Relationship between time reversal and linear equalization in digital communications

Abstract

Iterative time reversal has been suggested as both an efficient method of creating a spatio-temporal focus and for use in telecommunications as a form of equalization. In this paper, the equivalence of a passive, i.e., via computation, iterative time reversal to the Moore-Penrose pseudo-inverse of the propagation matrix is shown. In the context of communications, however, any received signal is corrupted by noise. Therefore, a regularization term is introduced to the iterative equations, causing convergence to the canonical minimum mean-squared error linear equalizer. Hence, a relationship between time reversal and equalization is demonstrated.