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Copy pathmain_cplx_2d_qam.cpp
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main_cplx_2d_qam.cpp
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/*********************************************************
Simulation of OFDM Receiver Based on Generalized
Approximate Message Passing Algorithm for Polar
Nonlinearity Type
For more details on the algorithm see the paper:
S.Zhidkov, R.Dinis “Belief Propagation Receivers for
Near-Optimal Detection of Nonlinearly Distorted OFDM
Signals,” IEEE 89th Vehicular Technology Conference
(VTC2019-Spring), May, 2019
Copyright (c) 2017-2019 Sergey Zhidkov
Licensed under the MIT license.
See LICENSE file in the project root for details.
*********************************************************/
#define ARMA_USE_CXX11
#include <iostream>
#include <fstream>
#include <armadillo>
#include <iostream>
#include "cfg_parser.h"
using namespace std;
using namespace arma;
// Nonlinear function f(z). Some examples:
// 0 - Soft envelope limiter (G=1.7 for M=1 or 3.4 for M=4)
// 1 - 'Chaotic' nonlinearity (for N=2048)
// 100 - Phase-only nonlinearity
// 102 - TWTA model (G0=1.4 for M=1 or 2.8 for M=4)
#define NONLINEARITY_TYPE 100
#define DEBUG_SAVE 0
#define DEBUG_PRINT 0
cx_vec nln_func(cx_vec z, double G0);
cx_vec slicer(cx_vec x, double power_scale, int qam_order);
int main(int argc, char** argv)
{
cx_double j = sqrt(-1);
// Get simulation parameters from configuration file
ConfigFile cfg("cfg.txt");
int N = cfg.getValueOfKey<int>("N", 8192);
int Nu = cfg.getValueOfKey<int>("Nu", N/4);
double G0 = cfg.getValueOfKey<double>("G0", 0.51);
double s_scale = cfg.getValueOfKey<double>("s_scale", 1.0);
double B = cfg.getValueOfKey<double>("B", 1.0);
int rand_seed = cfg.getValueOfKey<int>("rand_seed", 0);
int I_max_gamp = cfg.getValueOfKey<int>("I_max", 50);
string EbNo_init = cfg.getValueOfKey<string>("EbNo", "3.5 3.75 4.0 4.25 4.5 4.75 5.0");
string L_SNR_init = cfg.getValueOfKey<string>("L_SNR", "500 500 500 500 500 500 500");
int QAM_ORDER = cfg.getValueOfKey<int>("qam_order", 4);
bool ENABLE_MULTIPATH_CHANNEL = cfg.getValueOfKey<int>("enable_multipath_channel", false);
int N_ch = cfg.getValueOfKey<int>("N_ch", 56);
double t_ch = cfg.getValueOfKey<double>("t_ch", 14.0);
bool ENABLE_OOB_FILTERING_TX = cfg.getValueOfKey<int>("enable_oob_filtering_tx", false);
bool ENABLE_OOB_FILTERING_RX = cfg.getValueOfKey<int>("enable_oob_filtering_rx", false);
bool enable_post_correction = cfg.getValueOfKey<bool>("post_correction", false);
int QAM_BIT = 2;
double POWER_SCALE = 1;
double LEVEL2_16QAM = 2.0/sqrt(10.0);
double LEVEL2_64QAM = 2.0/sqrt(42.0);
double LEVEL4_64QAM = 4.0/sqrt(42.0);
if (rand_seed == 0) {
arma_rng::set_seed_random();
}
else {
arma_rng::set_seed(rand_seed);
}
vec EbNo(EbNo_init);
ivec L_SNR(L_SNR_init);
ofstream clog("log.txt");
cout << "Reading simulation parameters from configuration file:" << endl;
cout << "N = " << N << endl;
cout << "Nu = " << Nu << endl;
cout << "I_max = " << I_max_gamp << endl;
cout << "G0 = " << G0 << endl;
cout << "s_scale = " << s_scale << endl;
cout << "B = " << B << endl;
