In this paper, we study the capacity of cognitive networks. We focus on the network model consisting of two overlapping ad hoc networks, called the primary ad hoc network (PaN) and secondary ad hoc network (SaN), respectively. PaN and SaN operate on the same space and spectrum. For PaN (or SaN resp.) we assume that primary (or secondary resp.) nodes are placed according to a Poisson point process of intensity n (or m resp.) over a unit square region. We randomly choose ns (or ms resp.) nodes as the sources of multicast sessions in PaN (or SaN resp.), and for each primary source v p (or secondary source v s), we pick uniformly at random nd primary nodes (or md secondary nodes) as the destinations of v p (or v s). Above all, we assume that PaN can adopt the optimal protocol in terms of the throughput. Our main work is to design the multicast strategy for SaN by which it can achieve the optimal throughput, without any negative impact on the throughput for PaN in order sense. Depending on nd and n, we choose the optimal strategy for PaN from two ones called percolation strategy and connectivity strategy, respectively. Subsequently, we design the corresponding throughput-optimal strategy for SaN. We further derive the regimes for n, nd, m and md where the throughput for PaN and SaN can simultaneously be achieved of the upper bound of their capacities asymptotically. Specifically, we show that (1) when n = o( m (log m) 2),

Abstract—We study the general scaling laws of the capacity for random wireless networks under the generalized physical model. The generality of this work is embodied in three dimensions denoted by (λ ∈ [1, n], nd ∈ [1, n], ns ∈ (1, n]). It means that: (1) We study the random network of a general node density λ ∈ [1, n], rather than only study either random dense network (RDN, λ = n) or random extended network (REN, λ = 1) as in most existing works. (2) We focus on the multicast capacity to unify unicast and broadcast capacities by setting the number of destinations of each session nd ∈ [1, n]. (3) We allow the number of sessions changing in the range ns ∈ (1, n], rather than assuming that ns = Θ(n) as in most existing works. We derive the general lower and upper bounds on the capacity for the arbitrary case of (λ, nd, ns). Particularly, when the general results are applied to the special cases (λ = 1, nd ∈ [1, n], ns = n) and (λ = n, nd ∈ [1, n], ns = n), we show that our results close the previous gaps between upper and lower bounds on the multicast capacity under the generalized physical model. I.

Abstract—We study the multicast capacity for hybrid wireless networks consisting of ordinary ad hoc nodes and base stations under Gaussian Channel model, which generalizes both the unicast capacity and broadcast capacity for hybrid wireless networks. Assume that all ordinary ad hoc nodes transmit at a constant power P, and the power decays along the path, with attenuation exponent α> 2. The data rate of a transmission is determined by the SINR (Signal to Interference plus Noise Ratio) at the receiver as B log(1 + SINR). The ordinary ad hoc nodes are placed in the square region A(a) of area a according to a Poisson point process of intensity n/a. Then, m additional base stations (BSs) acting as the relaying communication gateway are placed regularly in the region A(a), and are connected by a high-bandwidth wired network. Let a = n and a = 1, we construct the hybrid extended network (HEN) and hybrid dense network (HDN), respectively. We choose randomly and independently ns ordinary ad hoc nodes to be the sources of multicast sessions. We assume that each multicast session has nd randomly chosen terminals. Three broad categories of multicast strategies are proposed. The first one is the hybrid strategy, i.e., the multihop scheme with BSsupported, which further consists of two types of strategies called connectivity strategy and percolation strategy respectively. The second one is the ordinary ad hoc strategy, i.e., the multihop scheme without any BS-supported. The third one is the classical BSbased strategy under which any communications between ordinary ad hoc node pairs are relayed by some specific BSs. According to the different scenarios in terms of m, n and nd, we select the optimal scheme from the three categories of strategies, and derive the achievable multicast throughput based on the optimal decision.

