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sim_OFDM_jammer.m
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sim_OFDM_jammer.m
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% ==========================================================================
% -- Single-Antenna Jammers in MIMO-OFDM Can Resemble Multi-Antenna Jammers
% --------------------------------------------------------------------------
% -- (c) 2023 Gian Marti
% -- e-mail: gimarti@ethz.ch
% --------------------------------------------------------------------------
% -- If you use this simulator or parts of it, then you must cite our paper:
%
% -- Gian Marti and Christoph Studer,
% -- "Single-Antenna Jammers in MIMO-OFDM Can Resemble Multi-Antenna Jammers,"
% -- IEEE Communication Letters, 2023
% ==========================================================================
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% configurable parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%
par.B = 8; % number of receive antennas
par.U = 2; % number of transmit antennas and data streams
par.L = 4; % number of channel taps
par.P = 16; % cyclic prefix length
par.N_sc = 64; % number of total subcarriers
par.tonelist = [-26:-22, -20:-8, -6:-1, 1:6, 8:20, 22:26] + 32; % list of used subcarriers, only meaningful for par.N_sc = 64;
par.num_tones = length(par.tonelist);
par.num_ofdm_symbols = 50; % number of OFDM symbols sent per channel realization
par.rho_dB = 30; % jammer strength relative to signal strength (in dB)
par.mod = 'QPSK'; % transmit constellation
par.random_jammer_power = 0; % if true, then the jammer-power is uniformly (in dB) sampled from
% the range [0, par.rho_dB] for every trial.
% Otherwise, it is deterministically equal par.rho_dB.
par.trials = 100; % number of Monte-Carlo trials (different channel realizations)
par.SNRdB_list = -5:1:20; % list of SNR values (in dB) to be simulated
par.plot = 1; % whether or not to plot the results
par.printmsg = 1; % whether or not to print log messages
rng(0); % random seed
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% simulation start
%%%%%%%%%%%%%%%%%%%%%%%%%%%
par.simName = [num2str(par.B) 'x' num2str(par.U) '_' par.mod '_L', num2str(par.L) '_P' num2str(par.P) ...
'_Nsc' num2str(par.N_sc) '_Nofd' num2str(par.num_ofdm_symbols) '_rho' num2str(par.rho_dB) ...
'_' num2str(par.trials) 'Trials'];
switch (par.mod)
case 'BPSK'
par.symbols = [ -1 1 ];
case 'QPSK'
par.symbols = [ ...
-1-1i,-1+1i, ...
+1-1i,+1+1i ];
case '16QAM'
par.symbols = [ ...
-3-3i,-3-1i,-3+3i,-3+1i, ...
-1-3i,-1-1i,-1+3i,-1+1i, ...
+3-3i,+3-1i,+3+3i,+3+1i, ...
+1-3i,+1-1i,+1+3i,+1+1i ];
case '64QAM'
par.symbols = [ ...
-7-7i,-7-5i,-7-1i,-7-3i,-7+7i,-7+5i,-7+1i,-7+3i, ...
-5-7i,-5-5i,-5-1i,-5-3i,-5+7i,-5+5i,-5+1i,-5+3i, ...
-1-7i,-1-5i,-1-1i,-1-3i,-1+7i,-1+5i,-1+1i,-1+3i, ...
-3-7i,-3-5i,-3-1i,-3-3i,-3+7i,-3+5i,-3+1i,-3+3i, ...
+7-7i,+7-5i,+7-1i,+7-3i,+7+7i,+7+5i,+7+1i,+7+3i, ...
+5-7i,+5-5i,+5-1i,+5-3i,+5+7i,+5+5i,+5+1i,+5+3i, ...
+1-7i,+1-5i,+1-1i,+1-3i,+1+7i,+1+5i,+1+1i,+1+3i, ...
