Univ. Of Maryland at College Park, ECE Department
ENEE324 Fall 2002 Instructor: Masoud Olfat
Quiz #: 4 Section: 0202 date: 10/31/02
Name: ID: Section:
Problem 1. A signal X taking the values -1 and 1 (corresponding to binary values 0 and 1) with
probabilities 1/3 and 2/3 is transmitted over a noisy channel. The noise, Z is
a Gaussian r.v with zero mean and variance
2
σ
. The receiver decodes the
received signal Y=X+Z as 0 if Y<a and 1 otherwise. Find a relation between a and
2
σ
, such that the Bit Error Rate( BER) or the probability of error is below
3
10
−
.
You might not need this, but just in case the pdf of a Gaussian r.v with mean
µ
and variance
2
σ
is:
2
2
()
2
1
() (,)
2
x
X
fxex
µ
σ
πσ
−
−
=∈−∞∞