An ASAPPP Approach to the Spectrum Allocation in General Heterogeneous Cellular Networks

The increasing heterogeneity of cellular networks makes the signal-to-interference-ratio (SIR) distribution challenging to derive, which restricts the further analysis of metrics that depend on it. In this paper, we establish a general heterogeneous cellular network (HCN) model to investigate the problem of spectrum allocation to the different tiers and propose an equivalent orthogonal network (EON) model to formulate the optimization problems. Specifically, we first employ the ASAPPP method which refers to “an approximate SIR analysis based on the Poisson point process” to provide accurate approximations to the spectral and energy efficiency in the EON. The approximations are then applied to spectrum allocation optimization problems, where the optimal SIR thresholds are derived, and, in turn, the optimal solutions are obtained that maximize the area spectral efficiency (ASE) and network energy efficiency (NEE), respectively. Interestingly, the optimal SIR threshold can be well approximated by an extremely simple expression that merely depends on the path loss exponent alone. The results indicate that neither full spectrum sharing nor full spectrum partitioning is optimal for all network parameters, such as density, transmit power, and so on, in terms of both the ASE and NEE. Instead, a hybrid scheme may perform the best. Moreover, different constraints on the spectrum efficiency can have a drastic impact on the performance of spectrum allocation schemes.