Probability Of Error For Coherent Bpsk
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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 simulation scripts error probability of bpsk show good agreement with the derived theoretical results. With Binary Phase Shift Keying (BPSK), the
Probability Of Error In Qpsk
binary digits 1 and 0 maybe represented by the analog levels and respectively. The system model is as shown in the Figure below. bpsk probability of error derivation Figure: Simplified block diagram with BPSK transmitter-receiver Channel Model The transmitted waveform gets corrupted by noise , typically referred to as Additive White Gaussian Noise (AWGN). Additive : As the noise gets ‘added' (and not multiplied) to the
Bit-error-probability-for-bpsk-modulation
received signal White : The spectrum of the noise if flat for all frequencies. Gaussian : The values of the noise follows the Gaussian probability distribution function, with and . Computing the probability of error Using the derivation provided in Section 5.2.1 of [COMM-PROAKIS] as reference: The received signal, when bit 1 is transmitted and when bit 0 is transmitted. The conditional probability distribution function (PDF) of for the two cases are: . Figure: Conditional probability probability of error for bpsk and qpsk density function with BPSK modulation Assuming that and are equally probable i.e. , the threshold 0 forms the optimal decision boundary. if the received signal is is greater than 0, then the receiver assumes was transmitted. if the received signal is is less than or equal to 0, then the receiver assumes was transmitted. i.e. and . Probability of error given was transmitted With this threshold, the probability of error given is transmitted is (the area in blue region): , where, isĀ the complementary error function. Probability of error given was transmitted Similarly the probability of error given is transmitted is (the area in green region): . Total probability of bit error . Given that we assumed that and are equally probable i.e. , the bit error probability is, . Simulation model Matlab/Octave source code for computing the bit error rate with BPSK modulation from theory and simulation. 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. Click here to download Matlab/Octave script for simulating BER for BPSK modulation in AWGN chnanel. Figure: Bit error rate (BER) curve for BPSK modulation - theory, simulati
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