On the Multicast Capacity of the Wireless Broadcast Channel

For a multicast network, in which a common source is transmitted to
$N$
users, the problem of maximizing the average rate subject to a coverage constraint (minimum quality of service) is studied. Considering such a network with single-antenna nodes and assuming that the channel state information is available only at the receiver side, the highest expected rate achievable by a random user in the network, called the expected typical rate, is derived in two scenarios: hard coverage constraint and soft coverage constraint. In the first case, the coverage is expressed in terms of the outage probability, while in the second case, the expected rate should satisfy a certain minimum requirement. It is shown that the optimum solution (achieving the highest expected typical rate for given coverage requirements) in both cases is achieved by an infinite layer superposition code for which the optimal power allocation among different layers is derived. The analysis is extended to a scenario with multiple transmit antennas. For the MISO case, a suboptimal coding scheme is proposed, which is shown to be asymptotically optimal, when the number of transmit antennas grows at least logarithmically with the number of users in the network.