Descripción: Probabilidad de error y tasa de error en Telecomunicaciones
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This paper focuses mainly on Bit Error Rate BER , Signal to Noise Ratio and different Rayleigh channels. We have designed four Rayleigh channels. This paper describes the comparative analysis of different digital modulation techniques like BPSK, QPSK
Direct Sequence Spread Spectrum Binary Phase Shift Keying with jamming Signal
Descripción: Well step test
Modern embedded processors include both scratchpad memory SPM and cache memory in their architectures. SPM's are prone to soft errors like Single event upsets SEUs and Single event multiple upsets SEMUs . For correcting soft errors, we use Error Corr
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Bitbisler
Descripción: to mitigate bit balling
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Bit Error Rate (BER) for BPSK modulation In this post, we will derive the theoretical equation for bit error error rate (BER) with Binary Phase Shift Keying (BPSK) modulation scheme in Additive White Gaussian Noise (AWGN) channel. The BER results obtained using using Matlab simulation scripts show good agreement with the derived theoretical results. With Binary Phase Shift Keying (BPSK), (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 tran transmi smitte tted d wavefo waveform rm gets gets corr corrupte upted d by noise noise Gaussian Noise (AWGN).
, typica typically lly refe referre rred d 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.
values of the the noise noise Gaussian : The values with
follow followss the Gaussi Gaussian an probab probabili ility ty distri distribut bution ion funct function ion,, and
.
Computing the probability of error 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
, the threshold 0 forms
Assuming that and are equally probable i.e. the optimal decision boundary. •
•
if the received signal is
is greater than 0, then the receiver assumes
was transmitted.
if the received signal is transmitted.
is less than or equal to 0, then the receiver assumes
was
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,
is 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 error probability is,
and
are equally probable i.e.
, the bit
.
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. http://www.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/
Figure: Bit error rate (BER) curve for BPSK modulation – theory, simulation
