Estimation in the Presence of Doppler Shifts
J.O. Coleman, Jiangsheng You, Hakan Ali Çırpan, M.K. Tsatsanis · 1997
The convergence of LMS adaptive algorithms is typically limited by the eigenvalue spread of a Toeplitz autocorrelation matrix with elements from the central portion of an autocorrelation function. If that autocorrelation function describes a random process input to an FIR filter, the ratio of the filter output power to that obtained in response to a unit-power white input varies, as the filter response is changed, across the closed interval from the minimum eigenvalue to the maximum eigenvalue of the autocorrelation matrix. This simple fact permits important relationships between these extreme eigenvalues and the spectrum at the filter input to be understood easily and without resorting to the classic asymptotic approximation with a cyclic matrix. In particular, we have the following: 1) A pure line spectrum with fewer distinct lines than the matrix order leads to a singular matrix. 2) The spectral minimum/maximum is a lower/upper bound on the minimum/maximum eigenvalue. 3) Those bounds are approached asymptotically with increasing ma- trix order (the classic result). Further, filter-optimization experience may offer the system designer some intuition for the variation of extreme eigenvalues with matrix order and key spectral parameters. Abstract— In this paper, we extend and analyze spatial smoothing with uniform circular arrays (UCA's). In particular, we study the performance of the Root-MUSIC with smoothing in the presence of correlated sources, finite data perturbations, and errors in transformed steering vector that arise due to some approximations made to enable the extension of the Root-MUSIC with smoothing to the UCA. Expressions are derived for the asymptotoic performance of the Root-MUSIC with smoothing applied to the transformed UCA data. An attempt has been made to bring out the impact of both the forward and forward-backward smoothing. We consider UCA's with isotropic as well as directional sensors in our study. Computer simulations are provided to demonstrate the usefullness of the analysis. Abstract— In a previous issue of this TRANSACTIONS, Cadzow proposed an iterative procedure and a one-step procedure to extrapolate a bandlim- ited signal from its limited observations. However, it was found that the convergence's proof of the iterative procedure contains some expressive errors, and the signal needed in the one-step extrapolation procedure does not always exist in general. These errors were pointed out and investigated in this note. Abstract— Transmitter/receiver motion in mobile radio channels may cause frequency shifts in each received path due to Doppler effects. Most blind equalization methods, however, assume time-invariant channels and may not be applicable to fading channels with severe Doppler' spread. In this paper, we address the problem of simultaneously estimating the Doppler shift and channel parameters in a blind setup. Both de- terministic and stochastic maximum likelihood methods are developed and iterative solutions proposed. The stochastic maximum likelihood solution is based on the modified version of the Baum-Welch algorithm, which originated in the study of hidden Markov models. The proposed methods are well suited for short data records, appearing in TDMA systems. Identifiability and performance analysis issues are discussed, and Cramer-Rao bounds are derived. In addition, some illustrative simulations are presented. Abstract— The asymptotic distribution of the deterministic (condi- tional) maximum likelihood estimates of signal parameters is derived by asymptotic properties of the correlation matrix. It is shown that the previously obtained result is valid with weaker assumptions than was assumed. The eigenvalues of the correlation matrix are not restricted to be distinct.