Wireless-powered communication networks have garnered significant attention due to their potential to enhance energy efficiency and extend network lifetime. One critical aspect of such networks is ensuring the security and confidentiality of communication, particularly in the presence of eavesdroppers. This section provides an overview of recent research related to secrecy outage probability minimization in wireless-powered communications. In their work, Cao et al. [1] introduced a joint artificial noise and power allocation (JAP) scheme for ensuring reliability and security in wireless-powered non-orthogonal multiple access (NOMA) systems. The study presents closed-form expressions for connection outage probability (COP), SOP, and effective secrecy throughput (EST). The proposed JAP scheme was found to outperform benchmark schemes, making it a notable contribution in the field of wireless-powered secure communications. Lee et al. [2] addressed secrecy outage minimization in wireless-powered relay networks with destination-assisted cooperative jamming. Their work introduced power splitting-based relaying (PSR) and time switching-based relaying (TSR) protocols to control energy harvesting and minimize secrecy outages. The results demonstrated that these protocols could achieve near-optimal secrecy outage performance, even without precise knowledge of eavesdropper locations, under high signal-to-noise ratio (SNR) conditions. Chen et al. [3] focused on the secrecy communication of a wirelessly powered network, proposing protocols that combine maximum ratio transmission with zero-forcing (ZF) jamming to enhance physical layer security. They provided closed-form expressions for connection and secrecy outage probabilities, along with optimal time-switching ratio and power allocation for secrecy throughput maximization in high SNR regimes. Their proposed schemes effectively improved security in wireless-powered networks. Moon et al. [4] considered a wireless-powered communication network with an energy harvesting (EH) jammer, addressing secrecy performance optimization. Their work involved the transmission of energy signals and information in separate phases, effectively thwarting eavesdropping attempts. The research provided insights into maximizing secrecy rates under various channel state information scenarios, emphasizing the advantage of optimal power allocation for security in EH systems. Li et al. [5] explored the performance of friendly jammer selection-aided multiuser scheduling for wireless networks. They proposed random jammer selection-aided multiuser scheduling (RJS-MUS) and optimal jammer selection-aided multiuser scheduling (OJS-MUS) schemes, analyzing their impact on secrecy outage probability. Their research demonstrated that, under specific SNR conditions, the proposed schemes outperformed conventional non-jammer selection-aided multiuser scheduling (NJS-MUS), highlighting the potential of power allocation strategies to enhance security. Yan et al. [6] investigated transmit antenna selection in a multiple-input-multiple-output (MIMO) energy-harvesting system. Their work introduced optimal antenna selection (OAS) and suboptimal antenna selection (SAS) schemes, examining the secrecy performance of these schemes under various channel state information scenarios. Notably, their results showed that full knowledge of CSI led to better secrecy performance, emphasizing the importance of CSI in achieving security in MIMO systems.

Jiang et al. [7] contributed to the field by studying secrecy performance in wirelessly powered wiretap channels. Their work involved exploring multi-antenna transmission schemes and deriving closed-form expressions for achievable secrecy outage probability and average secrecy rate. It emphasized the role of channel state information in achieving substantial secrecy diversity gain, furthering our understanding of security in wireless-powered networks. Zen et al. [8] explored wirelessly powered backscatter communications in the context of smart sustainable cities. Their work addressed the secrecy performance of WP-BackComs using a stochastic geometry framework. They considered factors such as imperfect successive interference cancellation, non-linear energy harvesting, and energy-causality constraints in the analysis. The results emphasized the importance of optimizing reflection coefficients to minimize SOP and the potential benefits of optimal strategies in WP-BackComs. Xu et al. [9] studied resource allocation for secure communications in cooperative cognitive wireless-powered communication networks. Their research proposed a cooperative protocol for secondary users, focusing on maximization of the secondary user’s ergodic rate while ensuring primary user security. Their algorithms considered perfect and imperfect channel state information and addressed both collusive and non-collusive eavesdroppers, highlighting the significance of secure resource allocation in cognitive wireless-powered networks. Tang et al. [10] addressed secrecy outage probability in wireless-powered cognitive radio networks. Their work focused on secure information transmission for secondary systems sharing the spectrum with primary networks and considered the presence of eavesdroppers. The closed-form analytical expressions revealed the trade-offs between primary outage probability, secondary secrecy outage probability, and the probability of non-zero secrecy capacity. Their research also discussed optimal time-switching and power-splitting strategies to maximize secondary secrecy outage probability under primary constraints, highlighting the importance of securing cognitive radio networks. The work by Lee et al. [11] delved into deep-learning-assisted wireless-powered secure communications with imperfect channel state information. They aimed to find robust transmit power control strategies to maximize secrecy rates while accounting for imperfect channel state information (CSI). Their research included iterative methods and a deep learning (DL)-assisted approach to tackle the no convexity of the problem, demonstrating the robustness of DL-assisted strategies against channel errors. Liu et al. [12] proposed a tag selection scheme to enhance security in passive backscatter communication systems with multiple tags and eavesdroppers. They analyzed SOP while considering a non-linear energy harvesting model. Their research introduced dynamic reflection coefficient optimization and tag selection to maximize the instantaneous secrecy capacity.

