Estimation of remaining capacity is essential for ensuring the safety and reliability of lithium-ion batteries. In actual operation, batteries are seldom fully discharged. For a constant current-constant voltage charging mode, the incomplete discharging process affects not only the initial state but also processed variables of the subsequent charging profile, thereby mainly limiting the applications of many feature-based capacity estimation methods which rely on a whole cycling process. Since the charging information of the constant voltage profile can be completely saved whether the battery is fully discharged or not, a geometrical feature of the constant voltage charging profile is extracted to be a new aging feature of lithium-ion batteries under the incomplete discharging situation in this work. By introducing the quantum computing theory into the classical machine learning technique, an integrated quantum particle swarm optimization–based support vector regression estimation framework, as well as its application to characterize the relationship between extracted feature and battery remaining capacity, are presented and illustrated in detail. With the lithium-ion battery data provided by NASA, experiment and comparison results demonstrate the effectiveness, accuracy, and superiority of the proposed battery capacity estimation framework for the not entirely discharged condition. Owing to the remarkable advantages of high energy density, environmentally friendly features, low self-discharge rate and long service life, lithium-ion batteries have been broadly used in various applications, such as hybrid electric vehicles (HEVs), electric vehicles (EVs) and consumer electronics , 2. As tTo prevent possible accidents and help users make maintenance policies before batteries reach hazard levels, it is essential for the battery management system (BMS) to estimate the state of charge (SOC) and the state of health (SOH) of lithium-ion batteries. SOC is defined as the percentage of the battery remaining charge to the current maximum capacity , SOH chaActual battery capacity is a significant health indicator (HI) for describing the aging status, and monitoring this parameter can be applied for the SOH estimation . When thThe model-based methods depend on an electrochemical model (EM), an equivalent circuit model (ECM) or an empirical model to describe the physical essence of the lithium-ion battery capacity degradation. The electrochemical model applies partial differential equations (PDEs) to describe the actual electrochemical reaction process inside batteries, which can capture dynamic behaviors with high accuracy . For exaIn contrast, the feature-based methods have a strong realistic significance. Since the battery capacity is related with several easily measured features, it is convenient to estimate capacity by using trained connections with multiple features from the current, voltage and temperature profiles. Those methods avoid understanding complex reaction mechanisms inside batteries to construct mathematical or physical models, thereby having been widely investigated by many researchers. For instance, Li et al.  extracteAlthough the above feature-based methods can achieve relatively satisfactory estimation results, they require batteries should be fully discharged and charged, which can hardly be applicable in real operation. The discharging profiles of each cycle of batteries used in various conditions are diverse. During everyday usage, batteries are seldom fully discharged to the 0% SOC level but are usually recharged from a partially discharged state to the 100% SOC level. This incomplete discharging process will affect the initial state  and processed variables (such as the charging time) of the subsequent charging process, thereby restricting the extraction of external features depending on a deterministic and intact charging/discharging process, such as the time ratio of CC phase to CV phase , image iIn fact, with the popular CC-CV charging mode, the CV profile is relatively robust with the incomplete discharging process and unstable initial charging state, and the BMS can reserve the corresponding charging data integrallty. Since the aim is to realize a credible online estimation of battery capacity whether the battery is fully discharged or not, therefore, illuminated by the data integrity and gradually aging phenomena in the CV profile, we extract a typical geometrical feature from the CV profile to be the aging indicator of battery capacity in this paper.Based on the extracted aging feature, a data-driven remaining capacity estimation model is established by using a classical machining learning technique named support vector regression (SVR). SVR can deal with the nonlinear systems and outperform ordinary regression methods due to its robustness to small variations, excellent generalization capability and not directly affected by the dimension of regressed entities. Accordingly, SVR is often adopted as the learning model in studies of lithium batteries –32. SincThe structure of this paper is organized as follows: In section 2, the capacity degradation property of the lithium-ion battery is illustrated, and the aging feature from the CV charging profile for the capacity estimation is extracted. Section 3 briefly introduces the related estimation model and intelligent algorithm including the SVR model and the QPSO algorithm. The proposed capacity estimation framework based on the QPSO-SVR is described in detail in section 4. Experiment results are presented and analyzed in section 5. Finally, the conclusions are discussed in section 6.t0 and tend are the begin and end time of a charging/discharging cycle, I(t) denotes the charging/discharging current. Particularly, the capacity researched in this paper refers to the charging capacity.Since the monitoring impedance is too complicated in real application, the battery capacity is often employed as the indicator to reflect actual health condition of the lithium-ion battery. The capacity represents the total available charge that the lithium-ion battery can supply over time, which can be expressed as:The remaining capacity of a lithium-ion battery is affected by many factors, such as external environmental loads, the number of charging and discharging cycles, the value of discharging current and so on. With the battery cycling, the capacity tends to be lower than the initial nominal value due to the loss of cyclic lithium and loss of active materials. Based on the data repository measured by NASA Ames PCoE, the charging capacity curves of battery No.5 and No.7 under nominal conditions are shown in In actual operation, the partial discharging process not only limits the applications of some useful aging features which rely on an intact discharging process, but also does have underlying influences on the subsequent charging process. In order to avoid the negative effects caused by the incomplete discharging process as possible, the aging feature of the lithium-ion battery is extracted from the more controllable charging process in this work. The charging mode to be investigated in this paper is the CC-CV charging mode. As the most popular charging mode of lithium-ion batteries, the CC-CV protocol can be divided into two consecutive processes: the CC charging and the CV charging. As shown in For the CC-CV mode, it is worth pointing out that only the CC profile is affected by the previous discharging state. Since if the battery goes through an incomplete discharging process, namely, the battery is not discharged to the predetermined cut-off voltage value, thus the initial battery voltage of the subsequent charging step will be higher than usual. As a result, the charging time will be undoubtedly decreased and the battery voltage trajectory will become uncertain, thereby making the CC profile not suitable for the aging feature extraction in practice. By contrast, as the battery turns into the CV phase when the voltage reaches the predefined maximum, it is evident that the CV profile is comparably robust with the unpredictable initial charging voltage. In other words, despite whether the battery is fully discharged or not, the process information can be completely saved and recorded in the dynamic data of the CV profile. Consequently, the CV profile is appropriate for the aging feature extraction under the condition of incomplete discharging.tCV and tend are the begin and end time of the CV profile, I(t) denotes the time-varying charging current. Based on the aging feature extracted from the CV profile, the next step is to build an accurate and reliable model for the battery capacity estimation.The more visualized aging phenomena during the CV profile can be explained by plotting the external measuring data of the lithium-ion battery. xi is the input vector, yi is the real output value, and N is the number of data samples. The SVR function can be described as:f(x) denotes the output value of prediction, WbSVR is a famous and powerful machine learning technique for both linear and nonlinear data regression. The basic SVR is formulated as convex quadratic programming (QP) problem which can condense the substantial training data into a dramatically smaller set of support vectors (SVs). Consider a dataset f(x) with the training dataset is less than the predefined error term ε, the estimated value of W and b can be obtained by solving the following QP problem:Aiming at finding a proper function (Eq ) such thC is the penalty parameter which represents the degree of attention paid to the outliers. Generally, the larger C is, the more attention will be paid to the outliers.For the cases that training samples in the dataset are not linearly separable, the relevant constraints are relaxed by introducing defined slack variables To solve the above optimization problem, the Lagrangian is adopted here:L,α(*),η(*)) with respect to original variables and substituting the results into Eq (xi ⋅ xj) denotes the dot-product of two input vectors. Hypothesizing that x*, the design function of the SVR can be then given by:Taking the partial derivative of  into Eq , the finHowever, many problems show nonlinear features in the actual application. To realize the linear regression, a mapping function is exploited to transfer the nonlinear data in the original dimension space to the high dimension space. In the high dimension space, the kernel function is adequate to replace the dot-product of two vectors as well as prevent the curse of dimensionality.