The WSSUS Pulse Design Problem in Multicarrier Transmission

TL;DR

This paper develops a mathematical framework for optimizing pulse shapes in multicarrier systems over WSSUS channels, demonstrating potential SINR gains through joint transmitter-receiver design.

Contribution

It introduces a novel trace class operator optimization approach for WSSUS pulse shaping, linking it to quantum fidelity optimization and providing iterative algorithms for large-scale problems.

Findings

3-6 dB SINR gain with channel statistics knowledge

Framework reveals non-convex nature of pulse design

Algorithms applicable to large-scale constellations

Abstract

Optimal link adaption to the scattering function of wide sense stationary uncorrelated mobile communication channels is still an unsolved problem despite its importance for next-generation system design. In multicarrier transmission such link adaption is performed by pulse shaping, i.e. by properly adjusting the transmit and receive filters. For example pulse shaped Offset--QAM systems have been recently shown to have superior performance over standard cyclic prefix OFDM (while operating at higher spectral efficiency).In this paper we establish a general mathematical framework for joint transmitter and receiver pulse shape optimization for so-called Weyl--Heisenberg or Gabor signaling with respect to the scattering function of the WSSUS channel. In our framework the pulse shape optimization problem is translated to an optimization problem over trace class operators which in turn is related to fidelity optimization in quantum information processing. By convexity relaxation the problem is shown to be equivalent to a \emph{convex constraint quasi-convex maximization problem} thereby revealing the non-convex nature of the overall WSSUS pulse design problem. We present several iterative algorithms for optimization providing applicable results even for large--scale problem constellations. We show that with transmitter-side knowledge of the channel statistics a gain of $3 - 6$dB in $\SINR$ can be expected.