On sparse multimode zero forcing transceivers

This paper introduces sparse multimode zero forcing transceivers in which a combination of ℓ1-norm minimization and the Farrow structure allows efficient low-cost channel equalization. Specifically, the Farrow structure (i) realizes multimode pulse shaping filters, and (ii) equalizes the amplitude distortion. The phase distortion is equalized using a complex nonlinearphase filter. Consequently, a multimode operation over the (equalized) channel is obtained. The ℓ1-norm minimization allows to efficiently determine the filter orders/coefficients and also to reduce the arithmetic complexity. Besides multimode operation, the Farrow structure also reduces the number of unknown parameters, to be optimized during the filter design.