An upper bound on the capacity of multiple-input multiple-output (MIMO) Gaussian fading channels is derived under peak amplitude constraints. The upper bound is obtained borrowing concepts from convex geometry and it extends to MIMO channels notable results from the geometric analysis on the capacity of scalar Gaussian channels. Relying on a sphere packing argument and on the renowned Steiner's formula, the proposed upper bound depends on the intrinsic volumes of the constraint region, i.e., functionals defining a measure of the geometric features of a convex body. The tightness of the bound is investigated at high signal-to-noise ratio (SNR) for any arbitrary convex amplitude constraint region, for any channel matrix realization, and any dimension of the MIMO system. In addition, two variants of the upper bound are proposed: one is useful to ensure the feasibility in the evaluation of the bound and the other to improve the bound's performance in the low SNR regime. Finally, the upper bound is specialized for two practical transmitter configurations, either employing a single power amplifier for all transmitting antennas or a power amplifier for each antenna.
翻译:在峰值振幅限制下,对多投入多重输出能力(MIMO)高斯淡化渠道的上限值来自峰值振幅限制。上界值是从锥形几何学中借款的概念,并扩展到MIMO频道,这通过对斜面高斯海峡频道能力的几何分析得出显著结果。依靠球体包装参数和著名的施泰纳公式,拟议的上界值取决于制约区域的内在量,即功能界定对锥体几何特征的测量。最后,对约束的紧度以高信号对噪音比率(SNR)来调查,对任何任意的锥形振幅限制区域、任何频道矩阵的实现和MIMO系统的任何层面,都采用高端线分析结果。此外,还提出了上界值的两个变式:一个有助于确保评估约束区的可行性,另一个有助于改进低层SNR系统中受约束的性能。最后,上界值是两种实用的发报器配置,即所有传输天线或每个天线都使用单一的电力放大器。