Analyzing randomly placed multiple antennas for MIMO wireless communication

We present an analytical approach for determining the signal-to-noise-ratio (SNR) of m multiple antennas in the line-of-sight case. The antennas are placed at random positions within a disc of given diameter d. We characterize the angular signal strength with three sectors: the main beam, the side beams and an area of white Gaussian noise. The SNR and the sector angles depend on d, m, and the wavelength λ. It turns out that for randomized antenna positions the analysis can be reduced to the analysis of a random geometric walk in two dimensions. The angle of the main beam is approximately λ/d with a SNR proportional to √m. For the side beams the SNR is proportional to sinc(2αd=λ) where α denotes the angle deviating from the target. The range of the side beams is limited to an approximate angle of λ/d√m. Beyond this angle we observe average white Gaussian noise.