Scaling Laws of Cognitive Ad Hoc Networks over General Primary Network Models

We study the capacity scaling laws for the cognitive network that consists of the primary hybrid network (PhN) and secondary ad hoc network (SaN). PhN is further comprised of an ad hoc network and a base station-based (BS-based) network. SaN and PhN are overlapping in the same deployment region, operate on the same spectrum, but are independent with each other in terms of communication requirements. The primary users (PUs), i.e., the ad hoc nodes in PhN, have the priority to access the spectrum. The secondary users (SUs), i.e., the ad hoc nodes in SaN, are equipped with cognitive radios, and have the functionalities to sense the idle spectrum and obtain the necessary information of primary nodes in PhN. We assume that PhN adopts one out of three classical types of strategies, i.e., pure ad hoc strategy, BS-based strategy, and hybrid strategy. We aim to directly derive multicast capacity for SaN to unify the unicast and broadcast capacities under two basic principles: 1) The throughput for PhN cannot be undermined in order sense due to the presence of SaN. 2) The protocol adopted by PhN does not alter in the interest of SaN, anyway. Depending on which type of strategy is adopted in PhN, we design the optimal-throughput strategy for SaN. We show that there exists a threshold of the density of SUs according to the density of PUs beyond which it can be proven that: 1) when PhN adopts the pure ad hoc strategy or hybrid strategy, SaN can achieve the multicast capacity of the same order as it is stand-alone; 2) when PhN adopts the BS-based strategy, SaN can asymptotically achieve the multicast capacity of the same order as if PhN were absent, if some specific conditions in terms of relations among the numbers of SUs, PUs, the destinations of each multicast session in SaN, and BSs in PhN hold.