Secure Diversity-Multiplexing Tradeoff of Zero-Forcing Transmit Scheme at Finite-SNR

TL;DR

This paper analyzes the finite-SNR diversity-multiplexing tradeoff of a MIMO wiretap channel using a Zero-Forcing transmit scheme, providing bounds and asymptotic analysis to characterize secrecy diversity gains.

Contribution

It introduces a finite-SNR secrecy multiplexing gain definition and derives tight bounds on secrecy diversity gain for ZF schemes in MIMO wiretap channels.

Findings

Upper bound underestimates secrecy diversity gain

Lower bound is tight at high-SNR

Asymptotic analysis confirms the lower bound as the actual secrecy diversity gain

Abstract

In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secrecy multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secrecy diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secrecy diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secrecy diversity gain of the MIMO wiretap channel.