cout << "rand seed = " << rand_seed << endl;
cout << "EbNo = [ ";
for (int i = 0; i < EbNo.n_elem; i++) {
cout << EbNo(i) << " ";
}
cout << "]" << endl;
cout << "L_SNR = [ ";
for (int i = 0; i < L_SNR.n_elem; i++) {
cout << L_SNR(i) << " ";
}
cout << "]" << endl;
cout << "Modulation: " << QAM_ORDER << "-QAM" << endl;
cout << "Post correction = " << enable_post_correction << endl;
cout << "Nonlinearity type = " << NONLINEARITY_TYPE << endl;
cout << "OOB filtering (TX) = " << ENABLE_OOB_FILTERING_TX << endl;
cout << "OOB filtering (RX) = " << ENABLE_OOB_FILTERING_RX << endl;
cout << "Multipath channel = " << ENABLE_MULTIPATH_CHANNEL << endl;
if (ENABLE_MULTIPATH_CHANNEL) {
cout << "Channel taps = " << N_ch << endl;
cout << "Channel delay spread = " << t_ch << endl;
}
// Copy to log
clog << "Reading simulation parameters from configuration file:" << endl;
clog << "N = " << N << endl;
clog << "Nu = " << Nu << endl;
clog << "I_max = " << I_max_gamp << endl;
clog << "G0 = " << G0 << endl;
clog << "s_scale = " << s_scale << endl;
clog << "B = " << B << endl;
clog << "rand seed = " << rand_seed << endl;
clog << "EbNo = [ ";
for (int i = 0; i < EbNo.n_elem; i++) {
clog << EbNo(i) << " ";
}
clog << "]" << endl;
clog << "L_SNR = [ ";
for (int i = 0; i < L_SNR.n_elem; i++) {
clog << L_SNR(i) << " ";
}
clog << "]" << endl;
clog << "Modulation: " << QAM_ORDER << "-QAM" << endl;
clog << "Post correction = " << enable_post_correction << endl;
clog << "Nonlinearity type = " << NONLINEARITY_TYPE << endl;
clog << "OOB filtering (TX) = " << ENABLE_OOB_FILTERING_TX << endl;
clog << "OOB filtering (RX) = " << ENABLE_OOB_FILTERING_RX << endl;
clog << "Multipath channel = " << ENABLE_MULTIPATH_CHANNEL << endl;
if (ENABLE_MULTIPATH_CHANNEL) {
clog << "Channel taps = " << N_ch << endl;
clog << "Channel delay spread = " << t_ch << endl;
}
if (QAM_ORDER == 64) {
QAM_BIT = 6;
}
else if (QAM_ORDER == 16) {
QAM_BIT = 4;
}
else {
QAM_BIT = 2;
}
vec SNR = EbNo + 10.0 * log10(double(QAM_BIT) * double(Nu) / double(N));
vec BER_lin = zeros<vec>(SNR.n_elem);
vec BER_clip = zeros<vec>(SNR.n_elem);
vec BER_gamp = zeros<vec>(SNR.n_elem);
vec FER_lin = zeros<vec>(SNR.n_elem);
vec FER_clip = zeros<vec>(SNR.n_elem);
vec FER_gamp = zeros<vec>(SNR.n_elem);
double init_std = 1.0;
vec C;
if (QAM_ORDER == 64) {
C = { -7.0, -5.0, -3.0, -1.0, 1.0, 3.0, 5.0, 7.0 };
POWER_SCALE = sqrt(42.0);
}
else if (QAM_ORDER == 16) {
C = { -3.0, -1.0, 1.0, 3.0 };
POWER_SCALE = sqrt(10.0);
}
else {
C = { -1.0, 1.0 };
POWER_SCALE = sqrt(2.0);
}
C = C * (1.0 / POWER_SCALE);
const uword N_z = 512;
double Z_range;
if (QAM_ORDER == 64) {
Z_range = 5.0;
}
else if (QAM_ORDER == 16) {
Z_range = 5.0;
}
else {
Z_range = 5.0;
}
cx_vec z_all = zeros<cx_vec>(N_z * N_z);
for (int k = 0; k < N_z; k++) {
for (int n = 0; n < N_z; n++) {
z_all(n*N_z + k).real(Z_range * ((double(k) / double(N_z / 2)) - 1.0));
z_all(n*N_z + k).imag(Z_range * ((double(n) / double(N_z / 2)) - 1.0));
}
}
cx_vec z_all_nln = nln_func(z_all, G0);
#if DEBUG_SAVE == 1
vec a = linspace(0, 5.0, 1024);
vec p = zeros<vec>(1024);
cx_vec x = cx_vec(a%cos(p), a%sin(p));
