| Abstrakt: |
Nonstationary complex random signals are in general improper (not circularly symmetric), which means that their complementary covariance is nonzero. Since the Karhunen-Loève (K-L) expansion in its known form is only valid for proper processes, we derive the improper version of this expansion. it produces two sets of eigenvalues and improper observable coordinates. We then use the K-L expansion to solve the problems of detection and estimation of improper complex random signal in additive white Gaussian noise. We derive a general result comparing the performance of conventional processing, which ignores complementary covariances, with processing that takes these into account in particular, for the detection and estimation problems considered, we find that the performance gain, as measured by deflection and mean-squared error (MSE), respectively, can be as large as a factor of 2 In a communications example, we show how this finding generalizes the result that coherent processing enjoys a 3-dB gain over noncoherent processing. [ABSTRACT FROM AUTHOR] |
