In a mobile ad hoc network (MANET), effective prediction of time-varying interferences can enable adaptive transmission designs and therefore improve the communication performance. This paper investigates interference prediction in MANETs with a finite number of nodes by proposing and using a general-order linear model for node mobility. The proposed mobility model can well approximate node dynamics of practical MANETs. In contrast to previous studies on interference statistics, we are able through this model to give a best estimate of the time-varying interference at any time rather than long-term average effects. Specifically, we propose a compound Gaussian point process functional as a general framework to obtain analytical results on the mean value and moment-generating function of the interference prediction. With a series form of this functional, we give the necessary and sufficient condition for when the prediction is essentially equivalent to that from a binomial point process (BPP) network in the limit as time goes to infinity. These conditions permit one to rigorously determine when the commonly used BPP approximations are valid. Finally, our simulation results corroborate the effectiveness and accuracy of the analytical results on interference prediction and also show the advantages of our method in dealing with complex mobilities.
However, the existing analysis methods only considered special or limiting scenarios where statistics of interference are identical at every time instant. For the random walk and Brownian motion models in @cite_30 @cite_33 , the means or pdfs (probability density functions) of aggregate interference at every time instant are the same due to the assumption that the initial node distribution is uniform. Consequently, node dynamics do not provide any useful information in the interference analysis. For the random waypoint model in @cite_30 @cite_33 , the idea was to wait an infinite time for the node distribution to converge to one limiting distribution that can be regarded as a PPP with a quadratic polynomial intensity @cite_23 . Based on that kind of PPP, mean, outage and approximated distribution for aggregate interference were given. As a result, not only do node dynamics not contribute to the analysis, but also the results are only valid in infinite time. It should be noted that in many applications what we would like to know are the statistics of aggregate interference within a finite time window rather than an infinite one.
@cite_30 @cite_33 @cite_23
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In wireless networks, distance variations caused by node mobility generate fluctuations of the channel gains. Such fluctuations can be treated as another type of fading besides multi-path effects. In this paper, we characterize the interference statistics in mobile random networks by mapping the distance variations of mobile nodes to the channel gain fluctuations. Network performance is evaluated in terms of the outage probability. A nearest-interferer approximation is employed. This approximation provides a tight lower bound on the outage probability. Comparing to a static network, we show that the interference distribution does not change under high mobility and random walk models, but random waypoint mobility increases interference. In mobile networks, distance variations caused by node mobility generate fluctuations in the channel gains. Such fluctuations can be treated as another type of fading besides multipath effects. In this paper, the interference statistics in mobile random networks are characterized by incorporating the distance variations of mobile nodes to the channel gain fluctuations. The mean interference is calculated at the origin and at the border of a finite mobile network. The network performance is evaluated in terms of the outage probability. Compared to a static network, the interference in a single snapshot does not change under uniform mobility models. However, random waypoint mobility increases (decreases) the interference at the origin (at the border). Furthermore, due to the correlation of the node locations, the interference and outage are temporally and spatially correlated. We quantify the temporal correlation of the interference and outage in mobile Poisson networks in terms of the correlation coefficient and conditional outage probability, respectively. The results show that it is essential that routing, MAC, and retransmission schemes need to be smart (i.e., correlation-aware) to avoid bursts of transmission failures. The random waypoint model is a commonly used mobility model in the simulation of ad hoc networks. It is known that the spatial distribution of network nodes moving according to this model is, in general, nonuniform. However, a closed-form expression of this distribution and an in-depth investigation is still missing. This fact impairs the accuracy of the current simulation methodology of ad hoc networks and makes it impossible to relate simulation-based performance results to corresponding analytical results. To overcome these problems, we present a detailed analytical study of the spatial node distribution generated by random waypoint mobility. More specifically, we consider a generalization of the model in which the pause time of the mobile nodes is chosen arbitrarily in each waypoint and a fraction of nodes may remain static for the entire simulation time. We show that the structure of the resulting distribution is the weighted sum of three independent components: the static, pause, and mobility component. This division enables us to understand how the model's parameters influence the distribution. We derive an exact equation of the asymptotically stationary distribution for movement on a line segment and an accurate approximation for a square area. The good quality of this approximation is validated through simulations using various settings of the mobility parameters. In summary, this article gives a fundamental understanding of the behavior of the random waypoint model.