Probability Of Error In Bpsk
Contents |
In this post, we will derive the theoretical equation for bit error rate (BER) with Binary Phase Shift Keying probability of error in qpsk (BPSK) modulation scheme in Additive White Gaussian Noise (AWGN) channel. The BER
Bpsk Probability Of Error Derivation
results obtained using Matlab/Octave simulation scripts show good agreement with the derived theoretical results. With Binary Phase Shift
Bit-error-probability-for-bpsk-modulation
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
Probability Of Error For Bpsk And Qpsk
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 received signal White : The spectrum of the noise if flat for all frequencies. Gaussian : The values of the noise follows the calculate probability of error for bpsk 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 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 equ
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