Universal Linear Precoding for NBI-Proof Widely Linear Equalization in MC Systems

In multicarrier (MC) systems, transmitter redundancy, which is introduced by means of finite-impulse response (FIR) linear precoders, allows for perfect or zero-forcing (ZF) equalization of FIR channels (in the absence of noise). Recently, it has been shown that the noncircular or improper nature of some symbol constellations offers an intrinsic source of redundancy, which can be exploited to design efficient FIR widely-linear (WL) receiving structures for MC systems operating in the presence of narrowband interference (NBI). With regard to both cyclic-prefixed and zero-padded transmission techniques, it is shown in this paper that, with appropriately designed precoders, it is possible to synthesize in both cases WL-ZF universal equalizers, which guarantee perfect symbol recovery for any FIR channel. Furthermore, it is theoretically shown that the intrinsic redundancy of the improper symbol sequence also enables WL-ZF equalization, based on the minimum mean output-energy criterion, with improved NBI suppression capabilities. Finally, results of numerical simulations are presented, which assess the merits of the proposed precoding designs and validate the theoretical analysis carried out.