Imane Oussakel
email: imane.oussakel@laas.fr

Philippe Owezarski
email: philippe.owezarski@laas.fr

Pascal Berthou
email: pascal.berthou@laas.fr

Cellular Uplink Bandwidth Prediction Based on Radio Measurements

Keywords: QoS monitoring, cellular networks, bandwidth prediction, machine learning, software defined radio

In 4G networks, the emergence of machine communications such as connected vehicles increases the high demand of uplink transmissions, thus, degrading the quality of service per user equipment. Enforcing quality-of-service in such cellular network is challenging, as radio phenomenon, as well as user (and their devices) mobility and dynamics, are uncontrolled. To solve this issue, estimating what the quality of transmissions will be in a short future for a connected user is essential. For that purpose, we argue that radio metrics are key features whose evolutions can help predicting the bandwidth that the considered connections can take advantage of in the following hundreds of milliseconds. The paper then describes how a 4G testbed has been deployed in order to study the correlation between radio noise and throughput in uplink transmissions. Based on radio measurements, the main supervised machine learning algorithms are used, such as Random Forest and Support Vector Machine to predict the uplink received bandwidth. For a specific user service, we are able to predict the end-to-end received bandwidth, i.e. the amount of received data on the server side during a specific period at a very low scale of 100 ms. Results also prove that uplink bandwidth predictions are less accurate compared to bandwidth prediction for downlink based on radio measurements.

I. INTRODUCTION

In the scope of smart cities, where everything is connected at anytime and anywhere, the Intelligent Transport System -ITS -emphasizes many services relying on car communication system. In such system, the vehicle is connected to pedestrians, other vehicles and the ITS servers via wireless networks. Many car companies have been engaged in a research effort to tackle the upcoming ITS issues. For instance, Continental Digital Service France (CDSF) and LAAS-CNRS have launched a collaboration in the framework of the eHorizon project (2017-2021) to cope with ITS systems [6]. As cellular networks are well known for their high throughput and low latency, especially the 4G standard, recent researches endorse the use of LTE-A for the middle term services of connected cars. In such communication, most applications send data (i.e. data uploading) to remote internet servers through LTE-A interface. Thus, contrary to the Human-to-Human applications where downlink (DL) transmission dominates, cars services use mostly uplink (UL) communication. For instance, automotive data analytics [START_REF]The Connected Vehicle: Big Data[END_REF] forecast a production of up to 30 terabytes of data per day by an average car. Therefore, the conventional roles are inverted: when all the vehicles are sending their information, a large amount of data must be received by the ITS server with a high quality of service (QoS). Eventhough, 4G is expected to satisfy the high demand of high throughput, several researches show that LTE suffers from congestion [START_REF] Phan | A capacity analysis for the transmission of event and cooperative awareness messages in LTE networks[END_REF], [START_REF] Vinel | 3GPP LTE Versus IEEE 802.11p/WAVE: Which Technology Is Able to Support Cooperative Vehicular Safety Applications[END_REF], especially in UL with the growth of machine traffic. This implies a QoS degradation, and sometimes, the inaccessibility to the network, that limits the envisaged applications and services.

Over years, researchers were focused on enhancing downlink (DL) transmission as only DL was challenging. They improved DL schedulers and congestion control mechanisms while taking predicted throughput as an input parameter [START_REF] Lu | CQIC: revisiting cross-layer congestion control for cellular networks[END_REF], [START_REF] Kwan | On pre-emption and congestion control for LTE systems[END_REF]. For that, DL LTE throughput prediction has been the ultimate goal of research, as it improves many use cases, such as video streaming quality. Although schedulers and congestion control mechanisms are different in UL and DL, we forecast an improvement of UL LTE-A in a similar way as DL, by incorporating UL predicted throughput. Machine application servers may avoid saturation based on the forecasted bandwidth, hence reducing UL QoS degradation. Thereby, UL bandwidth prediction is valuable in the machine-to-machine context.

In wireless networks, throughput is one of the high performance metrics that changes rapidly depending on the environmental situations. However, radio phenomena affect the different performance metrics. It is increasingly hard to understand how such phenomena degrade the QoS, as they are uncontrolled. In this article, we tackle one radio phenomenon, i.e. noise, to understand how it influences the throughput performance in uplink 4G. In the framework of eHorizon project, we study the case of a connected car transmitting a fixed amount of data to a specific server based on LTE-A network. The aim is to estimate/predict the uplink-received bandwidth by the server. To that end, a 4G testbed is deployed, where the radio propagation is controlled in an Anechoic Room (AR) while injecting a specific noise profile. We investigate our work on UL bandwidth prediction based on radio measurements over a small time granularity, from 100 ms to 1 s scales. Different machine-learning (ML) algorithms are tested to validate the impact of wireless channel on bandwidth prediction in UL transmissions.

The remaining of this paper is organized as follows. Section II points out the 4G background of the experimentation. The related work is reviewed in section III. Section IV describes the testbed deployment inside an anechoic room. Section V covers the prediction methodology used in this article.

Section VI presents and discusses the obtained results for uplink bandwidth prediction. Finally, section VII concludes this paper.

II. LTE-A BACKGROUND

Our work is based on 4G communications, as uplink cellular traffic has become dense with the introduction of M2M communications, especially connected cars. This section presents a quick overview of the main 4G metrics and techniques that our study is based on.

Fig. 1 shows a basic architecture of the 4G network when a User Equipment (UE) is connected via the LTE access network to the Evolved Packet Core network (EPC). The EPC maintains the sessions, registration procedures and routing of UE IP-packets. The base station for LTE-A radio is named evolved NodeB (eNB); it ensures mainly Radio resource management and scheduling in both uplink and downlink. 4G is known as a flexible standard as it proposes the use of different bandwidths {3,5Mhz, 4 MHz, 5 MHz, 10 MHz, 20Mhz} and can be deployed on many frequency bands. To ensure the multiple users access, 4G uses OFDMA in downlink and SC-FDMA in uplink. Orthogonal Frequency Division Multiple Access (OFDMA) is a multiple carrier system, where each OFDM data symbol is transmitted over one subcarrier. This transmission of multiple data symbols in a parallel manner leads to a high PAPR (Peak to Average Power Ratio). PAPR causes a high-energy consumption for the transmitter. For uplink transmissions, the efficiency of power amplifier becomes crucial as the UE has a limited battery power. To avoid this OFDMA drawback in uplink, the 4G deploys the single-Carrier Frequency Division Multiple Access (SC-FDMA), where data symbols are transmitted in series and each symbol is carried by a wider bandwidth. Such difference with downlink motivates our investigation on uplink.

