Heterogeneous cellular networks (HCNs) present an attractive solution to increased demands in mobile user capacity. Comprehensive studies have been conducted in stochastic geometric models that represent the relatively random placement of base transmitting stations (BTSs) operating at different power levels. This study considers the design of two-tier HCNs for which picocell BTSs from the second tier are separated simultaneously from each other and from their tier-1 macrocell counterparts.

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... separations, introduced in detail in the study, are termed the co-tier and cross-tier separations, with each parameter characterised by a minimum distance separation. Subsequently, expressions are obtained for distance distributions of BTSs from specific tiers to typical users, followed by conditional probabilities of association with each tier. We show that a minimum radius of association can be guaranteed for a tier-2 BTS based on the values of co-tier and cross-tier separations. Furthermore, we analyse the Laplace transform of interference to the typical user and the resultant formulae for coverage probability, and by extension, area spectral efficiency. Numerical results demonstrating the effect of co-tier and cross-tier separation on these performance parameters support the analysis and provide insights into cell planning based on this concept. Nomenclature Φ k , λ k set of active BTSs from the kth tier, and the respective density, where k = 1, 2 δ 1, 2 cross-tier separation parameter, which is the minimum distance from any tier-1 BTS to any tier-2 BTS δ 2 co-tier separation parameter, which is the minimum distance between any pair of tier-2 BTSs Φ 2, i , λ 2i largest set of potential tier-2 BTS locations before reduction of locations due to co-tier separation, and its density Φ 2, b , λ 2, b set of all potential tier-2 BTS locations that are separated by δ 2 , before cross-tier separation is imposed and its density x ki location of the ith nearest BTS from the kth tier, taken with respect to the location of the user at the origin X ki variable distance from the user to x ki P k , h x ki transmission power level of the kth tier, and instantaneous fading gain on the signal transmitted by BTS at Probability of an event P A ( ⋅ ) Probability of an event describing the association of a user to a BTS P c ( ⋅ ) Probability of an event describing the coverage of a user associated to a BTS