+3-7i,+3-5i,+3-1i,+3-3i,+3+7i,+3+5i,+3+1i,+3+3i ];
end
% normalize transmission constellation
par.constellation_energy = mean(abs(par.symbols).^2);
par.symbols = par.symbols/sqrt(par.constellation_energy);
par.Es = mean(abs(par.symbols).^2); % equal to 1
% precompute bit labels
par.Q = log2(length(par.symbols)); % number of bits per symbol
par.bits = de2bi(0:length(par.symbols)-1,par.Q,'left-msb');
% track simulation time
time_elapsed = 0;
% intermediate results
y_jl_f = zeros(par.B,par.N_sc,par.num_ofdm_symbols);
y_oj_comp_f = zeros(par.B,par.N_sc,par.num_ofdm_symbols);
y_oj_noncomp_f = zeros(par.B,par.N_sc,par.num_ofdm_symbols);
y_comp_f = zeros(par.B,par.N_sc,par.num_ofdm_symbols);
y_noncomp_f = zeros(par.B,par.N_sc,par.num_ofdm_symbols);
% results
Y_oj_comp = zeros(par.trials, par.num_tones,par.B, par.num_ofdm_symbols);
Y_oj_noncomp = zeros(par.trials, par.num_tones,par.B, par.num_ofdm_symbols);
MSE_jl = zeros(1, length(par.SNRdB_list));
MSE_comp = zeros(1, length(par.SNRdB_list));
MSE_noncomp = zeros(1, length(par.SNRdB_list));
res.BER_jl = zeros(1, length(par.SNRdB_list));
res.BER_comp = zeros(1, length(par.SNRdB_list));
res.BER_noncomp = zeros(1, length(par.SNRdB_list));
res.BER_projs = zeros(par.L, length(par.SNRdB_list));
res.spatial_interference_distr = zeros(par.B,par.num_tones);
% generate bit stream
bits = randi([0 1],par.trials,par.num_ofdm_symbols,par.U,par.Q,par.num_tones);
idx = zeros(par.trials, par.num_ofdm_symbols, par.U,par.num_tones);
% trials loop
tic
for t=1:par.trials
% generate jammer's channel in the time domain
j_ = sqrt(0.5)*randn(par.B,par.L) + 1j*sqrt(0.5)*randn(par.B,par.L);
j_f = (1/sqrt(par.N_sc))*fft(j_,par.N_sc,2);
% generate the UEs' channel in the time domain
H_ = sqrt(0.5)*randn(par.B,par.U,par.L) + 1j*sqrt(0.5)*randn(par.B,par.U,par.L);
H_f = (1/sqrt(par.N_sc))*fft(H_,par.N_sc,3); % E[||H_f(:,:,i)||_F^2] = B*U*L/N_sc for all i=1,...,N_sc
% so the expected receive signal energy per subcarrier is E_s*B*U*L/N_sc = B*U*L/N_sc
if par.random_jammer_power
par.rho = par.U*10^(par.rho_dB*rand()/10);
else
par.rho = par.U*10^(par.rho_dB/10);
end
for snrindex = 1:length(par.SNRdB_list)
par.N0 = par.L*par.U*10^(-par.SNRdB_list(snrindex)/10);
for k=1:par.num_ofdm_symbols
%%% generate transmit signals
% generate jammer's transmit signal in the frequency domain for OFDM-compliant case
w_f = sqrt(0.5)*randn(1,par.N_sc)+ 1j*sqrt(0.5)*randn(1,par.N_sc);
w_no_cp = sqrt(par.N_sc)*ifft(w_f); %this does in fact not change the Gaussian statistics
w = [w_no_cp(:,par.N_sc-par.P+1:par.N_sc), w_no_cp];
w = sqrt(par.rho)*w;
% generate the jammer's transmit signal in the time domain for OFDM-noncompliant case
w_noncomp = sqrt(0.5)*randn(1,par.N_sc+par.P)+ 1j*sqrt(0.5)*randn(1,par.N_sc+par.P);
w_noncomp = sqrt(par.rho)*w_noncomp;
% generate UEs' transmit signal in the frequency domain for OFDM-compliant case
for n=1:par.num_tones
