Detection and estimation of improper complex random signals

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