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Unformatted text preview: Carleton University SYSC 5504 Department of Systems and Computer Engineering ELG 6154 Principles of Digital Communications Fall 2010/11 Assignment #2 Due on Tuesday October 26, 2010 1. Suppose that for some binary communication system the output of the matched filter is distributed with likelihood functions of f R ( r | 0 sent) = r 2 exp r 2 2 2 f R ( r | 1 sent) = r E b + 2 exp r 2 2( E b + 2 ) for r 0, where E b is the transmitted energy per bit and 2 is the variance of additive noise. Assume that 0 and 1 are equally likely to be transmitted. (a) Derive an expression for the optimal decision rule. Provide the simplest expression you can. (b) Find an expression for the probability of a bit error in terms of E b / 2 . (c) Evaluate this expression for E b / 2 = 1. 2. Consider the 4-PAM signalling scheme with the constellation shown below, which is used for transmission over an AWGN channel with single-sided noise PSD of N ....
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This note was uploaded on 01/25/2011 for the course SCE 5201 taught by Professor Huang during the Spring '10 term at Carleton CA.
- Spring '10