Large Wireless Networks Research Articles

Low Complexity and Provably Efficient Algorithm for Joint Inter and Intrasession Network Coding in Wireless Networks

The performance of wireless networks can be enhanced by performing network coding on the intermediate relay nodes. To enhance the throughput of large wireless networks, we can decompose them into a superposition of simple relay networks called two-hop relay networks. Previously, the capacity region of two-hop relay networks with multiple unicast sessions and limited feedback was characterized where packet erasure channels are used. A near-optimal coding scheme that exploits the broadcast nature and the diversity of the wireless links was proposed. However, the complexity of the scheme is exponential in terms of the number of sessions, as it requires the knowledge of the packets that are received by any subset of the receivers. In this paper, we provide a polynomial time coding scheme and characterize its performance using linear equations. The coding scheme uses random network coding to carefully mix intra and intersession network coding and makes a linear, not exponential, number of decisions. For two-hop relay networks with two sessions, we provide an optimal coding scheme that does not require the knowledge of the channel conditions. We also provide a linear programming formulation that uses our two-hop relay network results as a building block in large lossy multihop networks.

A Hierarchical QoS Routing Protocol for the Wireless Sensor Networks

The large wireless sensor networks are often structured hierarchically by grouping nodes into different domains in order to deal with the scaling problem. This paper proposes a new protocol called hierarchical QoS routing protocol (HQRP) that achieves scalability by organizing the network as a hierarchy of domains using the full-mesh aggregation technique. In HQRP, each local node just only needs to maintain local routing and summary information of other domains, but does not requires any global states maintained. The HQRP uses a Reverse Best Metric Path Forwarding approach with hierarchical, topological and QoS forwarding conditions to construct the multicast tree while minimizing message overhead and satisfying delay-bandwidth and minimum energy consumption. The paper presents proof of correctness and complexity analysis of the HQRP. Simulation results show very good performance in terms of success ratio and message overhead.

Scheduling Partition for Order Optimal Capacity in Large-Scale Wireless Networks

The capacity scaling property specifies the change of network throughput when network size increases. It serves as an essential performance metric in large-scale wireless networks. Existing results have been obtained based on the assumption of using a globally planned link transmission schedule in the network, which is however not feasible in large wireless networks due to the scheduling complexity. The gap between the well-known capacity results and the infeasible assumption on link scheduling potentially undermines our understanding of the achievable network capacity. In this paper, we propose the scheduling partition methodology that decomposes a large network into small autonomous scheduling zones and implements a localized scheduling algorithm independently in each partition. We prove the sufficient and the necessary conditions for the scheduling partition approach to achieve the same order of capacity as the widely assumed global scheduling strategy. In comparison to the network dimension $(\sqrt{n})$, scheduling partition size $(\Theta (r(n)))$ is sufficient to obtain the optimal capacity scaling, where $(r(n))$ is the node transmission radius and much smaller than $(\sqrt{n})$. We finally propose a distributed partition protocol and a localized scheduling algorithm as our scheduling solution for maximum capacity in large wireless networks.

The placement-configuration problem for intrusion detection nodes in wireless sensor networks

The deployment and configuration of a distributed network intrusion detection system (NIDS) in a large Wireless Sensor Network (WSN) is an enormous challenge. A reduced number of devices equipped with detection capabilities have to be placed on strategic network locations and then appropriately configured in order to maximise the detection rate and minimise the amount of computational and physical resources consumed – fundamentally energy, which in turn depends on CPU, memory, and network usage. In practice, a major difficulty lies in the fact that the relationship between each node’s tuning parameters and the overall cost/benefit rate achieved by the deployment is poorly understood. We call this the Placement-Configuration Problem (PCP). In this paper we formalise and study this problem both theoretically and empirically. We introduce a formal model of distributed NIDS upon which the cost/benefit tradeoffs can be appropriately derived. Subsequently we show that, in general, the PCP is hard (NP-complete) and present a heuristic local search algorithm to find near-optimal solutions for practical scenarios. Our analysis framework is general in the sense that it is applicable to a number of existing detection technologies for WSNs, and we discuss how further aspects can be easily introduced if required.