σ denotes the predefined bandwidth of the RBF kernel. Therefore, the final design function of the SVR can be rewritten as:There are several types of the kernel function, such as radial basis function (RBF) kernel, polynomial kernel, sigmoid kernel and so on. Due to only one parameter to be set and excellent generalization ability, the RBF kernel is the most choice when facing with nonlinear regression . Consequi at iteration k, i after k iterations, gbestk denotes the global optimal solution after k iterations, ω is the inertia weight coefficient, r1 and r2 are two random numbers sampled from , c1 and c2 are learning factors. However, the traditional PSO algorithm also confronts some intractable problems in actual applications: its global convergence is not guaranteed; it is easily trapped in the local optimal solution; the algorithm requires too many parameters which are hard to be predetermined.PSO is a heuristic swarm intelligent algorithm broadly adopted in solving the optimization problems. The main idea of PSO derives from the imitation of biological and sociological predation behavior of birds swarm: the behavior of each particle (candidate solution) is subject to the Newtonian dynamics. Thus the update of each particle in the search space can be decided by its velocity and position:pi which is used to constrain the movement of the particle i, so the wave function ψ of the particle i can be depicted by:xi is the position of particle i, Li represents the Delta potential well. To address the possibility of a particle’s appearance in the quantum space, the probability density function (PDF) of the particle i is computed as:To overcome these disadvantages of PSO, QPSO was developed by introducing the quantum mechanics into the convergence process of PSO. From the quantum mechanics perspective, the velocity and position of the particle cannot be determined simultaneously due to the famous uncertainty principle . Therefoi can be updated as follows:u and β are two random number distributed uniformly in , and the value of α is called the contraction-expansion coefficient which controls the convergence speed of the particle and is the only parameter needs to be determined in QPSO, M particles at k iteration:By applying the Monte Carlo method, the position of the particle Finally, substitute Eq  into Eq xi, φ denotes a random number distributed uniformly in .Additionally, considering the convergence of Aiming to estimate the capacity of the lithium-ion battery by only using the charging data of the CV step, herein, we focus on how to construct an effective and accurate estimation model. By introducing the quantum computing theory into the classical machine learning technique, a fusion framework based on QPSO-SVR for the lithium-ion battery capacity estimation is proposed in this work. The schematic diagram of the proposed fusion framework is shown in During the charging process of the lithium-ion battery, the monitored parameters including current, voltage, and temperature can be well recorded by a variety of sensors inside electrical appliances. The raw data required for the model construction is the charging current time series.Since the aging feature presented in this paper is extracted from the CV charging phase, the CV current time series should be separated from the whole charging dataset. The initial point of the CV step can be determined by recognizing whether the charging voltage reaches the predefined maximum value or not, while the endpoint can be detected by recognizing whether the load current falls to the predefined terminal value or not. Based on the separated data, the CV capacity series can be extracted by computing the area under the current curve. The extracted CV capacity and the total charging capacity are regarded as the input and output in the estimation model, respectively.To ensure the generalizability of the estimation model, we divide the extracted sample sets into two parts: one part for the model training and the other part for the model testing. Training sample set is exploited to determine the optimal combination of the unknown parameters in the SVR model. To ensure the global optimization ability and improve the estimation accuracy of the SVR model, a novel QPSO-SVR method is presented, and the corresponding flowchart is shown as The procedure of implementing the QPSO-SVR method is briefly described as below:C, the error term ε, and the bandwidth σ), the population of particles M, the maximum number of iterations MT, and the fitness function Ffitness. It is worth pointing out that since the fitness function is used to judge the optimal position of particles in the quantum space, we select the mean square error (MSE) to be the fitness function, which can be given by:yj and jth sample in N training samples.Define the search space of parameters to be optimized  appearing in the quantum space,i is out of the search space or not. If its position is out of the search space, set the corresponding fitness value equal to the infinity; otherwise, substitute the candidate parameter combination into the SVR model and train the model with the training sample set, then calculate this particle’s fitness value based on Eq  until the maximum iterations are reached.By iteratively performing the above procedures, the optimal combination Training sample set can be utilized to train the estimation model, but not to test the generalizability of the trained SVR. Consequently, we build a supervised learning step in this framework and some typical evaluation criteria are adopted to evaluate the performance of the trained model based on the testing sample set. The more details about this step can be found in section 5. According to the evaluation results, we can decide whether we need to retrain the estimation model or not.Finally, based on the above framework, a well-trained capacity estimation model can be employed for lithium-ion batteries.To make our work more detailed and comprehensible, experimental data from NASA battery dataset is used in this paper. In NASA accelerative aging test procedure, the commercial 18650 sized lithium-ion batteries (No.5 & No.7) went through three diverse operational profiles, namely, charging, discharging and impedance at room temperature. Charging was carried out in the CC mode at 1.5A until the battery voltage reached 4.2V. Afterward, batteries were continued charging in the CV mode until the charge current fell to 20mA. Discharging was conducted at the CC level of 2A until the battery voltage reduced to 2.7V and 2.2V for batteries No.5 and No.7, respectively. What’s more, 168 charging and discharging cycles were recorded.By using the NASA lithium-ion battery datasets, aging features merely extracted from the CV step of battery No.5 and No.7 are shown in To quantitatively demonstrate this underlying relationship, Pearson’s linear correlation coefficient and the Spearman’s rank correlation coefficient are calculated and analyzed, respectively.Q denotes the capacity vector with the standard deviation σQ, QCV denotes the extracted CV capacity vector with the standard deviation ρ ranges from −1 to 1, and the closer its absolute value near to 1, the stronger the linear dependence between two vectors.The Pearson’s linear correlation coefficient is usually used to measure the linear dependence between two variables, which can be calculated as:Q and QCV in descending order. Similarly, the coefficient r also ranges from −1 to 1, and the closer its absolute value near to 1, the stronger the monotonic correlation between two vectors.Another statistical index is the Spearman’s rank correlation coefficient which is defined as the Pearson correlation between the rank values of two variables in descending order:ρ and r are very close to -1 for both battery No.5 and No.7, which imply a strong negative correlation between the battery capacity and the extracted aging feature. In other word, the quantitative correlation analysis verifies the feasibility of the building the capacity estimation model based on the extracted aging feature once again.Based on the previous two indices, the results of correlation analysis are listed in yi is the actual capacity value, N is the sample size.Before implementing the presented QPSO-SVR approach to estimate capacity of the lithium-ion battery, some metrics are necessary to evaluate the estimating performance and accuracy. Here we employ the mean absolute percentage error (MAPE) and root mean square error (RMSE) to act as the evaluation criteria of different methods:ea and the relative error er are exploited in RUL estimation:Since the lithium-ion battery is recognized as invalid when the charging capacity decreases to 70% or 80% of the rated capacity , we defiThe experimental datasets of battery No.5 and No.7 are used to evaluate our extracted aging feature and proposed remaining capacity estimation framework. Each dataset is separated into two parts: one part for the model construction and the other part for the capacity estimation. To demonstrate the superiority of the presented QPSO-SVR method, this paper compares the capacity estimation results obtained by the standard SVR (denoted as SVR) and the SVR optimized by PSO algorithm (denoted as PSO-SVR). Furthermore, considering the practical meanings for maintenance and logistics support of lithium-ion batteries, we also choose different charging cycles  as the estimation starting point.The whole experiments are operated on the MSI brand laptops by Intel Core i7 2.5 GHz CPU and 16 GB Memory. The software platform is the MATLAB R2014a.For battery No.5, the estimation results of different methods at different starting points are shown in ea is only three cycles, which is observably less than the value of ea based on SVR (eight cycles) and PSO-SVR (seven cycles). The same conclusions can be drawn for the other two starting points, manifesting that the proposed method can be well applied to RUL estimation no matter when the estimation performs.Since the capacity of battery No.7 does not reach the threshold during the aging test, we only perform the capacity estimations at different starting points for battery No.7. The results are displayed in In conclusion, the abovementioned discussions prove that the geometrical feature extracted from the CV profile can be used to estimate the battery capacity, and the proposed QPSO-SVR approach observably outperforms the SVR and PSO-SVR approaches in a real application. By using the presented framework, we can obtain an accurate and credible capacity estimation result for the lithium-ion battery for the not entirely discharged condition.To avoid being affected by the conventional incomplete discharging process of lithium-ion batteries, a novel data-driven framework is presented for the battery remaining capacity estimation. Since the CV charging profile is relatively robust with the unpredictable initial charging state, and the corresponding process information can be completely recorded, a geometrical feature of the CV charging curve, namely the CV charging capacity, is extracted to be the aging feature of lithium-ion batteries under the incomplete discharging condition. By introducing the quantum computing theory into the classical machine learning technique, a QPSO-SVR framework, as well as its application to the battery remaining capacity estimation problems, are presented and illustrated in detail.With the data repository provided by NASA Ames PCoE, correlation analysis confirms that there is a distinct and strong relationship between the battery capacity and the extracted aging feature. The corresponding estimated remaining capacity further demonstrates the potential usefulness of the extracted CV capacity to be an independent aging feature for the not entirely discharged condition. Besides, compared with the conventional SVR and PSO-SVR under various evaluation metrics, the proposed QPSO-SVR framework also has the least estimation errors and shows stronger generalization performance in both capacity estimation and RUL estimation. Therefore, we can conclude that our extracted aging feature and the proposed framework are promising and credible for the remaining capacity estimation of lithium-ion batteries under the incomplete discharging process.


