Optimal Antenna Spacing for Linear Arrays in NLOS MIMO Channels

This paper investigates optimal antenna array configurations for multiple-input-multiple-output (MIMO) systems. The array configuration, particularly the element spacing, significantly affects the correlation between elements, which can lead to channel rank deficiency or deterioration in condition number. In practical sparse channels, deploying a massive number of antenna elements can become redundant. Therefore, exploring optimal array configurations is crucial for enhancing MIMO communication system. Although substantial theoretical analyses have been conducted for antenna configurations in line-of-sight (LOS) environments, analyses in non-line-of-sight (NLOS) environments remain limited. Through theoretical analysis, this paper demonstrates that in NLOS environments, the optimal condition number of MIMO channels is achieved when the antenna array configuration renders the antenna array matrix orthogonal, with the optimal condition number being determined by the wireless propagation environment. Building upon this finding, we show that there always exists an antenna spacing that makes the antenna array matrix orthogonal in a two-cluster environment, and we provide a closed-form solution for this spacing. For three-cluster environments, we derive the conditions that cluster angles must satisfy to achieve antenna array matrix orthogonality and provide a closed-form solution for optimal antenna spacing under these conditions. Furthermore, we propose a systematic solution based on Newton descent algorithm to calculate optimal antenna spacing, aimed at reducing analytical complexity in environments with more clusters. Finally, numerical simulations validate the theoretical analysis and provide recommendations for optimizing antenna placement in IoT devices operating in sparse channel environments.