A Compressed Sensing Approach to Block-Iterative Equalizers

The universality of underdetermined systems has nurtured a variety of novel compressed sensing (CS) algorithms that ingeniously exploit data sparsity. Whereas well-studied greedy and iterative threshold-based CS recursions take the form of an adaptive filter followed by a proximal operator, this is no different in spirit from the role of block iterative equalizers, where structure is roughly exploited by the signal constellation slicer. By capitalizing on the intrinsic sparsity of signal modulations, we approach the concept of interblock interference (IBI) more proficiently in light of CS concepts, where the optimal feedback of detected symbols is devised adaptively. This should be contrasted with standard forms of IBI estimation/cancellation commonly seen in block DFEs, where detection is restricted to a contiguous set of entries within the transmitted vector. A significant consequence of the latter is that, while block transceivers commonly employ some form of redundancy that accounts for IBI, a CS algorithm applied to the same transmitted vector may require no redundancy whatsoever, and is capable of retrieving both target symbol and IBI altogether. The CS-based iterative DFE acts as a more efficient re-estimation procedure, proposed under recursive-least-squares based adaptations. Besides maximizing system throughput, the new algorithms exhibit significantly higher performance when compared to existing methods that focus solely on minimized redundancy. Simulations in several scenarios illustrate the merits of the unified approaches.