Difference Antenna Selection and Power Allocation for Wireless Cognitive Systems

In this paper, we propose an antenna selection method in a wireless cognitive radio (CR) system, namely difference selection, whereby a single transmit antenna is selected at the secondary transmitter out of $M$ possible antennas such that the weighted difference between the channel gains of the data link and the interference link is maximized. We analyze mutual information and outage probability of the secondary transmission in a CR system with difference antenna selection, and propose a method of optimizing these performance metrics of the secondary data link subject to practical constraints on the peak secondary transmit power and the average interference power as seen by the primary receiver. The optimization is performed over two parameters: the peak secondary transmit power and the difference selection weight $\delta\in [0, 1]$. We show that, difference selection using the optimized parameters determined by the proposed method can be, in many cases of interest, superior to a so called ratio selection method disclosed in the literature, although ratio selection has been shown to be optimal, when impractically, the secondary transmission power constraint is not applied. We address the effects that the constraints have on mutual information and outage probability, and discuss the practical implications of the results.Comment: 29 pages, 9 figures, to be submitted to IEEE Transactions on Communication

Connectivity of confined 3D Networks with Anisotropically Radiating Nodes

Nodes in ad hoc networks with randomly oriented directional antenna patterns typically have fewer short links and more long links which can bridge together otherwise isolated subnetworks. This network feature is known to improve overall connectivity in 2D random networks operating at low channel path loss. To this end, we advance recently established results to obtain analytic expressions for the mean degree of 3D networks for simple but practical anisotropic gain profiles, including those of patch, dipole and end-fire array antennas. Our analysis reveals that for homogeneous systems (i.e. neglecting boundary effects) directional radiation patterns are superior to the isotropic case only when the path loss exponent is less than the spatial dimension. Moreover, we establish that ad hoc networks utilizing directional transmit and isotropic receive antennas (or vice versa) are always sub-optimally connected regardless of the environment path loss. We extend our analysis to investigate boundary effects in inhomogeneous systems, and study the geometrical reasons why directional radiating nodes are at a disadvantage to isotropic ones. Finally, we discuss multi-directional gain patterns consisting of many equally spaced lobes which could be used to mitigate boundary effects and improve overall network connectivity.Comment: 12 pages, 10 figure

On the Distribution of Random Geometric Graphs

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random topology, properties (e.g., connectedness), or Shannon entropy as a measure of the graph's topological uncertainty (or information content). Moreover, the distribution is also relevant for determining average network performance or designing protocols. However, a major impediment in deducing the graph distribution is that it requires the joint probability distribution of the $n(n-1)/2$ distances between $n$ nodes randomly distributed in a bounded domain. As no such result exists in the literature, we make progress by obtaining the joint distribution of the distances between three nodes confined in a disk in $\mathbb{R}^2$. This enables the calculation of the probability distribution and entropy of a three-node graph. For arbitrary $n$, we derive a series of upper bounds on the graph entropy; in particular, the bound involving the entropy of a three-node graph is tighter than the existing bound which assumes distances are independent. Finally, we provide numerical results on graph connectedness and the tightness of the derived entropy bounds.Comment: submitted to the IEEE International Symposium on Information Theory 201

More is less: Connectivity in fractal regions

Ad-hoc networks are often deployed in regions with complicated boundaries. We show that if the boundary is modeled as a fractal, a network requiring line of sight connections has the counterintuitive property that increasing the number of nodes decreases the full connection probability. We characterise this decay as a stretched exponential involving the fractal dimension of the boundary, and discuss mitigation strategies. Applications of this study include the analysis and design of sensor networks operating in rugged terrain (e.g. railway cuttings), mm-wave networks in industrial settings and vehicle-to-vehicle/vehicle-to-infrastructure networks in urban environments.Comment: 5 page

Connectivity in Dense Networks Confined within Right Prisms

We consider the probability that a dense wireless network confined within a given convex geometry is fully connected. We exploit a recently reported theory to develop a systematic methodology for analytically characterizing the connectivity probability when the network resides within a convex right prism, a polyhedron that accurately models many geometries that can be found in practice. To maximize practicality and applicability, we adopt a general point-to-point link model based on outage probability, and present example analytical and numerical results for a network employing $2 \times 2$ multiple-input multiple-output (MIMO) maximum ratio combining (MRC) link level transmission confined within particular bounding geometries. Furthermore, we provide suggestions for extending the approach detailed herein to more general convex geometries.Comment: 8 pages, 6 figures. arXiv admin note: text overlap with arXiv:1201.401

Adaptive OFDM Index Modulation for Two-Hop Relay-Assisted Networks

In this paper, we propose an adaptive orthogonal frequency-division multiplexing (OFDM) index modulation (IM) scheme for two-hop relay networks. In contrast to the traditional OFDM IM scheme with a deterministic and fixed mapping scheme, in this proposed adaptive OFDM IM scheme, the mapping schemes between a bit stream and indices of active subcarriers for the first and second hops are adaptively selected by a certain criterion. As a result, the active subcarriers for the same bit stream in the first and second hops can be varied in order to combat slow frequency-selective fading. In this way, the system reliability can be enhanced. Additionally, considering the fact that a relay device is normally a simple node, which may not always be able to perform mapping scheme selection due to limited processing capability, we also propose an alternative adaptive methodology in which the mapping scheme selection is only performed at the source and the relay will simply utilize the selected mapping scheme without changing it. The analyses of average outage probability, network capacity and symbol error rate (SER) are given in closed form for decode-and-forward (DF) relaying networks and are substantiated by numerical results generated by Monte Carlo simulations.Comment: 30 page

Capacity and Power Scaling Laws for Finite Antenna MIMO Amplify-and-Forward Relay Networks

In this paper, we present a novel framework that can be used to study the capacity and power scaling properties of linear multiple-input multiple-output (MIMO) $d\times d$ antenna amplify-and-forward (AF) relay networks. In particular, we model these networks as random dynamical systems (RDS) and calculate their $d$ Lyapunov exponents. Our analysis can be applied to systems with any per-hop channel fading distribution, although in this contribution we focus on Rayleigh fading. Our main results are twofold: 1) the total transmit power at the $n$th node will follow a deterministic trajectory through the network governed by the network's maximum Lyapunov exponent, 2) the capacity of the $i$th eigenchannel at the $n$th node will follow a deterministic trajectory through the network governed by the network's $i$th Lyapunov exponent. Before concluding, we concentrate on some applications of our results. In particular, we show how the Lyapunov exponents are intimately related to the rate at which the eigenchannel capacities diverge from each other, and how this relates to the amplification strategy and number of antennas at each relay. We also use them to determine the extra cost in power associated with each extra multiplexed data stream.Comment: 16 pages, 9 figures. Accepted for publication in IEEE Transactions on Information Theor