A Framework for Transceiver Designs for Multi-Hop Communications with Covariance Shaping Constraints

TL;DR

This paper develops a comprehensive framework for designing MIMO transceivers in multi-hop relay systems under covariance shaping constraints, unifying linear and nonlinear methods with closed-form solutions and simulation validation.

Contribution

It introduces a unified framework for multi-hop MIMO transceiver design under covariance shaping constraints, encompassing linear and nonlinear methods with explicit solutions.

Findings

Closed-form optimal solutions for shaping and power constraints.

Relaying operations as matrix weighting operations.

Performance validation through simulations.

Abstract

For multiple-input multiple-output (MIMO) transceiver designs, sum power constraint is an elegant and ideal model. When various practical limitations are taken into account e.g., peak power constraints, per-antenna power constraints, etc., covariance shaping constraints will act as an effective and reasonable model. In this paper, we develop a framework for transceiver designs for multi-hop communications under covariance shaping constraints. Particularly, we focus on multi-hop amplify-and-forward (AF) MIMO relaying communications which are recognized as a key enabling technology for device-to-device (D2D) communications for next generation wireless systems such as 5G. The proposed framework includes a broad range of various linear and nonlinear transceiver designs as its special cases. It reveals an interesting fact that the relaying operation in each hop can be understood as a matrix version weighting operation. Furthermore, the nonlinear operations of Tomolision-Harashima Precoding (THP) and Decision Feedback Equalizer (DFE) also belong to the category of this kind of matrix version weighting operation. Furthermore, for both the cases with only pure shaping constraints or joint power constraints, the closed-form optimal solutions have been derived. At the end of this paper, the performance of the various designs is assessed by simulations.