Ergodic Capacity Optimization for Single-Stream Beamforming Transmission in MISO Rician Fading Channels

Abstract

The maximization of the ergodic capacity for singlestream beamforming, which is a (constrained) transmission scheme referred to as "optimum beamforming," has been extensively addressed in the open literature for multiple-inputsingle-output (MISO) Rayleigh fading channels and spatially uncorrelated MISO Rician fading channels with a unit transmit covariance matrix, and closed-form solutions have been derived for these cases. However, optimum beamforming for spatially correlated or uncorrelated MISO Rician fading channels with a nonunit transmit covariance matrix has received less attention and remains a complex multidimensional optimization problem. This paper first proves that this convex constrained optimization problem can be reduced to only one dimension; hence, it can be solved very fast using standard 1-D search algorithms. Then, simulations mainly performed for linear equispaced antenna arrays demonstrate that: 1) the proposed method for the calculation of the optimum beamformer has significantly lower computational complexity compared with other currently used multidimensional algorithms; and 2) the optimum beamformer further improves capacity compared with the (single-stream) beamforming transmission that maximizes the signal-to-noise ratio (SNR) at the receiver, whereas in some operational environments, it achieves ergodic capacity that is very close or equal to the maximum ergodic capacity. Index Terms-Beamforming, capacity optimization, Rician fading channels.George V. Tsoulos (SM'02) received the M.Eng. degree from National Technical University of Athens, Athens, Greece, and the Ph.D. degree from the University of Bristol, Bristol, U.K.Since the early 1990s, he has been involved in several pioneering research collaborative projects in smart antennas (e.g., TSUNAMI I and II, SUNBEAM) and has worked for a range of leading companies around the world in the design and analysis of advanced wireless communication systems. He is currently an Associate Professor with the Department of Telecommunication Science and Technology, University of Peloponnese, Tripoli, Greece. His research interests include smart antenna/multiple-input-multiple-output systems, Green Wireless Systems, very large antenna array systems, and emerging wireless communication technologies.

Tight Logarithmic Approximations and Bounds for Generic Capacity Integrals and Their Applications to Statistical Analysis of Wireless Systems

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“…[6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [32], [33], [34], [35], [36], [37] has a similar form to that of the Nakagami capacity integral as…”