cx_vec y = nln_func(x, 1.0);
y.save("y.txt", raw_ascii);
return(0);
#endif
for (int m_snr = 0; m_snr < SNR.n_elem; m_snr++) {
double snr = SNR(m_snr);
int L = int(L_SNR(m_snr));
cout << endl << "---- EbNo = " << EbNo(m_snr) << "(dB) [" << L << " symbols] ----" << endl;
clog << endl << "---- EbNo = " << EbNo(m_snr) << "(dB) [" << L << " symbols] ----" << endl;
// Allocate channel impulse responce array
cx_mat h = zeros<cx_mat>(N_ch, L);
// Generate signals
cx_vec X = zeros<cx_vec>(N*L);
cx_vec z = zeros<cx_vec>(N*L);
cx_vec X0 = zeros<cx_vec>(N);
cx_vec z0 = zeros<cx_vec>(N);
for (int l = 0; l < L; l++) {
if (QAM_ORDER == 64) {
X0.set_real(4.0 * sign(randu<vec>(N) - 0.5) + 2.0 * sign(randu<vec>(N) - 0.5) + sign(randu<vec>(N) - 0.5));
X0.set_imag(4.0 * sign(randu<vec>(N) - 0.5) + 2.0 * sign(randu<vec>(N) - 0.5) + sign(randu<vec>(N) - 0.5));
}
else if (QAM_ORDER == 16) {
X0.set_real(2.0 * sign(randu<vec>(N) - 0.5) + sign(randu<vec>(N) - 0.5));
X0.set_imag(2.0 * sign(randu<vec>(N) - 0.5) + sign(randu<vec>(N) - 0.5));
}
else {
X0.set_real(sign(randu<vec>(N) - 0.5));
X0.set_imag(sign(randu<vec>(N) - 0.5));
}
X0 = X0 * (1.0/POWER_SCALE);
// Set to zero unused subcarriers
if (Nu < N) {
X0.subvec(Nu,N-1) = zeros<cx_vec>(N-Nu);
}
X.subvec(N*l, N*(l + 1) - 1) = X0;
z0 = ifft(X0)*sqrt(N);
z.subvec(N*l, N*(l + 1) - 1) = z0;
}
#if DEBUG_SAVE == 2
z.save("z.txt", raw_ascii);
return(0);
#endif
cout << "Signal generation complete!" << endl;
cx_vec z_nln = zeros<cx_vec>(N*L);
z_nln = nln_func(z, G0);
double IBO = max(abs(z_nln)) / stddev(G0*z);
cout << "IBO = " << IBO << endl;
clog << "IBO = " << IBO << endl;
// Out-of-band filtering (optional)
if (ENABLE_OOB_FILTERING_TX && (Nu < N)) {
for (int l = 0; l < L; l++) {
z0 = z_nln.subvec(N*l, N*(l + 1) - 1);
X0 = fft(z0) / sqrt(N);
// Set to zero unused subcarriers
X0.subvec(Nu, N - 1) = zeros<cx_vec>(N - Nu);
z0 = ifft(X0)*sqrt(N);
z_nln.subvec(N*l, N*(l + 1) - 1) = z0;
}
}
#if DEBUG_SAVE == 3
z_nln.save("z_nln.txt", raw_ascii);
return(0);
#endif
double CF = 20.0 * log10(max(abs(z_nln)) / stddev(z_nln));
CF = (CF < 0.0) ? 0.0 : CF;
cout << "PAPR = " << CF << " (dB)" << endl;
clog << "PAPR = " << CF << " (dB)" << endl;
if (ENABLE_MULTIPATH_CHANNEL) {
// Exponentially decaying multipath channel profile
// (equivalent to Channel C, from Thompson, "Constant-Envelope OFDM", with N_ch=56, t_ch=14.0)
vec h_abs = zeros<vec>(N_ch);
for (int k = 0; k < N_ch; k++) {
h_abs(k) = exp(-double(k) / t_ch);
}
h_abs = h_abs / sqrt(sum(square(h_abs)));
for (int l = 0; l < L; l++) {
for (int k = 0; k < N_ch; k++) {
h(k, l).real(sqrt(N) * h_abs(k) * arma::randn());
h(k, l).imag(sqrt(N) * h_abs(k) * arma::randn());
//h(k, l).real((k == 0) ? (sqrt(N)) : (0.0));
//h(k, l).imag(0.0);
}
}
#if DEBUG_SAVE == 4
h.save("h.txt", raw_ascii);
return(0);
#endif
for (int l = 0; l < L; l++) {
cx_vec h_zp = zeros<cx_vec>(N);
h_zp.subvec(0, N_ch - 1) = h(span::all, l);
cx_vec H = fft(h_zp) / sqrt(N);
z.subvec(N * l, N * (l + 1) - 1) = ifft((fft(z.subvec(N * l, N * (l + 1) - 1)) % H) / sqrt(N)) * sqrt(N);
z_nln.subvec(N * l, N * (l + 1) - 1) = ifft((fft(z_nln.subvec(N * l, N * (l + 1) - 1)) % H) / sqrt(N)) * sqrt(N);
