@article{3025149,
    title = "Ergodic capacity optimization for single-stream beamforming transmission in MISO rician fading channels",
    author = "Kontaxis, D.E. and Tsoulos, G.V. and Karaboyas, S.",
    journal = "IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY",
    year = "2013",
    volume = "62",
    number = "2",
    pages = "628-641",
    publisher = "Institute of Electrical and Electronics Engineers, Inc. (IEEE)",
    issn = "0018-9545",
    doi = "10.1109/TVT.2012.2227151",
    keywords = "Algorithms;  Antenna arrays;  Channel capacity;  Constrained optimization;  Covariance matrix;  Rayleigh fading;  Signal to noise ratio;  Transmissions, Beam formers;  Capacity optimization;  Closed form solutions;  Constrained optimi-zation problems;  Ergodic capacity;  Multidimensional optimization;  One dimension;  Operational environments;  Optimum beamforming;  Rician fading channel;  Search Algorithms;  Signaltonoise ratio (SNR);  Transmission schemes, Beamforming",
    abstract = "The maximization of the ergodic capacity for single-stream beamforming, which is a (constrained) transmission scheme referred to as 'optimum beamforming,' has been extensively addressed in the open literature for multiple-input-single-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. © 1967-2012 IEEE."
}