The number of small sophisticated wireless sensors which share the electromagnetic spectrum is expected to grow rapidly over the next decade and interference between these sensors is anticipated to become a major challenge. In this paper we study the interference mechanisms in one such sensor, automotive radars, where our results are directly applicable to a range of other sensor situations. In particular, we study the impact of radar waveform design and the associated receiver processing on the statistics of radar–radar interference and its effects on sensing performance. We propose a novel interference mitigation approach based on pseudo-random cyclic orthogonal sequences (PRCOS), which enable sensors to rapidly learn the interference environment and avoid using frequency overlapping waveforms, which in turn results in a significant interference mitigation with analytically tractable statistical characterization. The performance of our new approach is benchmarked against the popular random stepped frequency waveform sequences (RSFWS), where both simulation and analytic results show considerable interference reduction. Furthermore, we perform experimental measurements on commercially available automotive radars to verify the proposed model and framework. The rapidly increasing deployment of small, low cost wireless based remote sensing devices is leading to an increasing concern about spectrum crowding and device interference. A prominent example is the small scale radar used for vehicle safety and autonomy, for UAV navigation, for collision avoidance and mapping and for hand gesture recognition , where iCurrently automotive radars are limited to high-end vehicles due to development and integration costs. However, very low-cost consumer radar technology is imminent ,3,4,5 anInterference in automotive radar systems can arise from vehicles traveling in opposite directions, vehicles traveling in the same direction fitted with forward-looking and backward-looking radars and vehicles at intersections . The intIn this paper, we propose a novel technique to mitigate multi-radar interference in an automotive radar context by designing an adaptive family of radar waveform sequences which are easily learnable by other radars. These sequences always maintain a minimum frequency separation (or a frequency gap) between a radar’s instantaneous transmitting frequencies. Thus, forming a frequency guard which guarantees orthogonality between sequences. Using this scheme, the available spectrum can be efficiently shared among radars in a fully decentralized manner, avoiding the need for a centralized control system. Thus, radars can adaptively manage frequency separation according to the current interference environment.Development of a mathematical model for the mutual interference in automotive radar systems.Development of an analytic framework to characterize the effective interfering power parametrized according to the frequency separation between radars. This framework is applicable to a large class of radar waveforms.Representation of a new family of waveform sequences which are capable of mitigating the effects of multi-radar interference without the need for any centralized co-ordination.Development of a new statistical characterization of mutual interference in an analytically tractable form.The main contributions of this paper are:There are many projects around the world aimed at developing practical mitigation techniques for automotive radar interference. For example, the project MOSARIM  is one oThe interference between radars which use FMCW waveform is investigated in ,11, wherInterference mitigation in automotive radars could be achieved by various techniques using different antenna polarization ,15,16, sIn order to reduce the received power from the direction of interferer, the concept of digital beam forming is applied in ,24. AnotShort range radars (SRR) for distances of 0.15–30 mMedium range radars (MRR) for distances of 1–100 mLong range radars (LRR) for distances of 10–250 mFuture vehicles with advanced driver assistance are likely to be equipped with 8–10 radars which will give an overall 360coverage  to scan SRR/MRRs are typically used for blind spot detection, lane changing assistance, parking assistance, side impact and self-parking, while LRRs are used for automatic cruise control, collision avoidance, cross traffic alert, etc. LRRs are more vulnerable to interference because of the long range, where typically such radars have narrow beam-width antennas for detecting far objects.The main cause of interference is vehicles traveling in the opposite direction equipped with LRRs operating in the same spectral band. A simplified typical automotive radar interference scenario is shown in G is the gain of the radar’s antenna, Referring to equation  as, (2)PFrom Equations (1) and (2) it is clear that the target echo will have far less power than the interfering signal by a factor of at-least Assuming that the victim receiver is not blinded then depending on the particular characteristic of the victim radar receiver there will be an effective interfering power that makes its way to the intermediate frequency (IF)/baseband section of the receiver. We define this fraction of total interfering power as Spectrum regulators impose certain restrictions on the maximum allowed transmitting power )  and the In order to characterize the interference, it is important to understand the architecture of next generation radar front-end . As depiA digital signal processing (DSP) unit drives a digital-to-analog converter (DAC) that in turn controls the frequency of a voltage controlled oscillator (VCO). Thus, the frequency can be stepped, or swept, according to the desired transmit waveform. The receive signal, on the other hand, is coherently down-converted at the mixer and low pass filter (LPF) using the same frequency produced by the VCO into an in-phase (I) and quadrature (Q) baseband component which are sampled by two analog-to-digital converters (ADC) and then fed to the DSP.In the context of interference, the performance of the VCO is very important because the oscillator phase noise spreads the signal (and interference) energy across adjacent frequencies. Moreover, while each radar can have an accurate crystal locked oscillator there is no radar–radar frequency or phase synchronization, so individual radar oscillators effectively drift with respect to each other. Thus, there is a high chance of interfering signals even if the interferer is not at exactly the same frequency as the victim radar operating frequency. If the interfering signal passes through the IF/baseband filters in the receiver, it will degrade the performance of the victim radar.d between the victim and interfering radars. With this model we calculate the statistical parameters to characterize the performance of the new transmit waveform in terms of signal-to-interference ratio (SIR).In order to mitigate the mutual interference in automotive radars, it is important first to study the interference characteristics and behaviour. The last box in  a radar , such thTo design a waveform with tractable properties we use the concept of pseudo-random stepped frequency hopping. Practical advantages of using random stepped frequency waveforms in automotive radar applications often refer to its high SIR due to its narrow instantaneous bandwidth at each tone . The wavN is the number of frequency tones. The frequency tones are randomly selected without replacement from the pool of allowed frequencies and transmitted as a pulse train. This pulse train where each pulse has a different frequency (tone) is equivalent to a narrow synthetic pulse when processed using the inverse Fourier transform (IDFT) [In a random stepped frequency waveform , the avam (IDFT)  to provim (IDFT) ,36,37,38m (IDFT) .The randomization in the sequence of tones can significantly reduce the interference compared to its linear version , which iN.All available frequencies need to be used within the pulse train of length The sequence does not have repeated elements within a pulse train, since it is sufficient to probe the scene once at each frequency tone.N pulses.The sequence is cyclic, thus it repeats itself periodically after The design of a proper waveform sequence or a family of sequences can significantly mitigate the interference arising from a large number of radars operating in close spatial and spectral proximity. We introduce a new family of sequences called pseudo random cyclic orthogonal sequences (PRCOS) which are capable of adaptively reducing the effects of mutual interference in dense multiple radar situations such as those found in automotive radars or UAV swarms. The proposed PRCOS is peculiar due to its generation and each sequence shared among the radars are cyclic shifted versions of each other. By orthogonal we mean that the transmitting frequencies of the radars will always maintain a minimum frequency gap between the radars, which aids in limiting the effective interfering power. The PRCOS are easy to learn, thus enabling a radar to dynamically learn the sequence being used by another radar and consequently avoid spectral collision. The sequence is pre-shared among the radars, such that each radar entering the new environment listens to the other radars and learns (from the beat frequency) which frequency tones others are using. The proposed sequence is constructed under the following assumptions:In general, a unique sequence, i.e., with non-repeated elements, is taken from the set Suppose a single unique cyclic sequence N elements. Suppose there exists a certain frequency guard, where two tones used by two different radars should be spaced by more than this frequency guard g, then the permitted phases M is the number of non-overlapping sequences calculated as g columns of tones of the permitted phases can reconstruct the full sequence, where Since all sequences are permutations of the ordered set, we start from g columns are permuted vertically, then M orthogonal (none-overlapping) sequences can be generated. A summary of the steps required to generate this kind of PRCOS is:Generate the seed matrix Permute the columns so that the resulting matrix Re-order the matrix in a vector, where the vector We also note from the example that the elements in the columns separated by a cyclic distance g columns and M rows, where each column is randomly permuted g columns permute The seed matrix has In order to evaluate the interference performance of the proposed PRCOS, the metric we adopt is in terms of signal-to-interference ratio. It is also important to note that there is a direct monotonic relationship between the SIR and the detection probability of a radar , such thThe spectrum of an ideal oscillator is an impulse at the generated frequency, but due to the effects of phase noise the spectrum of a practical oscillator is broadened. Phase noise in