Moon et al.’s research [13] delved into the intricacies of enhancing security in wireless-powered communication networks by introducing an energy harvesting (EH) jammer, where an eavesdropper seeks to intercept communication between a user and a hybrid access point (H-AP). Their study presents a novel approach to this challenge, dividing the communication process into two key phases: energy transfer (ET) and information transfer (IT). During the ET phase, the H-AP transmits an energy signal to replenish the batteries of both the EH user and the EH jammer. In the subsequent IT phase, the user sends its information signal to the H-AP, while the EH jammer leverages the harvested energy to generate jamming signals aimed at interfering with the eavesdropper. This innovative approach assumes only knowledge of the channel distribution information (CDI) of the eavesdropper, and it focuses on minimizing the secrecy outage probability through an optimized time allocation between the two phases. To manage complexity, Moon et al. offered a simplified closed-form solution, demonstrating through simulations that their method closely approaches the optimum performance. Their research provides insights into secure wireless-powered communication networks, particularly in scenarios with energy-harvesting jammers and partial channel information. Chen et al. [18] researched a unique hierarchical game model for enhancing physical layer security (PLS) through dynamic three-party collaborations. This system focuses on legitimate users (LUs) who strive to securely send confidential data to their respective base stations (BSs) via uplink channels, contending with potential eavesdroppers (EVs). Additionally, jammers (JAs) exist, which can opt to align with either LUs to boost their secure data transmission or with EVs to enhance eavesdropping capabilities, in return for possible rewards. They introduced a deep reinforcement learning (DRL) strategy for achieving equilibrium with long-term performance assurances in this hierarchical game. Through simulations, they demonstrated the effectiveness of their method, highlighting its advantages over similar approaches.

The challenges involved in SOP minimization span the realms of both cyber security and system optimization. It requires the development of efficient algorithms [21–25]. That can adapt to evolving network conditions, effectively allocate power and resources, and dynamically adjust to potential security threats [5–8]. Furthermore, the integration of machine learning (ML) techniques introduces a new layer of complexity, but also the potential for groundbreaking advancements [26–28]. In the literature of wireless-powered communication, there have been notable efforts aimed at minimizing SOP as we investigated in Subsection 1.1. However, it is evident that while significant progress has been made, particularly in enhancing security against eavesdroppers, most existing research tends to focus on scenarios with specific conditions, such as high or perfect CSI. These studies often present strategies optimized for idealized conditions and may not fully encapsulate the challenges encountered in more variable and realistic wireless network environments. Additionally, many of these approaches concentrate on theoretical models and may not sufficiently address the practical challenges of deployment in real-world scenarios. Moreover, proposing an efficient optimization scheme to tackle this challenge has proven to be a formidable task. The primary motivation of this work lies in advancing the state-of-the-art in wireless-powered communications. By minimizing SOP and, in turn, enhancing the secrecy performance, this paper not only contributes to the evolution of wireless-powered communication but also exemplifies the potential of combining nature-inspired optimization methods with advanced ML methods to address complex communication challenges [3–5]. ML techniques are now extensively and effectively utilized across various sectors [29–31]. Specifically, recurrent neural networks (RNNs) are increasingly used to reduce outage probabilities in wireless-powered communication, offering a smart solution to key challenges in today’s wireless networks [25]. Their role is crucial for improving the dependability and effectiveness of these systems, particularly in managing the fluctuating and hard-to-predict nature of wireless channels. RNNs become essential in such scenarios because wireless communication faces various uncertainties like constantly changing channel conditions, variable energy harvesting rates, and unpredictable movements of users. They excel in fine-tuning power distribution and managing resources to lower the chances of outages, thereby boosting system reliability. Consequently, RNNs play a pivotal role in enhancing the performance of wireless-powered communication systems by continuously fine-tuning energy and resource allocation [26].

