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Optimal linear precoding in multi-user MIMO systems: A large system analysis

机译：多用户MIMO系统中的最佳线性预编码：大型系统分析

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We consider the downlink of a single-cell multi-user MIMO system in which the base station makes use of N antennas to communicate with K single-antenna user equipments (UEs) randomly positioned in the coverage area. In particular, we focus on the problem of designing the optimal linear precoding for minimizing the total power consumption while satisfying a set of target signal-to-interference-plus-noise ratios (SINRs). To gain insights into the structure of the optimal solution and reduce the computational complexity for its evaluation, we analyze the asymptotic regime where N and K grow large with a given ratio and make use of recent results from large system analysis to compute the asymptotic solution. Then, we concentrate on the asymptotically design of heuristic linear precoding techniques. Interestingly, it turns out that the regularized zero-forcing (RZF) precoder is equivalent to the optimal one when the ratio between the SINR requirement and the average channel attenuation is the same for all UEs. If this condition does not hold true but only the same SINR constraint is imposed for all UEs, then the RZF can be modified to still achieve optimality if statistical information of the UE positions is available at the BS. Numerical results are used to evaluate the performance gap in the finite system regime and to make comparisons among the precoding techniques.
机译：我们考虑了单小区多用户MIMO系统的下行链路，其中基站利用N根天线与随机位于覆盖区域中的K个单天线用户设备（UE）进行通信。特别是，我们专注于设计最佳线性预编码的问题，以在满足一组目标信号干扰加噪声比（SINR）的同时，将总功耗降至最低。为了深入了解最优解的结构并降低计算的复杂度，我们分析了N和K以给定比率增长的渐近形式，并利用大型系统分析的最新结果来计算渐近解。然后，我们集中在启发式线性预编码技术的渐近设计上。有趣的是，事实证明，当SINR要求与平均信道衰减之比对于所有UE相同时，正则归零强制（RZF）预编码器等效于最佳编码器。如果该条件不成立，而是仅对所有UE施加相同的SINR约束，则如果UE位置的统计信息在BS可用，则可以将RZF修改为仍然达到最佳状态。数值结果用于评估有限系统方案中的性能差距，并进行预编码技术之间的比较。

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