oscillators can be modelled as random fluctuations in phase over time, which results in the spreading of energy to adjacent frequencies .Phase noise can be seen as the combination of white Gaussian noise and coloured noise , where tf is the frequency offset from the center frequency.One of the widely used models for phase noise is the Lorentzian spectrum . By ignoFor short range radars the effect of phase noise is significantly mitigated by the range correlation effect  because The model in nput PSD .T is the pulse width. Therefore the normalized PSD at the output of the pulse modulator is given as, In the case of a square pulse the power transfer function is given by, T and amplitude E represented as, The spectral characteristics of a random stepped frequency waveform are studied by considering an individual rectangular pulse of width When this pulse is modulating an ideal carrier of frequency Therefore, the overall frequency spectrum of a stepped frequency waveform can be seen to be an overlap of multiple sinc functions centered at each tone In this section, we explore the statistical distribution of the distances between two tones based on the suggested PRCOS. Assuming two radars randomly select two tones  follows:ζo(d)=∫−∞ follows:ζo(d)=∫−∞A and C are empirical parameters, A is proportional to the power of the signal and C represents the spread of the signal. The expression of Equation =∫−BK interferers is given as, The actual SIR resulting from a single interfere is given by, Q well-separated targets in the range–Doppler domain, the SIR of each target can be calculated as, In multiple target scenario the interference affects each target individually depending on its parameters, i.e., radar cross section (RCS) and distance of the target from the receiver. Therefore, if there are d between the tones increases. As we previously indicated, a PRCOS sequence will have orthogonality between its allowed phases, that is, at any given time instance two tones are separated by a frequency difference (frequency distance) denoted as d, where g. This will limit the maximum number of users allowed to use the sequence, The relation between the effective normalized interfering power M elements.When we consider the ordered sequences, we observe the interesting property that the distance statistics within a single column are in fact the same for all other columns refer to ; thus, wM nodes  of the distance can be derived as follows. Consider a phase, This can be explained by taking an example from As depicted in refer to . Similarg of d, we can find the PMF of d are related. Therefore the PMF of Since the normalized SIR depends on the frequency distance M users using the PRCOS with a frequency guard of g, as follows, Thus, we obtain the expected SIR with In order for a radar to detect a target a minimum SIR needs to be achieved; we denote this threshold as g of 500 kHz. From g. We generated the proposed PRCOS sequence using the algorithm explained in B is taken as g, is switched from 100 kHz to 500 kHz and the number of interferers considered is nine. In order to place the interferers we create a road strip with the first interferer at a distance The performance of the PRCOS is analyzed by comparing the SIR with the well-known random sequence using simulations as the number of users increases for different frequency guards f 100 m2 .g, the mean SIR is computed for different cases of numbers of interferers starting from one to nine. It is obvious that, as the number of interferers increases, SIR will decrease because of the increase in the interfering power as is shown in g which is 0 Hz. The mean SIR is calculated for different cases of numbers of interferers from one to nine. It is evident from We first generate the PRCOS with Equation  and SIR Equation . The intT of the DAC). The transmitted signal from the radar is captured using a dipole antenna and fed into a spectrum analyser. The experiment diagram and the actual setup are shown in In order to verify the proposed model for the effective interference power, we observe the PSD spreading in a commercially available radar module, K-MC3 . Since t4.15 GHz  which is®. We extract the spectrum of a single pulse peaked at The PSDs of the pulses are acquired from the spectrum analyser using MATLABAlong with the spectrum obtained from the experiment , we depict the proposed empirical model and the analytic Lorentzian model obtained from the numerical analysis in In this paper we presented an analytic framework for characterizing the mutual interference between automotive radars by modelling the phase noise and the effect of pulsed waveform on the interference. Compared to the existing studies on interference mitigation, the proposed interference model is generic and can be applied to a large class of waveforms. We introduced a novel approach in designing a family of waveform sequences for automotive radars based on pseudo-random frequency hopping that has a tractable performance. Therefore, depending on traffic densities and SIR requirements, the radars can adjust the frequency distance without a centralized control system. One of the main challenges of implementing PRCOS is that it requires a fast digital-to-analog converter (DAC) to drive/modulate the VCO; however, the modulator of existing automotive radar chipsets is based on an FMCW ramp generator. With the proposed approach using PRCOS waveforms, it is possible to predict the statistics of the radar signal-to-interference plus noise ratio based on given scenario parameters. Simulation results showed that the proposed PRCOS waveforms outperform random stepped frequency waveforms in terms of the signal-to-interference ratio by at least 7 dB. Furthermore, the presented experimental verification asserted the plausibility of the proposed analytic framework based on commercially available radar modules.


The rapid development of digital health poses a critical challenge to the personal health data protection of patients. The European Union General Data Protection Regulation (EU GDPR) works in this context; it was passed in April 2016 and came into force in May 2018 across the European Union. This study is the first attempt to test the effectiveness of this legal reform for personal health data protection. Using the difference-in-difference (DID) approach, this study empirically examines the policy influence of the GDPR on the financial performance of hospitals across the European Union. Results show that hospitals with the digital health service suffered from financial distress after the GDPR was published in 2016. This reveals that during the transition period (2016–2018), hospitals across the European Union indeed made costly adjustments to meet the requirements of personal health data protection introduced by this new regulation, and thus inevitably suffered a policy shock to their financial performance in the short term. The implementation of GDPR may have achieved preliminary success. Public health increasingly appears to be a science of information . Having Although digital health has so many meaningful applications, its high dependence on sensitive information with respect to patients’ personal health can inevitably trigger data security problems. Vast amounts of personal health data have been collected, often without of the awareness of patients. Patients cannot control their data, and do not have sufficient levels of awareness to give free and informed consent . The devThese potential risks of digital health have received the attention of legislators. In legislative efforts for protecting personal privacy, Europe has been at the forefront . The mosFacing the challenges of health data protection in the digital health age, this new regulation aims to address them and advance the level of health data protection in the European Union. Yet, it is unclear whether this legal reform is effectively implemented by public health sectors across the European Union . It is tOn the one hand, the GDPR’s implementation by hospitals and healthcare institutions across the European Union can reflect the actual effectiveness of the GDPR for personal health data protection. It is thus necessary to examine the current levels of compliance with the GDPR by these healthcare organizations. Before becoming enforceable in May 2018, the GDPR was published in April 2016. This transition period from April 2016 to May 2018 was allowed for making preparations for this new legislation. Hospitals and healthcare institutions across the European Union needed to make adjustments for the GDPR in various ways, such as staff training on the GDPR, staff recruitment of some key GDPR roles, the purchase of equipment, and system installation for the new requirements of the GDPR. The costly adjustments may have led to financial distress, but the temporary financial distress reflects their efforts in preparation. Hence, by making comparison of financial performance before and after 2016, the effectiveness of this regulation can be accurately tested. On the other hand, the adjustment for this new legislation by these organizations actually indicates that their levels of personal health data protection before the GDPR came into effect had not spontaneously reached the new standards introduced by the GDPR. Such an existing gap, again, shows the effectiveness and necessity of the GDPR for personal health data protection. The GDPR is needed to remedy deficiencies in personal health data protection. Its articles should reflect the current limitations and further improvement directions of personal health data protection for hospitals and healthcare institutions across the European Union. Thus, the possible financial distress resulting from costly adjustments can be considered as measurable evidence to verify the existence of the gap in personal health data protection and then reflect the effectiveness of the GDPR. As such, to test the effectiveness of the European Union GDPR for personal health data protection, this study will empirically examine the effect of the GDPR on financial performance of hospitals and healthcare institutions across the European Union using the difference-in-difference (DID) approach. The digital health business is not viewed as being equally important for all hospitals across the European Union. Some hospitals regard the information, communication, and telecommunication business surrounding health as the largest primary business aside from the provision of common hospital services, while others do not. Based on the practice recommended by the difference-in-difference (DID) approach , the forThe present study is the first empirical research to test the effectiveness of the European Union GDPR for personal health data protection. The test results will reveal the aggregate level of the GDPR’s implementation by public health sectors across the European Union, and from other side reflect the existing level of personal health