The radio transmission is based on either Time Division Duplex (TDD) or FDD (Frequency Division Duplex) mode. Different frequency bands are used for downlink and uplink in FDD; in contrast, the uplink and downlink in TDD mode are separated in time while sharing the same frequency band. For each duplex mode, a frame structure type has been defined. For instance, in FDD, frame type 1 is used in Half and full duplex mode. As shown in fig. 2, the frame-type 1-length is fixed to 10 ms, containing 10 sub-frames of 1 ms (two adjacent slots). Each slot is defined as a resource block of 0.5 ms over 12 subcarriers spaced by 15 khz when a simple Cyclic prefix (CP) is used and spaced by 7.5 kHz in the case of extended cyclic prefix. Then, data symbols are transmitted over one or several resource blocks. Each resource block holds six or seven SC-FDMA data symbols depending on the used cyclic prefix. In the physical layer, the LTE-A radio resource is referred as Physical Resource Block (PRB) that forms 180 khz x 0.5 ms. Our measurements are mainly based on the specified PRB. In time domain, the PRB contains seven SC-FDMA data symbols expanded over 12 subcarriers in frequency domain. The eNB allocates for each user a specific number of resource blocks based on its resource-scheduling algorithm, UE's capability and the channel quality. Although schedulers are vendor specific, it is reported to consider one TTI (Transmission Time Interval) of 1 ms as the smallest scheduling time unit [START_REF] Trivedi | Comparison of Different Scheduling Algorithm for LTE[END_REF]. Thus, based on the used bandwidth, a defined number of useful resource blocks is available. For example, for a 5 MHz bandwidth, 25 physical resource blocks of 180 kHz could be assigned to the users attached in the cell. In order to handle the communication between the UE and eNB, the use of these PRBs is standardized by using channels formats in the lower layers. For instance, for uplink transmissions at Physical layer level, the UE activates the PRACH, Physical Random Access Channel to demand access to the network; it communicates the control signaling information using the Physical Uplink Control Channel (PUCCH). PUCCH is mainly located in the bounds of the used bandwidth in frequency domain. The UE transmits its data on the Physical Uplink Shared Channel (PUSCH), which uses the remaining PRBs.

In the wireless system, channel is changing rapidly, resulting in QoS degradation. In order to adapt to channel's change and guarantee a high quality of service over time in downlink and uplink communications, the UE and eNB accomplish many measurements and reports. The 3GPP has normalized the main measures for each side of the network. The difference between the UE and eNB composition results in many dissimilarities between downlink and uplink measurements. As we are interested in uplink communication, we cover in more details the main uplink measurements used for prediction in section Vpart V.A.

III. RELATED WORK

Over years, bandwidth estimation and prediction has been widely studied in wired networks and WLAN. D. Kout-sonikolas et al. [START_REF] Koutsonikolas | On the feasibility of bandwidth estimation in 1xEVDO networks[END_REF] reveal the ineffectiveness of using those techniques in cellular networks as they are characterized by the large short-scale fluctuation of bandwidth. Although, [START_REF] Winstein | Stochastic Forecasts Achieve High Throughput and Low Delay over Cellular Networks[END_REF]- [START_REF] Liu | Experiences in a 3G Network: Interplay Between the Wireless Channel and Applications[END_REF] show the possibility of throughput estimation and prediction in wireless networks essentially in Downlink. Their proposed methods are based on higher layer measurements. In cellular networks, based on radio measurements, multiple performance tasks are introduced at different layers of the protocol stack. For instance, when a bad signal is received HARQ (Hybrid automatic repeat request) is triggered in the second layer. Given this, we are interested in using the radio measurements to predict bandwidth instead of higher layer measurements.

Even though, both client and network throughput are important in cellular networks, link bandwidth prediction related work considered only Downlink channel. F. Lu et al. [START_REF] Lu | CQIC: revisiting cross-layer congestion control for cellular networks[END_REF] use CQI (Channel quality indicator) and DRX (Discontinuous Transmission) to predict instantaneous downlink throughput in 3G networks. The study in [START_REF] Chakraborty | Coordinating cellular background transfers using LoadSense[END_REF] classifies bandwidth into high and low categories in order to increase user equipment coordination efficiency for transmission in cellular background. Margolies et al. [START_REF] Margolies | Exploiting mobility in proportional fair cellular scheduling: Measurements and algorithms[END_REF] investigate the reproducibility of signal quality over the same path to predict throughput based on user trajectory tracking. Authors of [START_REF] Yue | Cellular Link Bandwidth Prediction in LTE Networks[END_REF], [START_REF] Samba | Instantaneous throughput prediction in cellular networks: Which information is needed[END_REF] proposed the use of machine learning techniques, especially Random Forest, to predict instantaneous throughput in LTE-A networks. However, A. Samba et al. [START_REF] Samba | Instantaneous throughput prediction in cellular networks: Which information is needed[END_REF] predict throughput based on both eNB and UE information before the connection is established for content providers. They conclude that applying RF on radio measurements leads to a promising prediction: 52% of the relative prediction errors are within ±20%. C Yue et al. [START_REF] Yue | Cellular Link Bandwidth Prediction in LTE Networks[END_REF] consider a set of lower layer measurements and historical throughput to predict real-time LTE-A throughput. Accurate predictions were obtained: 69% of the relative prediction errors are within ±10% for walking scenario.

