发表机构
University of Tennessee, Knoxville; University of California, San Diego（田纳西大学诺克斯维尔分校; 加州大学圣地亚哥分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对方形比值的MIMO信道，通过三角参数化方法获得有限SNR下容量的闭式解，填补了该比值仅能数值计算的空白，还给出了低SNR下容量斜率的闭式结果。
AI 中文摘要
针对经典的独立同分布（IID）单用户多输入多输出（MIMO）信道，当发射端拥有完整的信道状态信息（CSIT）时，每个接收天线的渐近容量是对马尔琴科-帕斯图尔（Marčenko-Pastur）分布的注水积分，其形状仅取决于发射天线数与接收天线数的比值。对于除方形比值外的所有比值，闭式解均已存在；而对于方形比值，仅在有限信噪比（SNR）以上存在闭式解。方形比值表现不同是因为马尔琴科-帕斯图尔分布的支撑集延伸至原点，此时注水截止点在所有有限SNR下均严格处于支撑集内部，且注水电平仅能通过数值方法获取。本研究通过对方形分布采用经典三角参数化方法填补了这一空白，该方法消除了边缘奇异性，将移动截止点替换为单一角度。SNR和容量均成为该角度的显式函数，因此容量曲线可通过扫描角度而非在每个工作点求解标量约束来绘制。该参数化方法还以闭式解形式给出了低SNR下的特性，此时容量相对于SNR的斜率等于极限频谱的上边缘。
英文摘要
For the canonical independent and identically distributed (IID) single-user multiple-input multiple-output (MIMO) channel with full channel state information at the transmitter (CSIT), the asymptotic capacity per receive antenna is a waterfilling integral over the Marčenko-Pastur law, whose shape depends only on the ratio of transmit to receive antennas. Closed forms are known for every ratio other than the square one, and there only above a finite signal-to-noise ratio (SNR). The square ratio behaves differently because the Marčenko-Pastur support reaches the origin. The waterfilling cutoff then stays strictly inside the support at every finite SNR, and the water level has been available only numerically. This letter closes that gap with a classical trigonometric parametrization of the square law, which removes the edge singularity and replaces the moving cutoff by a single angle. Both the SNR and the capacity become explicit functions of that angle, so the capacity curve is traced by sweeping the angle rather than by solving a scalar constraint at each operating point. The same parametrization delivers the low-SNR behavior in closed form, where the slope of capacity in SNR equals the upper edge of the limiting spectrum.