data protection before the introduction of the GDPR. The empirical findings can help legislators grasp the situation of current preparations for the GDPR, whereby they will make plans to further promote comprehensive implementation of the GDPR. This paper is structured as follows. In the following sections, this paper first describes the development of digital health, and analyzes the challenges for personal health data protection which the digital health is facing. Then this paper discusses the new requirements and standards introduced by the European Union GDPR in protecting personal health data. Combining these two sections, this paper then analyzes the potential impacts of GDPR shock on operations of public health sectors across the European Union. In the following section of method, this paper gives an empirical examination to reveal the actual effectiveness of the GDPR in protecting personal health data across the European Union. To clarify the difference-in-difference (DID) approach, this paper offers the relevant technique details. Meanwhile, this paper makes a series of robust tests to confirm the robustness of our findings. Finally, in the last section, this study concludes that the existing conditions of design and deployment of healthcare technologies have not fully met new standards introduced by the GDPR in relation to personal health data protection. The European Union GDPR is indeed represented a significant shock for the financial performance of public health sectors across the European Union. There is a need for urgent and further adjustments in design and deployment of healthcare technologies to ensure the balance between personal data protection and data usage for public health interests. Future research directions and implications of the present research are also discussed. Digital health is broadly regarded as healthcare practices using information and communication technologies . It coveHowever, the sharing of personal health data among health service providers, health professionals, health information networks, and patients, is accompanied by the issue of sensitivity of personal data, which has raised specific concern from personal data protection laws . Out of The GDPR appears much more adequate to respond to challenges of personal health data protection in the digital health era . It provThe GDPR, at first, gives the more detailed definition of “data concerning health” than before, referring to personal data related to the physical or mental health of a natural person, including all data about his or her past, current, or future health status collected in the course of the registration for or the provision of healthcare services to him or her . More imTo be specific, the GDPR sets the higher standards concerning informed consent and notification duties. As Article 7 states, a patient needs to be informed of the possible risks of data collection “in an intelligible and easily accessible form, using clear and plain language”. In addition, since excessive data collection can make consent invalid, the data controller, before data collection, must state whether the provision of personal health data is required by a law or contract, or whether it is a necessary condition to entry into a contract, whether the patient has an obligation to provide personal data, as well as the potential consequences when such data will not be provided (Article 13). Also, to improve the inefficiency of long and complicated privacy notices, the GDPR advocates for using short text with standardized icons to aid immediate awareness of the intended data processing . The GDPR also strengthens the protection for the right of access to personal health data. Healthcare organizations are required to respond to patient access requests in a shorter deadline (30 days) than before (40 days). To enhance transparency between patients and healthcare service providers, the GDPR introduces the duty of data protection impact assessment (DPIA). Data controllers are required to carry out a DPIA before processing the sensitive information concerning health to identify the possible risks of data processing and find ways to solve them. Further, some provisions  aim to clarify for patients the decisions made by automated processing, including profiling, and the logic involved in data processing, as well as the consequences. In this way, the risks incurred when decision-making algorithms are used are made transparent to patients, enabling them to exercise human intervention in the decision . The GDPConsidering the great technical development in the healthcare field can directly cause the increasing loss of “legibility” of health data processing , the GDPIn addition, especially for health data collected via wearable devices, privacy by design is viewed as the most important provisions of health data protection in the GDPR . It asksTherefore, with the new standards ranging from informed consent, notification duties, data access, data protection impact assessment (DPIA), algorithmic transparency, automated decision-making, data portability to privacy by design, privacy by default, and high sanctions applying across the European Union, the GDPR increases the level of legal protection for personal health data, making the balance between health data uses (business interests) and personal health data protection  lean to the latter . The existing solutions to meet requirements of previous regulations on data protection have not adapted to the new and more stringent standards in the GDPR. Hospitals and healthcare institutions across the European Union thus need to make further adjustments from staff recruitment, staff training, business adjusting, and technical upgrades, etc., by doing so, aim to look for the balance between their profit maximization and effective protection for personal health data. The health data protection training for staff needs a further update to cope with this new legislation. In general, most data breaches are internal rather than external hacks; the internal training of data protection is thus necessary for all staff . InadequIt is also necessary to recruit staffs that are well qualified for the key roles of the GDPR, such as data protection officers that take charge of informing, advising, and monitoring compliance, data privacy teams, and IT project and program managers. The shortage of such staff is expected to be disruptive to healthcare organizations with the digital health as the primary business . They shMoreover, healthcare organizations should review how their current data have been collected as soon as possible. Early evaluation can guide them in how to address the challenges of the GDPR. For those that find themselves unable to deal with the GDPR, it may be the better practice to leave the current market to avoid serious financial losses, and then create business in accordance with new survival opportunities. Information technologies used in personal health data protection are also needed to display advanced functions that can meet the new GDPR requirements, such as carrying out data protection impact assessment (DPIA), new specifications for consent and notification, new deadlines for data breaches (72 h), reduced processing time for data access requests (30 days), and the other measures mentioned earlier.These devoted efforts in improving personal health data protection can bring more business opportunities for healthcare organizations in the long term, however, huge costs are incurred to fulfil all these adjustments . Hence, This data protection reform is, for some, far beyond the scope of any previous experience. The effectiveness of this legal policy for health data protection can be examined through testing whether the pre–post change in hospitals’ financial performance is significantly negative. This is based on the fact that the GDPR proposes higher requirements of health data protection, which in turn inevitably induces greater input for hospitals and thus causes a shock to their financial performance.In this study, considering the digital health business is not viewed equally important for all hospitals across the EU, financial performance seems to be highly vulnerable to the policy shock of the GDPR in those institutions that consider digital health service as the largest primary business except for traditional hospital services, whereas those without or with the digital health service as only a small proportion of their operating business are is less likely to suffer from this shock. Accordingly, comparing the pre–post change in financial performance between these two groups can test the policy effect of the GDPR on promoting health data protection in the digital health age.Statistique des activités économiques dans la communauté européenne . The database can be accessed via the website https://amadeus.bvdinfo.com/. The sample period of this study is 2013–2017. The return of asset  is used to measure hospitals’ financial performance [Our sample comes from Bureau Van Dijk (BVD)-Amadeus. The Bureau Van Dijk is a part of the database of Moody’s Analytics, a top-3 rating institution located in the United States. This database reports on the financial performance of hospitals in EU-28 countries using the NACE classification. The NACE classification is the industry standard classification system used in the European Union, and is the abbreviation of the French formance . In lineformance ,28. Moreformance . Firm siformance . Cash flformance .The difference-in-difference (DID) approach is widely used as the effective way to investigate the policy influence. The core idea of DID approach is to test the policy influence on outcomes by evaluating the significance of pre–post change (change in outcomes before and after the policy). In the DID design, two differences are important: (1) the difference of the outcome variable after vs. before the policy change in the group exposed to the policy (named B2-B1), and (2) the difference of the outcome variable after vs. before the date of policy change in the group unexposed to the policy (named A2-A1). The DID approach is to separate out the policy influence by evaluating the outcome change related to the policy implementation beyond the background change, that is (B2-B1) – (A2-A1). Statistically, the policy influence on outcomes is tested through the interaction term between the pre-post and exposed-unexposed variables. The policy influence is statistically present if the estimated parameter of interaction term is significantly different from zero.According to the DID approach, in this study, hospitals with the information, communication, and telecommunication business surrounding health as their largest business except for the provision of common hospital services are viewed as the treatment group , and the rest of the hospitals are correspondingly viewed as the control group. Thus the control group not only includes hospitals without