Analysis on Transmit Antenna Selection for Spatial Multiplexing Systems: A Geometrical Approach

TL;DR

This paper introduces a geometric framework to analyze the diversity order in transmit antenna selection for spatial multiplexing MIMO systems, providing theoretical bounds and insights into the diversity-multiplexing tradeoff.

Contribution

It offers a novel geometric approach to rigorously analyze and bound the diversity order in transmit antenna selection for spatial multiplexing systems.

Findings

Achieves a diversity order of (Nt-1)(Nr-1) with 2 antennas selected.

Provides bounds for diversity order when selecting more than 2 antennas.

Evaluates diversity-multiplexing tradeoff curves using the proposed geometric approach.

Abstract

Recently, the remarkable potential of a multiple-input multiple-output (MIMO) wireless communication system was unveiled for its ability to provide spatial diversity or multiplexing gains. For MIMO diversity schemes, it is already known that. by the optimal antenna selection maximizing the post-processing signal-to-noise ratio, the diversity order of the full system can be maintained. On the other hand, the diversity order achieved by antenna selection in spatial multiplexing systems, especially those exploiting practical coding and decoding schemes, has not been rigorously analyzed thus far. In this paper, from a geometric standpoint, we propose a new framework for theoretically analyzing the diversity order achieved by transmit antenna selection for separately encoded spatial multiplexing systems with linear and decision-feedback receivers. We rigorously show that a diversity order of (Nt-1)(Nr-1) can be achieved for an Nr by Nt SM system when L=2 antennas are selected from the transmit side; while for L>2 scenarios, we give bounds for the achievable diversity order and show that the optimal diversity order is at least (Nt-L+1)(Nr-L+1) . Furthermore, the same geometrical approach can be used to evaluate the diversity-multiplexing tradeoff curves for the considered spatial multiplexing systems with transmit antenna selection.