Full-dimensional (FD) multi-user massive multiple input multiple output (m-MIMO) systems employ large two-dimensional (2D) rectangular antenna arrays to control both the azimuth and elevation angles of signal transmission. We introduce the sum of two outer products of the azimuth and elevation beamforming vectors having moderate dimensions as a new class of FD beamforming. We show that this low-complexity class is capable of outperforming 2D beamforming relying on the single outer product of the azimuth and elevation beamforming vectors. It is also capable of performing close to its FD counterpart of massive dimensions in terms of either the users minimum rate or their geometric mean rate (GM-rate), or sum rate (SR). Furthermore, we also show that even FD beamforming may be outperformed by our outer product-based improper Gaussian signaling solution. Explicitly, our design is based on low-complexity algorithms relying on convex problems of moderate dimensions for max-min rate optimization or on closed-form expressions for GM-rate and SR maximization.
翻译:全维(FD)多用户大规模多输入多重输出(m-MIMO)系统采用大型二维(2D)矩形天线阵列,以控制信号传输的方位角和高角角角;我们采用平方和高波波束矢量中两个外产中度尺寸的合成物之和,作为FD波束成形的新类别;我们表明,这种低复合度等级能够超过2D波束成型,依赖方位和高波形矢量的单外产物;它还能够以用户最低速率或其几何平均速率(GM-速率)或总速率(SR)等大方度的方位接近方位阵形。此外,我们还表明,即使是方位成型也可能因基于外部产品不当的高频信号溶液而超过。我们的设计依据的低兼容性算法,依靠最大速率优化的中等尺寸的方位方位的方位的方位问题或GM-SR最大度和最大方位的闭式表达方式。