A bidirectional LMS algorithmfor estimation of fast time-varying channels

Yapıcı, Yavuz
Effort to estimate unknown time-varying channels as a part of high-speed mobile communication systems is of interest especially for next-generation wireless systems. The high computational complexity of the optimal Wiener estimator usually makes its use impractical in fast time-varying channels. As a powerful candidate, the adaptive least mean squares (LMS) algorithm offers a computationally efficient solution with its simple first-order weight-vector update equation. However, the performance of the LMS algorithm deteriorates in time-varying channels as a result of the eigenvalue disparity, i.e., spread, of the input correlation matrix in such chan nels. In this work, we incorporate the L MS algorithm into the well-known bidirectional processing idea to produce an extension called the bidirectional LMS. This algorithm is shown to be robust to the adverse effects of time-varying channels such as large eigenvalue spread. The associated tracking performance is observed to be very close to that of the optimal Wiener filter in many cases and the bidirectional LMS algorithm is therefore referred to as near-optimal. The computational complexity is observed to increase by the bidirectional employment of the LMS algorithm, but nevertheless is significantly lower than that of the optimal Wiener filter. The tracking behavior of the bidirectional LMS algorithm is also analyzed and eventually a steady-state step-size dependent mean square error (MSE) expression is derived for single antenna flat-fading channels with various correlation properties. The aforementioned analysis is then generalized to include single-antenna frequency-selective channels where the so-called ind ependence assumption is no more applicable due to the channel memory at hand, and then to multi-antenna flat-fading channels. The optimal selection of the step-size values is also presented using the results of the MSE analysis. The numerical evaluations show a very good match between the theoretical and the experimental results under various scenarios. The tracking analysis of the bidirectional LMS algorithm is believed to be novel in the sense that although there are several works in the literature on the bidirectional estimation, none of them provides a theoretical analysis on the underlying estimators. An iterative channel estimation scheme is also presented as a more realistic application for each of the estimation algorithms and the channel models under consideration. As a result, the bidirectional LMS algorithm is observed to be very successful for this real-life application with its increased but still practical level of complexity, the near-optimal tracking performa nce and robustness to the imperfect initialization.


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Citation Formats
Y. Yapıcı, “A bidirectional LMS algorithmfor estimation of fast time-varying channels,” Ph.D. - Doctoral Program, Middle East Technical University, 2011.