{"department":[{"_id":"263"}],"type":"journal_article","user_id":"43497","author":[{"last_name":"Schreier","full_name":"Schreier, Peter J.","first_name":"Peter J."},{"last_name":"Scharf","full_name":"Scharf, Louis L.","first_name":"Louis L."},{"full_name":"Mullis, Clifford T.","last_name":"Mullis","first_name":"Clifford T."}],"issue":"1","volume":51,"title":"Detection and estimation of improper complex random signals","year":"2005","date_created":"2023-01-30T11:52:08Z","date_updated":"2023-01-30T11:53:47Z","doi":"10.1109/TIT.2004.839538","status":"public","_id":"40896","citation":{"apa":"Schreier, P. J., Scharf, L. L., &#38; Mullis, C. T. (2005). Detection and estimation of improper complex random signals. <i>IEEE Trans.\\ Inform.\\ Theory</i>, <i>51</i>(1), 306–312. <a href=\"https://doi.org/10.1109/TIT.2004.839538\">https://doi.org/10.1109/TIT.2004.839538</a>","ieee":"P. J. Schreier, L. L. Scharf, and C. T. Mullis, “Detection and estimation of improper complex random signals,” <i>IEEE Trans.\\ Inform.\\ Theory</i>, vol. 51, no. 1, pp. 306–312, 2005, doi: <a href=\"https://doi.org/10.1109/TIT.2004.839538\">10.1109/TIT.2004.839538</a>.","chicago":"Schreier, Peter J., Louis L. Scharf, and Clifford T. Mullis. “Detection and Estimation of Improper Complex Random Signals.” <i>IEEE Trans.\\ Inform.\\ Theory</i> 51, no. 1 (2005): 306–312. <a href=\"https://doi.org/10.1109/TIT.2004.839538\">https://doi.org/10.1109/TIT.2004.839538</a>.","short":"P.J. Schreier, L.L. Scharf, C.T. Mullis, IEEE Trans.\\ Inform.\\ Theory 51 (2005) 306–312.","ama":"Schreier PJ, Scharf LL, Mullis CT. Detection and estimation of improper complex random signals. <i>IEEE Trans\\ Inform\\ Theory</i>. 2005;51(1):306–312. doi:<a href=\"https://doi.org/10.1109/TIT.2004.839538\">10.1109/TIT.2004.839538</a>","mla":"Schreier, Peter J., et al. “Detection and Estimation of Improper Complex Random Signals.” <i>IEEE Trans.\\ Inform.\\ Theory</i>, vol. 51, no. 1, 2005, pp. 306–312, doi:<a href=\"https://doi.org/10.1109/TIT.2004.839538\">10.1109/TIT.2004.839538</a>.","bibtex":"@article{Schreier_Scharf_Mullis_2005, title={Detection and estimation of improper complex random signals}, volume={51}, DOI={<a href=\"https://doi.org/10.1109/TIT.2004.839538\">10.1109/TIT.2004.839538</a>}, number={1}, journal={IEEE Trans.\\ Inform.\\ Theory}, author={Schreier, Peter J. and Scharf, Louis L. and Mullis, Clifford T.}, year={2005}, pages={306–312} }"},"publication":"IEEE Trans.\\ Inform.\\ Theory","page":"306–312","abstract":[{"lang":"eng","text":"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 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."}],"intvolume":"        51"}