BER and Outage Probability Approximations for LMMSE Detectors on Correlated MIMO Channels

• Published in: IEEE transactions on information theory Vol. 55; no. 10; pp. 4386 - 4397
• Main Authors: Kammoun, A., Kharouf, M., Hachem, W., Najim, J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-10-2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antenna theory; Antennas; Applied sciences; Asymptotic properties; Bit error rate; Bit-error rate (BER); Channels; correlated channels; Correlation; Data transmission; Detectors; Distributed computing; Error analysis; Exact sciences and technology; gamma approximation; Gaussian; Information theory; Information, signal and communications theory; large random matrices; Mathematical analysis; Matrix theory; Mean square errors; Measurement; MIMO; minimum mean-square error (MMSE); multiple-input multiple-output (MIMO); Normal distribution; outage probability; Outages; Radiocommunications; Random variables; Receivers; Receiving antennas; Signal to noise ratio; signal-to-noise ratio (SNR); Telecommunications; Telecommunications and information theory; Transmitting antennas; Performance evaluation; MIMO system; signal-to-noise ratio (SNR); Random matrix; Outage; Bit error rate; Wireless telecommunication; correlated channels; gamma approximation; multiple-input multiple-output (MIMO); large random matrices; minimum mean-square error (MMSE); Mean square error; Gamma distribution; Accuracy; outage probability; Simulation; Transmitting antenna; Matrix method; Metric; Receiving antenna; Random variable; Bit-error rate (BER); Signal to noise ratio
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2009.2025531

This paper is devoted to the study of the performance of the linear minimum mean-square error (LMMSE) receiver for (receive) correlated multiple-input multiple-output (MIMO) systems. By the random matrix theory, it is well known that the signal-to-noise ratio (SNR) at the output of this receiver behaves asymptotically like a Gaussian random variable as the number of receive and transmit antennas converge to + infin at the same rate. However, this approximation being inaccurate for the estimation of some performance metrics such as the bit error rate (BER) and the outage probability, especially for small system dimensions, Li proposed convincingly to assume that the SNR follows a generalized gamma distribution which parameters are tuned by computing the first three asymptotic moments of the SNR. In this paper, this technique is generalized to (receive) correlated channels, and closed-form expressions for the first three asymptotic moments of the SNR are provided. To obtain these results, a random matrix theory technique adapted to matrices with Gaussian elements is used. This technique is believed to be simple, efficient, and of broad interest in wireless communications. Simulations are provided, and show that the proposed technique yields in general a good accuracy, even for small system dimensions.