# Integer-Forcing Linear Receivers: A Design Criterion for Full-Diversity STBCs

## TL;DR

This paper establishes a design criterion for full-diversity space-time block codes (STBCs) when using Integer-Forcing (IF) linear receivers in MIMO channels, demonstrating that NVS property ensures full diversity through theoretical bounds and simulations.

## Contribution

It introduces a new design criterion for full-diversity STBCs tailored for IF linear receivers, extending the understanding of their performance in MIMO systems.

## Key findings

- NVS property ensures full diversity for IF receivers.
- Derived an upper bound on decoding error probability.
- Simulation confirms linear designs with NVS achieve full diversity.

## 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 work we address the design of full-diversity STBCs for IF linear receivers. We derive an upper bound on the probability of decoding error, and show that STBCs that satisfy the non-vanishing singular value (NVS) property provide full-diversity for the IF receiver. We also present simulation results to demonstrate that linear designs with NVS property provide full diversity for IF receiver. As a special case of our analysis on STBCs, we present an upper bound on the error probability for the V-BLAST architecture presented by Zhan \emph{et al.}, and demonstrate that the IF linear receivers provide full receive diversity. Our results supplement the existing outage probability based results for the IF receiver.