While DL algorithms can play a crucial role in reducing SOP, the primary difficulty is in adjusting the DL’s hyper-parameters. Currently, meta-heuristic algorithms are used for fine-tuning network parameters. Training RNNs poses significant challenges, particularly with traditional gradient-based techniques, which often encounter limitations such as getting trapped in local minima and struggling with non-differentiable objectives [32–34]. These issues highlight the need for alternative optimization strategies to enhance RNN training. Biogeography-based optimization (BBO) emerges as a promising approach, illustrating the effectiveness of meta-heuristic methods in addressing these challenges. BBO offers a unique way of balancing exploration and exploitation, potentially avoiding local minima and improving training results. However, standard BBO has its drawbacks, including a propensity to get stuck in local optima and inefficient exploration of the search space, leading to suboptimal outcomes [35]. Improving BBO could lead to more powerful and versatile optimization algorithms, better equipped to address the complex problems encountered in real-world optimization scenarios. In light of these challenges and the pressing need for heightened security, this paper introduces a novel approach aimed at the minimization of SOP in wireless-powered communications. Our proposed method harnesses the power of an improved BBO (IBBO) to effectively train an RNN. This unique synergy between the IBBO and the RNN’s capacity for learning complex relationships within wireless-powered communication scenarios promises to enhance system performance significantly. The main contributions of this paper can be summarized as follows:

Our work introduces a novel approach to address the pressing challenge of minimizing SOP in the context of WPC. SOP, a pivotal metric, quantifies the vulnerability of communication links to information leakage, and our scheme offers a fresh perspective on how to effectively reduce it.

The structure of the paper is organized as follows: Section 2 delves into the research model, encompassing the system model, SOP problem formulation, the proposed IBBO, and the evolutionary RNN. Section 3 presents the experimental findings and discussions, providing crucial insights. The paper concludes in Section 4 with a summary of the key contributions and the broader implications of the research.

The considered system model, as illustrated in Fig. 1, consists of a wireless-powered communication network. Within this setup, a legitimate user we refer to as Alice receives her power wirelessly from a distant power beacon (PB). The objective for Alice is to securely send a private message to Bob, another authorized receiver, across a wireless channel subject to fading. Concurrently, an eavesdropper, whom we call Eve, is attempting to capture and decipher the message from the signals that reach her.

For ease of analysis while maintaining the system’s generality, it is assumed that each node in the network is equipped with only one antenna. Consequently, the power that Alice receives at any specific instant can be quantified by the Eq. (1):

(1)PR=PTLTdTαgT

Here, PT represents the power transmitted by the power beacon (PB), LT combines the effects of antenna gains and frequency-dependent propagation losses, dT is the distance between the power beacon and Alice, α>2 is the path-loss exponent, and gT=|hT|2 signifies the normalized fading power channel coefficient between the power beacon and Alice, where E[gT]=1 (indicating an average value of 1). With these assumptions, the instantaneous SNR at user K, where K can be either Bob (B) or Eve (E), can be defined as Eq. (2):

(2)γK=PTLTσK2dTαdKα|hT|2|hK|2=γ¯KgTgK

Here, σK2 represents the noise power at Bon/Eve, γ¯K is the average SNR, and gK=|hK|2 is the corresponding fading coefficient with an average value of 1. Furthermore, we assume that all channels in the system are quasi-static fading channels, meaning they remain constant during the transmission of an entire code word and change randomly from one transmission block to another. These channels are modeled using the independent Rayleigh distribution. The goal of this paper is to minimize the SOP, which is the probability that the instantaneous secrecy capacity falls below a threshold target secrecy rate; RS. The secrecy capacity CS is given by the difference between the capacities of the main channel (Alice to Bob) and the eavesdropper’s channel (Alice to Eve):

(3)CS=[CB−CE]+where CB=log2⁡(1+γB) and CE=log2⁡(1+γE), and [X]+ denotes the positive part of X as max{CB−CE,0}. Therefore, the SOP can be given by Eq. (4):

(4)PSOP=Pr(CS≤RS)

Using the definition of CS, we can deduce a mathematical representation for SOP:

(5)PSOP=Pr(log2⁡1+γB1+γE≤RS)

Thus, according to Eq. (2), the cost function can be formulated as Eq. (6):

(6)f(PT,LT,dT,α,σB2,σE2,dB,dE,hT,hB,hE)=Pr(log2⁡1+γB1+γE≤RS)

Under the following constraints:

0≤PT≤Pmax

α>2 is a constant value.

hT,hB, and hE follow independent Rayleigh distributions with the mean value of aT, aB, and aE, respectively.

