Two Results on the Unicast Capacity of Static Multi-channel Multi-radio Wireless Networks: Separability and Multi-channel Routing

The first result concerns whether the capacity of a static multi-channel multi-radio wireless network is equal to the sum of the capacities of the corresponding single-channel singleradio wireless networks. For the Arbitrary Network model, the former in general is not equal to the latter, i.e., the network capacity is not separable in channels. However, if the number of radio interfaces at each node is equal to the number of channels, the separability property holds provided that the time under consideration is sufficiently long. For the Random Network model, the separability property holds under the same condition. The second result concerns the impact of multi-channel routing (i.e., routing a fixed bit through multiple channels as opposed to a single channel) on the network capacity. For both network models, if again the number of radio interfaces at each node is equal to the number of channels, multi-channel routing does not improve network capacity, but yields the same network capacity as single-channel routing.