All of the above studies focus on predicting bandwidth for only DL transmissions. Our work differs in that we are interested in UL that takes advantage of a different transmitter and receiver composition. In fact, contrarily to DL that uses OFDMA reducing/vanishing the inter-symbol interference (ISI), UL 4G uses SC-FDMA, where data symbols are transmitted in series and each symbol is carried by a wider bandwidth. Hence, SC-FDMA is susceptible to ISI, which reduces data-rate when no compensation is present. For that the eNB deploys as a first step a complex frequency equalizer to mitigate such distortion. Therefore, UL data-symbols are not only affected differently by the channel variation compared to DL, but signal treatment is also different in the receiver (eNB). This difference with downlink motivates our work on uplink performance study to investigate the possibility of estimating/predicting the bandwidth in SC-FDMA based systems, that could be different from related work focusing on downlink only. For estimating/predicting UL traffic, we apply mainly Support Vector Machine (SVM) [START_REF] Smola | A tutorial on support vector regression[END_REF] and Random Forest (RF) [START_REF] Breiman | Random forests[END_REF] as machine learning techniques to predict the UL bandwidth based on Radio measurements. Both algorithms provide good predictions in different application domains with accurate time series and are insensitive to high dimensional feature spaces [START_REF] Zekić Sušac | A Comparison of Machine Learning Methods in a High-Dimensional Classification Problem[END_REF], which corresponds to the case study in this article.

IV. TESTBED DEPLOYMENT

The testbed objective is to limit the uncontrolled effects during a wireless communication, and study the impact of disturbing features on high level QoS metrics. The wireless system is LTE-A as already mentioned in the paper. Fig. 3 schematizes the testbed deployment. Openairinterface (OAI) software based platform [START_REF] Nikaein | Openairinterface: A flexible platform for 5g research[END_REF] is implemented. It spans the full LTE 3GPP protocol stack (including features from LTE-Advanced and LTE-Advanced-Pro) for both radio access and core network. For a full access to radio measurements, the 4G network is based on the Software defined radio (SDR). The OAI softmodem is connected with a hardware platform for SDR: USRP B210. The later is connected to a host computer to perform processing, and then connected to a PC running core network, and accessing the internet and a server. Cars are going to be connected using a 4G sim card in their system. To emulate a connected car communication system, a commercial UE (Samsung Galaxy J3 2017) is used and controlled remotely. To simplify the preliminary experimentations, the network transmission mode is Single Input Single Output (SISO). The eNB antennas (Tx and Rx antennas) and the UE are placed inside an AR, where the RF propagation is controlled thanks to the microwave absorbers materiel on the walls, scattering any wireless signal that comes across. Then the room inside is free from any multipath phenomena and radio perturbation or degradation. The testbed works on frequency band 7 (regulated to be used for ITS communications) with 5 MHz bandwidth and uses Frequency Division Duplex (FDD) mode, which corresponds to the traditional and stable version of OAI platform with USRPB210. As our objective is to observe the impact of radio perturbation on the bandwidth variation, the server and the intermediate PCs are well provisioned for not behaving as a bottleneck during communication. Throughput deterioration is mainly caused by environment phenomena.

IPERF3 generates traffic at the UE side and IPERF3server monitors throughput reception in the server. As TCP (Transport Control Protocol) changes the transmission window based on the perceived packet losses in the window, we instead use UDP (User Datagram Protocol) in order to have a fixed transmission amount of data during the whole test duration. Given this, any observed bandwidth degradation is essentially due to channel quality variation. Using a speed test throughput application in the UE, the maximum UL data-rate achieved in the testbed is around 8Mbps. Further, the traffic consists of a UDP flow with a constant throughput of 8 Mbps, which allows the use of all the available PRBs. The size of the packets is set to 1350 bytes to avoid any segmentation during transmission.

Noise profile: In real environments, multiple radio phenomena are scrambling the communications. Example phenomena include multipath fading leading to InterSymbol Interference (ISI) noise, pathloss and random processes such as AWGN (Additive White Gaussian Noise). These phenomena tend to attenuate aggressively the transmitted signal which causes a significant amount of signal strength reduction. Thus, in time varying scenarios, the received signal amplitude undergoes rapid fluctuation that is often modeled as a random variable with a particular distribution. In this paper, we consider a Gaussian distribution, AWGN, which is characterized by its amplitude that affects the signal strength. Moreover, noise (AWGN) is introduced as it causes transmission errors and may disrupt the communication with ISI production for high power noise [START_REF] Bolat | Study of OFDM Performance Over AWGNn Channels[END_REF]. Contrarily to work in literature where AWGN is often taken with constant attenuation, we introduce randomness in the attenuation in order to have attenuation fluctuations of the signal over time. For that, we developed an assisted labVIEW program on the noise generator. Given an interval of maximum and minimum noise levels, each 10s the noise level takes randomly a value in the specified interval. The programmed step for noise level change (10s) is chosen as to have sufficient samples for each noise level. Therefore, low noise level values keep the channel flat, while high noise level disrupt totally the communication, with the probability of introducing ISI. Also, the abrupt changes in noise levels during the transmission tend to reflect the real environments, where the user's mobility across different shadowers leads to aggressive/alleviated signal attenuation. The noise is injected inside the anechoic room using a signal generator with a directional antenna toward the eNB receiver. The bandwidth is fixed to 5Mhz to scramble the full UL bandwidth.

V. PREDICTION METHODOLOGY

Given the LTE testbed in the anechoic room, we are able to generate 4G traffic with noise perturbation. During the whole test duration, noise level changes by the programmed step (10s). This way, samples of same duration for every noise level are generated. In this section, we present the prediction methodology.

A. Data collection

The eNB performs different radio measures in order to decode the received data and adapt to channel variation. With SDR at eNB side, we are able to collect all the performed eNB measurements (as depicted by the 3GPP standard), especially from the lower layers. After a benchmark of physical layer measurements, we present in the following the main radio measures having a minimum correlation with bandwidth variation:

• RIP: Received Interference Power measured within the bandwidth of each PRB. The eNB measures the noise power over the PRBs each 1 ms. One of our objectives is to compare the bandwidth predictions over different time granularity. The bandwidth measurements are performed in a discrete time manner, each δt. As the minimum time report interval in IPERF3 is 100 ms, we fix δt=100ms. The predictions are then made every δt. The eNB measurements are performed per subframe scale (1ms). In order to have a representative measure per δt, we compute the maximum, minimum, and the mean of each measure per δt to construct the datasets. Table I depicts the constitution of datasets used as input for learning algorithms. The first column represents the datasets labels, and the second column explicits the constitution of datasets in the form of samples. We built 5 datasets based on the aforementioned metrics. Four of them are based on a single feature and the last one combines all the features. For instance, dataset RSSI contains the single UL RSSI feature. Each sample in dataset RSSI is composed of the maximum, minimum and mean measured UL RSSI over δt, i.e. {UL RSSI min, UL RSSI max, UL RSSI mean}, dataset All is a combination of the four features.

