Full-Diversity Space-Time Block Codes for Integer-Forcing Linear Receivers

TL;DR

This paper investigates the design of full-diversity space-time block codes for Integer-Forcing linear receivers in MIMO channels, establishing new criteria and proving the full-diversity property for certain code classes.

Contribution

It introduces the RNVS property as a new criterion for full-diversity STBCs with IF receivers and proves its sufficiency, expanding the class of codes beyond perfect STBCs.

Findings

RNVS property guarantees full-diversity with IF receivers

All known non-vanishing determinant codes satisfy RNVS

Existence of full-diversity codes outside perfect STBCs

Abstract

In multiple-input multiple-output (MIMO) fading channels, the design criterion for full-diversity space-time block codes (STBCs) is primarily determined by the decoding method at the receiver. Although constructions of STBCs have predominantly matched the maximum-likelihood (ML) decoder, design criteria and constructions of full-diversity STBCs have also been reported for low-complexity linear receivers. A new receiver architecture called Integer-Forcing (IF) linear receiver has been proposed to MIMO channels by Zhan et al. which showed promising results for the high-rate V-BLAST encoding scheme. In this paper, we address the design of full-diversity STBCs for IF linear receivers. In particular, we are interested in characterizing the structure of STBCs that provide full-diversity with the IF receiver. Along that direction, we derive an upper bound on the probability of decoding error, and show that STBCs that satisfy the restricted non-vanishing singular value (RNVS) property provide full-diversity for the IF receiver. Furthermore, we prove that all known STBCs with the non-vanishing determinant property provide full-diversity with IF receivers, as they guarantee the RNVS property. By using the formulation of RNVS property, we also prove the existence of a full-diversity STBC outside the class of perfect STBCs, thereby adding significant insights compared to the existing works on STBCs with IF decoding. Finally, we present extensive simulation results to demonstrate that linear designs with RNVS property provide full-diversity for IF receiver.