idx(t,k,:,n) = bi2de(bits(t,k,:,:,n),'left-msb')+1;
end
S_f_used_tones = par.symbols(squeeze(idx(t,k,:,:))); % symbol vectors
S_f = zeros(par.U, par.N_sc);
S_f(:,par.tonelist) = S_f_used_tones; % only transmit signal over the used subcarriers
S_no_cp = sqrt(par.N_sc)*ifft(S_f,par.N_sc,2);
S = [S_no_cp(:,par.N_sc-par.P+1:par.N_sc), S_no_cp];
%%% generate receive signals
y_jl = zeros(par.B, par.N_sc+par.P+par.L-1); % jammerless receive signal
y_oj_comp = zeros(par.B, par.N_sc+par.P+par.L-1); % only compliant jammer
y_oj_noncomp = zeros(par.B, par.N_sc+par.P+par.L-1); % only noncompliant jammer
y_comp = zeros(par.B, par.N_sc+par.P+par.L-1); % full receive signal, jammer compliant
y_noncomp = zeros(par.B, par.N_sc+par.P+par.L-1); % full receive signal, jammer noncompliant
for b=1:par.B
for u=1:par.U
y_jl(b,:) = y_jl(b,:) + conv(squeeze(H_(b,u,:)),S(u,:));
end
y_oj_comp(b,:) = conv(j_(b,:),w);
y_oj_noncomp(b,:) = conv(j_(b,:),w_noncomp);
end
y_comp = y_jl + y_oj_comp;
y_noncomp = y_jl + y_oj_noncomp;
%%% generate noise in the time domain
N = sqrt(0.5)*randn(par.B,par.N_sc)+ 1j*sqrt(0.5)*randn(par.B,par.N_sc);
N = sqrt(par.N0)*N;
%%% truncate signals in time-domain to remove cylic prefix and channel reverberation
y_jl_trunc = y_jl(:,par.P+1:par.P+par.N_sc) + N;
y_oj_comp_trunc = y_oj_comp(:,par.P+1:par.P+par.N_sc); % no noise
y_oj_noncomp_trunc = y_oj_noncomp(:,par.P+1:par.P+par.N_sc); % no noise
y_comp_trunc = y_comp(:,par.P+1:par.P+par.N_sc) + N;
y_noncomp_trunc = y_noncomp(:,par.P+1:par.P+par.N_sc) + N;
%%% convert to frequency domain
y_jl_f(:,:,k) = (1/sqrt(par.N_sc))*fft(y_jl_trunc, par.N_sc, 2);
y_oj_comp_f(:,:,k) = (1/sqrt(par.N_sc))*fft(y_oj_comp_trunc, par.N_sc, 2);
y_oj_noncomp_f(:,:,k) = (1/sqrt(par.N_sc))*fft(y_oj_noncomp_trunc, par.N_sc, 2);
y_comp_f(:,:,k) = (1/sqrt(par.N_sc))*fft(y_comp_trunc, par.N_sc, 2);
y_noncomp_f(:,:,k) = (1/sqrt(par.N_sc))*fft(y_noncomp_trunc, par.N_sc, 2);
%%% remove subcarriers that are not used
y_jl_f_tones = y_jl_f(:,par.tonelist,:);
y_oj_comp_f_tones = y_oj_comp_f(:,par.tonelist,:);
y_oj_noncomp_f_tones = y_oj_noncomp_f(:,par.tonelist,:);
y_comp_f_tones = y_comp_f(:,par.tonelist,:);
y_noncomp_f_tones = y_noncomp_f(:,par.tonelist,:);
H_f_tones = H_f(:,:,par.tonelist);
%%% collect jammer statistics for later analysis
for n=1:par.num_tones
Y_oj_comp(t,n,:,k) = y_oj_comp_f_tones(:,n,k);
Y_oj_noncomp(t,n,:,k) = y_oj_noncomp_f_tones(:,n,k);
end
end % iterate over OFDM symbols with same channel realization
for n=1:par.num_tones
%%% extract jammer statistics
[U_comp,S_comp,~] = svd(squeeze(Y_oj_comp(t,n,:,:)));
[U_noncomp,S_noncomp,~] = svd(squeeze(Y_oj_noncomp(t,n,:,:)));
res.spatial_interference_distr(:,n) = res.spatial_interference_distr(:,n) + diag(S_noncomp); % interference distribution over different spatial dimensions
% form best rank-(B-1) projectors: those that remove most of the
% jammer interference per subcarrier