B. Methodology

In this article, Python scikit-learn library is used for all the tests. GridsearchCV [START_REF] Geisser | The Predictive Sample Reuse Method with Applications[END_REF] is applied to choose the optimal hyper-parameters for each estimator. It combines both gridsearch and cross-validation methods. Gridsearch consists of an exhaustive search over subset values of parameters for a given estimator and cross-validation (CV) technique [START_REF] Kohavi | A study of cross-validation and bootstrap for accuracy estimation and model selection[END_REF] estimates the prediction error of a model. CV is categorized

VI. UPLINK BANDWIDTH PREDICTION EVALUATION

This part presents and discusses the results obtained on bandwidth prediction using machine learning techniques. Five datasets are tested with two ML techniques RF and SVM. Because of place constraint, we only present the results with RF model; the results for SVM are pretty similar. The evaluation is based on the performance metric RMSE.

A. Sensitivity to forecast window

In order to exhibit the influence of window forecast size on predictions, each dataset from table I is evaluated over iδt, with i ∈ {1, .., 10} and w = 0. That is, we predict bandwidth based on the instantaneous radio measurements. The forecast window changes from 1δt to 10δt. The maximum, minimum and mean observed RMSE with K 2 -fold CV is represented in fig. 4. For each dataset, dashes represent the maximum and minimum of the observed RMSE per δt, and the line links the mean of the observed metric per δt. The predictions errors range from 29 Kbytes to 36 Kbytes. In fact, the lower RMSE value is obtained for predictions based on dataset Rx power, which doesn't exceed 31 Kbytes. Dataset SNR reaches 36.5 Kbytes of RMSE for a window forecast of 1δt. We point that the minimum, maximum and mean received bandwidth during the experimentation are 0 Kbytes, 128 Kbytes and 51.1 Kbytes respectively. When combining all the features in dataset all, the RMSE is not reduced compared with dataset Rx power. It is surprising that the SNR achieves the lower scores over the tested features, eventhough it combines the strength of the received signal and the noise measure.

In order to figure out whether the cause is the length of training samples per noise level, another test is performed, where the time step is 60s instead of 10s. Hence, 600 samples are available for each noise level, and a total of 26 noise levels are tested. The same methodology is applied, and similar results of RMSE are obtained (fig. 4). It clearly exhibits that the cause behind the observed values of RMSE is not the low number of training samples per noise level. Further, the overall received signal power could be considered the most relevant metric of channel quality in an environment with random noise variation. It is worth noting that the obtained UL predictions are less accurate compared with DL predictions based radio measurements, already mentioned in part III. Over the different forecasted windows, there is no major change in terms of RMSE, thus exhibiting the insensitivity of the model to the forecast window.

B. Prediction bias

In order to generalize the estimated error predictions and be sure that the 10-fold nested CV doesn't introduce any bias during the prediction stage, we study CV bias with varying folds. Different K values for the K-fold method are tested. A small value of K forms folds containing multiple noise level transitions, while higher values of K forms folds with a low number of samples per noise level. For K=26, the number of folds is exactly the number of noise levels. In this part K 2 =K 1 for the nested CV. Fig. 5 shows the distribution of the observed RMSE per CV size for a forecast window of 1δt with dataset SNR. For each K-fold, a vertical boxplot is drawn. It consists of a box from the lower quartile of the observed RMSE to the upper quartile, with a crossbar in the mean of RMSE. The upper and lower fences outside the box represent respectively 95% and 5% of the estimated RMSE. For all the tested K-folds, the mean RMSE is around 36Kbytes. Then, the generalized prediction error for dataset SNR in an environment with random noise is approximately 36Kbytes.

C. Sensitivity to lag size

In this part, the importance of having numerous past radio measurements for good predictions is analyzed. The main lag sizes w tested are 3, 7 or 10, i.e. using the past three, seven and ten δt measurements. Fig. 6 shows the obtained RMSE for a window forecast of δt with the three values of w for all the datasets. Adding the past measures improves smoothly the predictions based on dataset SNR and dataset RSSI. On the other hand, historical information doesn't necessary improve the performance, however, it might degrade it. The reason behind that might be the random and brutal change of the signal attenuation caused by the generated noise profile. In fact, it reflects real radio environment, where the upcoming attenuation is uncontrolled. Hence, forthwith the past measurements become obsolete. Therefore, in the rest of the paper, we fix w = 0.

D. Sensitivity to training data length

Machine learning techniques leverage on training sets to give accurate predictions. The size and variance of a given training set should then impact the prediction performance. In this part, we investigate the sensitivity of our model to the training dataset size. For that, we train RF model with various datasets of different lengths. In order to have a significant

