Scaling Laws of Multicast Capacity for Power-Constrained Wireless Networks under Gaussian Channel Model

We study the asymptotic networking-theoretic multicast capacity bounds for random extended networks (REN) under Gaussian channel model, in which all wireless nodes are individually power-constrained. During the transmission, the power decays along path with attenuation exponent \alpha > 2. In REN, n nodes are randomly distributed in the square region of side length \sqrt{n}. There are n_s randomly and independently chosen multicast sessions. Each multicast session has n_d+1 randomly chosen terminals, including one source and n_d destinations. By effectively combining two types of routing and scheduling strategies, we analyze the asymptotic achievable throughput for all n_s=\omega (1) and n_d. As a special case of our results, we show that for n_s=\Theta (n), the per-session multicast capacity for REN is of order \Theta ({1\over \sqrt{n_d n}}) when n_d=O({n\over ({\log n})^{\alpha +1}} ) and is of order \Theta ({1\over n_d} \cdot (\log n)^{-{\alpha \over 2} }) when n_d=\Omega ({n\over \log n} ).