}
#if DEBUG_SAVE == 5
z.save("z2.txt", raw_ascii);
return(0);
#endif
} // Multipath channel
// Channel (AWGN)
double Sw = stddev(z) * pow(10.0, -0.05*snr) / sqrt(2);
double Sw_nln = stddev(z_nln) * pow(10.0, -0.05*snr) / sqrt(2);
double Sw2 = Sw * Sw;
double Sw2_nln = Sw_nln * Sw_nln;
//cout << "Sw2 = " << Sw2 << endl;
//cout << "Sw2_nln = " << Sw2_nln << endl;
cx_vec y = z + Sw*(cx_vec(arma::size(z), fill::randn));
cx_vec y_nln = z_nln + Sw_nln*(cx_vec(arma::size(z), fill::randn));
#if DEVUG_SAVE == 6
y.save("y.txt", raw_ascii);
y_nln.save("y_nln.txt", raw_ascii);
return(0);
#endif
// Decoding linear OFDM
cout << endl << "Linear OFDM simulation" << endl;
clog << endl << "Linear OFDM simulation" << endl;
double ber = 0;
double fer = 0;
cx_vec R0 = zeros<cx_vec>(N);
for (int l = 0; l < L; l++) {
R0 = fft(y.subvec(N * l, N * (l + 1) - 1)) / sqrt(N);
if (ENABLE_MULTIPATH_CHANNEL) {
// Linear MMSE equalizer
cx_vec h_zp = zeros<cx_vec>(N);
h_zp.subvec(0, N_ch - 1) = h(span::all, l);
cx_vec H = fft(h_zp) / sqrt(N);
R0 = R0 % (conj(H) / (square(abs(H)) + Sw2));
}
#if DEBUG_SAVE == 7
R0.save("r.txt", raw_ascii);
return(0);
#endif
uvec err_real = (sign(real(R0)) != sign(real(X.subvec(N*l, N*(l + 1) - 1))));
uvec err_imag = (sign(imag(R0)) != sign(imag(X.subvec(N*l, N*(l + 1) - 1))));
if (QAM_ORDER == 64) {
err_real += (sign(abs(real(R0)) - LEVEL4_64QAM) != sign(abs(real(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL4_64QAM));
err_imag += (sign(abs(imag(R0)) - LEVEL4_64QAM) != sign(abs(imag(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL4_64QAM));
err_real += (sign(abs(abs(real(R0)) - LEVEL4_64QAM) - LEVEL2_64QAM) != sign(abs(abs(real(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL4_64QAM) - LEVEL2_64QAM));
err_imag += (sign(abs(abs(imag(R0)) - LEVEL4_64QAM) - LEVEL2_64QAM) != sign(abs(abs(imag(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL4_64QAM) - LEVEL2_64QAM));
}
else if (QAM_ORDER == 16) {
err_real += (sign(abs(real(R0)) - LEVEL2_16QAM) != sign(abs(real(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL2_16QAM));
err_imag += (sign(abs(imag(R0)) - LEVEL2_16QAM) != sign(abs(imag(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL2_16QAM));
}
if (Nu < N) {
err_real.subvec(Nu, N - 1) = zeros<uvec>(N - Nu);
err_imag.subvec(Nu, N - 1) = zeros<uvec>(N - Nu);
}
ber = ber + sum(err_real) + sum(err_imag);
if ((sum(err_real) > 0) || (sum(err_imag) > 0)) {
fer += 1;
}
}
ber = ber / double(L * QAM_BIT * Nu);
fer = fer / double(L);
cout << "BER (linear) = " << ber << endl;
cout << "FER (linear) = " << fer << endl << endl;
clog << "BER (linear) = " << ber << endl;
clog << "FER (linear) = " << fer << endl << endl;
clog.flush();
BER_lin(m_snr) = ber;
FER_lin(m_snr) = fer;
wall_clock timer;
// GAMP decoder simulation
int I_max_gamp2 = I_max_gamp;
if ((B != 1.0) || (s_scale != 1.0)) {
I_max_gamp2 = int(2 * I_max_gamp2);
}
double Sw2_nln_0 = Sw2_nln;
double B0 = B;
if (NONLINEARITY_TYPE == 100) {
cout << "PO-OFDM simulation" << endl;
clog << "PO-OFDM simulation" << endl;
}
else {
cout << "Nonlinear OFDM simulation" << endl;
