On the Second Order Statistics of the Multihop Rayleigh Fading Channel

Second order statistics provides a dynamic representation of a fading channel and plays an important role in the evaluation and design of the wireless communication systems. In this paper, we present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one and can be modeled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and the AFD of the product of N Rayleigh fading envelopes (or of the recently so-called N*Rayleigh channel). Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the corresponding ones of the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations

Level Crossing Rate and Average Fade Duration of the Multihop Rayleigh Fading Channel

We present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one, which can be modelled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and AFD of the product of N Rayleigh fading envelopes, or of the recently so-called N*Rayleigh channel. Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations

Throughput Scaling of Wireless Networks With Random Connections

This work studies the throughput scaling laws of ad hoc wireless networks in the limit of a large number of nodes. A random connections model is assumed in which the channel connections between the nodes are drawn independently from a common distribution. Transmitting nodes are subject to an on-off strategy, and receiving nodes employ conventional single-user decoding. The following results are proven: 1) For a class of connection models with finite mean and variance, the throughput scaling is upper-bounded by $O(n^{1/3})$ for single-hop schemes, and $O(n^{1/2})$ for two-hop (and multihop) schemes. 2) The $\Theta (n^{1/2})$ throughput scaling is achievable for a specific connection model by a two-hop opportunistic relaying scheme, which employs full, but only local channel state information (CSI) at the receivers, and partial CSI at the transmitters. 3) By relaxing the constraints of finite mean and variance of the connection model, linear throughput scaling $\Theta (n)$ is achievable with Pareto-type fading models.Comment: 13 pages, 4 figures, To appear in IEEE Transactions on Information Theor

DESIGN AND IMPLEMENTATION OF INFORMATION PATHS IN DENSE WIRELESS SENSOR NETWORKS

In large-scale sensor networks with monitoring applications, sensor nodes are responsible to send periodic reports to the destination which is located far away from the area to be monitored. We model this area (referred to as the distributed source) with a positive load density function which determines the total rate of traffic generated inside any closed contour within the area. With tight limitations in energy consumption of wireless sensors and the many-to-one nature of communications in wireless sensor networks, the traditional definition of connectivity in graph theory does not seem to be sufficient to satisfy the requirements of sensor networks. In this work, a new notion of connectivity (called implementability) is defined which represents the ability of sensor nodes to relay traffic along a given direction field, referred to as information flow vector field $\vec{D}$. The magnitude of information flow is proportional to the traffic flux (per unit length) passing through any point in the network, and its direction is toward the flow of traffic. The flow field may be obtained from engineering knowledge or as a solution to an optimization problem. In either case, information flow flux lines represent a set of abstract paths (not constrained by the actual location of sensor nodes) which can be used for data transmission to the destination. In this work, we present conditions to be placed on $\vec{D}$ such that the resulting optimal vector field generates a desirable set of paths. In a sensor network with a given irrotational flow field $\vec{D}(x,y)$, we show that a density of $n(x,y)=O(|\vec{D}(x,y)|^2)$ sensor nodes is not sufficient to implement the flow field as $|\vec{D}|$ scales linearly to infinity. On the other hand, by increasing the density of wireless nodes to $n(x,y)=O(|\vec{D}(x,y)|^2 \log |\vec{D}(x,y)|)$, the flow field becomes implementable. Implementability requires more nodes than simple connectivity. However, results on connectivity are based on the implicit assumption of exhaustively searching all possible routes which contradicts the tight limitation of energy in sensor networks. We propose a joint MAC and routing protocol to forward traffic along the flow field. The proposed tier-based scheme can be further exploited to build lightweight protocol stacks which meet the specific requirements of dense sensor networks. We also investigate buffer scalability of sensor nodes routing along flux lines of a given irrotational vector field, and show that nodes distributed according to the sufficient bound provided above can relay traffic from the source to the destination with sensor nodes having limited buffer space. This is particularly interesting for dense wireless sensor networks where nodes are assumed to have very limited resources