,pilot_gt,Hhat_fr,gf,gt,'v4');
HhatLSf = mean(HhatLS,2);
Rhh = HhatLSf*HhatLSf';
Rhh = Rhh./Frame_size;
W = Rhh*inv(Rhh+(beta/lsnr)*eye(N));
Glsfr = W*HhatLSf;
Glsfr = repmat(Glsfr, 1, Frame_size);
elseif eq_idx == 8
% LMMSE Estimator Uniform PDP
HhatLS = griddata(pilot_gf,pilot_gt,Hhat_fr,gf,gt,'v4');
HhatLS = mean(HhatLS,2);
Rhh = Rhh_uni;
W = Rhh/(Rhh+(beta/lsnr)*eye(N));
for ii = 1: Frame_size
Glsfr(:,ii) = W*HhatLS(:,ii);
end
elseif eq_idx == 9
% LMMSE Estimator Exponential PDP
HhatLS = griddata(pilot_gf,pilot_gt,Hhat_fr,gf,gt,'v4');
HhatLS = mean(HhatLS,2);
Rhh = Rhh_exp; %HhatLS*HhatLS';
W = Rhh/(Rhh+(beta/lsnr)*eye(N));
for ii = 1: Frame_size
Glsfr(:,ii) = W*HhatLS(:,ii);
end
elseif eq_idx == 10
% fast LMMSE Estimator with long term Rhh
HhatLS = griddata(pilot_gf,pilot_gt,Hhat_fr,gf,gt,'v4');
Glsfr = zeros(N, Frame_size);
for ii = 1: Frame_size
Glsfr(:,ii) = Wfast*HhatLS(:,ii);
end
elseif eq_idx == 5
% LS with CP exploitation
HhatLS = griddata(pilot_gf,pilot_gt,Hhat_fr,gf,gt,'v4');
HhatLSf = mean(HhatLS,2);
HhatLSf = repmat(HhatLSf, 1, Frame_size);
[Xdata, Glsfr] = cpenhanced(Rx_Freq(:,j), HhatLSf, y(:,j), Frame_size, N, Ncp);
Xe_Freq(:, j) = reshape(Xdata, N*Frame_size, 1);
elseif eq_idx == 6
% Enhance ALMMSE with CP exploitation
HhatLS = griddata(pilot_gf,pilot_gt,Hhat_fr,gf,gt,'v4');
HhatLS = mean(HhatLS,2);
Rhh = HhatLS*HhatLS';
W = Rhh*inv(Rhh+(beta/lsnr)*eye(N));
Glmmse = zeros(N, Frame_size);
for ii = 1: Frame_size
Glmmse(:,ii) = W*HhatLS;
end
[Xdata, Glsfr] = cpenhanced(Rx_Freq(:,j), Glmmse, y(:,j), Frame_size, N, Ncp);
Xe_Freq(:, j) = reshape(Xdata, N*Frame_size, 1);
else
error('Unsupported Channel Estimator Option');
end
Gls(:,j) = reshape(Glsfr,N*Frame_size,1);
end
end
% Gls = reshape(Gls,N,Frame_size*Nframes);
if eq_idx == 5
Rx_Freq = Xe_Freq;
else
Rx_Freq = Rx_Freq./Gls;
end
end
% 2.3.3 Reshape to Frame size
FFT_Data = reshape(Rx_Freq,N*Frame_size,[]);
% 2.3.4 Extract Data Cells
FFT_Data = reshape(FFT_Data(data_sc_frame,:), [], Nframes);
% 2.3.5 Demodulation
slice_idx = [1:ceil(Nframes./poolsize):Nframes];
slice_size = diff([slice_idx, Nframes+1]);
[r1, c1] = size(FFT_Data);
FFT_Data_sliced = mat2cell(FFT_Data, [r1], slice_size);
Rx_Data_sliced = cell(1,poolsize);
parfor ip=1:poolsize
Rx_Data_sliced{ip} = qamdemod(FFT_Data_sliced{ip},M,'gray');
end
Rx_Data = cell2mat(Rx_Data_sliced);
Rx_gray = Rx_Data; % gray2bin(Rx_Data,'qam',M);
rxbits = de2bi(Rx_gray(:));
% Step 2.4 Collect BER and SER
[bitErrors,ber] = biterr(txbits,rxbits);
[symErrors,ser] = symerr(Rx_Data(:),D(:));
serofdm(i) = ser;
berofdm(i) = ber;
% Export data for Test in python
if save_tx_data
if longcp
filename = sprintf('./mat/ofdm_%s_%s_%ddB.mat',lower(channel),mod_names{m_ary},snr(i));
else
filename = sprintf('./mat/ofdm_%s_%s_%ddB_shortcp.mat',lower(channel),mod_names{m_ary},snr(i));
end
parsave(filename, y, txbits, rxbits);
end
toc
end
berofdm_all(m_ary+1,:) = berofdm;
serofdm_all(m_ary+1,:) = serofdm;
end
%% Step 3: Result Presentation: Plot BER
parsave(mat_name, berofdm_all, serofdm_all, mat_name);
csvwrite(csv_name, berofdm_all);
figure;
semilogy(SNRs,berofdm_all(2:5,:),'--x','LineWidth',1);
grid('on');
xlabel('SNR (dB)');
ylabel('BER');
legend(mod_names);
titletxt = sprintf('%s Channel',channel);
title(titletxt);
savefig(fig_name);
saveas(gcf, png_name);
end