Investigating the Gaussian Convergence of the Distribution of the Aggregate Interference Power in Large Wireless Networks (original) (raw)
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Communications (QBSC), 2010
The distribution of the aggregate interference power in large wireless networks has gained increasing attention with the emergence of different types of wireless networks such as ad-hoc networks, sensor networks, and cognitive radio networks. The interference in such networks is often characterized using a Poisson Point Process (PPP). As the number of interfering nodes increases, there might be a tendency to approximate the distribution of the aggregate interference power by a Gaussian random variable given that the individual interference signals are independent. However, some observations in literature suggest that this Gaussian approximation is not valid except under some specific scenarios. In this paper, we cast these observations in a single mathematical framework and express the conditions for which the Gaussian approximation will be valid for the aggregate interference power generated by a Poisson field of interferers. Furthermore, we discuss the effect of different system and channel parameters on the convergence of the distribution of the aggregate interference power to a Gaussian distribution.
Gaussian Approximation for the Wireless Multi-Access Interference Distribution
IEEE Transactions on Signal Processing, 2012
This paper investigates the problem of Gaussian approximation for the wireless multi-access interference distribution in large spatial wireless networks. First, a principled methodology is presented to establish rates of convergence of the multi-access interference distribution to a Gaussian distribution for general bounded and power-law decaying path-loss functions. The model is general enough to also include various random wireless channel dynamics such as fading and shadowing arising from multipath propagation and obstacles existing in the communication environment. It is shown that the wireless multi-access interference distribution converges to the Gaussian distribution with the same mean and variance at a rate 1 √ λ , where λ > 0 is a parameter controlling the intensity of the planar (possibly non-stationary) Poisson point process generating node locations. An explicit expression for the scaling coefficient is obtained as a function of fading statistics and the path-loss function. Second, an extensive numerical and simulation study is performed to illustrate the accuracy of the derived Gaussian approximation bounds. A good statistical fit between the interference distribution and its Gaussian approximation is observed for moderate to high values of λ. Finally, applications of these approximation results to upper and lower bound the outage capacity and ergodic sum capacity for spatial wireless networks are illustrated. The derived performance bounds on these capacity metrics track the network performance within one nats per second per hertz.
Large Deviations of the Interference in a Wireless Communication Model
IEEE Transactions on Information Theory, 2000
Interference from other users limits the capacity, and possibly the connectivity, of wireless networks. A simple model of a wireless ad-hoc network, in which node locations are described by a homogeneous Poisson point process, and node transmission powers are random, is considered in this paper. A large deviation principle for the interference is presented under different assumptions on the distribution of transmission powers.
A Cumulant-Based Characterization of the Aggregate Interference Power in Wireless Networks
2010 IEEE 71st Vehicular Technology Conference, 2010
The importance of characterizing the aggregate interference power generated by a wireless network has increased with the emergence of different types of wireless networks such as ad-hoc networks, sensor networks, and cognitive radios. A cumulant-based characterization of this aggregate interference is an attractive approach. A number or recent papers in literature have dealt with cumulants of the aggregate interference but under specific scenarios. In this paper, we introduce a simple yet comprehensive method to determine the cumulants of the aggregate interference power originating from a wireless network. This method is quite general and applicable for finite and infinite network sizes, and it is flexible to encompass different system and propagation parameters such as large-scale fading, small-scale fading or even composite fading. We also investigate the behavior of these cumulants with respect to changes in the network size and fading distributions.