clog << "Nonlinear OFDM simulation" << endl;
}
ber = 0;
fer = 0;
cx_vec y0 = zeros<cx_vec>(N);
cx_vec x_hat = zeros<cx_vec>(N);
cx_vec x_flat = zeros<cx_vec>(N);
vec mu_x = init_std * ones<vec>(N);
vec mu_r = zeros<vec>(N);
cx_vec r_hat = zeros<cx_vec>(N);
cx_vec s_hat = zeros<cx_vec>(N);
vec mu_s = zeros<vec>(N);
cx_vec p_hat = zeros<cx_vec>(N);
vec mu_p = zeros<vec>(N);
cx_vec z_hat = zeros<cx_vec>(N);
vec mu_z = zeros<vec>(N);
cx_vec ifft_x = zeros<cx_vec>(N);
cx_vec fft_s = zeros<cx_vec>(N);
vec p_out = zeros<vec>(N_z * N_z);
vec P_x_re = zeros<vec>(arma::size(C));
vec P_x_im = zeros<vec>(arma::size(C));
cx_vec x_hat_best = zeros<cx_vec>(N);
cx_vec y0_oob = zeros<cx_vec>(N);
cx_vec y0_ref = zeros<cx_vec>(N);
double min_ber;
double E_min;
//vec mu_x_best = zeros<vec>(N);
//vec s_hat_best = zeros<vec>(N);
for (int l = 0; l < L; l++) {
// int l = l_k(ii);
timer.tic();
y0 = y_nln.subvec(N*l, N*(l + 1) - 1);
// Out-of-band filtering in the receiver (optional)
if (ENABLE_OOB_FILTERING_RX && (Nu < N)) {
X0 = fft(y0) / sqrt(N);
// Set to zero unused subcarriers
X0.subvec(Nu, N - 1) = zeros<cx_vec>(N - Nu);
y0 = ifft(X0)*sqrt(N);
}
if (ENABLE_MULTIPATH_CHANNEL) {
// Linear MMSE equalizer
cx_vec h_zp = zeros<cx_vec>(N);
h_zp.subvec(0, N_ch - 1) = h(span::all, l);
cx_vec H = fft(h_zp) / sqrt(N);
X0 = fft(y0) / sqrt(N);
X0 = X0 % (conj(H) / (square(abs(H)) + Sw2_nln_0));
y0 = ifft(X0) * sqrt(N);
}
y0_ref = y0;
// Initialize priors
x_hat = zeros<cx_vec>(N);
x_flat = zeros<cx_vec>(N);
mu_x = init_std * ones<vec>(N);
if (Nu < N) {
mu_x.subvec(Nu, N - 1) = 0.000001 * ones<vec>(N - Nu);
}
mu_r = zeros<vec>(N);
r_hat = zeros<cx_vec>(N);
s_hat = zeros<cx_vec>(N);
mu_s = zeros<vec>(N);
p_hat = zeros<cx_vec>(N);
mu_p = zeros<vec>(N);
z_hat = zeros<cx_vec>(N);
mu_z = zeros<vec>(N);
// PO-OFDM
int N_phi = 512;
const double PI = datum::pi;
const double sPI = sqrt(PI);
vec phi_z = linspace<vec>(0, 2*PI, N_phi);
cx_vec exp_z = zeros<cx_vec>(N_phi);
exp_z.set_real(cos(phi_z));
exp_z.set_imag(sin(phi_z));
double A_r, phi_r, A_p, phi_p;
double a, I0, I2, K1, exp_K1;
cx_double I1;
vec b = zeros<vec>(N_phi);
vec c = zeros<vec>(N_phi);
vec b2 = zeros<vec>(N_phi);
vec E0 = zeros<vec>(N_phi);
vec E1 = zeros<vec>(N_phi);
vec E2 = zeros<vec>(N_phi);
vec U0 = zeros<vec>(N_phi);
vec U1 = zeros<vec>(N_phi);
vec U2 = zeros<vec>(N_phi);
double min_ber = datum::inf;
double E_min = datum::inf;
vec E = zeros<vec>(I_max_gamp2);
double ber_k = 0;
int t = 0;
bool reset_flag = true;
Sw2_nln = s_scale * Sw2_nln_0;
B = B0;
//cout << endl;
//clog << endl;
vec sc_alp = ones<vec>(I_max_gamp2);
for (t = 0; t < I_max_gamp2; t++) {
// Output nodes
ifft_x = ifft(x_hat) * sqrt(N);
double mu0 = mean(mu_x);
for (int k = 0; k < N; k++) {
//mu_p(k) = B * mu0 + (1 - B) * mu_p(k);
mu_p(k) = mu0;
p_hat(k) = ifft_x(k) - mu_p(k) * s_hat(k);
#if (NONLINEARITY_TYPE == 100)
// Version for PO-OFDM: semi-analytical solution: 2D integral becomes 1D
// For more details see: S.Zhidkov and R.Dinis, "Phase-only OFDM"
A_r = abs(y0(k));
phi_r = arg(y0(k));
A_p = abs(p_hat(k));
phi_p = arg(p_hat(k));
a = 1.0 / (2.0*mu_p(k));
K1 = (A_p*A_p) / (2.0*mu_p(k));
