Scaling Laws of Cognitive Networks

We consider a cognitive network consisting of n random pairs of cognitive transmitters and receivers communicating simultaneously in the presence of multiple primary users. Of interest is how the maximum throughput achieved by the cognitive users scales with n. Furthermore, how far these users must be from a primary user to guarantee a given primary outage. Two scenarios are considered for the network scaling law: (i) when each cognitive transmitter uses constant power to communicate with a cognitive receiver at a bounded distance away, and (ii) when each cognitive transmitter scales its power according to the distance to a considered primary user, allowing the cognitive transmitter-receiver distances to grow. Using single-hop transmission, suitable for cognitive devices of opportunistic nature, we show that, in both scenarios, with path loss larger than 2, the cognitive network throughput scales linearly with the number of cognitive users. We then explore the radius of a primary exclusive region void of cognitive transmitters. We obtain bounds on this radius for a given primary outage constraint. These bounds can help in the design of a primary network with exclusive regions, outside of which cognitive users may transmit freely. Our results show that opportunistic secondary spectrum access using single-hop transmission is promising.Comment: significantly revised and extended, 30 pages, 13 figures, submitted to IEEE Journal of Special Topics in Signal Processin

Product Multicommodity Flow in Wireless Networks

We provide a tight approximate characterization of the $n$-dimensional product multicommodity flow (PMF) region for a wireless network of $n$ nodes. Separate characterizations in terms of the spectral properties of appropriate network graphs are obtained in both an information theoretic sense and for a combinatorial interference model (e.g., Protocol model). These provide an inner approximation to the $n^2$ dimensional capacity region. These results answer the following questions which arise naturally from previous work: (a) What is the significance of $1/\sqrt{n}$ in the scaling laws for the Protocol interference model obtained by Gupta and Kumar (2000)? (b) Can we obtain a tight approximation to the "maximum supportable flow" for node distributions more general than the geometric random distribution, traffic models other than randomly chosen source-destination pairs, and under very general assumptions on the channel fading model? We first establish that the random source-destination model is essentially a one-dimensional approximation to the capacity region, and a special case of product multi-commodity flow. Building on previous results, for a combinatorial interference model given by a network and a conflict graph, we relate the product multicommodity flow to the spectral properties of the underlying graphs resulting in computational upper and lower bounds. For the more interesting random fading model with additive white Gaussian noise (AWGN), we show that the scaling laws for PMF can again be tightly characterized by the spectral properties of appropriately defined graphs. As an implication, we obtain computationally efficient upper and lower bounds on the PMF for any wireless network with a guaranteed approximation factor.Comment: Revised version of "Capacity-Delay Scaling in Arbitrary Wireless Networks" submitted to the IEEE Transactions on Information Theory. Part of this work appeared in the Allerton Conference on Communication, Control, and Computing, Monticello, IL, 2005, and the Internation Symposium on Information Theory (ISIT), 200

The Balanced Unicast and Multicast Capacity Regions of Large Wireless Networks

We consider the question of determining the scaling of the $n^2$-dimensional balanced unicast and the $n 2^n$-dimensional balanced multicast capacity regions of a wireless network with $n$ nodes placed uniformly at random in a square region of area $n$ and communicating over Gaussian fading channels. We identify this scaling of both the balanced unicast and multicast capacity regions in terms of $\Theta(n)$, out of $2^n$ total possible, cuts. These cuts only depend on the geometry of the locations of the source nodes and their destination nodes and the traffic demands between them, and thus can be readily evaluated. Our results are constructive and provide optimal (in the scaling sense) communication schemes.Comment: 37 pages, 7 figures, to appear in IEEE Transactions on Information Theor

Scaling Laws for Heterogeneous Wireless Networks

Thesis Supervisor: Devavrat Shah Title: Associate Professor Thesis Supervisor: Gregory W. Wornell Title: ProfessorThis thesis studies the problem of determining achievable rates in heterogeneous wireless networks. We analyze the impact of location, traffic, and service heterogeneity. Consider a wireless network with n nodes located in a square area of size n communicating with each other over Gaussian fading channels. Location heterogeneity is modeled by allowing the nodes in the wireless network to be deployed in an arbitrary manner on the square area instead of the usual random uniform node placement. For traffic heterogeneity, we analyze the n × n dimensional unicast capacity region. For service heterogeneity, we consider the impact of multicasting and caching. This gives rise to the n × 2n dimensional multicast capacity region and the 2n × n dimensional caching capacity region. In each of these cases, we obtain an explicit informationtheoretic characterization of the scaling of achievable rates by providing a converse and a matching (in the scaling sense) communication architecture.National Science Foundation. DARPA, and Hewlett-Packard under the MIT/HP Alliance

On outer bounds to the capacity region of wireless networks

Abstract — We study the capacity region of a general wireless network by deriving fundamental upper bounds on a class of linear functionals of the rate tuples at which joint reliable communication can take place. The widely studied transport capacity is a specific linear functional: the coefficient of the rate between a pair of nodes is equal to the Euclidean distance between them. The upper bound on the linear functionals of the capacity region is used to derive upper bounds to scaling laws for generalized transport capacity: the coefficient of the rate between a pair of nodes is equal to some arbitrary function of the Euclidean distance between them, for a class of minimum distance networks. This upper bound to the scaling law meets that achievable by multihop communication over these networks for a wide class of channel conditions; this shows the optimality, in the scaling-law sense, of multihop communication when studying generalized transport capacity of wireless networks. Index Terms — Ad-hoc wireless networks, capacity region, cutset bounds, isometric embedding, multi-hop, transport capacit