Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/24622
- Detection and estimation of improper complex random signals
Schreier, Peter J.;
Scharf, L. L.;
Mullis, C. T.
- Nonstationary complex random signals are in general improper (not circularly symmetric), which means that their complementary covariance is nonzero. Since the Karhunen-Love (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 signals 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.
- IEEE Transactions on Information Theory Vol. 51, no. 1, p. 306-312
- Institute of Electrical and Electronics Engineers
improper complex random signal;
widely linear transformations;
- Resource Type
- journal article