Wireless link prediction and triggering using modified Ornstein–Uhlenbeck jump diffusion process
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Abstract
Through time domain observation, typical wireless signal strength values seems to exhibit some forms of meanreverting and discontinuous “jumps” behaviour. Motivated by this fact, we propose a wireless link prediction and triggering (LPT) technique using a modified meanreverting Ornstein–Uhlenbeck (OU) jump diffusion process. The proposed technique which we refer as OULPT is an integral component of wireless mesh network monitoring system developed by ICT FP7 CARrier grade wireless MEsh Network project. In particular, we demonstrate how this technique can be applied in the context of wireless mesh networks to support link switching or handover in the event of predicted link degradation or failure. The proposed technique has also been implemented and evaluated in a realtime experimental testbed. The results show that OULPT technique can significantly enhance the reliability of wireless links by reducing the rate of false triggers compared to a conventional linear prediction technique and therefore offers a new direction on how wireless link prediction, triggering and switching process can be conducted in the future.
Keywords
Wireless mesh networks Monitoring system Link prediction Link triggering Data analysis1 Introduction
Monitoring of a wireless link is a tough challenge due to the nature of the wireless link which is constantly affected by interference and temporary fading. An efficient and reliable network monitoring system is generally expected to collect information regarding current system configuration, observe current values of parameters influencing performance metrics, detect abnormal behaviour of a node or link and in some cases, predict the performance degradation events. Accurate and timely prediction is critical to ensure that there is sufficient time for mitigation actions such as self (re)configuration or healing to take place [3]. In wireless multihop [4] or mesh [5] environment, the behaviour of links particularly those which are closer to a gateway is becoming the primary concern as they carry the traffic of other nodes further down the hops. Through time domain observation typical wireless signals’ signal strength seem to exhibit some forms of meanreverting behaviour (converging towards a long term mean) as well as discontinuous “jumps” (missing values for a certain period of time). Therefore it is natural for us to look at models with these properties. One such stochastic model which we are considering in this paper is the Ornstein–Uhlenbeck (OU) diffusion process which was first applied in physics [7] to describe Brownian motion of particles suspended in a fluid with friction. In this paper due to the inherent jump properties of wireless signal strength or received signal strength indicator (RSSI) values, we propose the modelling of this behaviour using a modified Ornstein–Uhlenbeck jump diffusion process. The proposed technique is an integral part of the monitoring system developed by ICT FP7 CARMEN (CARrier grade wireless MEsh Network) project [1, 2, 6, 8].
The remainder of this paper is organised as follows. Section 2 discusses the related works and motivations behind this research. Section 3 presents the modelling, and calibration of the proposed method and the novel link prediction and triggering algorithms. Section 4 shows the OULPT analysis. It also demonstrates the design and realtime implementation of OULPT technique. Finally conclusions are drawn in Sect. 5.
2 Related work
Many studies have been done on wireless link monitoring in general and each of them provided us with different approaches, methods or techniques. On work to improve monitoring accuracy, the efficient and accurate linkquality monitor (EAR) developed by [9] exploits three complementary measurement schemes namely: passive, cooperative and active monitoring. It maximizes the measurement accuracy by dynamically and adaptively adopting one of the above mentioned measurement schemes. For link quality monitoring, many are using signal to noise ratio (SNR) or RSSI measurement as quality measure [10, 11, 12, 13]. According to MadWiFi driver [14], the reported RSSI for each frame is actually equivalent to the SNR and therefore the terms can actually be used interchangeably except that the definition of RSSI usually varies between vendors. The work in [10] confirms that the SNR is a very good indicator for choosing the optimum bit rate for IEEE802.11 [15] in general when trained on a particular link. Authors in [13] found that RSSI is an appropriate metric for quantifying the link quality and channel dynamics when compared with the value measured by a spectrum analyzer. The work in [12] proposes an accurate, lowcomplexity, online prediction mechanism for the long range prediction of wireless link quality. Similarly this work also uses RSSI as the basic measure for signal strength. Here the past measurements of the received signal strength are employed and then through segmentation, filtering