Biography matlab code for 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 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 , 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 Gaussian probability distribution function, with and .
Computing the probability of error
Using the derivation provided in Section 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
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To test the correctness of various CSP estimators, we need a sampled signal with known cyclostationary parameters. Additionally, the signal should be easy to create and understand. A good candidate for this kind of signal is the binary phase-shift keyed (BPSK) signal with rectangular pulse function.
PSK signals with rectangular pulse functions have infinite bandwidth because the signal bandwidth is determined by the Fourier transform of the pulse, which is a sinc() function for the rectangular pulse. So the rectangular pulse is not terribly practical&#;infinite bandwidth is bad for other users of the spectrum. However, it is easy to generate, and its statistical properties are known.
So let&#;s jump in. The baseband BPSK signal is simply a sequence of binary ( 1) symbols convolved with the rectangular pulse. The MATLAB script make_rect_bpsk.m does this and produces the following plot:
The signal alternates between amplitudes of +1 and -1 randomly. After frequency shifting and adding white Gaussian noise, we obtain the power spectrum estimate:
The power spectrum plot shows why the rectangular-pulse BPSK signal is not popular in practice. The range of frequencies for which the signal possesses non-zero average power is infinite, so it will interfere with signals &#;nearb
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Modulation Techniques MATLAB Code
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