the digital service, but also those that do not take it as the secondary business just behind the common hospital service. This study uses the DID approach to compare the financial performance difference between these two groups. The period 2013–2015 is defined as the pre-legislation period and 2016–2017 is defined as the post-legislation period. Thus, there are 24,637 valid hospital-year observations in the control group and 1289 valid hospital-year observations in the treatment group after excluding missing values in dependent and control variables  which captures the change in financial performance of the treatment hospitals relative to the control hospitals subsequent to the legislation of the GDPR. A significant negative (positive) coefficient of 4β indicates a decrease (increase) in financial performance after the legislation.In the above regression equation, the subscript To clarify the concern of potential self-selection bias, this study re-examines the above treatment effect using the combination of the propensity score matching (PSM) and difference-in-difference (DID) procedure. The PSM-DID procedure has been widely used to examine the causal treatment effect and is appropriate to deal with the potential self-selection bias problem ,32,33,34Under the background of this study, the potential self-selection bias represents that the hospitals with poorer financial performance at the beginning may be more motivated to provide digital services to attract patients compared to their counterparts, and thus their poorer financial performance is pre-determined and preexisting, regardless of whether the legislation of the GDPR is in force or not. According to previous studies, the decision of a public health institution to provide digital health services depends on its capital input, human input, cash flow and leverage ,36,37. MFollowing the PSM-DID procedure, this study uses these variables as matching variables to predict the propensity score and re-match the new control and treatment group. The matching variables should not display significant differences between the new control and treatment group. The newly matched control and treatment group will meet the requirement that whether a hospital decides to provide digital services or not is quasi-random. After that, the use of DID on the new matched groups no longer suffers from any possible self-selection bias theoretically. More specifically, the above procedure can be clearly divided into three steps. In Step 1, the logit regression is used to obtain the estimated propensity scores, where the binary dependent variable is whether or not the hospital takes the digital health as the largest business except for the common hospital service. The estimated propensity scores enable us to construct a new matched treatment group and a control group that are similar in the matching variables. The main matching method used in this study is “nearest-neighbor (NN) matching”, which takes the observation with the closest propensity score for comparison. The reason why the nearest neighbor is chosen rather than other matching methods is that it allows the repetitive use of objects for matching, and thus is capable to overcome the shortcoming of inefficiency and matching bias induced by one-to-one matching . Such a 4β) of the interaction term “treatment group × post legislation” is expected to not be significant when assuming a pseudo legislation year. Besides, this study also re-examines the treatment effect when deleting the first legislation year 2016 and retaining the post legislation year 2017. The estimate of the interaction term is expected to remain significant if the treatment effect is robust.Further, this study performs a series of placebo tests. The purpose of these tests is to examine the sensitivity of DID results ,40,41. Sp < 0.05, Panel A). The propensity score matching difference-in-difference (PSM-DID) result shows that the above influence remains robust and significantly negative . Besides identifying the existence of the treatment effect, we also provide an estimate of the magnitude of the effect ). For the PSM-DID regression, the results of matching quality check of variables are also presented  or 2014 . In the last column, this study repeats previous analysis when deleting the first legislation year 2016, and finds that the interaction term “treatment group × post legislation” remains significantly negative . These results confirm the treatment effect of GDPR policy is robust and insensitive. Results of placebo tests are shown in The empirical results validate the effectiveness of the GDPR for health data protection. By identifying the negative pre–post change of hospitals’ financial performance, this study tests and confirms the effectiveness of the policy. Based on the fact that much greater financial input than ever before is needed to meet the stricter requirements of data protection, a subsequent decline of financial performance will inevitably happen to hospitals that attach great importance to digital health services.Since hospitals do not equally emphasize the digital health business, the GDPR that urges greater financial input for stricter health data protection is more likely to impact the financial performance of hospitals that view the digital health service as the largest primary business except for traditional hospital services. In contrast, for hospitals without or just having the digital health service as a small share in their operating business, the influence of the GDPR will be much smaller. Through identifying the negative pre–post change of financial performance of hospitals in the treatment group compared with those in the control group, the effectiveness of the GDPR for health data protection can be validated.This study has several managerial and academic implications. First, the GDPR by its very nature has captured much attention from industry and academics alike. Due to its relative modernity and novelty, there is no vast body of academic literature present, although articles and opinion pieces discussing it are fairly numerous. So far, there are no deeply empirical studies into organizational compliance with this new regulation. Most relevant studies appear to focus on reporting the concrete preparations made for compliance, for example, the budget sizes expended or the increase in workforce size. There is yet to be in-depth empirical research to precisely test whether this new regulation is effectively implemented (or complied with) by organizations, and what the actual extent of the compliance has been. This study addresses that gap. Second, in recent years, digital health has become a forefront issue in the health field. Much attention has been devoted to the important role of digital health services in attracting potential and retaining existing patients. For example, digital health services have been found as a good channel to improve patients’ adherence to a range of healthcare practices, including interaction with health service providers, engagement in medical consultations, online health information seeking, and self-monitoring of health ,45. WithThird, this study is the first attempt to empirically examine the policy effect of the GDPR, the latest legislation on data protection, on digital public health sectors across the European Union. The timely evaluation of this policy influence can give legislators and healthcare organizations the timely and valid findings, helping them promote the GDPR’s implementation. The decline of financial performance suggests that digital public health sectors are making costly adjustments to the GDPR’s requirements of patients’ personal health data protection, which demonstrates the implementation of this new regulation have achieved preliminary success. However, this finding also reflects the existing conditions of design and deployment of healthcare technologies in these organizations have not fully met the new standards of personal health data protection required by this new regulation. Thus, European Union legislators need to further promote the level of GDPR implementation, and digital public health sectors across the European Union need to make urgent and further adjustments in the design and deployment of healthcare technologies to ensure the balance between personal data protection and data usage.This study is not free of limitations. First, due to the availability of data, this study still could not answer how long this negative impact lasts. The issue can help understand the whole course of the GDPR’s implementation by digital public health sectors across the European Union. Thus, as new data become available, future research can investigate this issue to complement our analysis. Second, given the huge cost expended in adjustments to the GDPR, it is necessary to investigate whether or not this policy shock would deter the new entry of hospitals into the digital public health market. Future research can use new data to make deeper explorations in this field. Third, this new regulation is designed to protect the health privacy of European Union citizens, regardless of the location of their health data, and it gives European Union courts the power to severely punish any healthcare organizations in the world that misuse European Union citizens’ health data. As such, the sample of this study focusing on the public health sectors across the European Union may limit the application of research findings at the local level. Future research can make extensions by using global samples to investigate the policy effect of the GDPR. Digital health has become an increasingly important trend and has been highly emphasized by medical and healthcare institutions. The policy effect of the General Data Protection Regulation (GDPR) was found to be effective in preventing a savage development of this wave of digitalization. The digital public health sectors across the European Union have made some costly adjustments to comply with this new regulation that requires much more stringent protection for patients’ health data. Their financial distress may reflect the huge cost of re-adaptation to this new regulation. Meanwhile, this financial distress also reveals the fact that the protection for patients’ personal health data has been insufficient in the past. If digital public health sectors already have enough input and support in the protection for patients’ health data before the unexpected legislation, this new legislation on data protection may not cause a sudden decline in their financial performance. Moreover, the negative impact of the GDPR on financial performance could be the watershed of digital public health development. It forecasts the beginning of a shuffle of digital public health markets, and only those institutions capable of affording the capital and human input in the effective protection for patients’ personal health data will survive in the future.


