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Consider the detection, using a matched-filter receiver, of the BPSK signals s,(t) = A cos w,t and s2(t) = A cos(@,t + 1) in additive white Gaussian noise with a received E, /N, = 6.8 dB, where A = /2E/T ; E and T denote the symbol energy and period, respectively. Assume that the signals have the same probability of occurrence and that the mean value of the sampled matched-filtered output is equal to ±VE. For this system: a) Detemine the minimum probability of bit error b) Detemine the minimum probability of bit error given that the threshold yopt = 0.1VE c) Now consider that Yopt = 0.1vE is optimum for a particular set of a prior probabilities, P(s,) and P(s2). Determine the values of these probabilities.

Consider the detection, using a matched-filter receiver, of the BPSK signals s,(t) = A cos w,t and s2(t) = A cos(@,t + 1) in additive white Gaussian noise with a received E, /N, = 6.8 dB, where A = /2E/T ; E and T denote the symbol energy and period, respectively. Assume that the signals have the same probability of occurrence and that the mean value of the sampled matched-filtered output is equal to ±VE. For this system: a) Detemine the minimum probability of bit error b) Detemine the minimum probability of bit error given that the threshold yopt = 0.1VE c) Now consider that Yopt = 0.1vE is optimum for a particular set of a prior probabilities, P(s,) and P(s2). Determine the values of these probabilities.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Consider the detection, using a matched-filter receiver, of the BPSK signals s, (t) = A cos w,t and s,(t) = A cos(w,t +n) in additive white Gaussian noise with a received E, /N, = 6.8 dB, where A = /2E /T ; E and T denote the symbol energy and period, respectively. Assume that the signals have the same probability of occurrence and that the mean value of the sampled matched-filtered output is equal to ±VE. For this system: a) Determine the minimum probability of bit error b) Determine the minimum probability of bit error given that the threshold yopt = 0.1VE c) Now consider that Yopt = 0.1VE is optimum for a particular set of a prior probabilities, P(s1) and P(s2). Determine the values of these probabilities.
Transcribed Image Text:Consider the detection, using a matched-filter receiver, of the BPSK signals s, (t) = A cos w,t and s,(t) = A cos(w,t +n) in additive white Gaussian noise with a received E, /N, = 6.8 dB, where A = /2E /T ; E and T denote the symbol energy and period, respectively. Assume that the signals have the same probability of occurrence and that the mean value of the sampled matched-filtered output is equal to ±VE. For this system: a) Determine the minimum probability of bit error b) Determine the minimum probability of bit error given that the threshold yopt = 0.1VE c) Now consider that Yopt = 0.1VE is optimum for a particular set of a prior probabilities, P(s1) and P(s2). Determine the values of these probabilities.
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