Too Much Mobility Limits the Capacity of Wireless Ad Hoc Networks

We show that for highly mobile ad hoc networks, the benefits of mobility are overshadowed by the cost of mobility in terms of the increased channel uncertainty and network homogeneity. We assume a block-fading channel model with jointly isotropic fading. We allow relays which can transmit and receive simultaneously. Under fairly general assumptions for the users' channel fades and additive noise distributions we show that increasing the number of transmit antennas M at any node beyond the channel coherence time T c (measured in units of channel uses) does not affect the capacity region of the ad hoc network. For a fast-fading (coherence time T c lesM) homogeneous network, we determine the exact capacity region of the ad hoc network for any partition of the nodes into source, destination, and relay nodes. The optimal strategy is such that only one pair of source-destination nodes is active at a time while all the other nodes are inactive. There is no benefit from relaying and at high signal-to-noise ratio (SNR) the total throughput grows at most double-logarithmically with the number of nodes. Even for the case of slow fading, where the channel variations are slow enough that the receiver can track the channel perfectly, the inability of the transmitter to track the network topology limits the total throughput growth rate to no more than logarithmic in the number of nodes. Spatial correlation is shown to enhance the capacity region of the Rayleigh-fading ad hoc network