E. Sensitivity to noise level linearity

In the previous parts, noise level was changing randomly during the test duration. Hence, the selected X train contains a significant amount of random noise level variations. In order to study the impact of the presence of such transitions in the training set, we set up another experimentation process. Keeping the same testbed, we changed the assisted LabVIEW program to control remotely the noise generator. This time, given an averaged granularity of 0.1 dBm as a step for noise level variation, the noise level is increasing every 10 s by the programmed step during the whole test duration (800s). This later experiment is aimed at providing a dataset less complex than the previous one in order to investigate the impairments introduced by the random change of noise levels on the system. The same process of data collection in part V.B is followed, and the two machine learning techniques, RF and SVM, are applied. We evaluate each dataset from table I over iδt, with i ∈ {1, .., 10} and w = 0. During bandwidth predictions, the forecast window changes from 1δt to 10δt. The maximum, minimum and mean observed RMSE with K 2 -fold CV is represented in fig. 8. For each dataset, dashes represent the maximum and minimum of the observed RMSE per δt, and the line links the mean of the observed metric per δt. Based on dataset SNR and dataset RIP, the RMSE Fig. 8: Impact of noise level variation. doesn't exceed 9.7 Kbytes and 13.4 Kbytes respectively for all the forecasted windows. It is to be noted that the minimum, maximum and mean received bandwidth are 1.32 Kbytes, 133 Kbytes and 75.04 Kbytes respectively. Comparatively, based only on the received power (dataset Rx power), poor predictions are obtained; an RMSE of 23.5 Kbytes is observed for a window forecast of 1δt. Dataset all that combines all the features, gives pretty similar results to the ones obtained with dataset SNR. This is explained by the presence of SNR measurements in dataset all. Therefore, this remarkable decrease of RMSE with the datasets containing linear generated noise levels is essentially due to the absence of randomness in noise level variation. In other words, the lower observed values of RMSE in the linear testbed are essentially due to the consecutive noise level variation in the training set for the model. Hence, the randomness in noise level variation leads to an increase in terms of RMSE, as expected.

F. Sensitivity to high noise level

The noise level changes each 10s by a step of 0.1 dBm during the whole test duration. After several tests, the maximum noise level is set to -12 dBm and the minimum to -20 dBm. Low values perturbate smoothly the radio environment, while the higher values, around -12 dBm, result in a packet loss above 90%(±5%) in the cell. In this part, we aim to see whether the prediction in linear testbed is sensitive to the high noise levels. To that end, we split the main dataset, for example, dataset RIP with bandwidth, into subsets of 1000 samples. Then, each subset contains 10 noise levels of 0.1 dBm difference, i.e. between -17.0 dBm to -16.0 dBm. We apply the methodology in V.B on each subset and plot in fig. 9, in 3D, the variation of the perceived RMSE over iδt with i ∈ {1..10} and per noise level. The RMSE is almost constant from -19 dBm to -16 dBm, then it increases brutally for the two levels of noise, -15 dBm and -14 dBm. Checking the corresponding bandwidth subsets, a high level of bandwidth variation is observed for these two levels. The increase of RMSE for those levels could be explained by the insufficiency of training samples, as only

VII. CONCLUSION

In this article, we investigated the uplink bandwidth prediction in cellular network and the radio phenomena impact on high-level QoS metrics, i.e. bandwidth. For that, a testbed is deployed in an anechoic room where the radio phenomena are controlled, and then noise is injected in a controlled manner to scramble the uplink transmissions. This allows a clear analysis of encountered behaviors. The noise profile is generated in a manner to emulate the amplitude attenuation variability present in real radio phenomena. Exhaustive radio measurements are performed to collect the main measures reflecting the uplink channel quality. In order to predict the received bandwidth at a granularity of 100 ms, machine learning techniques are used, mainly random forest and support vector machine. Nested cross-validation is used for each case study to generalize the obtained error predictions. As the features choice for machine learning is crucial, the sensitivity of the model to forecast window, lag size, high noise level and training data length are investigated for each feature. The model shows insensitivity in the different cases. We have emulated two types of environments and have shown that in an environment where noise level changes gradually, accurate predictions are achieved. On the other hand, when noise level changes brutally from lower to higher values and vice versa, thus emulating real radio communication systems, high prediction errors are obtained. Therefore, contrarily to downlink, where only radio measurements are sufficient to predict accurately the received bandwidth, uplink bandwidth prediction needs more investigation in a real environment with very versatile devices and users. Hence, cellular uplink is becoming the hotbed of improvements.

Fig. 1 :

 1 Fig. 1: Basic 4G architecture.

Fig. 2 :

 2 Fig. 2: Uplink resource grid for one slot.

Fig. 3 :

 3 Fig. 3: LTE-A Testbed deployment.

Fig. 4 :

 4 Fig. 4: Impact of forecast window.

Fig. 5 :

 5 Fig. 5: Cross-validation bias.

Fig. 6 :

 6 Fig. 6: Impact of lag size w.

Fig. 7 :

 7 Fig. 7: Impact of training dataset length.

Fig. 9 :

 9 Fig. 9: Sensitivity to high noise level.

  SNR: Signal to Noise Ratio compares the level of the desired received signal to the level of noise. Taking P signal and P noise as the average power of the received signal and noise respectively, SNR is defined (in decibels) as follows: SN R dB = 10.log 10 (P signal /P noise ).

	• UL RSSI: Uplink Received Signal Strength Indicator. It
	measures the total wideband received power over the full
	bandwidth -5 MHz -including noise and interference.
	UL RSSI states the quality in the cell. Too low RSSI
	reflects the inability of the cell to communicate with
	any UE, while too high value indicates a high level of
	interference in the cell.
	It is
	measured for each received PUSCH holding UE's data
	and PUCCH containing the UE's control signaling infor-
	mation. Let's denote PUSCH SNR and PUCCH SNR the
	corresponding metrics.

• • Rx power: The received power. It measures the received power in the eNB based on the demodulation reference signal (DMRS), which is used to get a coherent detection and demodulation of UL channels.

into exhaustive and non-exhaustive categories, the former is more computational for high dimensional datasets. For that, the non-exhaustive cross-validation is chosen, mainly the recommended K-fold method, with K=10 to have a good compromise between variance and bias of the model [START_REF] Friedman | The Elements of Statistical Learning[END_REF]. Varma and Simon [START_REF] Varma | Bias in error estimation when using cross-validation for model selection[END_REF] report that the estimated prediction error from the cross-validation used to tune hyper-parameters is biased, and recommend the use of nested cross-validation instead, where an inner CV is used to select the optimized model (executed with GridsearchCV) and an outer CV to estimate the prediction error. Let denote K 1 -fold and K 2 -fold the inner and the outer CV respectively. Given an input dataset, a random split is performed to construct training and test sets. In fact, the dataset is split into K 2 -folds, one fold is used for testing and the others K 2 -1 folds constitute the training set. For each hyper-parameter combination from the gridsearch, K 1 -fold is applied. It divides the training set into K 1 equal folds; K 1 -1 folds are used for training and the remaining fold for evaluation. It computes the prediction error and iterates until all the folds are used for both training and validation, then the prediction error is averaged over all the K 1 cases of CV. The hyper-parameter combination achieving a minimized prediction error is selected as the best optimized model. In order to generalize the selected model, the outer loop CV is used where the model is tested K 2 times on unseen data, i.e. the test set. Then, the generalized prediction error is the average of the estimated prediction error over the tested sets.

