BPSK modulation over an AWGN channel

As a first example we will generate a sequence of 500000 random bits {0,1} and BPSK modulate these. Thereafter the BPSK signals will be transmitted over an AWGN channel with a signal-to-noise ratio dB. The received signal is then decoded and the number of bit errors are calculated.

#include <itpp/itcomm.h>
using namespace itpp;
//These lines are needed for use of cout and endl
using std::cout;
using std::endl;
int main()
{
//Scalars
int N;
double N0;
//Vectors
bvec bits, dec_bits;
vec symbols, rec;
//Classes
BPSK bpsk; //The BPSK modulator/debodulator class
BERC berc; //The Bit Error Rate Counter class
//Init
N = 500000; //The number of bits to simulate
N0 = 1; //0 dB SNR
//Randomize the random number generator
RNG_randomize();
//Generate the bits:
bits = randb(N);
//Do the BPSK modulation
bpsk.modulate_bits(bits, symbols);
//Add the AWGN
rec = symbols + sqrt(N0 / 2) * randn(N);
//Decode the received bits
bpsk.demodulate_bits(rec, dec_bits);
//Count the number of errors
berc.count(bits, dec_bits);
//Print the results
cout << "There were " << berc.get_errors() << " received bits in error." << endl;
cout << "There were " << berc.get_corrects() << " correctly received bits." << endl;
cout << "The error probability was " << berc.get_errorrate() << endl;
cout << "The theoretical error probability is " << 0.5*erfc(1.0) << endl;
//Exit program:
return 0;
}

When you run this program, the output will look something like this:

There were 39224 received bits in error.
There were 460776 correctly received bits.
The error probability was 0.078448
The theoretical error probability is 0.0786496

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