j_est_comp = U_comp(:,1);
P_comp = eye(par.B) - j_est_comp*j_est_comp';
j_est_noncomp = U_noncomp(:,1);
P_noncomp = eye(par.B) - j_est_noncomp*j_est_noncomp';
Projs = zeros(par.L,par.B,par.B);
for b=1:par.L
Projs(b,:,:) = eye(par.B) - U_noncomp(:,1:b)*U_noncomp(:,1:b)';
end
%%% detect signals using zero-forcing (and, in some cases, jammer mitigation)
S_est_jl = (sqrt(par.N_sc)*(H_f_tones(:,:,n)))\squeeze(y_jl_f_tones(:,n,:));
S_est_comp = (sqrt(par.N_sc)*(P_comp*squeeze(H_f_tones(:,:,n))))\(P_comp*squeeze(y_comp_f_tones(:,n,:)));
S_est_noncomp = (sqrt(par.N_sc)*(P_noncomp*squeeze(H_f_tones(:,:,n))))\(P_noncomp*squeeze(y_noncomp_f_tones(:,n,:)));
S_est_projs = zeros(par.B,par.U,par.num_ofdm_symbols);
for b=1:par.L
S_est_projs(b,:,:) = (sqrt(par.N_sc)*(squeeze(Projs(b,:,:))*squeeze(H_f_tones(:,:,n))))\(squeeze(Projs(b,:,:))*squeeze(y_noncomp_f_tones(:,n,:)));
end
% -- compute bit outputs
S_est_jl_vec = reshape(S_est_jl, [par.num_ofdm_symbols*par.U,1]);
[~,idxhat_vec] = min(abs(S_est_jl_vec*ones(1,length(par.symbols))-ones(par.num_ofdm_symbols*par.U,1)*par.symbols).^2,[],2);
idxhat_jl = reshape(idxhat_vec, [par.U, par.num_ofdm_symbols]);
bithat_jl = par.bits(idxhat_jl,:);
S_est_comp_vec = reshape(S_est_comp, [par.num_ofdm_symbols*par.U,1]);
[~,idxhat_vec] = min(abs(S_est_comp_vec*ones(1,length(par.symbols))-ones(par.num_ofdm_symbols*par.U,1)*par.symbols).^2,[],2);
idxhat_comp = reshape(idxhat_vec, [par.U, par.num_ofdm_symbols]);
bithat_comp = par.bits(idxhat_comp,:);
S_est_noncomp_vec = reshape(S_est_noncomp, [par.num_ofdm_symbols*par.U,1]);
[~,idxhat_vec] = min(abs(S_est_noncomp_vec*ones(1,length(par.symbols))-ones(par.num_ofdm_symbols*par.U,1)*par.symbols).^2,[],2);
idxhat_noncomp = reshape(idxhat_vec, [par.U, par.num_ofdm_symbols]);
bithat_noncomp = par.bits(idxhat_noncomp,:);
bithat_projs = zeros(par.L,par.U*par.num_ofdm_symbols,par.Q);
for b=1:par.L
S_est_vec = reshape(S_est_projs(b,:,:), [par.num_ofdm_symbols*par.U,1]);
[~,idxhat_vec] = min(abs(S_est_vec*ones(1,length(par.symbols))-ones(par.num_ofdm_symbols*par.U,1)*par.symbols).^2,[],2);
idxhat = reshape(idxhat_vec, [par.U, par.num_ofdm_symbols]);
bithat_projs(b,:,:) = par.bits(idxhat,:);
end
% -- compute error metrics
bit_tensor = squeeze(bits(t,:,:,:,n));
bit_tensor = permute(bit_tensor,[3 2 1]);
true_bits = bit_tensor(:,:)';
res.BER_jl(snrindex) = res.BER_jl(snrindex) + sum(sum(true_bits~=bithat_jl));
res.BER_comp(snrindex) = res.BER_comp(snrindex) + sum(sum(true_bits~=bithat_comp));
res.BER_noncomp(snrindex) = res.BER_noncomp(snrindex) + sum(sum(true_bits~=bithat_noncomp));
for b=1:par.L
res.BER_projs(b,snrindex) = res.BER_projs(b,snrindex) + sum(sum(true_bits~=squeeze(bithat_projs(b,:,:))));
end
end
end % iterate over SNRs
% -- keep track of simulation time
if(par.printmsg)
if toc>10
time = toc;
time_elapsed = time_elapsed + time;
fprintf('estimated remaining simulation time: %3.0f min.\n', ...