Algorithm 1 represents the prediction model for bandwidth. For a given dataset (table I), we apply the algorithm summarized in the following. Let N be the size of the considered dataset. K 2 -fold CV is chosen for having randomly 25% of the dataset for testing which we denote X test ={X 1 test , .., X m test } with size m, and 75% for the training set denoted X train ={X 1 train , .., X n train } with size n, where X p train and X p test are the p th samples in their corresponding datasets. GridsearshCV is applied on the X train to select the optimized model, referred by M . Let w be the rolling window, it represents the past w time units, and i denotes the forecast window, where i ∈ {1δt...10δt}, with δt=100 ms. The maximum forecast window is then 1 second. For each lag w and forecast window i, M uses the historical measures (X t test , X t-1 test , .., X t-w test ) to predict for each sample X t test from X test the corresponding bandwidth BW t (i,w) , i ∈ {1..10}. For example, using Dataset RIP with i=1 and w=2, M uses the current and Algorithm 1 Bandwidth prediction from dataset i Input:

Historical radio measurements with lag size w, M: optimized prediction model. Output: BW =[( BW 1 (1δt,w) , .., BW 1 (i,w) ), .., ( BW m (1δt,w) , .., BW m (i,w) )] : the predicted bandwidth.

for each(w,i) do for t in range (1, m) do ( BW t (1δt,w) , BW t (2δt,w) , .., BW t (i,w) ))=M (X t test , X t-1 test , .., X


domain: spi phys

text:
C Chatelard

J Sanchis Muñoz

J.-C Krapez

C Mazel

V Olichon

J Barba Polo

Y.-M Frédéric

F Hélias

P Barillot

I Legoff

G Serra

LEAK DETECTION IN WATER TRANSMISSION SYSTEMS BY MULTISPECTRAL REMOTE SENSING WITH AIRPLANE AND UAV

Water leak detection in water transportation mains outside urban areas by airborne remote sensing has been assessed with a series of measurement campaigns in 2017 over SCP (Société du Canal de Provence -France) network in Provence (Fr). The most appropriate wavelengths and combination for revealing high moisture areas and artificial leaks coming from this image database (VNIR, SWIR, TIR spectral range) allowed us to select the best onboard instrumentation for both types of platforms (manned & unmanned). This work aims at validating the choice of this instrumentation associated with the multispectral approach (Triangle method) in the framework of a new airborne campaign in October 2018 with a plane and an UAV in operational environment.

INTRODUCTION

Water loss in the transmission networks is a perennial problem which challenges the efficiency of water transmission systems and represents a waste of limited natural resources. Water has become increasingly scarce and less predictable [START_REF] Sarni | Water Tech: A guide to investment, innovation and business opportunities in the wáter sector[END_REF]. In some places of Europe as much as 50% of water resources are being lost before they reach the end-user [START_REF]A water blueprint for Europe[END_REF]. Solutions shall address the problems Europe is facing, e.g. 60% of European cities over-exploit their groundwater resources and 50 percent of wetlands are endangered [START_REF]Water is for life: How the Water Framework Directive helps safeguard Europe's resources[END_REF], which could get worse if a more efficient and sustainable use of water resources is not achieved. Problems with leakages are not only related to the efficiency of the network but also to water quality. The detection of leakages in large diameter mains, which represent a high share of the total water losses, is key but it has been poorly addressed due to the challenges it faces (less frequent access to pipe, high frequency noise is quickly attenuated, multiple travel paths, etc.).

Currently, active leakages in water distribution networks (WDN) are detected and located by ground sensing and monitoring techniques based on the measurement of pressure differences, acoustic sounding and ground penetrating radar. These ground methods become difficult or inadequate for water transmission mains, especially out of urban areas, and for open canals. New efficient and cost-effective pipeline surveillance methods are required.

The water leaks induce soil moisture which can reach the upper surface by diffusion and capillarity depending on the pipe damage severity. In a vegetation context, water leaks increase the water content in the vegetation canopy and the vegetation vigour.

Remote sensing offers the possibility of large, medium and field-scale soil moisture monitoring and characterization relying on variations of reflectance in optical bands or emission in thermal bands. An increase of the soil moisture induces reflectance changes in both soil and vegetation, and emission changes related to surface emissivity (close to 1 for natural surfaces) and surface temperature. Some visible effects associated to the soil water content are surface darkening, temperature variations due to increased evaporation, thermal inertia of local areas, and on vegetation anomalous growth or vigour.

The Earth-atmosphere energy balance conditions the surface temperature. This balance is affected by the thermal properties of the surface and the underlying horizons. The water presence in soil or vegetation increases the latent heat losses through evaporation or evapotranspiration respectively. These losses reduce the amplitude of the temperature variations related to variations of the radiative flux (e.g. day-night variations) for both soil and vegetation.

