The problem of determining asymptotic bounds on the capacity of a random ad hoc network is considered. Previous approaches assumed a threshold-based link layer model in which a packet transmission is successful if the SINR at the receiver is greater than a fixed threshold. In reality, the mapping from SINR to packet success probability is continuous. Hence, over each hop, for every finite SINR, there is a non-zero probability of packet loss. With this more realistic link model, it is shown that for a broad class of routing and scheduling schemes, a fixed fraction of hops on each route have a fixed non-zero packet loss probability. In a large network, a packet travels an asymptotically large number of hops from source to destination. Consequently, it is shown that the cumulative effect of per-hop packet loss results in a per-node throughput of only O(1 n) (instead of Theta(1 sqrt n log n )) as shown previously for the threshold-based link model). A scheduling scheme is then proposed to counter this effect. The proposed scheme improves the link SINR by using conservative spatial reuse, and improves the per-node throughput to O(1 (K_n sqrt n log n )), where each cell gets a transmission opportunity at least once every K_n slots, and K_n tends to infinity as n tends to infinity.
How much information can be carried over a wireless network with a multiplicity of nodes, and how should the nodes cooperate to transfer information? To study these questions, we formulate a model of wireless networks that particularly takes into account the distances between nodes, and the resulting attenuation of radio signals, and study a performance measure that weights information by the distance over which it is transported. Consider a network with the following features. I) n nodes located on a plane, with minimum separation distance spl rho sub min >0. II) A simplistic model of signal attenuation e sup - spl gamma spl rho spl rho sup spl delta over a distance spl rho , where spl gamma spl ges 0 is the absorption constant (usually positive, unless over a vacuum), and spl delta >0 is the path loss exponent. III) All receptions subject to additive Gaussian noise of variance spl sigma sup 2 . The performance measure we mainly, but not exclusively, study is the transport capacity C sub T :=sup spl Sigma on sub spl lscr =1 sup m R sub spl lscr spl middot spl rho sub spl lscr , where the supremum is taken over m, and vectors (R sub 1 ,R sub 2 ,...,R sub m ) of feasible rates for m source-destination pairs, and spl rho sub spl lscr is the distance between the spl lscr th source and its destination. It is the supremum distance-weighted sum of rates that the wireless network can deliver. We show that there is a dichotomy between the cases of relatively high and relatively low attenuation. When spl gamma >0 or spl delta >3, the relatively high attenuation case, the transport capacity is bounded by a constant multiple of the sum of the transmit powers of the nodes in the network. However, when spl gamma =0 and spl delta <3 2, the low-attenuation case, we show that there exist networks that can provide unbounded transport capacity for fixed total power, yielding zero energy priced communication. Examples show that nodes can profitably cooperate over large distances using coherence and multiuser estimation when the attenuation is low. These results are established by developing a coding scheme and an achievable rate for Gaussian multiple-relay channels, a result that may be of interest in its own right. When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput spl lambda (n) obtainable by each node for a randomly chosen destination is spl Theta (W spl radic (nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is spl Theta (W spl radic An) bit-meters per second. Thus even under optimal circumstances, the throughput is only spl Theta (W spl radic n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance.