RealTime Estimation of the Interference in Random Waypoint Mobile Networks
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Abstract
It is well known that the stochastic nature of the interference deeply impacts on the performance of emerging and future wireless communication systems. In this work we consider an ad hoc network where the mobile nodes adopt the Random Waypoint mobility model. Assuming a timevarying wireless channel due to slow and fast fading and, considering the dynamic path loss caused by the node’s mobility, we start by characterizing the interference caused to a receiver by the moving nodes positioned in a ring. Based on the interference distribution, we evaluate two different methodologies to estimate the interference in realtime. The accuracy of the results achieved with the proposed methodologies in several simulations show that they may be used as an effective tool of interference estimation in future wireless communication systems, being the main contribution of this work.
Keywords
Interference estimation Ad hoc networks Mobility1 Introduction
Interference is an important metric in the future generation of wireless communication systems because the traditional single transmitter and receiver model is being progressively replaced by a different approach, where multiple nodes may transmit simultaneously for a single or even multiple receivers.
The interference in wireless mobile networks, and particularly its characterization, is important for many applications. In most wireless mobile scenarios the characterization of the interference is a nontrivial task. While several authors model the interference in nonmobile networks [1], the assumption nodes’ mobility introduces a novel degree related with the timevarying nature of nodes’ positions. The works already published approaching a formal description of the interference in mobile networks are mainly focused on modeling. The use of statistics describing the level of mobility of the interferers in the modeling process was considered in [2, 3, 4]. [2] models the aggregate interference caused by static interferers, being considered that the nodes’ mobility only causes a timevarying displacement with respect to the different nonmobile cells. [3] admits a mobile scenario where the nodes adopt the Random Direction mobility model. [4] considers that the mobile nodes adopt the Random Waypoint mobility model (RWP), but only the interference power from the nearest interferer to the receiver is considered. [5] proposes an interference model for ad hoc mobile networks where the nodes move in accordance with the RWP and all the contributions of the nodes located within a defined region are considered.
This work starts by characterizing the distribution of the interference caused to a receiver by multiple moving nodes located in a ring, considering path loss and slow and fast fading. Based on the interference distribution, we evaluate two different methodologies to estimate the interference in realtime. The major contribution of this work is the identification of a method to estimate the aggregate interference in random waypoint mobility networks, leading to accurate results when used in realtime.
The next section describes the main contributions of this work. Section 3 presents the general assumptions. In Sect. 4 the distribution of the interference values obtained through simulation is approximated by known distributions in order to identify possible approximations. Section 5 describes two estimation methodologies as well as the realtime estimates obtained through simulation and finally the conclusions are present in Sect. 6.
2 Relationship to CyberPhysical Systems
Recently, Cyberphysical Systems have attracted much attention from the academic community. These systems are mainly focused on the link between computation and physical processes in terms of their reciprocal interaction. Instead of considering standalone physical devices, CyberPhysical Systems adopt an integrated network of multiple physical devices to enrich the interactions and cooperation between the devices and the virtual worlds available through computation.
Recent advances in wireless communications systems and distributed wireless networks have supported a plethora of innovation in CyberPhysical Systems. Significant progresses have been observed in mobile ad hoc networks and wireless sensor networks. Examples of CyberPhysical Systems include mobile robotics and mobile sensors or actuators.
Our work contributes to the development of mobile CyberPhysical Systems, by studying interference phenomena in mobile wireless networks formed without a central coordinator. By characterizing the interference caused by multiple mobile nodes, the wireless communication process can be improved. Consequently, mobile CyberPhysical Systems may benefit when higher throughput or reliability is needed.
Basically, we show the impact of the mobility, in terms of average velocity of the cyberphysical devices, in the interference caused to a central receiver. We characterize the interference power at the receiver taking into account the specifics associated with the propagation and mobility scenario. In this way, we contribute to the advance of CyberPhysical Systems, by proposing an effective solution to estimate the interference, which may be used for different purposes ranging from wireless energy harvesting to the improvement of the wireless communication system.
3 System Description
3.1 Mobility Assumptions
This work considers that the nodes move in accordance with the RWP mobility model [6]. In a RWP model all nodes are firstly placed in a random position (\( x, y \)). (\( x, y \)) is sampled from an uniform distribution denoted by \( x \in [0, X_{max} ] \) and \( y \in [0, Y_{max} ] \). (\( x, y \)) denotes the starting point, and the following procedure is the definition of the ending point (\( x^{'} ,y^{'} \)), which is uniformly selected as the starting point (i.e.\( x^{'} \in [0, X_{max} ] \) and \( y^{'} \in [0, Y_{max} ] \)). Afterwards a node samples the velocity \( v \in [V_{min} ,V_{max} ] \) from an uniform distribution, which is adopted to travel from the starting point to the ending point.
After arriving at the ending point (\( x^{'} ,y^{'} \)), a node selects the duration of a pause (\( T_{p} \)) during which it remains stopped at the ending point. After the time \( T_{p} \), a node selects another value for the velocity to travel to a different ending point. After arriving at the ending point, a node repeats the same procedure as many times as parameterized in the mobility simulations.
3.2 Network Scenario
Parameters adopted in the simulations.
\( X_{max} \)  1000 m  \( n \)  100 
\( Y_{max} \)  1000 m  \( T_{p} \)  0 s; 300 s 
Simulation time  3000 s  \( R_{i} \)  20 m 
\( V_{min} \)  5 m/s  \( R_{o} \)  120 m 
\( V_{max} \)  20 m/s 
3.3 Radio Propagation Assumptions
This subsection describes the radio propagation scenario considered in this work.
4 Characterization of the Interference Distribution
Following the assumptions considered in the previous section, several simulations were performed considering two different mobility scenarios:

Mobility scenario 1  \( V_{min} = 5 \) m/s, \( V_{max} = 20 \) m/s, and \( T_{p} = 0 \) s, representing an average node’s velocity \( {\text{E}}\left[ V \right] = 10.82 \) m/s;

Mobility scenario 2  \( V_{min} = 5 \) m/s, \( V_{max} = 20 \) m/s, and \( T_{p} = 300 \) s, representing an average node’s velocity \( {\text{E}}\left[ V \right] = 1.50 \) m/s.
Regarding the propagation conditions, we have considered the following scenario:

Radio scenario – \( \alpha = 2 \) and \( \sigma_{\xi dB} = 3 \) dB.
5 Interference Estimation
A Maximum Loglikelihood estimator (MLE) and a Probability Weighted Moments (PWM) estimator are introduced in the next subsections, in order to be used in realtime to estimate the aggregate interference. Hereafter, we denote the elements of an interference sample set by \( \chi = X_{1} , X_{2} , \ldots ,X_{m} \). We also consider the ordered sample set, which is denoted by \( X_{1,m} \le \ldots \le X_{m,m} \).
5.1 LogLikelihood Estimator
5.2 PWM Estimator
5.3 Simulation Results
Regarding the accuracy of the proposed estimators, both MLE and PWM present high accuracy. As a final remark, the results presented in Fig. 3 validate the proposed estimation methodologies, being the PWM estimator more adequate for the realtime estimation due to its higher accuracy. Finally, we highlight that approximate results were observed for smaller sample set sizes using the PWM estimator, and similar results may be achieved using only \( m = 10 \) samples per sample set, which is a remarkable low number of samples. The results are not show in the paper due to lack of space.
6 Conclusions
In this work we consider an ad hoc mobile network where the nodes move in accordance with the Random Waypoint mobility model. Assuming a timevarying wireless channel due to slow and fast fading and, considering the dynamic path loss due to the mobility of the nodes, we start by characterizing the interference distribution caused to a receiver by the mobile interferers located in a ring. The simulation results confirmed that the distribution of the aggregated interference may be accurately approximated by a Generalized Extreme Value distribution. Based on the interference distribution, two different methodologies (MLE and PWM) were assessed to estimate the interference in realtime. The accuracy of the results achieved with the proposed methodologies show that they may used as an effective tool of interference estimation in future wireless communication systems. Moreover, the low number of required samples constitutes one of the advantages of the proposed PWM estimator, even when the samples are highly correlated.
Notes
Acknowledgments
The authors gratefully acknowledge financial support from the Portuguese Science and Technology Foundation (FCT/MEC) through the project ADINPTDC/EEITEL/2990/2012 and the grant SFRH/BD/108525/2015.
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