The fundamental limits of over-the-air computation (AirComp) are explored in a two-transmitter, two-receiver MIMO Gaussian network, where both receivers demand the same aggregation of source symbols originating at the two transmitters. An AirComp degrees of freedom (ACDoF) metric is defined, constrained by an asymptotic mean-squared error threshold. For a generic MIMO setting where the two transmitters are equipped with $M_1, M_2$ antennas, and the two receivers with $N_1, N_2$ antennas, the AirComp DoF value is shown to be almost surely equal to $\min\{M_1,M_2,N_1,N_2,(1/3)\max\{M_1+M_2,N_1+N_2\}\}$. For SISO settings results are extended beyond generic channels to arbitrary channel realizations. For finite signal-to-noise ratio(SNR) settings, an iterative alternating optimization algorithm is explored.

翻译：本文探讨了在两发射机、两接收机MIMO高斯网络中空中计算（AirComp）的基本极限，其中两个接收机均请求由两个发射机发出的源符号的相同聚合结果。定义了一个受渐近均方误差阈值约束的空中计算自由度（ACDoF）度量。对于一般MIMO场景，即两个发射机分别配备$M_1, M_2$根天线，两个接收机分别配备$N_1, N_2$根天线，空中计算自由度值几乎必然等于$\min\{M_1,M_2,N_1,N_2,(1/3)\max\{M_1+M_2,N_1+N_2\}\}$。对于SISO场景，结果从一般信道推广至任意信道实现。在有限信噪比（SNR）场景下，探索了一种迭代交替优化算法。