Panic disorder is associated with high productivity costs. These costs, which should be included in cost-effectiveness analyses (CEA) from a societal perspective, have a considerable impact on cost-effectiveness estimates. However, they are often omitted in published CEAs. It is therefore uncertain whether choosing a societal perspective changes priority setting in future research as compared to a healthcare perspective.To identify research priorities regarding the cost-effectiveness of an early intervention for subthreshold panic disorder using value of information (VOI) analysis and to investigate to what extent priority setting depends on the perspective.We calculated the cost-effectiveness of an early intervention for panic disorder from a healthcare perspective and a societal perspective. We performed a VOI analysis, which estimates the expected value of eliminating the uncertainty surrounding cost-effectiveness estimates, for both perspectives.From a healthcare perspective the early intervention was more effective at higher costs compared to usual care , whereas it was cost-saving from a societal perspective. Additional research to eliminate parameter uncertainty was valued at €129.7 million from a healthcare perspective and €29.5 million from a societal perspective. Additional research on the early intervention utility gain was most valuable from a healthcare perspective, whereas from a societal perspective additional research would generate little added value.Priority setting for future research differed substantially according to the perspective. Our study underlines that the health-economic perspective of CEAs on interventions for panic disorder must be chosen carefully in order to avoid inappropriate choices in research priorities. The results of model-based cost-effectiveness analyses (CEAs) are surrounded by uncertainty as the available information about costs and effectiveness of interventions in healthcare is rarely perfect . This unReimbursement decisions based on CEAs require a willingness-to-pay (WTP) threshold, which represents the maximum amount society is willing to pay for health gains. In cost-effectiveness research, health gains are preferably expressed in quality adjusted life-years (QALYs) as QALYs allow for comparison between health conditions due the generic character of this outcome measure. When a WTP threshold for a QALY is determined, the net monetary benefit (NMB) of the treatment alternatives of interest can be calculated by multiplying the WTP by the QALYs gained and subtracting the additional costs. The treatment alternative with the highest expected NMB is the preferred option.A value of information (VOI) analysis estimates the expected value of eliminating the uncertainty surrounding cost-effectiveness estimates , 4. ThisThe costs outside the healthcare sector are substantial among patients with mental disorders –8. In thIn a previously published paper , we consTo our knowledge, a VOI analysis applied to CEAs of interventions for (subthreshold) panic disorder has not yet been published. It therefore remains unclear whether additional research into specific model parameters to reduce uncertainty has additional value, and it also remains unclear whether these research priorities depend on the perspective that is applied. This information is valuable because decision makers not only have to decide which treatment alternative to adopt, but also whether more research regarding the decision is desirable . MoreoveThe VOI analysis was applied to a previously developed model-based CEA. Based on this Markov model constructed in Microsoft Excel , we analWe applied a cycle length of one year, meaning that patients remained in the same health state or switched to a connecting health state after one year. The time horizon of the analysis was five years. Because the long-term effect of the CBT-based early intervention is unknown we decided that applying the six months treatment effect to a CEA with a time horizon of >5 years would be inappropriate. In the previous cost-effectiveness study , a scenaUsual care consists of the currently available care for panic disorder in the Netherlands covering psychotherapy, pharmacotherapy, or a combination of these therapies . We inveIn addition to the previously published CEA from a societal perspective , we alsoIn the VOI analysis, the parameter uncertainty in the model was valued. Our VOI analyses consist of two parts: the expected value of perfect information (EVPI), and the expected value of partial perfect information (EVPPI). The EVPI represents the estimated value of eliminating the uncertainty in the model. More specific, the EVPI places an upper boundary on the costs of performing additional research to eliminate the uncertainty. It can thus be interpreted as the maximum of costs society should be willing to pay for additional evidence that eliminates the current decision uncertainty. Having perfect information regarding the cost-effectiveness of adding a CBT-based early intervention to usual care for panic disorder would protect against making suboptimal decisions regarding reimbursement and implementation as the cost-effectiveness estimate based on the model would be certain. The EVPI informs policy makers whether it is worthwhile to invest in further research that will contribute to the reduction of the current decision uncertainty.In the first step, the NMB for every model iteration of each treatment alternative  was calculated by multiplying the WTP by the QALYs and subtracting the costs. Thereafter we identified the preferred treatment alternative, which is the alternative that maximizes the NMB for the given WTP threshold based on current information in the model. Thereafter, the NMB when having perfect information (the EVPI) was calculated. Within each simulation run, the individual EVPI was equal to the difference between the NMB of the optimal treatment alternative based on the current information and the potential maximum NMB. The individual EVPI thus equals zero when the recommended option by the model under current uncertainty has the highest NMB. The individual EVPI was averaged over all 10,000 model runs. This method is illustrated in The population EVPI was calculated from a healthcare and a societal perspective by multiplying the average individual EVPI values by the number of STHPD patients in the Netherlands who receive the early intervention in the model . The population EVPI values from a healthcare perspective and a societal perspective were plotted against a range of different WTP thresholds, resulting in a population EVPI curve.Although the population EVPI provides insight into the NMB gained when having perfect information, it remains unclear which parameters in the model are associated with the greatest uncertainty. If the uncertainty in the current analysis mainly results from the healthcare costs parameters, it might not be worthwhile to further investigate the parameters on treatment effectiveness.To identify for which parameters future research is worthwhile for both perspectives, we calculated the EVPPI. The EVPPI is calculated as the difference between the expected NMB of a decision made with perfect information on a group of parameters and the expected NMB with current information on that group of parameters. In order to calculate the EVPPI, we performed the model simulations (inner loop) for a fixed randomly drawn value for the parameter(s) of interest given a WTP threshold of €20,000 per QALY. Subsequently, new fixed values of the same parameters were drawn and the simulation was performed again (outer loop). In line with Mohseninejad et al. , the numEstimates of the QALYs and costs per treatment alternative are shown in As an example, The uncertainty of subsets of parameters was valued in the EVPPI given a WTP threshold of €20,000 per QALY . BecauseIn this study, we aimed to identify research priorities regarding the cost-effectiveness of a CBT-based early intervention for STHPD using VOI analysis and to investigate to what extent priority setting depends on the perspective. The decision uncertainty was relatively high when a healthcare perspective was applied, and eliminating uncertainty was valued at a total of €129.7 million for a WTP of €20,000 per QALY. The decision uncertainty in our model is comparable to other cost-effectiveness analyses on psychological interventions in mental healthcare that applied a healthcare perspective , 24. AddOur results indicate that the cost-effectiveness estimates and the potential value of additional research substantially differed when we applied a societal perspective instead of a healthcare perspective. From a societal perspective, additional research would generate little additional value whereas further research from a healthcare perspective could be considered worthwhile, especially for the utility gain associated with the early intervention. When healthcare policy makers decide to invest in a CBT-based early intervention for STHPD at a WTP of €20,000 per QALY, the cost-effectiveness probability that the early intervention is cost-effective is only 61%. Because this decision uncertainty is relatively high, reducing decision uncertainty would be beneficial for healthcare policy makers. Investing in additional research on the early intervention utility gain, intervention costs, and health-state utilities in order to reduce uncertainty could be considered. For employers or others investors for whom the societal perspective is relevant, on the other hand, additional research is not likely to be worthwhile as additional information within the probabilistic sensitivity analysis would not generate additional value. It is unlikely that investing in additional research on the parameters included in the VOI will yield extra information regarding the decision from a societal perspective, which emphasizes the importance of identifying the relevant perspective for the CEA.In a comparable VOI analysis on a minimal intervention for depression , howeverTo our knowledge, our study is the first to apply a VOI analysis to cost-effectiveness research in the field of (subthreshold) panic disorder. A strength of the application of this analysis is that it values the uncertainty surrounding the cost-effectiveness estimate, which provides valuable input for policy decisions regarding investments in future research. There are also some limitations that require discussion. The VOI analysis in this article estimates the value of eliminating the parameter uncertainty of the presented model, but two other relevant sources of uncertainty may have influenced the results which were not captured by VOI analysis: structural and methodological uncertainty , 26.Structural uncertainty is likely to be present in our model. For example, we did not apply different health-state transition rates for individuals who received any treatment for panic disorder due to a lack of available information . InsteadThe second source of uncertainty is methodological uncertainty, which relates to the analytical methods used in the model. One aspect related to this uncertainty is the WTP threshold, which requires attention given its importance for our study. We applied a WTP of €20,000 per QALY in our study, which we used for the CEAs and VOI of both health economic perspectives. However, a WTP of €20,000 is mostly used for a healthcare setting , 27. AltThe effect of the early intervention that was applied in the model was largely based on one trial (n = 216) . AlthougIn order to incorporate the treatment effect of the early intervention in the transition probabilities, we applied a log-normal distributed relative risk to the STHPD to panic disorder transition. A limitation of our study is that the remaining transition parameters in the model were fixed. However, as the intervention’s cost-effectiveness is primarily the result of the intervention’s reduction in the STHPD to panic disorder transition, the uncertainty in the other transition rates can be considered of second-order importance.Although VOI analysis quantifies the value of uncertainty, in general and for specific model parameters, its practical application remains difficult . The EVPIn conclusion, our results showed that research priorities regarding an early intervention for STHPD differed according to the health-economic perspective applied to the CEA. The VOI analysis indicated that additional research to eliminate uncertainty surrounding the cost-effectiveness estimate is worthwhile when the CEA is performed from a healthcare perspective, but less so when a societal perspective was applied. When the probability that an intervention is more effective as well as cost-saving is high, the value of additional research is likely to be minimal. Because performing a VOI analysis is recommended in the new Dutch guidelines for economic evaluations in healthcare , a conscS1 Table(PDF)Click here for additional data file.S1 Fig(PDF)Click here for additional data file.


