Too much mobility limits the capacity of wireless ad-hoc networks

We consider a K user isotropic fast fading ad-hoc network with no channel state information at any transmitter or receiver. Assuming that the users' channels are identically distributed, we determine the capacity region of this ad-hoc network for any partition of the users into transmitters and receivers. The optimal strategy is such that only one pair of transmit-receive nodes is active at a time while all the other nodes are inactive. There is no benefit from cooperation and the total throughput grows at most double-logarithmically with the number of nodes. Even if 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. Our analysis extends Hochwald and Marzetta's single user Rayleigh fading AWGN channel result to show that under the more general model of an isotropic fading ad-hoc network with arbitrary distribution of additive noise there is no capacity benefit from increasing the number of transmit antennas beyond the channel coherence time T_c.