Abstract—This paper addresses three issues in the field of ad hoc network capacity: the impact of i) channel fading, ii) channel inversion power control, and iii) threshold–based scheduling on capacity. Channel inversion and threshold scheduling may be viewed as simple ways to exploit channel state information (CSI) without requiring cooperation across transmitters. We use the transmission capacity (TC) as our metric, defined as the maximum spatial intensity of successful simultaneous transmissions subject to a constraint on the outage probability (OP). By assuming the nodes are located on the infinite plane according to a Poisson process, we are able to employ tools from stochastic geometry to obtain asymptotically tight bounds on the distribution of the signal-to-interference (SIR) level, yielding in turn tight bounds on the OP (relative to a given SIR threshold) and the TC. We demonstrate that in the absence of CSI, fading can significantly reduce the TC and somewhat surprisingly, channel inversion only makes matters worse. We develop a threshold-based transmission rule where transmitters are active only if the channel to their receiver is acceptably strong, obtain expressions for the optimal threshold, and show that this simple, fully distributed scheme can significantly reduce the effect of fading. Index Terms—Ad hoc networks, channel inversion, fading, threshold scheduling, transmission capacity (TC). I.

Abstract—We study the multicast capacity of large-scale random extended multihop wireless networks, where a number of wireless nodes are randomly located in a square region with side length a = p n, by use of Poisson distribution with density 1. All nodes transmit at a constant power P, and the power decays with attenuation exponent> 2. The data rate of a transmission is determined by the SINR as B log(1 + SINR), where B is the bandwidth. There are ns randomly and independently chosen multicast sessions. Each multicast session has k randomly chosen terminals. n We show that when k 1 and ns (log n) 2n 1=2+, the capacity that each multicast p session can achieve, with high proba-n bility, is at least c8 p, where 1, 2, and c8 are some special con-n k stants and> 0 is any positive real number. We also show that for k = O( n), the per-flow multicast capacity under Gaussian log n p n channel is at most O ( p) when we have at least ns = (log n) n k random multicast flows. Our result generalizes the unicast capacity for random networks using percolation theory.

In this paper, we study the multicast capacity of a large scale random wireless network. We simply consider the extended multihop network, where a number of wireless nodes vi(1 ≤ i ≤ n) are randomly located in a square region with side-length a = √ n, by use of Poisson distribution with density 1. All nodes transmit at constant power P, and the power decays along path, with attenuation exponent α> 2. The data rate of a transmission is determined by the SINR as B log(1 + SINR). There are ns randomly and independently chosen multicast sessions. Each multicast has k ran-n domly chosen terminals. We show that, when k ≤ θ1 (log n) 2α+6, and ns ≥ θ2n 1/2+β, the capacity that each multicast session can n achieve, with high probability, is at least c8 √ , where θ1, θ2, ns k and c8 are some special constants and β> 0 is any positive real number. Our result generalizes the unicast capacity [3] for random networks using percolation theory.

Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communication-theoretic results accounting for the network’s geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs – including point process theory, percolation theory, and probabilistic combinatorics – have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue.

Abstract — We study two distinct, but overlapping, networks which operate at the same time, space and frequency. The first network consists of randomly distributed primary users, which form either an ad hoc network, or an infrastructuresupported ad hoc network in which additional base stations support the primary users. The second network consists of randomly distributed secondary or cognitive users. The primary users have priority access to the spectrum and do not change their communication protocol in the presence of secondary users. The secondary users, however, need to adjust their protocol based on knowledge about the locations of the primary users so as not to harm the primary network’s scaling law. Base on percolation theory, we show that surprisingly, when the secondary network is denser than the primary network, both networks can simultaneously achieve the same throughput scaling law as a stand-alone ad hoc network. I.

