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EE 6332, Spring, 2017 Wireless Telecommunication. Zhu Han Department of Electrical and Computer Engineering Class 17 Mar. 27 th , 2017. Outline. BER Performance AWGN Channel Fading Channel Chapter 6.1 AWGN Chapter 6.2. Baseline: Stationary Channel. BPSK modulation.
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EE 6332, Spring, 2017Wireless Telecommunication Zhu Han Department of Electrical and Computer Engineering Class 17 Mar. 27th, 2017
Outline BER Performance AWGN Channel Fading Channel Chapter 6.1 AWGN Chapter 6.2 ECE 6331, Spring 2009
Baseline: Stationary Channel BPSK modulation y: the received signal x: the transmitted signal with amplitude a w: white noise with power N0
Bit Error Probability Noisena(t) gTx(t) gRx(t) d(i) We assume: • binary transmission with • transmission system fulfills 1st Nyquist criterion • noise , independent of data source Probability density function (pdf) of Mean and variance
if • if Conditional pdfs The transmission system induces two conditional pdfs depending on
Example of samples of matched filter output for some bandpass modulation schemes
Figure 5.8 Illustrating the partitioning of the observation space into decision regions for the case when N 2 and M 4; it is assumed that the M transmitted symbols are equally likely.
Placing a threshold Probability of wrong decisions Probability of wrong decision When we define and as equal a-priori probabilities of and we will get the bit error probability s
Conditions for illustrative solution and With equivalently with substituting for
Special Case: Gaussian distributed noise • many independent interferers • central limit theorem • Gaussian distribution Motivation: é ù 2 - 1 2 ê ú ò 2 s = - 2 P 1 e d N ê ú b p s 2 2 0 N ê ú 0 ë û no closed solution Definition of Error Function and Error Function Complement
2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -3 -2 -1 0 1 2 3 Error function and its complement • function y = Q(x) y = 0.5*erfc(x/sqrt(2)); erf(x) erfc(x) erf(x), erfc(x) x
Expressions with and Bit error rate with error function complement antipodal: unipolar Q function
Bit error rate for unipolar and antipodal transmission • BER vs. SNR theoretical -1 simulation 10 unipolar -2 10 BER antipodal -3 10 -4 10 -2 0 2 4 6 8 10
Flat Fading Channel Assume h is Gaussian random: BPSK: Conditional on h, 6.154, 6.155 Averaged over h, which follows chi-square distribution at high SNR.
Effects of Fading Other modulation
Irreducible Bit Error Rate due to multipath Error floor
Homework 4 • 5.4, 5.5,5.9, 5.17,5.18, 6.1, 6.12, 6.16 • Due 4/10 ECE6331 Spring 2009