NNV: A NOVEL AI SAFETY VERIFICATION FRAMEWORK

Abstract

This paper studies the secrecy performance of multi-hop wireless-powered communications networks, where all nodes harvest energy from multiple power beacons (PBs) for conveying secret information in the presence of an eavesdropper. To enhance the secrecy outage probability (SOP), we propose and analyze a novel best node selection strategy, referred to as BNS, that selects the best data transmission node to decode and forward information to a destination over Nakagami-m fading channels. We derive the closed-form expression for SOP of the proposed BNS scheme. We then develop a deep neural network framework for secrecy performance evaluation based on this analysis. Numerical results show that the proposed deep learning approach achieves almost exact SOP of the analysis results while it drastically reduces the execution time, arising a real-time configuration in IoT networks.

Index Terms—Deep neural networks, energy harvesting, node selection schemes, multi-hop systems, physical-layer security.

I. INTRODUCTION

Recently, physical layer security (PLS) and wireless energy harvesting (WEH) have drawn significant attention from the academia and industry [1]. The objective of WEH is to prolong the smart devices operation without replacing their batteries artificially, while that of PLS is to guarantee the confidential exchanged data in the Internet-of-Things (IoT) networks [2,3,4]. Although the combination of PLS and WEH has been widely studied in IoT network, it is only recently that a few works have investigated PLS and EH in multi-hop energy harvesting IoT networks.

Recently, deep learning (DL) has emerged as a powerful solution to tackle a variety of practical problems in contemporary wireless IoT systems, including resource allocation, queue management, and congestion control [5]. By precisely estimating functions with high nonlinearity at a minimum of complexity, DL has been increasingly applied in wireless networks to improve various aspects of systems including resource allocation, throughput prediction, and channel estimation [6,7,8]. Furthermore, employing deep learning for performance prediction in IoT networks can expedite real-time configurations. DL-based models have the capability to precisely predict desired performance measurements from intricate datasets with high dimensionality, even in complex network scenarios and highly dynamic environments where mathematical derivations may not be practical.

Different from these works, we consider the secure multi-hop communications in IoT networks in Nakagami-m environments, where the node selection strategy is converted to a regression problem using DNN for SOP evaluation. The main contributions of the paper are summarized as follows:

• We propose the best node selection (BNS) scheme to improve the secure communications in multi-hop wireless powered IoT networks.

• We derive closed-form expressions for the SOP of BNS scheme under considered system setup. Based on such an expression, we develop a deep learning model for SOP prediction with high accuracy and short execution time, which promotes a real-time configuration for multi-hop communications in IoT networks.

• Numerical results show the SOP performance improvement of the BNS scheme over conventional one, arising as an efficient strategy for multi-hop transmissions in IoT networks.

Notations and Functions: Boldface represents vector and ||.|| designates the Frobenius norm. (.) H is the transpose conjugate. Γ(.) denotes the Gamma function [6, Eq. 8.310.1], and Kv(.) symbolizes the v order modified Bessel function of second kind [6, Eq. (8.432)].

II. SYSTEM MODEL

Let us consider a multi-hop energy harvesting IoT network as shown in Fig. 1, where a source (S) transmits its data to a destination (D) via multiple relays located in K-1 intermediate clusters. We assume that all nodes harvest energy from a multiple antennas power beacon (PB) for their operation. The PB is equipped with M antennas and uses energy beamforming to power the relays. Each IoT device is equipped with one single antenna and operates on half-duplex mode. We assume that the number of users is equal to the number of relays in each cluster and all channels experience the independent distributed Nakagami-m fading.

The time switching architecture is adopted for WEH and data transmission phases [2]. In the EH phase, the source and all relays harvest energy from PB in the duration of αT , where α and T denote time switching ratio and transmission block, respectively. In the data transmission phase, (1-α )T , K orthogonal subtime slots are used to transmit data over K hops [3]. The transmit power of Rk,i during a subtime slot of (1-α )T/ K can be calculated as Pk= P‖gk,i‖2 where κ is defined as =Kηα1-α, η with η∈(0,1] is the energy conversion efficiency, P is the transmit power of PB and gk,i is the channel coefficient of the PB ⟶ Rk,i link.

In this paper, we propose the best node selection criterion as

The instantaneous SNR at Rk,j and E can be expressed as

where Ψ = P/N0, hk,b,j is the is the channel coefficient of the Rk, i*⟶Rk, j link. In this paper, the large-scale path loss is modeled as Gf=PL(dd0)-β, where d denotes the distance (in meter) between two nodes, β is the path loss exponent, d0 presents the reference distance, and σPL is the measured path loss at d0. 

Fig. 1. The system model of interest.

III. SECRECY OUTAGE PROBABILITY ANALYSIS

The SOP of the considered system is given as

where Rth is the threshold.

