Performance Evaluation of MISO-SDMA in Heterogeneous Networks with Practical Cell Association

In this paper adopting stochastic geometry we investigate the system performance in heterogenous networks including multiple tiers of BSs with multiple-input single output spatial division multiple access (MISO-SDMA) technique. In the related literature on heterogenous systems, ideal cell association (CA) rules are often considered for simplicity, where each user equipment (UE) examines a very large number of pilots across the tiers before choosing its associated base station (BS). Here we consider practical cases where UEs are restricted to examine $K_H \geq 1$ pilots across all tiers before choosing their associated BS. We then obtain closed-form expressions for the system performance measured by the coverage probability and UE's data rate. Our analytical results provide quantitative insights on the impact of different factors on the system performance including the BS's spatial density, their transmission powers, number of transmit antennas, SIR thresholds, number of UEs served by each BS, and $K_H$. Interestingly, we observe that increasing $K_H$ always improves the coverage probability however, it only improves data rate up to a certain point. The data rate is then reduced by further increasing of $K_H$. Given $K_H$ pilots in practical cases, the issue is how to allocate the pilots among different tiers. We address this issue by developing an algorithm and show that by careful allocation of available pilots, the network performance is significantly improved even in cases with small $K_H$. Our results also indicate a fundamental tradeoff, as sharing strategies providing the best coverage performance yield very poor capacity and vice versa. Such trade-off provides a new degree of freedom in heterogeneous networks design.