Wet areas should show a lower radiance temperature as compared to drier areas during sunny day hours, whereas the opposite is expected after the sunset and before the dawn [START_REF] Myer | Crops and soils[END_REF]. Thermal infrared (TIR) sensors are used on this basis to assess the soil moisture or the evaporation rate over vegetation canopy areas [START_REF] Nellis | Application of thermal infrared imagery to canal leakage detection[END_REF][START_REF] Tracey | Hydrologic investigations in canal and aqueduct systems using airborne thermal infrared linescanning[END_REF][START_REF] Pickerill | Leak detection from rural aqueducts using airborne remote sensing[END_REF][START_REF] Mcgowen | Identifying channel seepage using pre-dawn thermal imagery[END_REF][START_REF] Huang | Airborne remote sensing for detection of irrigation canal leakage[END_REF][START_REF] Thomson | Potential and challenges in use of thermal imaging for humid region irrigation system management[END_REF][START_REF] Arshad | A remote sensing technique detecting and identifying water activity sites along irrigation canals[END_REF][START_REF] Cundill | Investigation of remote sensing for potential use of dike inspection[END_REF]. However, the detection accuracy of the TIR [START_REF] Nellis | Application of thermal infrared imagery to canal leakage detection[END_REF][START_REF] Tracey | Hydrologic investigations in canal and aqueduct systems using airborne thermal infrared linescanning[END_REF][START_REF] Thomson | Potential and challenges in use of thermal imaging for humid region irrigation system management[END_REF] is low leading to false positives and misinterpretations caused by diverse scenarios like dense vegetation or shadows. To overcome this limitation, TIR was combined with visible and NIR data from multispectral or hyperspectral cameras [START_REF] Pickerill | Leak detection from rural aqueducts using airborne remote sensing[END_REF][START_REF] Huang | Airborne remote sensing for detection of irrigation canal leakage[END_REF][START_REF] Arshad | A remote sensing technique detecting and identifying water activity sites along irrigation canals[END_REF][START_REF] Cundill | Investigation of remote sensing for potential use of dike inspection[END_REF]. A combined use of TIR and VIS-NIR data like in the Triangle Method can be used in water leak detection over water transmission pipes and canals to gain accuracy. This method consists in combining the apparent temperature and a vegetation index like NDVI to perform a temperature-NDVI scatterplot for all the pixels over an area with a wide diversity in terms of cover fraction and water content. The name is related to the (roughly) triangle shape of the obtained scatterplot [START_REF] Sandholt | A simple interpretation of the surface temperature-vegetation index space for assessment of surface moisture status[END_REF][START_REF] Carlson | An overview of the" triangle method" for estimating surface evapotranspiration and soil moisture from satellite imagery[END_REF][START_REF] Petropoulos | Surface soil moisture retrievals from remote sensing: Current status, products & future trends[END_REF][START_REF] Krapez | Comparison of three methods based on the temperature-NDVI diagram for soil moisture characterization[END_REF][START_REF] Krapez | A combination of temperature, vegetation indexes and albedo, as obtained by airborne hyperspectral remote sensing, for the evaluation of soil moisture[END_REF][START_REF] Krapez | Combined airborne thermography and visible-to-near infrared reflectance measurement for soil moisture mapping[END_REF][START_REF] Maltese | Surface soil humidity retrieval using remote sensing techniques: a triangle method validation[END_REF][START_REF] Maltese | Soil water content assessment: Critical issues concerning the operational application of the triangle method[END_REF][START_REF] Chatelard | Multispectral approach assessment for detection of losses in water transmission systems by airborne remote sensing[END_REF]. The vertex of the triangle is often truncated, giving a trapezoidal shape. The scatterplot yields to the calculation of a water index for each point or pixel by making a quotient between its relative position with respect to the dry edge and the wet edge of the triangle/trapezoid [START_REF] Sandholt | A simple interpretation of the surface temperature-vegetation index space for assessment of surface moisture status[END_REF][START_REF] Petropoulos | Surface soil moisture retrievals from remote sensing: Current status, products & future trends[END_REF][START_REF] Krapez | Combined airborne thermography and visible-to-near infrared reflectance measurement for soil moisture mapping[END_REF][START_REF] Maltese | Surface soil humidity retrieval using remote sensing techniques: a triangle method validation[END_REF][START_REF] Maltese | Soil water content assessment: Critical issues concerning the operational application of the triangle method[END_REF][START_REF] Chatelard | Multispectral approach assessment for detection of losses in water transmission systems by airborne remote sensing[END_REF].

An airborne remote sensing campaign was conducted during February, April and July 2017 over several areas belonging to the water network infrastructure provided by SCP to evaluate the applicability of the temperature/Vegetation Index space (i.e. the triangle/trapezoid method) in a water leak detection method based on airborne data. The campaigns were driven with ONERA's BUSARD aerial platform instrumented with two hyperspectral Hyspex VNIR and SWIR cameras and a microbolometer infrared camera (FLIR A325 or FLIR A655sc 7.5-12µm). The best results were obtained by applying the triangle method fusing a thermal infrared image and a vegetation index image based on a visible image and a NIR image [START_REF] Chatelard | Multispectral approach assessment for detection of losses in water transmission systems by airborne remote sensing[END_REF].

The aim of this work is to validate the T-VI (Temperature -Vegetation Index) method at different scales by means of a manned aircraft platform and an UAV with data acquired in October 2018 over an area with artificial water leaks (Fig. 1).

METHODS

An airborne and UAV remote sensing campaign was carried out on October 2018 over several areas belonging to the water network infrastructure of SCP. The aircraft was a Tecnam P2006T operated by Air Marine and instrumented with a Spectrocam VNIR multispectral camera (with 8 custom selected filters: 425, 550, 640, 660, 724, 820, 832.5 and 840 nm), a Noxant Noxcam cooled TIR camera (7.7 -9.3 µm) and a custom made acquisition software. The flights with the manned platform were performed at an altitude of 800 m which led to a spatial resolution of 0.30 m for the Spectrocam camera and 0.48 m for the Noxant camera. The UAV was a custom designed multicopter operated by Galileo Geosystems and instrumented with a Micasense RedEdge 3 VNIR multispectral camera (with five bands: 475, 560, 668, 717 and 840 nm) and a microbolometer uncooled FLIR Vue Pro R TIR camera (7.5 -13.5 µm). The flights with the unmanned platform were performed at an altitude of 50 m which led to a spatial resolution of 3.4 cm for the Micasense camera and 6.5 cm for the FLIR camera. Soil moisture ground measurements have been carried out during the flights in the 5 cm upper layer with a portable FDR probe over the area of interest to assess the results. The area of study in the present work is a plot located in Vauvenargues (Aix-en-Provence, France). A secondary pipe has been connected to the existing main pipe and buried at a depth of about 1m; the connection with the existing pipe was equipped with a valve, a flow meter, a recorder and a pressure regulator; calibrated holes have been drilled in the added pipe to generate leakages.. In the present work three bands have been used in both cases, manned aircraft and UAV (660 nm (red), 832,5 nm (NIR) and TIR for manned aircraft and 668 nm (red), 840 nm (NIR) and TIR for UAV). In both cases, the images have been preprocessed with the Pix4D photogrammetric software to obtain spectral orthomosaics. The multispectral aircraft data are uncalibrated raw data. A radiometric calibration based on spectralon calibration images has been applied as part of the radiometric calibration carried out by Pix4D in the case of the red and NIR bands of the UAV acquired data. Although the aircraft and the UAV TIR cameras are both radiometrically calibrated, the emissivity parameter has been set to 1 and no temperature function has been applied to the raw data to extract the true temperature from the brightness temperature. The work in [START_REF] Chatelard | Multispectral approach assessment for detection of losses in water transmission systems by airborne remote sensing[END_REF] has showed negligible differences between wetness indexes obtained from calibrated and uncalibrated optical or thermal data. The rest of the data processing pipeline is similar in both cases. As a first processing step, the spectral mosaics have been normalized and the data range limited to the range [0, 1] with the aim of eliminating the "no data" value added by Pix4D. The co-registration of the spectral orthomosaics has been done with Gefolki software developed by ONERA [START_REF] Brigot | Adaptation and evaluation of an optical flow method applied to coregistration of forest remote sensing images[END_REF] and Pix4D (only the UAV multispectral data). The coregistration has been done taking as master the TIR image as the lowest resolution image in both cases; for this purpose a resampling of the VNIR with a bi-cubic spline interpolation algorithm was performed.

