Performance Analysis of K-Tier Ultra-Dense Networks over Nakagami-m Fading Channels

Ultra-dense network (UDN) is emerging as a promising technology to satisfy the explosive data traffic requirement in the fifth generation wireless communication systems. In order to facilitate system design and evaluate performance, this paper develops a tractable analysis framework of K-tier UDNs over Nakagami-m fading channels, in which the base stations (BSs) of each tier have a particular spatial density and transmit power. Using stochastic geometry, we derive the closed-form expression of coverage probability for a typical user. The analytical expression reveals the signal-to-interference-plus-noise ratio (SINR) invariance property of UDNs with Rayleigh fading also holds in Nakagami-m fading scenario when each tier has the same fading parameter. The asymptotic expression with a simple form is also provided, from which it is convenient to observe the effects of system parameters on the coverage probability. The simulation results verify the asymptotic form is very accurate for moderate SINR targets, e.g., above 5 dB. The average outage rate of a typical user is also provided. Furthermore, an effective algorithm is proposed to find the optimal SINR threshold, maximizing the average outage rate with appropriate requirements of coverage probability.