Multicasting in Stochastic MIMO Networks

Physical-layer multicast transmission, which seeks to deliver information messages to all users simultaneously, is becoming more important in wireless systems with demand for various multimedia mobile applications such as Multimedia Broadcast Multicast Services. The spatial randomness of communicating nodes in a wireless network is one of inevitable uncertainties in the design and analysis of network information flow and connectivity. The use of multiple antennas at both transmitting and receiving nodes is the most promising strategy to increase spectral efficiency and communication reliability as well as to enhance physical-layer confidentiality of wireless systems. In this paper, we characterize multicasting in such a stochastic multiple-input multiple-output (MIMO) network where a probe transmitter broadcasts confidential data with sectorized transmission to legitimate receivers sitting in a region R. We first put forth a measure of the total amount of information flow, called the space-time capacity, into R in a spatial random field of legitimate receivers without accounting for intrinsic confidentiality at the physical layer. We then derive the space-time capacity into the sectoral region R and the nth nearest ergodic capacity in a Poisson field to characterize the spatial average and ordering of MIMO ergodic capacity achieved by legitimate receivers in R. Using the Maru{c}enko-Pastur law, we further assess the asymptotic space-time capacity and the nth nearest ergodic capacity per receive antenna as the antenna numbers tend to infinity. In the presence of eavesdropping, we determine a total amount of confidential information flow per receive antenna, called the space-time secrecy rate, into R in Poisson fields of receiving equivalents-with asymptotic arguments. Using an asymptotic secrecy graph on R, we also characterize local confidential connectivity such as the secrecy range, out-degree, and out-isolation probability of the probe transmitter. The framewor- developed in this work enables us to quantify the local information flow in random MIMO wireless networks by averaging first small-scale fading processes over time and then large-scale path losses over space.