sm10_1

Prévia do material em texto

Problem 10.1. Let be the event that a 0 is transmitted and let be the event that a 
0 is received. Define H
0H 0R
1 and R1, similarly for a 1. Express the BER in terms of the 
probability of these events when: 
(a) The probability of a 1 error is the same as the probability of a 0 error. 
(b) The probability of a 1 being transmitted is not the same as the probability of a 0 being 
transmitted. 
 
Solution 
In both cases, the probability of error may be expressed as 
 [ ] ( ) ( ) ( ) ( )001110 HHRHHRerror PPPPP += (1) 
 
(a) The BER is the same as the P[error] and with P(R0|H1) = P(R1/H0) = p then 
 [ ] ( )[ ] pHHperror =+= 01 )( PPP 
 
since P(H1)+P(H0) = 1. 
 
(b) With P(H0) ≠ P(H1), the answer is given by the general result of Eq. (1). 
 
 
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only 
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that 
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.