Connectivity of Large Wireless Networks Under A General Connection Model

This paper studies networks where all nodes are distributed on a unit square <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> = <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Δ</sup> [- [1/2], [1/2]] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> following a Poisson distribution with known density ρ and a pair of nodes separated by an Euclidean distance <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> are directly connected with probability <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gr</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> )= <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Δ</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> ), independent of the event that any other pair of nodes are directly connected. Here, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</i> :[0,∞)→ [0,1] satisfies the conditions of rotational invariance, nonincreasing monotonicity, integral boundedness, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> )= <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</i> (1/( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> )) ; further, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> =√{(logρ+ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> )/( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> ρ)} where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> =∫ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ℜ</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</i> (|| <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> ||) <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dx</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> is a constant. Denote the aforementioned network by <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gr</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> ). We show that as ρ→ ∞, 1) the distribution of the number of isolated nodes in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gr</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> ) converges to a Poisson distribution with mean <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> ; 2) asymptotically almost surely (a.a.s.) there is no component in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gr</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> ) of fixed and finite order <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> >; 1; c) a.a.s. the number of components with an unbounded order is one. Therefore, as ρ→ ∞, the network a.a.s. contains a unique unbounded component and isolated nodes only; a sufficient and necessary condition for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gr</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> ) to be a.a.s. connected is that there is no isolated node in the network, which occurs when <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> → ∞ as ρ→ ∞. These results expand recent results obtained for connectivity of random geometric graphs from the unit disk model and the fewer results from the log-normal model to the more general and more practical random connection model.

A Modified clustering for LEACH algorithm in WSN

Node clustering and data aggregation are popular techniques to reduce energy consumption in large Wireless Sensor Networks (WSN). Cluster based routing is always a hot research area in wireless sensor networks. Classical LEACH protocol has many advantages in energy efficiency, data aggregation and so on. However, determining number of clusters present in a network is an important problem. Conventional clustering techniques generally assume this parameter to be user supplied. There exist very few techniques that can solve the problem of automatic detection of number of clusters satisfactorily. Some of these techniques rely on user supplied information, while others use cluster validity indices. In this paper, we proposed a rather simple method to identify the number of clusters that can give satisfactory results. Proposed method is compared with classical LEACH protocol and found to be giving better results.

Reliable localised event detection in a wireless distributed radio telescope

We consider a large wireless network constituting a radio telescope. Each of the anticipated 3000 nodes is triggered to collect data for further analysis at a rate of more than 200 Hz, mostly caused by noisy environmental sources. However, relevant cosmic rays occur only a few times a day. As every trigger has an associated 12.5 KB of data, and considering the size of the telescope in number of nodes and covered area, centralised processing is not an option. We propose a fully decentralised event detection algorithm based on collaborative local data analysis, effectively filtering out only those triggers that need further centralised processing. As we show through performance evaluations, the crux in the design is finding the right balance between accuracy and efficient use of resources such as the communication bandwidth in the unreliable communication environment.

Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations

We introduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed byN, the number of nodes in the network. AsNgoes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.

Scalable Cluster-based Routing in Large Wireless Sensor Networks

Large control overhead is the leading factor limiting the scalability of wireless sensor networks (WSNs). Clustering network nodes is an efficient solution, and Passive Clustering (PC) is one of the most efficient clustering methods. In this letter, we propose an improved PC-based route building scheme, named Route Reply (RREP) Broadcast with Passive Clustering (in short RBPC). Through broadcasting RREP packets on an expanding ring to build route, sensor nodes cache their route to the sink node, which reduces the total route search times and thus the control overhead. Simulation results are also provided to show the efficiency of the proposed RBPC in terms of reduced overhead and energy consumption, and it is also shown that RBPC outperforms AODV/PC in the delivery ratio.

Asymptotic analysis of flooding in CSMA-based large scale ad-hoc wireless networks

Abstract Abstract In this article, we study the asymptotic behavior of flooding in large scale wireless networks. Specifically, we derive an upper bound on the coverage of flooding when the number of nodes n in the network goes to infinity. We consider two different regimes of transmission radii: first, the case of constant transmission radius r where the percentage of covered nodes scales as O ( n r 2 e − K S n r 2 ) for a constant K S &gt; 0. In this case, as an important result, we observe that the percentage of covered nodes is upper bounded by a decreasing function, vanishing as the network size grows. Second, the case of vanishing r n (i.e., r decreases as n increases) is considered where it is shown in the literature that the minimum value of r n which maintains connectivity is log n / Π n . In this case, a coverage percentage of at most O ( n − K S ′ log n ) is expected for a constant value of K S ′ &gt; 0 , leading to an infinite number of covered nodes. In such case, the rate at which the network coverage is decreased can be controlled and be considerably reduced by a proper choice of network parameters ( K S ′ ). Consequently, this result shows that flooding is a suitable strategy even for large networks.

