Line-of-Sight $2 \times n_r$ MIMO With Random Antenna Orientations

Abstract

Line-of-sight (LoS) multiple-input multiple-output (MIMO) gives full spatial-multiplexing gain when the antenna array geometry and orientation are designed based on the interterminal distance. These known design methodologies that hold for antenna arrays with fixed orientation do not provide full MIMO gains for arbitrary array orientations. In this paper, we study LoS MIMO channels with random array orientations when the number of transmit antennas used for signaling is 2. We study the impact of common array geometries on error probability, and identify the code design parameter that describes the high signal-to-noise ratio (SNR) error performance of an arbitrary coding scheme. For planar receive arrays, the error rate is shown to decay only as fast as that of a rank 1 channel, and no better than SNR $^{-3}$ for a class of coding schemes that includes spatial multiplexing. We then show that for the tetrahedral receive array, which uses the smallest number of antennas among nonplanar arrays, the error rate decays faster than that of rank 1 channels and is exponential in SNR for every coding scheme. Finally, we design a LoS MIMO system that guarantees a good error performance for all transmit/receive array orientations and over a range of interterminal distances.