time_elapsed*(par.trials/t-1)/60);
tic
end
end
end % iterate over MC trials
% normalize results
res.BER_jl = res.BER_jl/(par.trials*par.U*par.num_ofdm_symbols*par.Q*par.num_tones);
res.BER_comp = res.BER_comp/(par.trials*par.U*par.num_ofdm_symbols*par.Q*par.num_tones);
res.BER_noncomp = res.BER_noncomp/(par.trials*par.U*par.num_ofdm_symbols*par.Q*par.num_tones);
res.BER_projs = res.BER_projs/(par.trials*par.U*par.num_ofdm_symbols*par.Q*par.num_tones);
res.spatial_interference_distr = res.spatial_interference_distr./sum(res.spatial_interference_distr,1);
res.spatial_interference_distr_sc_std = std(res.spatial_interference_distr.');
res.spatial_interference_distr_sc_avg = mean(res.spatial_interference_distr.');
%%% plot results
if par.plot
figure(1)
semilogy(par.SNRdB_list, res.BER_jl, 'LineWidth', 2.5)
hold on
semilogy(par.SNRdB_list, res.BER_comp, 'LineWidth', 2.5)
semilogy(par.SNRdB_list, res.BER_noncomp, 'LineWidth', 2.5)
hold off
grid on
axis([min(par.SNRdB_list) max(par.SNRdB_list) 1e-4 1])
xlabel('average SNR per receive antenna [dB]','FontSize',12)
ylabel('uncoded bit error-rate (BER)','FontSize',12)
legend(["Jammerless", "OFDM-compliant jammer", "Cyclic prefix-violating jammer"],'FontSize',12,'Interpreter','none')
set(gca,'FontSize',12)
set(gcf,'position',[10,10,400,300])
figure(2)
bar(1:par.B,res.spatial_interference_distr_sc_avg)
hold on
er = errorbar(1:par.B,res.spatial_interference_distr_sc_avg, ...
2*res.spatial_interference_distr_sc_std, ...
2*res.spatial_interference_distr_sc_std);
er.Color = [0 0 0];
er.LineStyle = 'none';
hold off
axis([0.25 par.B+0.75 0 1])
grid on
xlabel('ordered spatial dimension index')
ylabel('fraction of receive interference')
set(gcf,'position',[10,10,400,300])
figure(3)
semilogy(par.SNRdB_list, res.BER_projs(1,:), 'LineWidth', 2.5)
hold on
for b=2:par.L
semilogy(par.SNRdB_list, res.BER_projs(b,:), 'LineWidth', 2.5)
end
hold off
grid on
axis([min(par.SNRdB_list) max(par.SNRdB_list) 1e-4 1])
xlabel('average SNR per receive antenna [dB]','FontSize',12)
ylabel('uncoded bit error-rate (BER)','FontSize',12)
numbers = {};
for b = 1:par.L
numbers{b} = "Null " + num2str(b) + " Dimensions";
end
legend(numbers,'FontSize',12,'Interpreter','none')
set(gca,'FontSize',12)
set(gcf,'position',[10,10,400,300])
end