Abstract—In this paper, we focus on the networking-theoretic multicast capacity for both random extended networks (REN) and random dense networks (RDN) under Gaussian Channel model, when all nodes are individually power-constrained. During the transmission, the power decays along path with the attenuation exponent α> 2. In REN and RDN, n nodes are randomly distributed in the square region with side-length √ n and 1, respectively. We randomly choose ns nodes as the sources of multicast sessions, and for each source v, we pick uniformly at random nd nodes as the destination nodes. Based on percolation theory, we propose multicast schemes and analyze the achievable throughput by considering all possible values of ns and nd. As a special case of our results, we show that for ns = Θ(n), the 1 per-session multicast capacity of RDN is Θ ( √ ndn) when nd = n O( (log n) 3) and is Θ ( 1) when nd = Ω( n n); the per-session log n 1 multicast capacity of REN is Θ ( √ ndn) when nd n = O( (log n) α+1) and is Θ ( 1 · (log n) nd − α 2) when nd = Ω ( n log n).

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Cognitive radios hold tremendous promise for increasing spectral efficiency in wireless systems. This paper surveys the fundamental capacity limits and associated transmission techniques for different wireless network design paradigms based on this promising technology. These paradigms are unified by the definition of a cognitive radio as an intelligent wireless communication device that exploits side information about its environment to improve spectrum utilization. This side information typically comprises knowledge about the activity, channels, codebooks and/or messages of other nodes with which the cognitive node shares the spectrum. Based on the nature of the available side information as well as a priori rules about spectrum usage, cognitive radio systems seek to underlay, overlay or interweave the cognitive radios ’ signals with the transmissions of noncognitive nodes. We provide a comprehensive summary of the known capacity characterizations in terms of upper and lower bounds for each of these three approaches. The increase in system degrees of freedom obtained through cognitive radios is also illuminated. This information theoretic survey provides guidelines for the spectral efficiency gains possible through cognitive radios, as well as practical design ideas to mitigate the coexistence challenges in today’s crowded spectrum.

Abstract — n source and destination pairs randomly located in a fixed area want to communicate with each other. It is well known that classical multihop architectures that decode and forward packets can deliver at most a √ n-scaling of the aggregate throughput. The performance is limited by the mutual interference between communicating nodes. We show however that a linear scaling of the capacity with n can in fact be achieved by more intelligent node cooperation and distributed MIMO communication. The key ingredient is a hierarchical and digital architecture for nodal exchange of information for realizing the cooperation. I.

Abstract—We present the first unified modeling framework for the computation of the throughput capacity of random wireless ad hoc networks in which information is disseminated by means of unicast routing, multicast routing, broadcasting, or different forms of anycasting. We introduce (n, m, k)-casting as a generalization of all forms of one-to-one, one-to-many and many-to-many information dissemination in wireless networks. In this context, n, m, and k denote the total number of nodes in the network, the number of destinations for each communication group, and the actual number of communication-group members that receive information (i.e., k ≤ m), respectively. We compute upper and lower bounds for the (n, m, k)cast throughput capacity in random wireless networks. When m = k = Θ(1), the resulting capacity equals the well-known capacity result for multi-pair unicasting by Gupta and Kumar. We demonstrate that Θ(1 / √ mn log n) bits per second constitutes a tight bound for the capacity of multicasting (i.e., m = k < n) when m ≤ Θ (n/(log n)). We show that the multicast capacity of a wireless network equals its capacity for multi-pair unicasting when the number of destinations per multicast source is not a function of n. We also show that the multicast capacity of a random wireless ad hoc network is Θ (1/n), which is the broadcast capacity of the network, when m ≥ Θ(n / log n). Furthermore, we show that Θ ( √ m/(k √ n log n)), Θ(1/(k log n)) and Θ(1/n) bits per second constitutes a tight bound for the throughput capacity of multicasting (i.e., k < m < n) when Θ(1) ≤ m ≤ Θ (n / log n), k ≤ Θ (n / log n) ≤ m ≤ n and Θ (n / log n) ≤ k ≤ m ≤ n respectively.