Precoding techniques for undersampled multireceiver communication systems

Although there have been extensive studies on the blind equalization problem for temporally or/and spatially oversampled communication signals, the literature is not equally rich for undersampled, and possibly multiuser, wireless systems. In this paper, we investigate the feasibility of blind signal recovery from undersampled data collected from a plurality of receivers. We show that although an undersampled communication system is not completely identifiable in general, such an obstacle can be overcome by employing proper precoding with an arbitrary amount of bandwidth expansion in the transmitter. The main contribution of this paper is the formulation of a generic framework for all undersampled systems and the derivation of necessary and sufficient conditions for a class of filters (which we term ambiguity resistant precoders) that allow the blind recovery of the transmitted signal. A family of such precoders is given. We discuss various related issues and show, for example, that block precoders, i.e., memoryless precoders, are not ambiguity resistant. In addition, we derive an algorithm that can accomplish blind equalization with a finite number of observations.