exp_K1 = exp(-K1);
b = A_p * cos(phi_p - phi_z) / mu_p(k);
c = exp(A_r * cos(phi_r - phi_z) / Sw2_nln);
b2 = square(b);
E0 = exp(b2 / (4.0*a) - K1);
E1 = (1.0 + erf(b / (2.0*sqrt(a)))) % E0;
U0 = 1.0 / (2.0*a) * exp_K1 + (sPI / (4.0*a*sqrt(a)) * b) % E1;
U1 = 1.0 / (4.0*a*a)*b*exp_K1 + (sPI / (4.0*a*sqrt(a)))*(1.0 + b2 / (2.0*a)) % E1;
U2 = 1.0 / (2.0*a*a) * (1.0 + b2 / (4.0*a))*exp_K1 + (b*sPI / (8.0*a*a*sqrt(a))) % (3.0 + b2 / (2.0*a)) % E1;
I0 = accu(c % U0);
I1 = accu(exp_z % c % U1);
I2 = accu(c % U2);
z_hat(k) = I1 / I0;
mu_z(k) = 0.5 * (I2 - abs(I1)*abs(I1) / (I0)) / (I0); // abs(I1) - since I1 is a complex number
#else
// General polar nonlinearity (2D integration - very slow)
p_out = exp(-real((y0(k) - z_all_nln)%conj(y0(k) - z_all_nln)) / (Sw2_nln * 2.0) - real((z_all - p_hat(k))%conj(z_all - p_hat(k))) / ( mu_p(k) * 2.0));
cx_double mp = accu(z_all % p_out);
double sp = accu(p_out);
if (sp == 0) {
mp = 0;
}
else {
mp = mp / sp;
}
cx_double vp = accu((z_all - mp)%conj(z_all - mp) % p_out);
if (sp == 0) {
vp = 0;
}
else {
vp = vp / sp;
}
z_hat(k) = mp;
mu_z(k) = 0.5 * real(vp);
#endif
s_hat(k) = B * (z_hat(k) - p_hat(k)) / mu_p(k) + (1 - B) * s_hat(k);
mu_s(k) = B * (1 - mu_z(k) / mu_p(k)) / mu_p(k) + (1 - B) * mu_s(k);
}
fft_s = fft(s_hat) / sqrt(N);
double mu1 = 1.0 / abs(mean(mu_s));
for (int n = 0; n < N; n++) {
if (reset_flag) {
x_flat(n) = x_hat(n);
reset_flag = false;
}
else {
x_flat(n) = B * x_hat(n) + (1 - B) * x_flat(n);
}
//mu_r(n) = B * mu1 + (1 - B) * mu_r(n);
mu_r(n) = mu1;
r_hat(n) = x_flat(n) + mu_r(n) * fft_s(n);
if (n < Nu) {
P_x_re = exp(-square(C - real(r_hat(n))) / (2.0 * mu_r(n)));
P_x_re = P_x_re / (sum(P_x_re) + 1e-15);
P_x_im = exp(-square(C - imag(r_hat(n))) / (2.0 * mu_r(n)));
P_x_im = P_x_im / (sum(P_x_im) + 1e-15);
// mmse g_in
x_hat(n).real(sum(C % P_x_re));
x_hat(n).imag(sum(C % P_x_im));
mu_x(n) = 0.5*(sum(square(C - real(x_hat(n))) % P_x_re) + sum(square(C - imag(x_hat(n))) % P_x_im));
}
else {
// Decision for unused subcarriers
x_hat(n) = 0;
mu_x(n) = 0.00001;
}
}
cx_vec y_rec = slicer(x_hat, POWER_SCALE, QAM_ORDER);
y_rec = ifft(y_rec)*sqrt(N);
E(t) = accu(square(abs(nln_func(y_rec, G0) - y0)));
uvec err_re = (sign(real(x_hat)) != sign(real(X.subvec(N*l, N*(l + 1) - 1))));
uvec err_im = (sign(imag(x_hat)) != sign(imag(X.subvec(N*l, N*(l + 1) - 1))));
if (QAM_ORDER == 64) {
err_re += (sign(abs(real(x_hat)) - LEVEL4_64QAM) != sign(abs(real(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL4_64QAM));
err_im += (sign(abs(imag(x_hat)) - LEVEL4_64QAM) != sign(abs(imag(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL4_64QAM));
err_re += (sign(abs(abs(real(x_hat)) - LEVEL4_64QAM) - LEVEL2_64QAM) != sign(abs(abs(real(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL4_64QAM) - LEVEL2_64QAM));
err_im += (sign(abs(abs(imag(x_hat)) - LEVEL4_64QAM) - LEVEL2_64QAM) != sign(abs(abs(imag(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL4_64QAM) - LEVEL2_64QAM));
}
else if (QAM_ORDER == 16) {
err_re += (sign(abs(real(x_hat)) - LEVEL2_16QAM) != sign(abs(real(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL2_16QAM));
