A Diversity Guarantee and SNR Performance for Unitary Limited Feedback MIMO Systems
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Research Article A Diversity Guarantee and SNR Performance for Unitary Limited Feedback MIMO Systems Bishwarup Mondal and Robert W. Heath Jr. Department of Electrical and Computer Engineering, The University of Texas at Austin, University Station C0803, Austin, TX 78712, USA Correspondence should be addressed to Robert W. Heath Jr., [email protected] Received 16 June 2007; Accepted 26 October 2007 Recommended by David Gesbert A multiple-input multiple-output (MIMO) wireless channel formed by antenna arrays at the transmitter and at the receiver offers high capacity and significant diversity. Linear precoding may be used, along with spatial multiplexing (SM) or space-time block coding (STBC), to realize these gains with low-complexity receivers. In the absence of perfect channel knowledge at the transmitter, the precoding matrices may be quantized at the receiver and informed to the transmitter using a feedback channel, constituting a limited feedback system. This can possibly lead to a performance degradation, both in terms of diversity and array gain, due to the mismatch between the quantized precoder and the downlink channel. In this paper, it is proven that if the feedback per channel realization is greater than a threshold, then there is no loss of diversity due to quantization. The threshold is completely determined by the number of transmit antennas and the number of transmitted symbol streams. This result applies to both SM and STBC with unitary precoding and confirms some conjectures made about antenna subset selection with linear receivers. A closed form characterization of the loss in SNR (transmit array gain) due to precoder quantization is presented that applies to a precoded orthogonal STBC system and generalizes earlier results for single-stream beamforming. Copyright © 2008 B. Mondal and R. W. Heath Jr. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Linear precoding uses channel state information (CSI) at the transmitter to provide high data rates and improved diversity with low complexity receivers in multiple-input multipleoutput (MIMO) wireless channels [1, 2]. The main idea of linear precoding is to customize the array of transmit signals by premultiplication with a spatial precoding matrix [3–8]. While precoding can be performed based on instantaneous CSI [9–19] or statistical CSI [20–23], the benefits are more in the instantaneous case assuming the CSI is accurate at the transmitter. Unfortunately, the system performance in terms of diversity and signal-to-noise ratio (SNR) depends crucially on the accuracy of CSI at the transmitter. In a limited feedback system, precoder information is quantized at the receiver and sent to the transmitter via a feedback channel [9– 17]. In such a system quantization errors significantly impact the system performance and this motivates the present investigation.
Prior work
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