Adaptive Equalization for Periodically VaryingFading Channels

The problem of identification and tracking of periodically varying systems is considered. Multipath fading channel imposes significant constraints and limitations on wireless communication applications. When the multipath is caused by a few strong reflectors, the channel behaves as a system with poly-periodically timevarying response. The channel impulse response is then modeled by a linear combination of a finite set of complex exponentials whose frequencies are termed by Doppler frequencies. This model is well-motivated in radio cellular telephony and aeronautical radio communication. While the system coefficients start varying rapidly in time, the commonly used adaptive least mean squares (LMS) and weighted least squares (WLS) algorithms are unable to track the variations effectively. The key point is to employ basis functions (BF) expansion algorithms, which are more specialized adaptive filters. Unfortunately, this type of estimators is numerically very demanding and has a limited mean square estimation error (MSE) performance. This thesis explores two existing adaptive equalization algorithms, namely, exponentially weighted basis function (EWBF), gradient basis function Gradient-BF, and contributes by proposing a new efficient BF estimator termed as recursive inverse basis function (RIBF) estimator. Furthermore, a frequency-adaptive version of RIBF estimator is derived. Computer simulations are carried out, using Matlab software package, to evaluate the proposed RIBF estimator performance. The new BF estimator outperforms the EWBF estimator by large computational complexity savings. Moreover, RIBF is superior to the Gradient-BF and EWBF estimators since it shows further reduction in the mean square parameter estimation error. These advantages results in significant gains when applied in wireless communications to reduce BER, SNR and channel bandwidth requirements.