The BBO algorithm, introduced by Dan Simon in 2008, is inspired by biogeography, a field that examines species distribution and their migration and adaptation processes in different geographic areas [35]. BBO utilizes the concepts of immigration, emigration, and speciation from biogeography to find optimal solutions in multi-objective optimization problems. In BBO, potential solutions are conceptualized as “habitats,” each with a habitat suitability index (HSI) indicating its fitness. The algorithm operates through migration, mutation, and elitism. Habitats with higher fitness values are more likely to share their features with others, facilitating the spread of advantageous features. Conversely, habitats with lower fitness levels are prone to receiving features from others, potentially enhancing their quality. The emigration rate of a habitat depends on its fitness relative to the population’s average fitness, with higher fitness habitats having higher emigration rates. Similarly, the likelihood of a habitat receiving immigrants correlates with the emigration rates of other habitats. The mathematical foundation of linear BBO is encapsulated in Eqs. (7), (8) that detail its operational mechanisms [35].

(7)μj(k)=E×(k(j)N) (8)λj(k)=I×(1−k(j)N)where μk(j) signifies the emigration rate, λk(j) denotes the immigration rate, kj refers to the species’ rank, N represents the total population size, E and I are the maximum rates of emigration and immigration, respectively. Within BBO, the information exchange between habitats is facilitated probabilistically through the emigration and immigration rates of each solution [35]. The migration process in standard BBO is described by Eq. (9):

(9)Hj(SIVs)←Hj(SIVs)+Hi(SIVs)where Hj is the host habitat and Hi is the guest habitat. According to the Eq. (9), the host habitat receives information from the guest habitat and itself. Also, the mutation operator defines as Eq. (10):

(10)mj=mmax×(1−pjpmax)where mmax is chosen by user, pj reveals the probability of species count and pmax is the highest value of pj.

The linear BBO algorithm, like other optimization methods, faces several challenges that affect its applicability and efficiency. Its performance is sensitive to the precise tuning of various parameters, such as migration and immigration rates, which need careful adjustment for different problem domains. This sensitivity can make BBO challenging to apply broadly without specific tuning. Additionally, BBO tends to converge slowly, particularly in complex and high-dimensional problems, often requiring numerous iterations due to its probabilistic migration and immigration rules. The algorithm also struggles with effectively exploring the entire search space, especially in rugged, multi-modal landscapes, as it tends to focus on regions with higher fitness values, potentially overlooking other viable areas. Scalability is another issue, particularly with very high-dimensional problems or those with numerous constraints, as maintaining and updating habitat populations can be computationally intensive. Furthermore, like many evolutionary algorithms, BBO faces difficulties in striking the right balance between exploration and exploitation, a critical aspect of its overall effectiveness [35].

To address these limitations, researchers have proposed various enhancements and modifications, such as hybridizing BBO with other techniques, introducing diversity-preserving mechanisms, or addressing parameter tuning issues. Recent research, particularly studies on Markov theory-based models, has explored the impact of different migration models on BBO’s efficiency. Various models like linear BBO, quadratic BBO, sinusoidal BBO, generalized sinusoidal BBO, and exponential-logarithmic BBO have been introduced. The paper under discussion introduces a novel migration model for BBO, described in Eqs. (11)–(13), which proposes unique migration rates for each habitat. This new approach aims to create a smarter migration structure to accelerate convergence to the best solution, differing from previous models that used a single function for migration rates and treated all habitats uniformly.

(11){μk(j)=2E3×(−cos(k(j)πN)+1)λk(j)=2I3×(cos(k(j)πN)+1)k(j)<N5 (12){μk(j)=E2×Ln(k(j)N+1)λk(j)=I2×exp(−k(j)N)N5≤k(j)≤2N5 (13){μk(j)=2E3×(tan h(k(j)πN−2π7)+1)λk(j)=2I3×(−tan h(k(j)πN−2π7)+1)k(j)>2N5

