On the Diversity Order of Spatial Multiplexing Systems With Transmit Antenna Selection: A Geometrical Approach

Abstract

In recent years, the remarkable ability of multiple-input multiple-output (MIMO) wireless communication systems to provide spatial diversity or multiplexing gains has been clearly demonstrated. For MIMO diversity schemes, it is well known that antenna selection methods that optimize the post-processing signal-to-noise ratio can preserve the diversity order of the original full-size MIMO system. On the other hand, the diversity order achieved by antenna selection in spatial multiplexing (SM) systems, especially those exploiting practical coding and decoding schemes, has not thus far been rigorously analyzed. In this paper, a geometrical framework is proposed to theoretically analyze the diversity order achieved by transmit antenna selection for separately encoded spatial multiplexing systems with linear and decisionfeedback receivers. When two antennas are selected from the transmitter, the exact achievable diversity order is rigorously derived, which previously only appears as conjectures based on numerical results in the literature. If more than two antennas are selected, we give lower and upper bounds on the achievable diversity order. Furthermore, the same geometrical approach is used to evaluate the diversity-multiplexing tradeoff curves for spatial multiplexing systems with transmit antenna selection.

On the Maximal Diversity Order of Spatial Multiplexing With Transmit Antenna Selection

“…Since M L = M U for L = 2 these bounds uniquely determine the maximal diversity in the case of two transmitting antennas and thereby analytically prove some previous observations made in the literature [4], [5]. Further, for the general case where 2 < L < min(N R , N T ) it was in [3] conjectured that the maximal diversity conicides with the lower bound, M L . Herein, we extend the anlysis of [3] by proving this conjecture for the case of the zero forcing (ZF) and ZF-decision-feedback (DF) receivers (with optimal detection ordering).…”

“…The effective noise,ñ, is spatially colored with covariance Q −1 j and the effective post-processing signal to noise ratio (SNR) of the kth data stream is given by [3]. A given data stream, k, is said to be in outage if the post-processing SNR drops below a given threshold, γ > 0 and the diversity order, d…”

“…The system model considered is covered in Section II, mainly in order to the introduce notation. The reader is referred to [3] for details regarding the systems model and a proper motivation of the problem considered. Our main contribution is then given in Section III in the form of Theorem 1.…”

Zero-forcing based MIMO two-way relay with relay antenna selection: Transmission scheme and diversity analysis

“…in (9) and its bounds in (14) are not equivalent in general. In this paper we mainly focus on the simple and effective suboptimal RAS schemes that are derived from the bounds in (14) or…”

“…Although the transmit antenna selection (TAS) with ZF receiver [14], [15], [20], [21] as well as the ZF transceivers [22], [23] have been carefully studied for point-to-point MIMO system, no previous research has been done to analyze RAS's effects in the ZF based MIMO-TWR system with DF protocal. Note that the straightforward analysis is very difficult, we carefully build the equivalent relation between the end-to-end diversity order and the BC phase diversity order.…”