Sensitivity and asymptotic analysis of inter-cell interference against pricing for multi-antenna base stations

We thoroughly investigate the downlink beamforming problem of a two-tier network in a reversed time-division duplex system, where the interference leakage from a tier-2 base station (BS) toward nearby uplink tier-1 BSs is controlled through pricing. We show that soft interference control through the pricing mechanism does not undermine the ability to regulate interference leakage while giving flexibility to sharing the spectrum. Then, we analyze and demonstrate how the interference leakage is related to the variations of both the interference prices and the power budget. Moreover, we derive a closed-form expression for the interference leakage in an asymptotic case, where both the charging BSs and the charged BS are equipped with a large number of antennas, which provides further insights into the lowest possible interference leakage that can be achieved by the pricing mechanism.