Multicast Throughput for Hybrid Wireless Networks under Gaussian Channel Model

We study the multicast capacity for hybrid wireless networks consisting of ordinary ad hoc nodes and base stations under Gaussian Channel model, which generalizes both the unicast and broadcast capacities for hybrid wireless networks. Assume that all ordinary ad hoc nodes transmit at a constant power P, and the power decays along the path, with attenuation exponent \alpha >2. The data rate of a transmission is determined by the Signal to Interference plus Noise Ratio (SINR) at the receiver as B \log (1 + {\rm SINR}). The ordinary ad hoc nodes are placed in the square region {\cal A}(a) of area a according to a Poisson point process of intensity n/a. Then, m additional base stations (BSs) acting as the relaying communication gateways are placed regularly in the region {\cal A}(a ), and are connected by a high-bandwidth wired network. Let a=n and a=1, we construct the hybrid extended network (HEN) and hybrid dense network (HDN), respectively. We choose randomly and independently n_s ordinary ad hoc nodes to be the sources of multicast sessions. We assume that each multicast session has n_d randomly chosen terminals. Three broad categories of multicast strategies are proposed. The first one is the hybrid strategy, i.e., the multihop scheme with BS-supported, which further consists of two types of strategies called connectivity strategy and percolation strategy, respectively. The second one is the ordinary ad hoc strategy, i.e., the multihop scheme without any BS-supported. The third one is the classical BS-based strategy under which any communication between two ordinary ad hoc nodes is relayed by some specific BSs. According to the different scenarios in terms of m, n, and n_d, we select the optimal scheme from the three categories of strategies, and derive the achievable multicast throughput based on the optimal decision.