On the scalability and capacity of single-user-detection based wireless networks with isotropic antennas

We extend the results of O. Arpacioglu and Z.J. Haas, (2004) on the capacity of single-user-detection based wireless networks, and we determine the implications of our results on the scalability of such networks. In particular, we consider a wireless network of N nodes that are equipped with isotropic antennas. The nodes are stationary or moving arbitrarily in a network domain of an arbitrary one, two, or three dimensional shape, as opposed to the two dimensional circular domain in O. Arpacioglu and Z.J. Haas, (2004). In this arbitrary dimensional setting, we derive bounds on the per node end-to-end throughput capacity and the maximum number of simultaneous transmissions whose SINRs exceed a given threshold. We derive these bounds with both the bounded propagation model in O. Arpacioglu and Z.J. Haas, (2004) and a large class of bounded propagation models, which we refer to as the general propagation model. Our results show that with the general propagation model, the maximum number of simultaneous transmissions, whose SINRs exceed the threshold has an upper bound that does not depend on N, and the per node end-to-end throughput capacity is O(1/N) for a large class of wireless networks. Moreover, we establish several required conditions for scalability. These conditions show that, for any propagation model, to achieve a desired per node end-to-end throughput as N grows, it is necessary to keep the average source-to-destination hop count bounded. Also, for the particular propagation model of O. Arpacioglu and Z.J. Haas, (2004), we show that the size of the network domain must grow with N at a rate that depends on the dimension of the network domain and the path loss exponent