Probability Theory Of Bit Error Rate
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All News & Analysis Products & Suppliers Standards Library Reference Library Community Acquired Engineering360 FreeRegistration HOME REFERENCE LIBRARY TECHNICAL ARTICLES OPTICAL COMPONENTS AND OPTICS CHAPTER 7 - PROBABILITY THEORY OF bit error rate example BIT ERROR RATE Chapter 7 - Probability Theory of Bit Error Rate
Bit Error Rate Vs Snr
By Stamatios V. Kartalopoulos From Optical Bit Error Rate 7.1 INTRODUCTION As data is transmitted over a medium, bit error rate matlab attenuation, combined noise, and jitter sources all distort the shape of the transmitted bits, both in amplitude and time, to such a degree that a receiver misinterprets some bit values
Acceptable Bit Error Rate
and detects them wrongly; that is, some logic “ones” are detected as logic “zeros” and some logic “zeros” as logic “ones.” In communications, the number of error bits in the number of bits transmitted provides a performance metric of the channel, from the transmitter to (and including) the receiver. However, this metric needs clarification. For example, if two data rates are 1 ber repair Mbit/s and 10 Gbit/s, 10 errors in a second mean 10/1,000,000 (or 10–5) and 10/10,000,000,000 (or 10–9) errors, respectively. Alter- natively, 10 errors in 1,000,000 bits transmitted means 10 errors per second for the 1 Mbit/s rate and 100,000 errors per second for the 10 Gbit/s rate. Thus, depending on performance limits set for a specific application, the channel performance may or may not be acceptable. That is, the frequency (or rate) of erroneous bits is very critical. Although it is impossible to predict if a particular bit will be received correctly or not, it is possible to predict with good confidence the performance of a channel if the parameters of the link are known, as well as the statistical behavior (Gaussian, Poisson) of noise and jitter sources. Then, the frequency of occurrence of erroneous bits and the signal-to-noise ratio can be reliably estimated. What we have stated without having defined yet are the bit error ratio and the bit error rate. What they are and what the difference between the two is is examined in the next section. Thus, to model a tran
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Packet Error Rate
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Symbol Error Rate
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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) http://www.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/ 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 error rate 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 5.2.1 of [COMM-PROAKIS] as reference: The received signal, when bit error rate 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 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) Demodulat
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