NDLI: On the joint characteristic function of the complex scalar LMS adaptive weight

Content Provider	IEEE Xplore Digital Library
Author	Bershad, N. Lian Qu
Copyright Year	1974
Abstract	In this paper, the joint characteristic function of the single weight complex scalar LMS adaptive algorithm is studied. An integral equation is derived for the joint characteristic function of the real and imaginary parts of the weight. This integral equation is used to obtain the weight moments and is approximately solved for a sufficiently small adaptation parameter μ. It is shown that, for small μ and in steady state, the real and imaginary parts of the weights are statistically independent Gaussian random variables with means equal to the Wiener weight. These results are applied to a detection problem using the weight magnitude square as the detection statistic. Assuming the weight is also Gaussian during the transient phase of adaptation, the detection performance is optimized over μ for a fixed number of data samples and a known observation interval. The optimum selection of μ approaches zero so that the adaptation process reduces to a cross-correlation operation. When the observation interval is not known a priori, a μ bounded away from zero is required. This detector is shown to be 3 dB degraded from the optimum narrow-band envelope detector using the same number of data samples.
Starting Page	1166
Ending Page	1175
Page Count	10
File Size	804811
File Format	PDF
ISSN	00963518
Volume Number	32
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1984-12-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Least squares approximation Integral equations Envelope detectors Adaptive algorithm Steady-state Random variables Statistics Phase detection Degradation Narrowband
Content Type	Text
Resource Type	Article
Subject	Signal Processing

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