Subspace approaches for blind equalization and identification

In this thesis we address the problem of blind equalization and identification with special reference to wireless communication systems. The problem of channel equalization has been important right from the days digital communication systems gained prominence. Until recently, most digital communications system could manage with just equalizing the channel once or very infrequently--this supported the use of long training sets for the purpose of equalization. But today the situation is changing. There is rapid growth in wireless systems and they are witnessing a huge increase in the number of users and applications. Due to the limited availability of the radio frequency spectrum, methods to increase the spectrum-efficiency of multiple access wireless networks are becoming more and more important. Apart from approaches like Time Division Multiple Access (TDMA) and Code Division Multiple Access (CDMA), a new approach to combat this problem is the concept of Spatial Division Multiple Access (SDMA) which takes into account the spatial discrimination provided by antenna arrays and allows multiple users located in different directions to share the same channel. Also the increase in efficiency that can be obtained by cutting down on the training sets has become very appealing. Therefore blind channel equalization techniques and methods which can make use of the spatial discrimination provided by an array antenna to simultaneously equalize and separate several co-channel signals have become very important.;In this thesis we develop deterministic algorithms for the blind equalization of systems with single and multiple co-channel users using only the data obtained by oversampling the received signal temporally and spatially. We assume that the user signals are digitally modulated with the same symbol rate and alphabet. The signals from each user arrive at the array antenna (or oversampler) through a multipath propagation channel. In the multiple sources case, the actual received signal is a superimposition of signals from all the users (and of course additive noise). Our objective is to estimate the channel and the information bits of each user, without using training sets. We do this by exploiting both the signal structure inherent in the oversampled received signal as well as the finite alphabet property of the digital signals.;We first study the problem for the single source case. We develop a block based approach (Basic Subspace Algorithm) to obtain an estimate of the transmitted signals using just the structure of the oversampled output data. This algorithm is computationally efficient and requires a very small observation to identify the channel accurately. We derive the identifiability conditions and prove the uniqueness of the estimates. The only problem with this algorithm is that it requires a well-conditioned channel matrix in order to obtain good estimates. We develop an error correcting approach (EC-LS Algorithm) based on the finite alphabet property to overcome this problem. We study and analyze the combined EC-LS Subspace algorithm and demonstrate its performance through simulations.;We next consider the channel equalization problem for the multiple sources case. We extend the ideas developed in the single user case to accommodate several users. The multi-user problem is in addition complicated by the fact that the signal are all mixed and have to be separated. We again resort to the finite alphabet property and develop a search procedure to separate the signals. The effectiveness of this approach is confirmed by simulations.