Signal Detection and Estimation, Second Edition
Packed with over 2,100 equations, 230 figures and 183 problems, this authoritative resource helps you apply the material to projects in the field involving signal processing, radar, and communications.
TABLE OF CONTENTS Signal Detection and Estimation, Second Edition
10.7: BINARY DETECTION IN COLORED NOISE
10.7 BINARY DETECTION IN COLORED NOISE
In the previous sections, we assumed that the additive Gaussian noise is zero mean and white. However, in many applications this assumption is not valid. We now consider detection of signals in nonwhite Gaussian noise. Consequently, the power spectral density is not constant in the filter bandwidth. The noise samples are no longer uncorrelated, and thus they are statistically dependent. One way to deal with this problem is to extend to colored Gaussian noise the concepts using Karhunen-Lo ve expansion for white Gaussian noise. Another way may be to use some preliminary processing for the noise (referred to as whitening) to make the colored noise white, and then use the Karhunen-Lo ve expansion.
The problem under consideration is to design a receiver to test for the general binary detection given by
where Y( t) is the received waveform, s 1( t) and s 0( t) are known deterministic signals, and N( t) is the additive colored Gaussian with mean zero and covariance function C nn ( t, u).
10.7.1 Karhunen-Lo ve Expansion Approach
The solution to the binary detection problem with Gaussian noise was relatively simple, since the coefficients of the Karhunen-Lo ve expansion generated by any set of orthonormal basis function resulted in independent samples. The coefficients Y 1, Y 2, , Y K were statistically independent Gaussian random variables, and thus the likelihood function was the joint probability density function of...
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