Uncoordinated Cooperative Communications with Spatially Random Relays

In traditional cooperative communications, coordination is required among relay nodes to help data transmission through distributed signal transmission or coding techniques. For large cooperative networks, the overhead for coordination is huge and the synchronization among relays is very difficult. In this paper, we propose uncoordinated cooperative communication schemes in a large wireless network that do not need the coordination among relays while realizing cooperative diversity for the source-destination link. Without a central controller, all relays that are spatially randomly placed contend for the channel to relay the packet from the source to the destination in a distributed fashion. The competition for the channel access is governed by the retransmission probability that is independently calculated by the relays according to the location or channel quality information. Three schemes of uncoordinated cooperative communications are proposed to determine the retransmission probabilities of the potential relays based on the local distance, direction, and channel quality, referred to as distance based, sectorized, and local SNR based schemes, respectively. Success probabilities for the proposed uncoordinated schemes are analyzed. Numerical and simulation results show that the local SNR based scheme has the best performance and the distance based scheme outperforms the sectorized scheme.

Enhanced Correlation Estimators for Distributed Source Coding in Large Wireless Sensor Networks

In this paper, we propose two estimators based on correlation parameters for the two key steps of a practical distributed source coding (DSC) scheme, namely: 1) the computation of the side-information at the receiver side and 2) the estimation of the required number of bits to compress the readings in order to guarantee a certain symbol error probability. We show that using the proposed estimators, the DSC algorithm performs better in terms of the compression rate and the symbol error rate. In particular, this improvement is especially significant when the number of snapshots used in the training phase is only slightly larger than the observation vector. However, when the number of snapshots is much higher than the observation dimension, our proposed estimators perform similarly to the classical estimators.

Analysis of routing protocols and interference-limited communication in large wireless networks via continuum modeling

The evaluation and assessment of the design of large wireless networks is an important problem in numerous applications. Direct simulation is a traditional approach for studying such networks but is severely limited in its utility as the size of the network increases. This necessitates other means for studying large networks, one of which is the modeling of large networks with continuum models. In this paper, we introduce nonlinear partial differential equations whose solutions approximate the expected behavior of large networks governed by probabilistic communication rules. The relative speed at which solutions can be obtained from the continuum models allows for the investigation of routing protocols and communication limitations due to interference—a feat that is not feasible via simulation methods. Specifically, we investigate the effects of a directed diffusion routing protocol and explore communication limitations in an interference-sensitive network. Network design studies using the approximating continuum models are then presented.

Flow-based XOR Network Coding for Lossy Wireless Networks

A practical way for maximizing the throughput of a wireless network is to decompose the network into a superposition of small two-hop networks such that network coding can be performed inside these small networks to resolve bottlenecks. We call these networks 2-hop relay networks. Therefore, studying the capacity of 2-hop relay networks is very important. Most practical network coding protocols that perform the superposition ignore the diversity among the links by turning off coding when the channels are lossy. Other protocols deal with the packets separately - not as members of flows - which makes the network coding problem with lossy links intractable. In this paper, we use a different approach by looking at flows or batches instead of individual packets. We characterize the capacity region of the 2-hop relay network with packet erasure channels when the coding operations are limited to XOR. We derive our results by constructing an upper bound on the capacity region and then providing a coding scheme that can achieve the upper bound. The capacity characterization is in terms of linear equations. We also extend our 2-hop relay networks results to multihop wireless networks by providing a linear program that can perform the superposition optimally. We perform extensive simulations for both the 2-hop relay and large wireless networks and show the superiority of our protocols over the network coding protocols that deal with the packets separately.

Group-Ordered SPRT for Decentralized Detection

The problem of decentralized detection in a large wireless sensor network is considered. An adaptive decentralized detection scheme, group-ordered sequential probability ratio test (GO-SPRT), is proposed. This scheme groups sensors according to the informativeness of their data. Fusion center collects sensor data sequentially, starting from the most informative data and terminates the process when the target performance is reached. Wald's approximations are shown to be applicable even though the problem setting deviates from that of the traditional sequential probability ratio test (SPRT). To analyze the efficiency of GO-SPRT, the asymptotic equivalence between the average sample number of GO-SPRT, which is a function of a multinomial random variable, and a function of a normal random variable, is established. Closed-form approximations for the average sample number are then obtained. Compared with fixed sample size test and traditional SPRT, the proposed scheme achieves significant savings in the cost of data fusion.

