Per-Antenna Power Distribution of a Zero-Forcing Beamformed ULA in Pure LOS MU-MIMO

Abstract

An analytical model is presented to determine the per-antenna power distribution of a beamformed $M$ -element uniform linear array (ULA) as a base station antenna (BSA). The analysis assumes a single sector cell serving two pieces of user equipment (UE) in a downlink multi-user multiple-input multiple-output system employing zero-forcing transmission. It is shown that the power distribution across the ULA antenna aperture is a periodic function whose characteristics mainly depend on the angular separation of two UEs and the number of BSA antenna elements. A significant variation between ULA input powers is seen to occur if the number of elements in the ULA is smaller than one period of this power distribution function. In order to mitigate the dynamic range of the power variation across the array, an upper bound for the inter-element spacing, depending on the field-of-view of the BSA, is defined. It is shown that, in a 20-element ULA, increasing the inter-element spacing from $0.5\lambda $ to $1.4\lambda $ reduces the power variation from 19 to 10 dB for differentiating two close-by UEs with 1° angular separation.