Optimality of beamforming condition for multiple antenna systems with mean feedback
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RESEARCH
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Optimality of beamforming condition for multiple antenna systems with mean feedback Wen Zhou1*, Hongyang Chen2 and Wong Hing Lam3
Abstract The necessary and sufficient condition for beamforming optimality for multiple-input multiple output (MIMO) systems with mean feedback has been derived and thoroughly investigated in this article. The condition is an inequality that contains parameters of the number of antennas, transmission power, and the singular values of channel mean matrix. When the beamforming optimality condition is satisfied, the Shannon capacity of MIMO system can be achieved by beamforming and hence scalar codes can therefore be used to achieve the maximum capacity. The channel is modeled as the sum of a scattering matrix of i.i.d zero mean, unit variance complex Gaussian random variables, and a mean matrix having its rank r ≥ 1. The beamforming condition inequality performance versus system parameters of signal-to-noise ratio and Ricean factor have thoroughly been investigated by numerical results. Computer simulations show that the beamforming strategy can be adopted on a relatively relaxed beamforming condition without the loss of capacity performance. Keywords: Multiple-input multiple output (MIMO), beamforming, mean feedback, rank
1. Introduction In the long-term evolution advanced (LTE-A) [1] of the 3rd Generation Partnership Project, multiple-input multiple output (MIMO) has been considered as a key technology in the physical layer. Telatar [2] and Foschini [3] first formulated the system capacity of the MIMO systems assuming independent and identically distributed fading at different antennas. Having acquired the perfect channel state information (CSI) in the MIMO systems, the transmitter performs a linear transform by multiplying the eigenvector of channel matrix and allocating the power of each data stream by waterfilling algorithm, its system capacity can be obtained. When the transmitter has only partial CSI such as the statistical information of the channel, acquiring the optimal transmission covariance matrix and deriving the condition for beamforming optimality are two major obstacles. A few studies on this aspect have been presented [4-11]. For one issue, to achieve maximum system capacity, the optimal transmission of covariance matrix is essential to the optimal transmitter. For another, by verifying whether the beamforming optimality condition is satisfied, we can determine whether the transmitter * Correspondence: [email protected] 1 Department of Electronic Engineering, Shantou University, Shantou, China Full list of author information is available at the end of the article
can adopt the beamforming strategy. If so, the operation at the transmitter will be simplified significantly since exhaustive searching for the optimal power allocation is no longer needed and therefore the scalar codes instead of vector codes can be adopted. Usually, there are two kinds of feedback mechanisms, namely, the mean and the covariance feedbacks [4,6-10]. Visotsky and Madhow [4
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