Design of ZF and MMSE filter-banks in relay networks with average and peak power constraints

In this paper we consider the design of jointly optimal filter-banks for transmission over frequency selective MIMO relay channels. Utilising block processing we present designs that maximise signal to noise ratio under the zero forcing constraint and minimise the mean square error. Both designs targetted in this paper assume limited power resource at the relaying stage of the network and we resort to techniques from convex optimisation theory to obtain the solutions to the constrained design problems.