HABITS: a Bayesian filter approach to indoor tracking and location

Using Wi-Fi signals is an attractive and reasonably affordable option to deal with the currently unsolved problem of widespread tracking in an indoor environment. History aware-based indoor tracking system (HABITS) models human movement patterns by applying a discrete Bayesian filter to predict the areas that will, or will not, be visited in the future. We outline here the operation of the HABITS real-time location system (RTLS) and discuss the implementation in relation to indoor Wi-Fi tracking with a large wireless network. Testing of HABITS shows that it gives comparable levels of accuracy to those achieved by doubling the number of access points. We conclude that HABITS improves on standard real-time location systems in term of accuracy (overcoming blackspots), latency (giving position fixes when others cannot), cost (less APs are required than are recommended by standard RTLS systems) and prediction (short, medium and longer-term predictions are available from HABITS).

Optimizing Cost and Throuhput Efficiency with Security in Wireless Ad HOC Networks Using Leach

Wireless ad hoc network (WANET) is a decentralized type of the wireless network. There are various challenges that are faced in the ad hoc environment. Wireless ad hoc networking is the enabling technology for paramount civilian and military applications requiring easy and quick (and often unmanned and cheap) network deployments. The security of communication in ad hoc wireless network is very important especially in military applications. The wireless nature of communication and any lack of network security infrastructure raise several security problems. Asymptotic notations solve the problem of large wireless networks. The main objective of the system is performance degradation of the secure network. In this paper mainly considering, order to reduce delay and increase throughput. The network performance can be calculated by using probability (p<1). Here we implemented LEACH algorithm for an efficient energy saving and thus increases the life time of wireless network. The simulation results show the presented algorithm is more efficient energy saving and fewer packets are damaged; thus provides secure wireless network.

MeshMon: a multi‐tiered framework for wireless mesh network monitoring

AbstractMonitoring and troubleshooting a large wireless mesh network (WMN) presents several challenges. Diagnosis of problems related to wireless access in these networks requires a comprehensive set of metrics and network monitoring data. Collection and offloading of a large amount of data are infeasible in a bandwidth constrained mesh network. Additionally, the processing required to analyze data from the entire network restricts the scalability of the system and impacts the ability to perform real‐time fault diagnosis. To this end, we propose MeshMon, a network monitoring framework that includes a multi‐tiered method of data collection. MeshMon, dynamically controls the granularity of data collection based on observed events in the network, thereby achieving significant bandwidth savings and enabling real‐time automated management. Our evaluation of MeshMon on a real testbed shows that we can diagnose a majority (87%) of network faults with a 66% savings in bandwidth required for network monitoring. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Aggregate Interference Distribution From Large Wireless Networks With Correlated Shadowing: An Analytical–Numerical–Simulation Approach

As the number and variety of wireless devices sharing spectrum increases, it becomes increasingly important to characterize the sum interference that is produced by a large number of interferers. We show that, in the case of several interferers, the assumption of independent shadowing paths is very inaccurate and must be replaced by an appropriate correlation model. We choose one such model, which has desirable mathematical and physical properties, is tunable, and is particularly well suited for simulation, although our approach can also be used with other correlation models. In addition, we allow a very versatile channel and system model. The simulation cost of such systems quickly grows for large numbers of interferers due to the time and memory constraints of the Monte Carlo simulation algorithm using the classic matrix factorization (e.g., Cholesky) approach. We show how an alternative simulation approach using shadowing fields can significantly reduce the order of the computational cost. In addition, we show how judicious random sample reuse and extrapolation based on a numerical analysis of moments can be used to further simplify the simulation. Through the combination of these three approaches, using a mixture of simulation, numerical, and analytical techniques, we can obtain accurate approximations of the distribution of the total interference power while reducing computational time by factors of more than 1000. We can also make some mathematical statements about the problem, which may be useful for further developments. We argue that our model is complex enough to accommodate a good degree of realism and that our approach is a viable alternative to the pure analysis of such a complex and versatile problem.

A Stochastic Geometry Model for Cognitive Radio Networks

We propose a probabilistic model based on stochastic geometry to analyze cognitive radio in a large wireless network with randomly located users sharing the medium with carrier sensing multiple access. Analytical results are derived on the impact of the interaction between primary and secondary users, on their medium access probability, coverage probability and throughput. These results can be seen as the continuation of the theory of priorities in queueing theory to spatial processes. They give insight into the guarantees that can be offered to primary users and more generally on the possibilities offered by cognitive radio to improve the effectiveness of spectrum utilization in such networks.