The empirical Triangle/Trapezoid method according to [START_REF] Sandholt | A simple interpretation of the surface temperature-vegetation index space for assessment of surface moisture status[END_REF] can be implemented by using either NDVI or OSAVI for the vegetation index. OSAVI is expected to have better immunity to the bare soil influence and then it is better correlated to the cover fraction [START_REF] Rondeaux | Optimization of soil adjusted vegetation indices[END_REF]. The water index (WI) is obtained by plotting each pixel of the scene in the temperature -VI space (T-VI). The resulting T-VI scatter plot shows a triangle/trapezoid shape of the pixel distribution. The WI of a pixel at temperature is calculated following the next expression: =

where and are the lowest and highest temperatures observed at the same VI as the considered pixel. The lowest temperature belongs to the so-called "cold" edge (or "wet" edge") of the triangle/trapezoid distribution, whereas the highest temperature belongs to the "warm" edge (or "dry" edge). In the classical Triangle method these edges are straight lines. They can be set automatically or manually, although the best results have been obtained by setting the edges manually.A software called WadiLeaks has been developed by Galileo Geosystems to carry out all the processing steps in a unique graphical user interface.

RESULTS

The OSAVI images obtained from the VIS and NIR images obtained onboard the airplane and the UAV are reported in Fig. 2. The flight line of the airplane was much larger than the image represented in Fig. 2-top. The latter has itself a much larger extent than the area covered by the UAV (black rectangle in the top image). The spatial resolution obtained by the UAV sensors is nevertheless from 7 to 9 times better. The Temperature-VI scatterplots obtained with the two sets of sensors are reported in Fig. 3. There are unavoidably some differences since the airplane explored a wider region; hence the corresponding scatterplot is more extensively covered.

For each scatterplot, the wet edge (low temperature border) and the dry edge (high temperature border) have been set manually, by excluding only a small number of pixels (outliers). The pixels that are excluded at bottom right of both scatterplot correspond to roads and paths.

The manned aircraft scatterplot is shifted towards lower VI values than those in the UAV scatterplot. This shift is due to the lack of calibration of the VNIR bands from the manned aircraft and doesn't affect the leaks' detection methodology. In the end, the inferred water index maps are reported in Fig. 4. The color scale is such that high moisture areas are in dark blue whereas low moisture areas are in light blue or even in white.

In the area where artificial leaks were present (see the red ellipse), a slight contrast can be observed in both WI images. The ground measurement have shown that the mean moisture level was about 30% and that it reached locally 60% at a few points along the leaking line (small puddles could then be seen as well). One should nevertheless admit that the contrast related to the leaks is quite faint; it is of about the same level as the other contrasts naturally developed across the considered field. In addition it is much lower than other false signals originating from the vegetation shadows. One explanation is that the campaign occurred one week after a rain period and the soil didn't have time to dry enough. In addition, in October, the solar radiation was not high enough to induce a tremendous difference regarding evaporation between the not-yet-dry surrounding soil and the soil wetted by the leaking line.

CONCLUSION

An airborne and UAV remote sensing campaign was performed in October 2018 over SCP water transportation means for acquiring airborne images with both platforms (aircraft and UAV) and for validating in operational conditions the WADI system (sensors, embedded software and on the ground) intended for the detection of water leaks. The multispectral approach has been validated on images of the Vauvenargues site where artificial leaks were introduced (new secondary pipe drilled with calibrated holes connected with the existing pipe) by applying the triangle method fusing a thermal infrared image and a vegetation index upon a visible image and a NIR.

The leaks induced a small contrast in the water index images obtained from both Airplane and UAV. Nevertheless, to achieve a level of contrast that would unarguably be detected against sources of false alarm (i.e. tree shadows), measurements should be done long after a rainy period and during warm seasons (around midday and with a powerful solar irradiance).

Figure 1 :

 1 Figure 1: Waterleaks test field. The green mark corresponds to the hydrant. The red line shows the leaking pipeline.

Figure 2 :

 2 Figure 2: OSAVI vegetation index from the manned aircraft (top) and from the UAV (bottom). The area covered by the UAV in the bottom corresponds approximately to the black rectangle in the top image.

Figure 3 :

 3 Figure 3: 2D scatterplots of Vegetation Index VI vs. normalized brightness temperature from the manned aircraft (left) and from the UAV (right). The wet edge is in blue and the dry edge is in red.

Figure 4 :

 4 Figure 4: Water index from the manned aircraft (top) and from the UAV (bottom). The leaking area is highlighted with a red ellipse (compare with Fig. 1).

ACKNOWLEDGEMENT

This work has been supported by the EU-funded H2020 project WADI -Water-tightness Airborne Detection Implementation (www.waditech.eu) under grant agreement N o 689239.