On outer bounds to the capacity region of wireless networks

Abstract

Abstract-In this correspondence, 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.

The Capacity of Wireless Networks: Information-Theoretic and Physical Limits

“…3, which shows the input-output relationship between transmitted and received signals. Such relationship is given by a chain of operators and corresponds to the information-theoretic channel model in (3). These operators are formally studied in the next sections according to the outline provided above.…”

“…Presence or absence of fading, choice of fading models, and choice of path loss models, lead to different lower and upper bounds on the scaling limit of the information rate. As a consequence, a plethora of articles appeared in the information-theoretic literature [2], [3], [9], [12], [17], [19], [20], [24]- [28], [40], [41], presenting bounds ranging from a per-node rate that rapidly decays to zero as the number of nodes in the network tends to infinity, to bounds predicting a slower decay, to bounds that are practically constant. In these works, while the lower bounds rely on different cooperative schemes employed by the nodes, the upper bounds follow from the application of the same mathematical tool: the information-theoretic cut-set bound [6,Ch.…”

Cognitive radio networks

“…Upper bounds based on the max-flow min-cut bound [29]- [31] as well as MIMO techniques [30] have been analyzed for various ranges of path loss exponent. For path loss α between two and three, a hierarchical scheme can achieve a throughput growth as n 2−α/2 [30] (asymptotically linear for α = 2).…”

Hierarchical Cooperation in <emphasis emphasistype="italic">Ad Hoc</emphasis> Networks: Optimal Clustering and Achievable Throughput

“…In summary, the required time for the double-stage scheme is Assume the channel gains are known at all nodes. All communication links in the first phase can operate at any rate less than the following: (9) Communications in the second phase are performed over the quantized MIMO channel of Fig. 4 where the notation is used for an i.i.d.…”