and regression process, the future trend in the received signal strength is forecasted. [11] proposes XCoPred, which is a pattern matching based scheme to predict link quality variations. The nodes monitor and store the links SNR values to their neighbours in order to obtain time series of SNR measurements. When a prediction on the future state of a link is required, the node looks for similar SNR patterns to the current situation in the past using a cross correlation function. MeshMon [13] on the other hand aims to actively cooperate and predict, detect, diagnose and resolve network problems in a scalable manner. It is independent of the underlying routing protocol and can operate even if the mesh routing protocol fails completely. In our work, we propose a novel technique that takes advantage of meanreverting behaviour of a RSSI as well as its discontinuous “jumps” characteristic.
As revealed in [10], it is understood that though RSSI or SNR alone is good enough for a single link, it may not achieve sufficient accuracy in deciding the endtoend or network wide transmission quality. In such situation, other cross layer metrics such as (MAC/IP layer) latency, throughput and loss may provide a more accurate means to evaluate the quality of a link. Metrics such as expected transmission count (ETX) and expected transmission time (ETT) have been widely proposed to support routing decision in wireless mesh [16]. However these metrics depend very much on the types of application and hence pose additional complexities when performing prediction. First and foremost, the monitoring system would need to know exact traffic pattern of the sender, then there is a foreseen challenge on trigger timeliness since a specific period is required to collect, compute and analyze crosslayer frame information. In this paper therefore, we only focus on the SNR/RSSI as it generally provides a reasonably good indication on the quality of the link without having to know the traffic characteristics, patterns or distribution. Despite saying that, the proposed link prediction and triggering technique can be applied on any desired metric such as throughput, delay, jitter or loss rate as long as it exhibits some forms of meanreverting behaviour and discontinuous “jump”.
3 Link prediction and triggering with OU diffusion process (OULPT)
To make a reliable forecast of local and neighbouring mesh links, we propose a diffusion process models for a selected window size of a series of RSSI values. The prediction can be applied to any channel info received from the neighbouring radios. Instead of using statistical time series modelling which involves comprehensive model identification process and then parameters estimation that are numerically intensive, we propose a much more simpler and effective way to estimate diffusion process model parameters from historical data.
3.1 Ornstein–Uhlenbeck jump diffusion process
3.2 Model calibration
To begin with, the jump diffusion model in its simplest form needs an estimate of probability of jump, measured by λ, and its size J _{ t }. However, this can be made more complicated by having a distribution for J _{ t }. Given that we have an array of parameters to estimate and if we were to set up a maximum likelihood method for the full model (mixing jumps and diffusion), it may be hard for the algorithm to distinguish what are jumps, and what are diffusions. Hence there is a need for us to subdivide the parameter estimation of jump components and mean reversion diffusion process into two parts.
Begin 
Set R = {r _{1}, r _{2}, …, r _{ N }} and its complement R ^{ C } = ϕ where N is the number of observations. 
Repeat 
• Find the mean \(\bar{r}\) and standard deviation σ _{ r } of the set R 
• For all elements in the set R, filter out the return r _{ t } if \(\left {r_{t}  \bar{r}} \right > 3\sigma_{r} .\) Set the filtered out set R ^{ C } = R ^{ C }∪{r _{ t }} and R = R – {r _{ t }} 
Until no further returns are filtered. 
End 
In this study, rather than accurately finding the parameter values using expensive maximum likelihood estimation method we can instead rely on simple regression analysis. As shown in Fig. 4, we can see that there is a strong linear relationship between X _{ t+1} and X _{ t } (we take Δt = 0.1 s) for all t values. Hence the first step in our parameter estimation using regression analysis is to find the best fit of the RSSI time series {X _{ t }} to its past values in order to make future forecasts.
3.3 Prediction algorithm
Thresholds for link handover trigger
LinkUp threshold (LU_TH)  \(\bar{X} + \Updelta_{x}^{U}\) 
Linkcomingup threshold (LCU_TH)  \(\bar{X} + \Updelta_{x}^{CU}\) 
Linkgoingdown threshold (LGD_TH)  \(\bar{X} + \Updelta_{x}^{GD}\) 
Linkdown threshold (LD_TH)  \(\bar{X}\) 
In order to reduce the probability of making false trigger and the probability of selecting the wrong AP to a wider margin, we can modify the above decision criteria to the following scheme:
3.4 Trigger algorithm
Based on the analysis so far, the following is the proposed algorithm in the form of a pseudocode:
 Step 1.