Selecting the six specified mathematical functions for migration rates, the IBBO employs a range of functions suited to combining habitats with diverse HSI, which enhances its overall effectiveness. In this paper, the GA’s crossover operator is employed to enhance the exploitation capabilities of the BBO. During the optimization process, in addition to the regular migration of BBO, the crossover operator can be applied to selected pairs of habitats. This operation allows for a more diversified exchange of features between habitats, potentially leading to more effective exploration and exploitation of the search space. It can help in overcoming local optima issues by providing a mechanism to escape and explore new areas of the solution space. Additionally, the mechanism of moving towards the Gbest from the PSO algorithm has been utilized to improve the performance of the BBO. This concept can be applied to BBO by allowing habitats to be influenced not just by their features but also by the best solutions found in their neighborhood. This mimics the way particles in PSO are influenced by their neighbors. By moving habitats towards the best experiences of their neighbors, the BBO algorithm can more effectively explore the solution space and exploit the best-known solutions. This approach encourages convergence towards optimal or near-optimal solutions by leveraging collective knowledge.

Fig. 2 presents an example of the operators in the IBBO. Moving towards a random habitat involves occasionally directing a habitat towards a completely random position in the solution space. Such random movements can prevent the algorithm from getting stuck in local optima. It introduces an element of randomness that helps to explore potentially unvisited regions of the search space. While the PSO-inspired mechanism focuses on exploiting known good solutions, the random habitat movement ensures that the algorithm does not overly focus on certain areas, thus maintaining a balance between exploration and exploitation. The key to effective optimization is balancing exploration and exploitation. Integrating moving towards a random habitat, the crossover operator from GA, and global best (Gbest) operator from PSO into BBO can help in maintaining this balance, as it introduces a new layer of complexity and adaptability to the search process. By incorporating these techniques, the BBO algorithm becomes more adaptable and robust, capable of handling a wider range of optimization problems.

RNNs are a unique subset of artificial neural networks tailored for processing sequential data, setting them apart from traditional feed-forward neural networks. Their defining feature is a feedback loop that maintains a ‘memory’ of previous inputs, enabling the handling of variable input lengths and the integration of past information into current input processing [25]. Comprising multiple layers, including an input layer for sequence data, a recurrent layer that refeeds outputs into the network, and an output layer for final outcomes, RNNs utilize activation functions such as sigmoid, tanh, and ReLU to learn complex patterns. These networks are highly effective in tasks like language modeling, sentiment analysis, machine translation, text generation, and speech recognition, as well as in predicting time series data and, in combination with CNNs, generating images and videos [26].

However, RNNs encounter significant challenges, notably in capturing long-term dependencies and grappling with vanishing or exploding gradients during training. Their primary training method, gradient-based optimization techniques, has inherent limitations, including the risk of getting trapped in local optima, leading to less than optimal training outcomes. Moreover, these methods are computationally complex and time-consuming, especially in large networks or with long sequences, due to the extensive computation of gradients across many layers and time steps. The vanishing gradient problem, where gradients become too small to effect meaningful learning, particularly hampers standard RNNs in handling long sequences and capturing long-term data dependencies. Conversely, the exploding gradient issue causes overly large updates to network weights, destabilizing training. These challenges collectively constrain the efficiency and applicability of RNNs in certain real-world applications.

Meta-heuristic algorithms [36–39], including BBO, are gaining recognition as effective tools for training the weights and biases of RNNs, offering several advantages over traditional gradient-based methods. One of their primary benefits is the ability to avoid getting trapped in local optima, a common issue with gradient-based techniques that follow the steepest descent. Meta-heuristics, in contrast, employ mechanisms to explore the search space more broadly and escape local minima, thus increasing the likelihood of identifying the global minimum. These algorithms are not dependent on the gradient of the error function, making them well-suited for optimizing functions that are non-differentiable, discontinuous, or highly nonlinear, which often poses challenges for gradient-based methods. This attribute is particularly beneficial in complex RNN architectures with a non-smooth error surface.

In this paper, the IBBO is utilized for training the RNN due to its ability to effectively balance exploration and exploitation. This equilibrium is key in training RNNs, as it allows the algorithm to investigate various weight and bias configurations without prematurely converging on a solution. The adaptive nature of the BBO, characterized by migration rates that change based on the quality of the habitats, enables the algorithm to modify its search strategy to suit the specific needs of the problem at hand. Such adaptability is particularly beneficial in training RNNs within dynamic environments, where data patterns may evolve over time. Fig. 3 shows the structure of the IBBO-RNN, and Fig. 4 shows the structure of a habitat in IBBO. Additionally, the cost function used in the IBBO is detailed in Eq. (14).

(14)Mean Square Error(MSE)=1k∑i=1k(Oi−Di)2where k = the total number of samples, Oi = System output, Di = Desire.