Bit Error Rate (BER) for BPSK modulationIn 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 simulation scripts show good agreement with the derived theoretical results. With Binary Phase Shift Keying (BPSK), the binary digits 1 and 0 maybe represented by the analog levels and respectively. The system model is as shown in the Figure below. Figure: Simplified block diagram with BPSK transmitter-receiver Channel Model The transmitted waveform gets corrupted by noise Gaussian Noise (AWGN). , typically referred to as Additive White Additive : As the noise gets ‘added’ (and not multiplied) to the received signal White : The spectrum of the noise is flat for all frequencies. Gaussian : The values of the noise with follows the Gaussian probability distribution function, and . Computing the probability of error The received signal, when bit 1 is transmitted and when bit 0 is transmitted. then the receiver assumes i. Probability of error given was transmitted is transmitted is (the area in blue region): With this threshold. • • . and . was is less than or equal to 0. .The conditional probability distribution function (PDF) of for the two cases are: . is greater than 0. Figure: Conditional probability density function with BPSK modulation Assuming that and are equally probable i. the optimal decision boundary.e. the probability of error given .e. then the receiver assumes was transmitted. the threshold 0 forms if the received signal is if the received signal is transmitted. com/2007/08/05/bit-error-probability-for-bpsk-modulation/ . Given that we assumed that error probability is. and are equally probable i. Simulation model Matlab/Octave source code for computing the bit error rate with BPSK modulation from theory and simulation.dsplog.where. Total probability of bit error . the bit . The code performs the following: (a) Generation of random BPSK modulated symbols +1′s and -1′s (b) Passing them through Additive White Gaussian Noise channel (c) Demodulation of the received symbol based on the location in the constellation (d) Counting the number of errors (e) Repeating the same for multiple Eb/No value. .e. is the complementary error function. Probability of error given was transmitted is transmitted is (the area in green region): Similarly the probability of error given . Click here to download Matlab/Octave script for simulating BER for BPSK modulation in AWGN chnanel. http://www. Figure: Bit error rate (BER) curve for BPSK modulation – theory. simulation .