Select a window size N from the latest smoothed RSSI values \(\left\{ {X_{i} } \right\}_{i = 1}^{N}\) of the current mesh node and also \(\left\{ {Y_{j}^{(i)} } \right\}_{j = 1}^{{N^{(i)} }}\) for each M neighbouring mesh nodes with their respective window size N ^{(i)}, i = 1, 2, …, M
 Step 2.

Extract out the jumpcomponents from \(\left\{ {X_{i} } \right\}_{i = 1}^{N}\) and \(\left\{ {Y_{j}^{(i)} } \right\}_{j = 1}^{{N^{(i)} }}\), i = 1, 2, …, M and estimate the OU jump diffusion process model parameters
 Step 3.

Forecast smoothed RSSI values for lead time \(\ell \ge \Updelta t\) for all current and neighbouring mesh nodes
 Step 4.
 Step 5.

Update the latest RSSI values and return to Step 1.
4 Analysis, design and implementation of OULPT technique
In the previous chapter we proposed the OU jump diffusion algorithm based on modified meanreverting diffusion process. It allows for a reliable forecast of RSSI values of local and neighbouring mesh links. This chapter contains some analyses of the proposed solution in Matlab simulation as well as in a realtime experimental testbed. The datasets adopted in our analyses represent two distinct environments namely the indoors and the outdoors. Further experimentations with different datasets may result in different levels of improvement but for initial proof of concept of our proposed OULPT, the existing datasets are believe to be sufficient to provide some valuable insights on what this technique may offer.
4.1 OULPT simulation analysis
In this section we evaluate the performance of the proposed OULPT technique using real RSSI data (courtesy from Intel and Fraunhofer FOKUS) using Matlab. For the Intel dataset, RSSI values of beacon frames were measured in an indoor office environment between a laptop and an IEEE 802.11g Access Point with transmission power of 15 dBm. The laptop moved with speed of approximately 0.5 m/s around the office. The Fraunhofer dataset on the other hand, were measured outdoor (open field) between two stationery wireless mesh nodes 50 m apart. Each node was equipped with IEEE802.11g radio card with transmit power of 14 dBm.
In this analysis we strictly follow the criteria set by Intel [20] in defining the LD and LGD thresholds using its RSSI. Here the LD threshold value is set at −80 dBm and LGD threshold is set at −76 dBm which results in a protection margin, \(\Updelta_{x}^{GD}\)of 4 dB. As the RSSI values do not seem to exhibit any trends or seasonal patterns and for fast computational results, the moving average (MA) technique is the best approach as all the weights are equally distributed to the data. As for other smoothing techniques such as weighted moving average (WMA), there is a need to choose the weighting factors in an ad hoc manner or through some estimation methods and is therefore impractical for our study. Detailed analysis on various smoothing techniques though desirable, is not the focus of this paper. In the following experiments, the OULPT parameters used are: N = 30, \(\ell = 5\), \(\Updelta_{x}^{GD} = 4\,{\text{dB}}\), m = 5, α = 0.60, \(\bar{\alpha } = 0.10\) and smoothing window size of 10.
By comparing Figs. 6, 7, 8 and 9 we can see by using the linear regression approach there is a higher likelihood that a false trigger would occur as compared with the approach taken by the proposed OULPT technique. In this paper we only compare OULPT with LR as both models are linear in construction and hence we are assessing likeforlike. Take note that the proposed OULPT is based on stochastic process modelling of the velocity of the random movements of RSSI values whilst the LR only looks into the relationship between explanatory and response variables. On the other hand time series models are not considered in this study as they are too computationally intensive such as there is a need to perform stationary test of the data, model identification, parameters estimation as well as diagnostic checking before one can fully use it. Therefore due to time constraints in the triggering process we have to exclude this technique. Furthermore time series models are not as practical as our OULPT technique from the implementation point of view.
Trigger results for Intel dataset of OULPT and linear regression techniques
Description of Trigger  OULPT (%)  LR (%)  Improvement (%) 

Triggers  24.20  36.49  −12.29 
False triggers  7.63  38.10  −30.47 
Nontriggers  75.80  63.51  +12.29 
False nontriggers  10.46  9.90  +0.56 
Although both methods have comparable lead time which is the time difference between the first successful trigger until the signal strength goes below the LD threshold, by reducing the chances of making a false trigger or missed trigger, the proposed OULPT technique is by far a more reliable method than linear regression.
4.2 OULPT module design and realtime implementation
Link state prediction result or trigger
Output/prediction  Description  Event type 

LINK_DOWN  Link completely down  State change 
LINK_GOING_DOWN  High probability of the link losing its connection status  Predictive 
LINK_UP  The Link is above the threshold value  State change 
LINK_GOING_UP  The probability of the link recovering its signal is high  Predictive 
Default settings for OULPT operation
General OULPT  
Data sample interval/step size  100 ms 
Moving average window size  10 
Jump diffusion algorithm  
Prediction Window size, N  30 
Prediction steps (or look ahead time)  5 steps (500 ms) 
Protection margin  4 db 
LD threshold  −80 dBm 
The visualizer shows the current smooth signal and also the predicted signal. The yellow markers indicate the LGD trigger events while the red markers indicate the LD events. The dark blue line represents the LD threshold. Other statistics such as trigger probability and false trigger probability of each trigger can be computed and shown in realtime.
5 Conclusions
Monitoring system is an integral part of every wireless mesh network. It provides to other modules accurate and timely information regarding the status of a network as well as to predict the quality of the wireless link. The results of prediction are used to reconfigure the network in advance to avoid service disruption. This paper proposes an novel link prediction and triggering technique based on a modified meanreverting diffusion process. The analysis shows that the proposed OULPT method can significantly enhance the reliability of wireless links which is particularly critical in wireless mesh environment. A significant improvement has been observed in reducing the rate of committing false trigger (from 38.1 to 7.63 % out of total trigger occurrences) as compared with the conventional linear regression method. The proposed method also incurs a very small percentage of false trigger when compared to the conventional linear regression method. On top of that when comparing the errors, OULPT experiences a smaller standard deviation implying that the errors are less dispersed. The linkup scenario is not addressed in this paper because it generally operates in the direct opposite manner as linkdown scenario. The prediction on linkup however can be used for early preparation of link to its normal operation. The proposed OULPT algorithm has also been successfully implemented and evaluated using a realtime embedded system board. Overall the OULPT technique is found to be promising and it offers a new direction on how wireless link prediction, triggering and switching process can be conducted in the future.
Notes
Acknowledgments
This work was partially funded by the European Commission within the 7th Framework Program in the context of the ICT project CarrierGrade Mesh Networks (CARMEN) (Grant Agreement No. 214994). The views and conclusions contained here are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the CARMEN project or the European Commission. The authors would also like to thank Intel and Fraunhofer FOKUS for contributing the datasets.
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