Load statistics and required spectrum in multi-tier heterogeneous networks

We obtain the minimum bandwidth required to meet an outage constraint in a multi-tier heterogeneous network assuming “maximum (biased) average received signal power” as the tier association metric. To do so, we model user and access point (AP) locations as Poisson point processes, and obtain the moment generating function (MGF) of the required spectrum; this analysis, in turn, is based on the cumulative distribution function of the bandwidth required by a typical user. Using this user load and the distribution of the coverage area of a typical AP, we derive the MGF of the AP load. We consider path loss attenuation and Rayleigh fading on both the desired and interfering signals; however, the expression for the AP load can be generalized to include arbitrarily distributed fading. An application of the results is to relate the AP outage rate and the tiers' allocated bandwidths.