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Adaptive recovery of a chirped signal using the RLS algorithm

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3 Author(s)
Wei, P.C. ; Dept. of Electr. & Comput. Eng., California Univ., San Diego, La Jolla, CA, USA ; Zeidler, J.R. ; Ku, W.H.

This paper studies the performance of the recursive least squares (RLS) algorithm in the presence of a general chirped signal and additive white noise. The chirped signal, which is a moving average (MA) signal deterministically shifted in frequency at rate ψ, can be used to model a frequency shift in a received signal. General expressions for the optimum Wiener-Hopf coefficients, one-step recovery and estimation errors, noise and lag misadjustments, and the optimum adaptation constant (βopt) are found in terms of the parameters of the stationary MA signal. The output misadjustment is shown to be composed of a noise (ξ0Mβ/2) and lag term (κ/(β2ψ2)), and the optimum adaptation constant is proportional to the chirp rate as ψ2/3 . The special case of a chirped first-order autoregressive (AR1) process with correlation (α) is used to illustrate the effect the bandwidth (1/α) of the chirped signal on the adaptation parameters. It is shown that unlike for the chirped tone, where the βopt increases with the filter length (M), the adaptation constant reaches a maximum for M near the inverse of the signal correlation (1/α). Furthermore, there is an optimum filter length for tracking the chirped signal and this length is less than (1/α)

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Signal Processing, IEEE Transactions on  (Volume:45 ,  Issue: 2 )