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Capacity Analysis and Optimal Spacing Design for Compact Array Massive MIMO Systems With Finite Aperture

To achieve large-scale antenna deployment in limited space, compact arrays should be widely used. In this letter, we discuss the mathematical relationship between system capacity and the aperture of compact uniform linear arrays (ULAs). In particular, the theoretical analysis benefits from the Marcenko-Pastur law and Toeplitz feature of the mutual coupling and correlation matrices. The element spacing optimization problem is then formulated to maximize the system capacity under a finite aperture. After illustrating its convexity, the optimal spacing can be obtained by applying one-dimensional search methods. Further, the discussions can be readily extended to compact uniform planar arrays (UPAs) with finite apertures. Numerical results show the superiority of optimal spacing in system capacity for both ULAs and UPAs to half-wavelength spacing.