Multiple-input multiple-output (MIMO) has become a key technology for contemporary wireless communication systems. For typical MIMO systems, antenna arrays are separated by half of the signal wavelength, which are termed collocated arrays. In this paper, we ask the following question: For future wireless communication systems, is it possible to achieve better performance than collocated arrays by using sparse arrays, whose element spacing is larger than half wavelength? The answer to this question is not immediately clear since while sparse arrays may achieve narrower beam for the main lobe, they also generate undesired grating lobes. In this paper, we show that the answer to the above question is affirmative. To this end, we first provide an insightful explanation by investigating the key properties of beam patterns of sparse and collocated arrays, together with the typical distribution of spatial angle difference \Delta, which all critically impact the inter-user interference (IUI). In particular, we show that sparse arrays are less likely to experience severe IUI than collocated arrays, since the probability of \Delta typically reduces with the increasing of |\Delta|. This naturally helps to reject those higher-order grating lobes of sparse arrays, especially when users are densely located. Then we provide a rigorous derivation of the achievable data rate for sparse and collocated arrays, and derive the condition under which sparse arrays strictly outperform collocated counterparts. Finally, numerical results are provided to validate our theoretical studies.

翻译：多输入多输出（MIMO）已成为当代无线通信系统的关键技术。在典型MIMO系统中，天线阵列的单元间距为信号波长的一半，这类阵列被称为共置阵列。本文探讨如下问题：对于未来无线通信系统，能否通过使用单元间距大于半波长的稀疏阵列获得优于共置阵列的性能？这一问题的答案并非显而易见，因为稀疏阵列虽能实现更窄的主瓣波束，但也会产生不期望的栅瓣。本文证明上述问题的答案是肯定的。为此，我们首先通过研究稀疏阵列与共置阵列波束图的关键特性，以及空间角度差Δ的典型分布，对影响用户间干扰（IUI）的关键因素进行深入解释。特别地，我们证明稀疏阵列比共置阵列更不易遭受严重IUI，因为Δ概率通常随|Δ|增大而减小。这自然有助于抑制稀疏阵列的高阶栅瓣，尤其是当用户密集分布时。随后，我们严格推导了稀疏阵列与共置阵列的可达数据速率，并给出了稀疏阵列严格优于共置阵列的条件。最后，通过数值结果验证了理论分析。