| As the data rate of a wireless communications system increases, imperfections in the channel begin to have a severe affect on the quality of the received signal. Consequently, almost all modern systems employ some type of channel equalization. Blind or self-recovering methods can estimate the parameters of the equalizer without extra bandwidth for training sequences or the co-operation of the transmitter. In particular, methods based on second-order cyclostationary statistics are attractive because of the ability to use shorter data records than the classic higher-order based methods. By fractionally-sampling the received communications signal, the observed sequence is rendered cyclostationary and second-order output statistics are sufficient for blind equalization of most channels. In this thesis, a blind nonlinear weighted correlation matching procedure for channel estimation is first described and a closed form expression for its asymptotic variance is given. For a particular choice of weights, this nonlinear matching approach gives the minimum variance estimate of the channel among all estimators based on second-order cyclostationary statistics. Furthermore, it provides useful estimates even when the channel is not strictly identifiable from second-order statistics. Next, methods for estimating the equalizer directly (i.e., without first estimating the channel) from the output data are described. These direct methods can be zero-forcing, minimum mean-square error, or even minimum mean-square error within the class of zero-forcing equalizers. In addition to being computationally and statistically more efficient, the direct methods can be made adaptive and thereby track time-varying channels. Since a tacit assumption of many blind equalization methods is that the channel length is known, we present two statistical methods for estimating the channel length. Recently, it was observed that certain types of coding at the transmitter also induced cyclostationarity in the received sequence. The advantage of transmitter induced cyclostationarity over fractional-sampling is that any FIR channel can be identified and equalized with second-order output only statistics. In the second part of this thesis, we explore a variety of methods for blind equalization of communications signals which use transmitter induced cyclostationarity. In addition to being valid for any channel, from a computational viewpoint, some of the methods available for transmitter induced cyclostationarity are extremely simple and, unlike existing blind methods, do not require matrix inversion. |