err_im += (sign(abs(imag(x_hat)) - LEVEL2_16QAM) != sign(abs(imag(X.subvec(N*l, N*(l + 1) - 1))) - LEVEL2_16QAM));
}
if (Nu < N) {
err_re.subvec(Nu, N - 1) = zeros<uvec>(N - Nu);
err_im.subvec(Nu, N - 1) = zeros<uvec>(N - Nu);
}
ber_k = double(sum(err_re) + sum(err_im));
if (E(t) < E_min) {
E_min = E(t);
min_ber = ber_k;
x_hat_best = x_hat;
}
#if DEBUG_PRINT == 1
cout << E(t) << "(" << ber_k << "), ";
cout << "BER (" << t << ") = " << ber_k / double(QAM_BIT * Nu) << endl;
//clog << E(t) << "(" << ber_k << "), ";
//clog << "BER (" << t << ") = " << ber_k / (2 * Nu) << endl;
#endif
if (ber_k <= 1) {
E_min = E(t);
min_ber = ber_k;
x_hat_best = x_hat;
break;
}
if (t==I_max_gamp) {
// Reset damping parameters and restart processing
B = 1.0;
Sw2_nln = Sw2_nln_0;
x_hat.zeros();
s_hat.zeros();
mu_s.zeros();
x_flat.zeros();
mu_r.zeros();
r_hat.zeros();
p_hat.zeros();
mu_p.zeros();
z_hat.zeros();
mu_z.zeros();
mu_x.fill(init_std);
reset_flag = true;
}
}
int post_corrected = 0;
// Post correction (assuming genuie CRC)
if (enable_post_correction && (min_ber > 0) && (min_ber<3)) {
// Step 1: single error correction
// If there is only a single error we can correct it by N bit-flips + CRC checks
uvec err_re = (sign(real(x_hat_best)) != sign(real(X.subvec(N*l, N*(l + 1) - 1))));
uvec err_im = (sign(imag(x_hat_best)) != sign(imag(X.subvec(N*l, N*(l + 1) - 1))));
if (min_ber <= 1) {
min_ber = 0; // We can correct single error by N bit-flips and CRC checks
ber_k = 0;
post_corrected = 1;
}
if ((post_corrected == 0) && (QAM_ORDER == 4)) {
// Step 2: try double errors
// Firsly, we select the lowest reliability bit and flip it
// And then try to flip other N bits (= N-times CRC check)
vec E_hat_re = square(sign(real(x_hat_best)) - real(x_hat_best));
double E_hat_max_re = E_hat_re.max();
vec E_hat_im = square(sign(imag(x_hat_best)) - imag(x_hat_best));
double E_hat_max_im = E_hat_im.max();
if (E_hat_max_re > E_hat_max_im) {
uword i_cand = E_hat_re.index_max();
err_re(i_cand) = 0;
}
else {
uword i_cand = E_hat_im.index_max();
err_im(i_cand) = 0;
}
if ((sum(err_re) + sum(err_im)) <= 1) {
min_ber = 0; // We can correct single error by N bit-flips and CRC checks
ber_k = 0;
post_corrected = 2;
}
}
}
ber = ber + min_ber;
fer = fer + (min_ber > 0);
double n_t = timer.toc();
double tmp_ber = ber / double((l + 1) * QAM_BIT * Nu);
double tt = t + post_corrected;
cout << "Current BER estimation (l=" << l << ") = " << tmp_ber << "/" << ber_k / double(Nu*QAM_BIT) << " (" << min_ber << "/" << tt << ") | " << n_t << " (sec.)" << endl;
clog << "Current BER estimation (l=" << l << ") = " << tmp_ber << "/" << ber_k / double(Nu*QAM_BIT) << " (" << min_ber << "/" << tt << ") " << endl;
clog.flush();
}
ber = ber / double(L*Nu*QAM_BIT);
fer = fer / L;
cout << "BER (nonlinear) = " << ber << endl;
cout << "FER (nonlinear) = " << fer << endl;
clog << "BER (nonlinear) = " << ber << endl;
clog << "FER (nonlinear) = " << fer << endl;
cout << endl << endl;
clog << endl << endl;
clog.flush();
BER_gamp(m_snr) = ber;
FER_gamp(m_snr) = fer;
EbNo.save("EbNo.txt", raw_ascii);
BER_gamp.save("BER.txt", raw_ascii);
FER_gamp.save("FER.txt", raw_ascii);