Theorem 1: The exact closed-form expression for the SOP of BNS scheme is expressed as

Proof:

First, the SOP of BRE scheme can be rewritten from (2) as

For notational convenience, let

Thus, I can be calculated as

Next, by substituting the cumulative distribution function (CDF) of Y, the probability density function (PDF) of X, and the PDF of Z, into (11), and then using [8, Eq. (3.471.9)], we arrive at

By plugging (15) into (10), the SOP of the BNS scheme is obtained as in (6), which concludes Theorem 1.

IV. DEEP NEURAL NETWORK EVALUATION

In this section, we design a DNN as a regression problem to evaluate the SOP performance. The DNN model includes an input layer, multiple hidden layers, and an output layer, as shown in Fig. 2. The values of the input variables are randomly chosen over the specific range shown in Table I. In this section, we present the proposed deep neural network for SOP evaluation, where the selection criteria (1) is modeled as regression problems. The DNN model for the regression problem is presented in Fig. 2, which includes an input layer, multiple hidden layers and an output layer. The number of hops, the positions of power beacon and eavesdropper, average SNR, number of antennas at the PB, number of relays in each cluster, and time switching ratio are extracted as input variables of a sample for training, as shown in Table I. The SOP of BNS scheme is generated based on the results in Theorem 1, which is served as output variable of training samples. The network is trained by using the adaptive moment estimation optimization algorithm to optimize the model parameters relied on training dataset. This process is done by calculating a loss function and updating weights and biases iteratively in the backpropagation procedure. It is noted that the training process is only performed at one time and can be reused several times to predict the SOP in communication processes. Thus, the computational complexity is brought to the offline training, which reduces significantly implementation cost and execution time in multi-hop energy harvesting IoT networks. We then use the generated data to train a deep neural network for SOP predictions.

Table 1: Input variables and their values for DNN model.

Fig. 2. The proposed DNN model for SOP evaluation.

V. SIMULATION RESULTS

In this section, the Monte-Carlo simulations are provided to verify the analytical expressions. We set dSD=10m, d0 =1m, PL=-30dB, β=3, η=0.8 and Rth=1bit/s/Hz. The positions of S, Rk,i, D, PB, and E are randomly located at (0,0), (k/K,O), (10,0), (7,5) and (10, -10), respectively. The DNN model is implemented in Python 3.7.4 associated with Keras 2.3.1 using TensorFlow 2.0.0. The neural network is end-to-end trained in 70 epochs, where weights are randomly initialized using Adam optimizer with the gradient decay factor of 0.95. The initial learning rate is set as 10-3 (dropped 90% after 20 epochs).

Fig. 3. RMSE of the DNN model with different number of hidden layers 

and number of hidden neurons.

Fig. 3 shows the root-mean-square error (RMSE) of the DNN model versus the number of hidden neurons with different hidden layers. It is observed that the more hidden layers the DNN model has, the lower RMSE the SOP is estimated. The reason is that the DNN model with multiple hidden layers has the ability to generalize dataset, resulting in high network capacity, while the single-layer neural network cannot learn the complex patterns in a highdimensional dataset, leading to the high RMSE.

As shown in Fig. 4, the deep learning approach achieves almost the same SOP as the considered relay selection scheme in all ranges of SNR, showing an accurate prediction of the deep learning approach. Furthermore, the system SOP is improved with the number of power beacon and eventually saturates at its given secrecy outage floors at high SNR. Thus, we can conclude that the system achieves the zero-diversity order. Furthermore, it can be observed that the analysis result is excellent agreement with the simulation one, validating the correctness of our derivations.

We also compare the execution time of Monte-Carlo simulation, theory evaluation, and DNN prediction.

The results show that DNN prediction takes the shortest execution time, only requiring 0.67 seconds to obtain a target SOP value. Evaluating the analysis follows with 3.51 seconds per SOP value. While the Monte-Carlo model takes 204.33 seconds per SOP value. Therefore, the DNN approach significantly reduces the execution time, suggesting a real-time configuration for multihop communications in IoT networks.

Fig. 5. SOP versus the number of hops.

Figure 5 illustrates the impact of the number of hops on the SOP performance of the BNS scheme. As the number of hops increases, the path loss effect diminishes, leading to an improvement in SOP performance. However, beyond a certain point, further increasing the number of hops results in degraded SOP due to the higher probability of errors associated with multihop transmission. Thus, there exists an optimal number of hops that minimizes the SOP.

VI. CONCLUSIONS

In this paper, we proposed the best relay selection scheme to improve the SOP performance for multi-hop communications in IoT networks. We derived the exact closedform expressions for the SOP of the BNS scheme over Nakagami-m fading channels. Based on the obtained analysis, we developed a DNN framework for the SOP evaluation with a short execution time. The numerical results showed that the DNN approach achieved almost the same SOP as compared to the BNS scheme. As a result, it could be a promising solution for future wireless sensor networks to enhance secrecy performance and reduce the execution time.

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