Simulation of turbo equalizer in multipath channels

The turbo equalizer uses a SISO NSC module and a SISO equalizer module. Optionally a precoder can be used at the channel input (by default the precoder is enabled).

Reference: R. Koetter, A. C. Singer, and M. Tuchler, ''Turbo equalization: an iterative equalization and decoding technique for coded data transmision,`` IEEE Signal Processing Magazine, pp. 67-80, Jan. 2004

#define USE_PRECODER
#include "itpp/itcomm.h"
using namespace itpp;
using std::cout;
using std::endl;
using std::string;
int main(void)
{
//general parameters
double threshold_value = 50;
string map_metric = "maxlogMAP";
ivec gen = "07 05";//octal notation
int constraint_length = 3;
int ch_nb_taps = 4;//number of channel multipaths
int nb_errors_lim = 3000;
int nb_bits_lim = int(1e6);
int perm_len = pow2i(14);//permutation length
int nb_iter = 10;//number of iterations in the turbo decoder
vec EbN0_dB = "0:0.5:10";
double R = 1.0 / 2.0;//coding rate of FEC
double Ec = 1.0;//coded bit energy
#ifdef USE_PRECODER
ivec prec_gen = "03 02";//octal notation
int prec_gen_length = 2;
#endif
//other parameters
int nb_bits_tail = perm_len / gen.length();
int nb_bits = nb_bits_tail - (constraint_length - 1);//number of bits in a block (without tail)
vec sigma2 = (0.5 * Ec / R) * pow(inv_dB(EbN0_dB), -1.0);//N0/2
int nb_blocks;//number of blocks
int nb_errors;
bvec bits(nb_bits);//data bits
bvec nsc_coded_bits(perm_len);//tail is added
bvec em_bits(perm_len);
bmat parity_bits;
ivec perm(perm_len);
ivec inv_perm(perm_len);
vec rec(perm_len);
//SISO equalizer
vec eq_apriori_data(perm_len);
vec eq_extrinsic_data;
//SISO NSC
vec nsc_intrinsic_coded(perm_len);
vec nsc_apriori_data(nb_bits_tail);
nsc_apriori_data.zeros();//always zero
vec nsc_extrinsic_coded;
vec nsc_extrinsic_data;
//decision
bvec rec_bits(nb_bits_tail);
int snr_len = EbN0_dB.length();
mat ber(nb_iter, snr_len);
ber.zeros();
register int en, n;
//CCs
Convolutional_Code nsc;
nsc.set_generator_polynomials(gen, constraint_length);
#ifdef USE_PRECODER
Rec_Syst_Conv_Code prec;
prec.set_generator_polynomials(prec_gen, prec_gen_length);
#endif
//BPSK
BPSK bpsk;
//AWGN
AWGN_Channel awgn;
//multipath channel impulse response (Rayleigh fading) with real coefficients
vec ch_imp_response(ch_nb_taps);
vec ini_state = ones(ch_nb_taps);//initial state is zero
MA_Filter<double, double, double> multipath_channel;
//SISO blocks
SISO siso;
siso.set_generators(gen, constraint_length);
siso.set_map_metric(map_metric);
#ifdef USE_PRECODER
siso.set_precoder_generator(prec_gen(0), prec_gen_length);
#endif
//BER
BERC berc;
//Randomize generators
RNG_randomize();
//main loop
for (en = 0;en < snr_len;en++) {
cout << "EbN0_dB = " << EbN0_dB(en) << endl;
awgn.set_noise(sigma2(en));
siso.set_noise(sigma2(en));
nb_errors = 0;
nb_blocks = 0;
while ((nb_errors < nb_errors_lim) && (nb_blocks*nb_bits < nb_bits_lim))//if at the last iteration the nb. of errors is inferior to lim, then process another block
{
//permutation
perm = sort_index(randu(perm_len));
//inverse permutation
inv_perm = sort_index(perm);
//bits generation
bits = randb(nb_bits);
//convolutional code
nsc.encode_tail(bits, nsc_coded_bits);//tail is added here to information bits to close the trellis
//permutation
em_bits = nsc_coded_bits(perm);
#ifdef USE_PRECODER
//precoder
prec.encode(em_bits, parity_bits);
em_bits = parity_bits.get_col(0);
#endif
//BPSK modulation (1->-1,0->+1) + multipath channel
ch_imp_response = randray(ch_nb_taps);
ch_imp_response /= sqrt(sum_sqr(ch_imp_response));//normalized power profile
multipath_channel.set_coeffs(ch_imp_response);
multipath_channel.set_state(ini_state);//inital state is zero
rec = awgn(multipath_channel(bpsk.modulate_bits(em_bits)));
//turbo equalizer
eq_apriori_data.zeros();//a priori information of emitted symbols
siso.set_impulse_response(ch_imp_response);
for (n = 0;n < nb_iter;n++)
{
//first decoder
siso.equalizer(eq_extrinsic_data, rec, eq_apriori_data, false);//no tail
//deinterleave+threshold
nsc_intrinsic_coded = SISO::threshold(eq_extrinsic_data(inv_perm), threshold_value);
//second decoder
siso.nsc(nsc_extrinsic_coded, nsc_extrinsic_data, nsc_intrinsic_coded, nsc_apriori_data, true);//tail
//decision
rec_bits = bpsk.demodulate_bits(-nsc_extrinsic_data);//assume that a priori info is zero
//count errors
berc.clear();
berc.count(bits, rec_bits.left(nb_bits));
ber(n, en) += berc.get_errorrate();
//interleave
eq_apriori_data = nsc_extrinsic_coded(perm);
}//end iterations
nb_errors += int(berc.get_errors());//get number of errors at the last iteration
nb_blocks++;
}//end blocks (while loop)
//compute BER over all tx blocks
ber.set_col(en, ber.get_col(en) / nb_blocks);
}
//save results to file
it_file ff("turbo_equalizer_bersim_multipath.it");
ff << Name("BER") << ber;
ff << Name("EbN0_dB") << EbN0_dB;
ff.close();
return 0;
}

When you run this program, the results (BER and EbN0_dB) are saved into turbo_equalizer_bersim_multipath.it file. Using the following MATLAB script

clear all
itload('turbo_equalizer_bersim_multipath.it');
figure
semilogy(EbN0_dB, BER, 'o-')
grid on
xlabel('E_b/N_0 [dB]')
ylabel('BER')

the results can be displayed.

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