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On the minimax robustness of the uniform transmission power strategy in MIMO systems

Shuangqing Wei, D. Goeckel

2003
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IEEE Communications Letters
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In this letter, it is shown that the uniform power allocation across transmit antennas is optimal in the sense that this strategy will maximize the minimum average mutual information of a multiple-inputmultiple-output (MIMO) system across the class of any arbitrary correlated fading channels, with constraints on the the total fixed transmit power (¢ ¤ £ ), total power of the fadings at the transmitter side (¢ ¤ ¥ ), and total power of the fadings at the receiver side (¢ ¤ ¦ ), if the channel
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... te information (CSI) is perfectly known at the receiver side only. Introduction Employing multiple antennas at both the transmitter and receiver of a communication system operating over a narrowband wireless communications channel can significantly increase the Shannon capacity in the scenario with independent fading [1] [2], or correlated fading [3] across different antenna pairs. Consider a MIMO system with § ¤ transmit antennas and § © receive antennas, and let be the fading coefficient between the th transmit antenna and the t h receive antenna. Assume the receiver has the perfect channel state information (CSI), while the transmitter does not have CSI. If and ! , for any disparte pairs , and " , # , are independent complex Gaussian random variables, it is shown in [2] that the optimal strategy to maximize the average mutual information of such a MIMO system is to transmit statistically independent Gaussian codewords across § antennas with equal power $ & % & ' ( § , where $ ) % is the total transmit power. If 0 and ! are correlated, and in addition to lacking CSI, the transmitter is also ignorant of values of the correlations, it is assumed without rigorous justification in [3]-[4] that in order to maximize the average mutual information of a MIMO system under correlated fadings, the uniform power distribution across transmit antennas will "naturally" be employed [3]. In [5], assuming that channel can play the role of a malicious nature by altering fading values to perform an inverse water-filling, it has been shown that the uniform power allocation strategy can maximize the minimum average mutual information of a MIMO system. However, under the constraints only on the variances of the fading values, when the channel can only set correlation properties of fadings, the optimality of the uniform power allocation strategy is still an open problem. In this paper, this strategy will be demonstrated to be minimax robust [6] , which maximizes

doi:10.1109/lcomm.2003.820103
fatcat:au65cgkilrdyfaxmgekguoty7u