Abstract—A critical function of wireless sensor networks (WSNs) is data gathering. While, one is often only interested in collecting a relevant function of the sensor measurements at a sink node, rather than downloading all the data from all the sensors. This paper studies the capacity of computing and transporting the specific functions of sensor measurements to the sink node, called aggregation capacity, for WSNs. It focuses on random WSNs that can be classified into two types: random extended WSN and random dense WSN. All existing results about aggregation capacity are studied for dense WSNs, including random cases and arbitrary cases, under the protocol model (ProM) or physical model (PhyM). In this paper, we propose the first aggregation capacity scaling laws for random extended WSNs. We point out that unlike random dense WSNs, for random extended WSNs, the assumption made in ProM and PhyM that each successful transmission can sustain a constant rate is over-optimistic and unpractical due to transmit power limitation. We derive the first result on aggregation capacity for random extended WSNs under the generalized physical model. Particularly, we prove that, for the type-sensitive perfectly compressible functions and type-threshold perfectly compressible functions, the aggregation capacities ( for random extended WSNs

Abstract—In this paper, we study the multicast capacity of a large scale random wireless network. We consider extended multihop networks, where a number of wireless nodes are randomly located in a square region with side-length a = √ n, by use of Poisson distribution with density 1. All nodes transmit at a constant power P, and the power decays along the path with attenuation exponent α> 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 n 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. We also show that for k = O( n), the per-flow log2 n multicast capacity under Gaussian channel is at most O ( √ n ns k when we have at least ns = Ω(log n) random multicast flows. Our result generalizes the unicast capacity [3] for random networks using percolation theory. Index Terms—Wireless ad hoc networks, capacity, multicast, unicast, scheduling, Gaussian channel, percolation theory. I.

Abstract—We study the asymptotic networking-theoretic multicast capacity bounds for random extended networks (REN) under Gaussian channel model, in which all wireless nodes are individually power-constrained. During the transmission, the power decays along path with attenuation exponent α>2. In REN, n nodes are randomly distributed in the square region of side length √ n. There are ns randomly and independently chosen multicast sessions. Each multicast session has nd+1 randomly chosen terminals, including one source and nd destinations. By effectively combining two types of routing and scheduling strategies, we analyze the asymptotic achievable throughput for all ns = ω(1) and nd. As a special case of our results, we show that for ns =Θ(n), the per-session multicast 1 capacity for REN is of order Θ ( √ ndn) when nd n = O( (log n) α+1) and is of order Θ ( 1 · (log n) nd − α 2) when nd = Ω( n log n).

Abstract — How to efficiently collect sensing data from all sensor nodes is critical to the performance of wireless sensor networks. In this paper, we aim to understand the theoretical limitations of data collection in terms of possible and achievable maximum capacity. Previously, the study of data collection capacity [1]–[6] has only concentrated on large-scale random networks. However, in most of practical sensor applications, the sensor network is not deployed uniformly and the number of sensors may not be as huge as in theory. Therefore, it is necessary to study the capacity of data collection in an arbitrary network. In this paper, we derive the upper and constructive lower bounds for data collection capacity in arbitrary networks. The proposed data collection method can lead to order-optimal performance for any arbitrary sensor networks. We also examine the design of data collection under a general graph model and discuss performance implications. I.

Abstract—We study the throughput capacity and transport capacity for both random and arbitrary wireless networks under Gaussian Channel model when all wireless nodes have the same constant transmission power P and the transmission rate is determined by Signal to Interference plus Noise Ratio (SINR). We consider networks with n wireless nodes {v1, v2, · · · , vn} (randomly or arbitrarily) distributed in a square region Ba with a side-length a. We randomly choose ns node as the source nodes of ns multicast sessions. For each source node vi, we randomly select k points and the closest k nodes to these points as destination nodes of this multicast session. We derive achievable lower bounds and some upper bounds on both throughput capacity and transport capacity for both unicast sessions and multicast sessions. We found that the asymptotic capacity depends on the size a of the deployment region, and it often has three regimes. Index Terms—Wireless networks, throughput capacity, transport capacity, unicast, multicast, Gaussian channel. I.

Abstract — We consider static ad hoc wireless networks comprising significant inhomogeneities in the node spatial distribution over the area, and analyze the scaling laws of their transport capacity as the number of nodes increases. In particular, we consider nodes placed according to a shot-noise Cox process, which allows to model the clustering behavior usually recognized in large-scale systems. For this class of networks, we propose novel scheduling and routing schemes which approach previously computed upper bounds to the per-flow throughput as the number of nodes tends to infinity. I. INTRODUCTION AND RELATED WORK In their seminal work, Gupta and Kumar [1] evaluated the capacity of a static ad-hoc wireless network consisting of n nodes randomly placed over a finite bi-dimensional domain and communicating among them (possibly in a multi-hop