Three-Dimensional Coprime Array for Massive MIMO: Array Configuration Design and 2D DOA Estimation

Abstract

In massive multiple-input multiple-output (MIMO) systems, it is critical to obtain the accurate direction of arrival (DOA) estimation. Conventional three-dimensional array mainly focuses on the uniform array. Due to the dense arrangement of the sensors, the array aperture is limited and severe mutual coupling effects arise. In this paper, a coprime cubic array (CCA) configuration design is presented, which is composed of two uniform cubic subarrays and can extend the interelement spacing with a selection of three pairs of coprime integers. Compared with uniform cubic array (UCA), CCA achieves the larger array aperture and less MC effects. And the analytical expression of Cramer–Rao Bound (CRB) for CCA is derived which verifies that the proposed CCA geometry outperforms the conventional UCA in two-dimensional (2D) DOA estimation performance in massive MIMO systems. Meanwhile, we propose a computationally efficient 2D DOA estimation algorithm with high accuracy for CCA. Specifically, we utilize array mapping to extract two uniform arrays from the nonuniform array by exploiting the relation derived from the signal subspace and the two directional matrices. Then, we operate a reduced dimension process on the uniform arrays and convert the 2D spectrum peak searching (SPS) problem into one-dimensional (1D) one, which significantly reduces the computational complexity. In addition, we employ the polynomial root finding technique with a lower complexity instead of 1D SPS to further relieve the computational complexity. Simultaneously, with coprime property, the phase ambiguity problem is solved, which results from the large interelement spacing. Numerical simulation results demonstrate that the proposed algorithm is very computationally efficient without degradation of DOA estimation performance.

Massive MIMO systems for 5G: A systematic mapping study on antenna design challenges and channel estimation open issues

“…The reported results show that both the coupled electric and magnetic fields were eliminated, using the FSS decoupling structure. A coprime cubic array (CCA) design configuration is proposed in [29]. The CCA consists of two uniform cubic subarrays, which can extend the antenna element spacing in a given array, by selection of three pairs of coprime integers.…”

Time Division Multiplexing: From a Co-Prime Sampling Point of View

“…Let us consider an example with M = 4, N = 3. In addition, we can assume d = 1 throughout the paper without affecting the behaviour for general values of d. For x 1 (t), the sub-sampler with inter-element spacing N d has samples at locations [0, 3,6,9,12,15,18,21] and sub-sampler with M d spacing has samples at [0, 4,8]. Refer Fig.…”

“…Now for x 2 (t) (Fig. 3b marked in red), the sub-sampler with inter-element spacing N d has samples at locations [0, 3,6,9,12,15,18,21]. This is same as the locations for x 1 (t) hence the self difference matrix is same.…”