Time-Varying FIR Transmultiplexers With Minimum Redundancy

In this paper, we derive conditions for existence of zero-forcing equalizers for FIR transmultiplexers. We extend theoretical results from the literature for zero-forcing equalization in transmultiplexer systems, and derive new conditions for a more general configuration that includes filter-bank based systems with long responses and time-varying filter banks. The time-varying filter banks can be used to model code division multiple access systems with long codes, as well as other practical problems. The results can be applied to both downlink and uplink scenarios, due to the general framework considered for the analysis. The derived relations allow the use of relatively simple equalizers, lead to transmitters using small amount of redundancy, and also allow the transmission through channels with long impulse responses. Experimental results obtained via computer simulations validate the derived expressions. The simulations were carried out for zero-forcing design and also for least-squares and minimum mean squared error designs that use the relations derived for existence of zero-forcing equalizers. The results show that the performance of all equalizers improve if the zero-forcing conditions derived in this paper are followed.