Eavesdropping attack is one of the most serious threats in industrial crowdsensing networks. In this paper, we propose a novel anti-eavesdropping scheme by introducing friendly jammers to an industrial crowdsensing network. In particular, we establish a theoretical framework considering both the probability of eavesdropping attacks and the probability of successful transmission to evaluate the effectiveness of our scheme. Our framework takes into account various channel conditions such as path loss, Rayleigh fading, and the antenna type of friendly jammers. Our results show that using jammers in industrial crowdsensing networks can effectively reduce the eavesdropping risk while having no significant influence on legitimate communications. Crowdsensing is a technique leveraging the crowd power to accomplish sensing tasks collaboratively at a low cost. The participants in crowdsensing networks sense the information and upload the sensed data to crowdsensing platforms voluntarily. As a result, the quality of sensing tasks heavily relies on whether the number of participants is sufficient. However, due to the consumption on time, battery and data, recruiting the participants in crowdsensing networks is difficult, although some incentive mechanisms were proposed . TherefoIn recent years, the combination of crowdsensing and Industrial Internet of Things (IIoT) has drawn extensive attention ,5. ThereWith the proliferation of wireless sensor devices, the security of transmitting data in such IIoT based crowdsensing networks deserves much attention, especially for the confidential data related with commercial interest and privacy concern. To protect the security of crowdsensing networks, some security encryption schemes were proposed, such as privacy-preserving participant selection scheme  and repuDifferent from the security encryption schemes, friendly-jamming schemes have been recognized as a promising approach to enhance the network security without bringing extra computing tasks ,11,12,13To mitigate the eavesdropping attack of crowdsensing networks, we propose a novel friendly jamming scheme in this paper. In this scheme, we place multiple jammers at a circular boundary around the protected communication area. Being implied by previous studies ,21, we aWe propose friendly jamming schemes (DFJ and OFJ) to protect confidential communications from eavesdropping attacks.probability of eavesdropping attacks and the probability of successful transmission to evaluate the effectiveness of our proposed scheme.We establish a theoretical model to analyze the We conduct extensive simulations to verify the accuracy of our theoretic model. The results also show that using jammers in crowdsensing networks can effectively reduce the eavesdropping risk while having no significant influence on legitimate communications.The main contributions of this paper are summarized as follows.Our proposed schemes have many more merits than other existing anti-eavesdropping schemes. Firstly, our schemes are less resource-intensive  and it does not require any modifications on existing network infrastructure. Secondly, our schemes are quite general since the circular area with jammers can essentially circumscribe any buildings due to the feature that every simple polygon  always has a circumscribed circle . As a reIn this section, we introduce the models used in this paper. We mainly focus on the uplink transmission from sensor devices (legitimate transmitter) to the receiver. The descriptions of notations are given in R, as shown in E with distance D away from the boundary of this communication area, trying to wiretap the confidential communications within the communication area. In order to protect the legitimate transmission, we place multiple friendly jammers at the circular boundary around the protected communication area.In this paper, we consider a finite disk communication area with radius r from a transmitter is h is a random variable following an exponential distribution with mean 1 and We assume the channel experience Rayleigh fading and path loss. Therefore, the received power of a receiver with distance omni-directional antenna and a directional antenna. Omni-directional antennas radiate/collect radio signals into/from all directions equally. The antenna gain of omni-directional antenna is a constant in all directions, i.e., There are two types of antennas used in our network: an  used in ,25, as sIn this paper, the receiver, the transmitters and the eavedropper are assumed to be equipped with omni-directional antennas. Then, with respect to jammers, we consider two jammer strategies in this network: (i) OFJ scheme, in which jammers are equipped with omni-directional antennas; (ii) DFJ scheme, in which jammers equipped with directional antennas. For comparison purposes, we also consider a scheme: NFJ scheme, in which no friendly jammers are deployed.Definition 1.The probability of successful transmission is the expectation of the probability that a reference transmitter can successfully transmit with the legitimate receiver according to the distance between the receiver and the reference transmitter.In this section, we investigate the impacts of different schemes on the legitimate communications. In particular, we consider the probability of successful transmission as a metric to evaluate the transmission quality of legitimate communications. The probability of successful transmission is defined as follows,T. In particular, when we consider the communication between a reference transmitter ith transmitter and the receiver), N jammers to the receiver  at the legitimate receiver, denoted by Thus, we have the probability of successful transmission, denoted by Then, we investigate the probability of successful transmission Theorem 1.In the NFJ scheme, the probability of successful transmission iswhere In NFJ scheme, there is no friendly jammer at the boundary of the communication area. Therefore, the cumulative interference from friendly jammers Proof. r. Since the receiver is located at the center of the circular area and each transmitter follows uniformly i.i.d., the probability density function of r is as follows,Let the distance between the receiver and a transmitter be After combining Equations  and 2),,2), we hh is a random variable following an exponential distribution with mean 1, Since Equation  can be eM, we can derive the expression of Next, we calculate Substituting Equation  into theAfter plugging Equation  into EquIn the OFJ scheme, the friendly jammers placed at the boundary of communication area are equipped with omni-directional antennas, i.e., the antenna gain of jammers is Equation  can be eTheorem 2.In the OFJ Scheme, the probability of successful transmission isProof. Similar to the proof of Theorem 1, the probability of successful transmission Equation , and EIjSubstituting Equations  and 13)13) into By plugging Equation  into EquIn DFJ scheme, the jammers placed at the boundary are equipped with directional antennas. In particular, we can find that the receiver can be only affected by the side lobe of directional antennas, as shown in Equation  can be eTheorem 3.In the DFJ scheme, the probability of successful transmission isProof. Similar to the proof of Theorems 1 and 2, Equation , and EIjAfter plugging Equations  and 17)17) into Definition 2.The probability of an eavesdropping attack is the probability that the eavesdropper can wiretap any of the transmitters.In this section, we analyze the influence of friendly jammers on the probability of an eavesdropping attack of this network. In particular, we use the probability of an eavesdropping attack as the metric to evaluate the possibility of being eavesdropped on in this network. We assume that if the eavesdropper can wiretap any of the transmitters, this network can be seen as being attacked. Based on this assumption, we give the definition of the probability of eavesdropping attack as follows.ith transmitter and the eavesdropper), Before we analyze the probability of an eavesdropping attack, we first analyze the probability that a certain transmitter can be wiretapped by the eavesdropper, denoted by Next, based on the analysis of The impact of friendly jammers on the eavesdropping attacks will then be investigated. In particular, we will derive the probability of an eavesdropping attack Firstly we consider the NFJ scheme in which there is no friendly jammer on the boundary of communication area. In this case, the interference from friendly jammers to eavesdropper Theorem 4.In the NFJ scheme, the probability of eavesdropping attack where Proof. l. The probability density function of l can be expressed as follows [We denote the distance between the eavesdropper and a transmitter by  follows ,(21)fl by Similarly, we denote Lemma 2.When where , andProof. We present the proof of Lemma 2 in With the interference from the jammers to the eavesdropper, we obtain the probability of eavesdropping attack Theorem 6.In DFJ scheme, the upper bound of probability of eavesdropping attack where Proof. We present the proof of Theorem 6 in In this section, we present the simulation results of probability of successful transmission M increases. Since the receiver only receives the information from the protected transmitter, the cumulative interference from legitimate transmitters to the receiver increases with M. When we introduce friendly jammers into the network, compared with the NFJ scheme, In M is larger than 2. For example, when M becomes 6 and 8, respectively. This result lies in the fact that the eavesdropper may eavesdrop any one of the M legitimate transmitters, rather than a specially appointed transmitter. When M increases, the interference on the eavesdropper increases. However, the eavesdropper may tap more transmitters as the total number of transmitters is increased. In addition, the performance of In From N. In N increases. The decrement of N increases, especially when friendly jammers are equipped with directional antennas . This result can help to verify the effectiveness of OFJ and DFJ schemes in reducing the probability of eavesdropping attacks The results as shown in T and D. From In another set of simulations as presented in In this section, we first discuss the impact of our friendly jamming schemes when the eavesdropper is located inside the network. Then we discuss the impact of our friendly jamming schemes on legitimate transmissions in other networks.In Regarding the case in which the eavesdropper is not located at the center of the network, we can first calculate the cumulative distance from the eavesdropper to each of friendly jammers via the approach proposed in  and usedIn In Then we analyze the second scenario. In this scenario, both the protected network and another network are using different channels. It is obvious that the analytical result in limit the jamming range or restrict the jamming period so that the impact on other legitimate communications will be minimized. The analytical results of OFJ and DFJ imply that the intensity of interference generated by our friendly jamming scheme heavily relies on the channel factors, for example, the transmitting power of jammers, antenna gain, path loss, etc. Therefore, we can adjust the transmitting power and the antenna gain of friendly jammers so that the jamming range can be minimized. Another approach of limiting the impact of friendly jamming schemes is restricting the time of the emitting jamming signal. For example, we can only send the jamming signal at the crucial stages .In this paper, we propose a novel friendly jamming scheme to protect confidential communications from eavesdropping attacks. To evaluate the effectiveness of our scheme, we establish a theoretical model to analyze the probability of eavesdropping attacks and the probability of successful transmission. Moreover, we verify our model with extensive simulations. The agreement between analysis and simulation results verifies the accuracy of our analysis.Our results show that our scheme can significantly decrease the eavesdropping risk compared with the no friendly jamming scenario and meanwhile that it maintains low decrease on the transmission probability. In addition, we find that using directional antennas compared with omni-directional antennas on friendly jammers can further decrease the eavesdropping risk while obviously mitigating the influence on the transmission probability.