Asymptotically optimum detection for large wireless networks with fading

This paper proves that CDMA with beam forming single user detection (SUD-CDMA) is asymptotically optimum, even if it is done on a user by user basis (naive CDMA), for many large wireless networks in the presence of unknown fading. The paper models the transmitters and receivers as uniformly distributed over a grid in a 3-D, 2-D or 1-D universe and allows every transmitter to broadcast to all receivers with a power inversely proportional to the second, third or the fourth power of its distance from the receiver. The channel between the transmitters and the receivers is a fading channel where the receivers do not have any knowledge of the fading realizations. The introduction of unknown fading (even if very slow) and interference from all the transmitters make the model and hence the result of this paper fundamentally different from previous results. The paper proves that, when the number of users increases while keeping the network expanse constant SUD-CDMA is optimal irrespective of the geometry of the network or the path loss exponent. When the number of users increases while keeping the network density constant SUD-CDMA is optimal for most geometries when the path loss exponent is low.