}
cout << "Simulation has finished!" << endl;
clog.close();
getchar();
}
/* Memoryless nonlinearity */
cx_vec nln_func(cx_vec z, double G0)
{
#if (NONLINEARITY_TYPE == 0)
vec T1 = { 0, 1 };
vec a = { 1, 0 };
vec b = { 0, 1 };
#elif (NONLINEARITY_TYPE == 1)
// Good at G0 = 0.45 (N=1024/512), 2D
vec T1 = { 0, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75, 3 };
vec a = { 1, 2, 2, -2, -2, 2, 2, -2, -2, -0.25 };
vec b = { 0, -2, -3.5, 4, 3.5, -4, -4.5, 6, 6.5, 1.75 };
#elif (NONLINEARITY_TYPE == 2)
// Good at G0 = 0.45 (N=1024/512), 2D
vec T1 = { 0.0000, 1.0000, 1.2500, 1.5000, 1.7500, 2.0000, 2.2500, 2.5000, 2.7500, 3.0000 };
vec a = { 1.0000, 2.0000, 2.0000, -2.0000, -2.0000, 2.0000, 2.0000, -2.0000, -2.0000, -0.5000 };
vec b = { 0.0000, -2.0000, -3.5000, 4.0000, 3.5000, -4.0000, -4.5000, 6.0000, 6.5000, 2.5000 };
#else
// Linear model (default)
vec T1 = { 0 };
vec a = { 1 };
vec b = { 0 };
#endif
#if (NONLINEARITY_TYPE < 100)
vec A = G0*abs(z);
vec phi = arg(z);
cx_vec y = zeros<cx_vec>(z.n_elem);
for (int k = 0; k < z.n_elem; k++) {
if (A[k] >= T1[T1.n_elem - 1]) {
A[k] = a[T1.n_elem - 1] * A[k] + b[T1.n_elem - 1];
}
else {
for (int m = 0; m < T1.n_elem - 1; m++) {
if ((A[k] >= T1[m]) && (A[k] < T1[m + 1])) {
A[k] = a[m] * A[k] + b[m];
break;
}
}
}
//A[k] = abs(A[k]);
y[k].real(A[k] * cos(phi[k]));
y[k].imag(A[k] * sin(phi[k]));
}
#else
#if (NONLINEARITY_TYPE == 100)
// Phase-only OFDM
vec phi = arg(z);
cx_vec y = zeros<cx_vec>(z.n_elem);
for (int k = 0; k < z.n_elem; k++) {
y[k].real(cos(phi[k]));
y[k].imag(sin(phi[k]));
}
#elif (NONLINEARITY_TYPE == 101)
// Rapp model
#elif (NONLINEARITY_TYPE == 102)
// Saleh TWTA model
double S_M = 1.0;
double PHI_M = 1.0472; // pi/3
vec A = G0*abs(z);
vec phi = arg(z);
cx_vec y = zeros<cx_vec>(z.n_elem);
for (int k = 0; k < z.n_elem; k++) {
phi[k] = phi[k] + 2.0 * PHI_M * (S_M*A[k]) * (S_M*A[k]) / (1.0 + (S_M*A[k])*(S_M*A[k]));
A[k] = 2.0 * (S_M*A[k]) / (1.0 + (S_M*A[k])*(S_M*A[k]));
y[k].real(A[k] * cos(phi[k]));
y[k].imag(A[k] * sin(phi[k]));
}
#elif (NONLINEARITY_TYPE == 103)
vec T_phi = { 0 };
vec a_phi = { 1 };
vec b_phi = { 0 };
//vec T_phi = { 0, 1.0, 1.25, 1.5, 2.0, 2.5};
//vec a_phi = { 1, 1, 1, 1, 1, 1};
//vec b_phi = { 0, -0.7854, 0.7854, -1.5708, 1.5708, 0};
// SEL with chaotic phase rotation model
vec A = G0*abs(z);
vec phi = arg(z);
cx_vec y = zeros<cx_vec>(z.n_elem);
for (int k = 0; k < z.n_elem; k++) {
if (A[k] >= T_phi[T_phi.n_elem - 1]) {
phi[k] = a_phi[T_phi.n_elem - 1] * phi[k] + b_phi[T_phi.n_elem - 1];
}
else {
for (int m = 0; m < T_phi.n_elem - 1; m++) {
if ((A[k] >= T_phi[m]) && (A[k] < T_phi[m + 1])) {
phi[k] = a_phi[m] * phi[k] + b_phi[m];
break;
}
}
}
if (A[k] > 1.0) {
A[k] = 1.0;
}
y[k].real(A[k] * cos(phi[k]));
y[k].imag(A[k] * sin(phi[k]));
}
#endif // Rapp/Saleh/Phase-only models
#endif // All models
return(y);
}
// QAM slicer
cx_vec slicer(cx_vec x, double power_scale, int qam_order)
{
int Nx = int(x.n_elem);
cx_vec y = zeros<cx_vec>(arma::size(x));
if (qam_order == 64) {
for (int k = 0; k < Nx; k++) {
if ((real(x(k))*power_scale) < -6.0) {
y(k).real(-7.0 * (1.0 / power_scale));
}