On distribution of aggregate interference in cognitive radio networks
2010 25th Biennial Symposium on Communications, 2010
This paper analyzes the distribution of aggregate interference in cognitive radio networks. Poisson point spatial distribution model and average propagation path loss model are considered. All possible scenarios are classified into three typical cases, based on typical outage events. When the average number of nodes in the forbidden region is much smaller than one, the aggregate interference can be well approximated by the nearest one (nearest node dominates outage events). When the average number of nodes in the forbidden range is greater than one, the aggregate interference can be approximated by a Gaussian random variable (many nodes contribute to outage). When the average number of nodes in the forbidden range is slightly smaller than one, neither the nearest node approximation nor Gaussian one is accurate (a few near-by nodes are dominant), and higher order cumulants approximations or others are required. We derive the nearest interference distribution and give a simpler way to calculate the cumulants of the aggregate interference. † Y. Wen, S. Loyka and A. Yongacoglu are with the
Modeling Heterogeneous Network Interference Using Poisson Point Processes
IEEE Transactions on Signal Processing, 2000
Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complicated, making evaluation of different communication strategies challenging in both analysis and simulation. This paper suggests a simplified interference model for heterogeneous networks. Leveraging recent applications of stochastic geometry to analyze cellular systems, this paper proposes to analyze downlink performance in a fixed-size cell in what is called the hybrid approach. The interference field consists of a contribution from out-of-cell interferers modeled as a superposition of marked Poisson point processes outside a guard region and a cross-tier contribution modeled as a marked Poisson point process. The guard region is used to avoid association issues that would occur if an interferer were located at the cell edge. Bounding the interference power as a function of distance from the cell center, the total interference is characterized through its Laplace transform. An equivalent marked process is proposed for the out-of-cell interference under additional assumptions. To facilitate simplified calculations, the interference distribution is approximated using the Gamma distribution with second order moment matching. The Gamma approximation simplifies calculation of the success probability and ergodic rate, incorporates small-scale and large-scale fading, and works with co-tier and cross-tier interference. Simulations show that the guard region can be tuned to give a reasonable match with performance in a hexagonal grid, and that the Gamma approximation provides a good fit over most of the cell.
Temporal Correlation of the Interference in Mobile Random Networks
2011 IEEE International Conference on Communications (ICC), 2011
In wireless networks, interference that is generated by undesired transmitters dominantly limits network performance. The correlation of node locations (in mobile or static networks) makes the interference temporally correlated. Such correlation affects network performance greatly, and hence needs to be quantified. In this paper, we quantify the temporal correlation of the interference in mobile Poisson networks. More specifically, we obtain closed-form expressions for the interference correlation coefficient ρ in Poisson line networks under various mobility models. When the mean speed of nodesv increases, we show that ρ is asymptotically proportional tov −1 . Moreover, multi-path fading and random MAC schemes reduce the temporal correlation of the interference. These results are extended to higher-dimensional networks.
Communication in a Poisson Field of Interferers-Part II: Channel Capacity and Interference Spectrum
IEEE Transactions on Wireless Communications, 2000
In Part I of this paper, we presented a mathematical model for communication subject to both network interference and noise, where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a wireless environment subject to path loss, shadowing, and multipath fading. We determined the distribution of the aggregate interference and the error performance of the link. In this second part, we characterize the capacity of the link subject to both network interference and noise. Then, we put forth the concept of spectral outage probability (SOP), a new characterization of the aggregate radio-frequency emission generated by communicating nodes in a wireless network. We present some applications of the SOP, namely the establishment of spectral regulations and the design of covert military networks. The proposed framework captures all the essential physical parameters that affect the aggregate network emission, yet is simple enough to provide insights that may be of value in the design and deployment of wireless networks.
Analysis of the simulated aggregate interference in random ad-hoc networks
2014 IEEE 15th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2014
In this paper, we propose a new method for bias correction in the simulation of random wireless ad-hoc networks (WANETs), when the distribution of the node locations is modeled as a Poisson-Point-Process (PPP). The aggregate interference is the main limiting factor in WANETs, and dominates the achievable rate and thus also the network capacity. In the proposed method, a bias correction constant is added to the aggregate interference that is measured in each simulation iteration. The value of the constant is derived through stochastic geometry analysis. We prove that the proposed method can reduce the computational complexity by several orders of magnitude, while producing more accurate simulation results. This improved accuracy is also demonstrated by simulations. As an example, we prove that a bias corrected simulation with only 100 transmitters is sufficient to estimate the aggregate interference with an accuracy of 1%.