  At present, operators address the explosive growth of mobile data demand by
densification of the cellular network so as to reduce the transmitter-receiver
distance and to achieve higher spectral efficiency. Due to such network
densification and the intense proliferation of wireless devices, modern
wireless networks are interference-limited, which motivates the use of
interference mitigation and coordination techniques. In this work, we develop a
statistical framework to evaluate the performance of multi-tier heterogeneous
networks with successive interference cancellation (SIC) capabilities,
accounting for the computational complexity of the cancellation scheme and
relevant network related parameters such as random location of the access
points (APs) and mobile users, and the characteristics of the wireless
propagation channel. We explicitly model the consecutive events of canceling
interferers and we derive the success probability to cancel the n-th strongest
signal and to decode the signal of interest after n cancellations. When users
are connected to the AP which provides the maximum average received signal
power, the analysis indicates that the performance gains of SIC diminish
quickly with n and the benefits are modest for realistic values of the
signal-to-interference ratio (SIR). We extend the statistical model to include
several association policies where distinct gains of SIC are expected: (i)
minimum load association, (ii) maxi- mum instantaneous SIR association, and
(iii) range expansion. Numerical results show the effectiveness of SIC for the
considered association policies. This work deepens the understanding of SIC by
defining the achievable gains for different association policies in multi-tier
heterogeneous networks.
