August 2007 - DSP LOG

Bit Error Rate (BER) for frequency shift keying with coherent demodulation

Following the request by Siti Naimah, this post discuss the bit error probability for coherent demodulation of binary Frequency Shift Keying (BFSK) along with a small Matlab code snippet.

Using the definition provided in Sec 4.4.4 of [DIG-COMM-SKLAR]), in binary Frequency shift keying (BFSK), the bits 0’s and 1’s are represented by signals $s_1$ and $s_2$ having frequencies $f_1$ and $f_2$ respectively, i.e.

$s_i(t) = \sqrt{\frac{2E}{T}}cos(2\pi f_it + \phi)$ ,

where

$E$ is the energy ,

$T$ is the symbol duration and

$\phi$ is an arbitrary phase (assume to be zero).

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CORDIC for phase rotation

My understanding of the CORDIC (Co-ordinate Rotation by DIgital Computer) thanks to the nice article in [DSPGURU-CORDIC].

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Bit Error Rate (BER) for BPSK modulation

In this post, we will derive the theoretical equation for bit error rate (BER) with Binary Phase Shift Keying (BPSK) modulation scheme in Additive White Gaussian Noise (AWGN) channel. The BER results obtained using Matlab/Octave & Python simulation scripts show good agreement with the derived theoretical results.

System Model

Transmitter

With Binary Phase Shift Keying (BPSK), the binary digits 1 and 0 maybe represented by the analog levels $+\sqrt{E_b}$ and $-\sqrt{E_b}$ respectively. The system model is as shown in the Figure below.