Communication over a wireless network with random connections

Abstract

Abstract-A network of nodes in which pairs communicate over a shared wireless medium is analyzed. We consider the maximum total aggregate traffic flow possible as given by the number of users multiplied by their data rate. The model in this paper differs substantially from the many existing approaches in that the channel connections in this network are entirely random: rather than being governed by geometry and a decay-versus-distance law, the strengths of the connections between nodes are drawn independently from a common distribution. Such a model is appropriate for environments where the first-order effect that governs the signal strength at a receiving node is a random event (such as the existence of an obstacle), rather than the distance from the transmitter. It is shown that the aggregate traffic flow as a function of the number of nodes is a strong function of the channel distribution. In particular, for certain distributions the aggregate traffic flow is at least (log ) for some 0, which is significantly larger than the ( ) results obtained for many geometric models. The results provide guidelines for the connectivity that is needed for large aggregate traffic. The relation between the proposed model and existing distance-based models is shown in some cases.

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

“…From (15) we have that, for any (47) where the first inequality follows from the triangle inequality; the second inequality follows from the fact that and have unit norm and from the Cauchy-Schwarz inequality; the third inequality follows from (due to the symmetry of Bessel functions of integer order) and the power constrain in (12). Thus, in order to prove the theorem, it suffices to show that there exists an , such that…”

“…223-232] (11) where is an element of area perpendicular to is the wavenumber, is the permittivity of the vacuum, is the Hankel function of the second kind and order , and a Fourier transform convention has been adopted, being the angular frequency, and being the permeability of the vacuum. Furthermore, we assume the following power constraint: (12) wherein is a normalization constant and is the individual power constraint of each source. This condition ensures that the power radiated by the sources is finite and linearly proportional to the number of sources in .…”

“…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.…”

“…Physics simply forbids it. Mathematical proofs of higher capacity scaling [2], [12], [24]- [26], [28], achieved using sophisticated cooperative communication schemes, rely on stochastic channel models and in a strict scaling limit sense are artifacts of such models. This highlights the importance of using appropriate mathematical models of reality to derive information-theoretic results.…”

Sum-Rate Maximization in Single-Hop Wireless Networks with the On-Off Power Scheme

“…The main contribution of this work is to determine the maximum throughput of the network in terms of different values of M and the probability of the shadowing effect, α. Our strategy differs from the model studied in [9] and [12]; primarily we use a decentralized on-off power allocation scheme for a single-hop wireless network with M subchannels, while [9] and [12] present a model with random connections for M = 1 and using relay nodes.…”