Multicast Capacity Scaling Laws for Multihop Cognitive Networks

In this paper, we study multicast capacity for cognitive networks. We consider the cognitive network model consisting of two overlapping ad hoc networks, called the primary ad hoc network (PaN) and secondary ad hoc network (SaN), respectively. PaN and SaN operate on the same space and spectrum. For PaN (or SaN, respectively), we assume that primary (or secondary, respectively) nodes are placed according to a Poisson point process of intensity n (or m, respectively) over a unit square region. We randomly choose n_s (or m_s, respectively) nodes as the sources of multicast sessions in PaN (or SaN, respectively), and for each primary source vp (or secondary source v^s, respectively), we pick uniformly at random nd primary nodes (or md secondary nodes, respectively) as the destinations of v^p (or v^s, respectively). Above all, we assume that PaN can adopt the optimal protocol in terms of the throughput. Our main work is to design the multicast strategy for SaN by which the optimal throughput can be achieved, without any negative impact on the throughput for PaN in order sense. Depending on nd and n, we choose the optimal one for PaN from two strategies called percolation strategy and connectivity strategy, respectively. Subsequently, we design the corresponding throughput-optimal strategy for SaN. We derive the regimes in terms of n, n_d, m, and m_d in which the upper bounds on multicast capacities for PaN and SaN can be achieved simultaneously. Unicast and broadcast capacities for the cognitive network can be derived by our results as the special cases by letting n_d = 1 (or m_d = 1) and n_d = n - 1 (or m_d = m - 1), respectively, which enhances the generality of this work.