1.1 Related work

In recent years, spectrum sensing techniques have transitioned from traditional methods such as energy detection to more advanced approaches based on machine learning (ML), deep learning (DL), reinforcement learning (RL), and artificial intelligence (AI). These advanced techniques significantly improve detection accuracy and robustness, especially in dynamic and noisy conditions, where traditional methods often struggle [12]. They improve CRN performance by automatically detecting environmental signal patterns and making accurate spectrum availability decisions. In [13] an ensemble learning framework has been introduced for cooperative spectrum sensing (CSS), highlighting significant improvements in detection and false alarm probabilities compared to conventional methods. The K nearest neighbor (KNN) algorithm in [14] has examined the accuracy, sensitivity, and confusion matrix to evaluate the classification of the PU channel. Similarly, multiple ML techniques, including KNN, are proposed in [15] to detect PU emulations in a mobile CRN environment. This method employs a prior learning process to create datasets using the SNR and received power entropy. In particular, it operates without the need for prior knowledge of modulation types or RF characteristics.

Building on advances in ML, recent work demonstrates how DL and convolutional neural networks (CNNs) can optimize spectrum sensing [16]. The integration of CNNs and recurrent neural networks (RNNs) in sensing has demonstrated superior performance over traditional methods, capturing spatial and temporal patterns in CR systems [17,18]. In [19], a novel DL-based sensing detector utilizing CNN and long-short-term memory (LSTM) is proposed to exploit energy correlation features and PU patterns without making assumptions from the signal-noise model. DL is also used to improve the classification of sensing by incorporating prior knowledge of PU with LSTM layers in [20]. The authors in [21] develop a multi-agent reinforcement learning scheme using distributed algorithms to help cognitive unmanned aerial vehicles (UAVs) decisions by linking sensing and access approaches. In this framework, the sensing phase is performed cooperatively, with binary decisions being exchanged between agents to inform the joint access strategy. Similarly, in [22], an RL-based CSS scheme improves the sensing performance in dynamic CR networks. In this approach, each SU acts as an agent that learns the behavior of channels and neighbors to improve detection efficiency, decrease scanning overhead, and reduce access delay.

Virtual CSS (VCSS) proposed in [23] tried to overcome power limitations in UAV networks by utilizing sequential decision fusion and ML techniques. The network in [24] is trained using the multilayer perceptron model to reduce the prediction error and mitigate the impact of collision factors. Furthermore, CNN-based method in [25] processes input from multiple secondary users (SUs). This approach specifically addresses how the combination of diverse sensing affects the detection performance. Reference [7] presents a GA method that computes optimal weighting coefficients for soft combination. These weights are then applied in soft decision fusion (SDF) for final decisions. Furthermore, [26] presents a hopping sequence module to increase the probability of detection when PUs and SUs are mobile. Finally, [27] and [28] use CSS with spatial variability in the classification of SU using SVM to reduce uncertainty in the global decision. Table 1 provides a summary of related work.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Literature summary of advanced spectrum sensing techniques.

https://doi.org/10.1371/journal.pone.0338915.t001

Multi-user CSS has emerged as a promising approach. However, existing cooperative methods face several challenges. Traditional methods often use fixed sensing times, which can lead to inefficiencies in spectrum utilization and reduced throughput. Similarly, the presence of FSUs in CSS degrades both the sensing performance and the error probabilities. To address these limitations, we propose a hybrid scheme that combines an ensemble classifier (EC) and a denoising autoencoder (DAE). The EC dynamically adjusts the sensing time, improving the efficiency and network throughput, while the DAE cleans the sensing data from FSU disturbances and noisy channel conditions, improving the sensing reliability.

In the cooperative model, increasing the number of sensing samples (more sensing time) leads to higher sensing accuracy. However, this also results in increased energy consumption and reduced channel throughput. In contrast, optimal choice of the sensing sample for the individual and the user in cooperation leads to benefits such as improved throughput, low sensing cost, and guaranteed sensing with minimum error. A similar problem of multichannel detection without the use of AI tools is investigated in [29,30]. The authors of [31] analyzed the performance of CSS in the presence of FSUs using a particle swarm optimization (PSO) scheme. In contrast, the work in [32] focused on a hybrid differential evolution-based ML (DE-ML) scheme to improve the FC decision with fixed sensing samples, but lacks denoising effects.

While existing approaches demonstrate progress, they possess critical limitations that are systematically summarized in Table 1. Our ECDAE framework bridges these gaps through : (1) dynamic sensing-time optimization through ensemble learning that adapts to real-time channel conditions, (2) integrated DAEs that purify sensing reports from both FSU distortions and channel noise with low latency, and (3) comprehensive validation across various FSU attack scenarios, demonstrating 82-100% error reduction compared to state-of-the-art methods. This paper is an extension of our previous work [33]. In this paper, a hybrid ensemble classifier-based DAE (ECDAE) scheme is suggested that integrates the ensemble classifier with the autoencoder as in Fig 1. The main contributions of this paper are summarized as follows:

• Novel Hybrid Architecture: We propose the first framework, to our knowledge, that integrates an ensemble classifier (EC) with a DAE for cooperative spectrum sensing. This ECDAE architecture uniquely addresses both sensing-time optimization and data purification in a single cohesive system.
• Dynamic Sensing-Time Optimization: We introduce an EC-based mechanism that dynamically reconfigures the sensing time for each user. This optimization is based on real-time signal-to-noise ratio (SNR) conditions and target detection (P_d) and false alarm (P_f) probabilities, significantly enhancing spectrum utilization efficiency and minimizing sensing overhead.
• Robustness Against sensing Attacks: Unlike prior work that often assume benign conditions, our framework is rigorously evaluated against a comprehensive suite of false-sensing user (FSU) attacks, including always no (NFS), always yes (YFS), always opposite (OFS) and random yes/no (YNFS) reporting strategies, ensuring practicality for adversarial real-world environments.
• Data Denoising: We employ a dedicated DAE to cleanse the aggregated sensing data at the FC. This step effectively mitigates distortions caused by both additive white Gaussian noise (AWGN) and malicious data injections from FSUs, providing a reliable input for the final decision fusion.
• Performance Validation: Through extensive simulations, we demonstrate that our proposed ECDAE framework consistently outperforms a wide range of state-of-the-art techniques, including traditional combination schemes (IGS, HGS), optimization algorithms (PSO, DE-ML), and deep learning models (CNN), across different tested attack scenarios and SNR conditions.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. CSS with reconfigurable sensing time.

https://doi.org/10.1371/journal.pone.0338915.g001

2.1 Attacker model and threat assumptions

To rigorously evaluate the robustness of the proposed ECDAE framework, we formalize the attacker model based on the FSU types introduced in Fig 3. This model defines the capabilities, knowledge, and goals of the adversaries.

• System Knowledge: FSUs are assumed to have perfect knowledge of the global hypothesis (H₀ or H₁) for each sensing interval. This represents a worst-case scenario where attackers can perfectly monitor the PU channel, allowing them to execute targeted attacks. This strong assumption ensures that our model is robust against highly informed adversaries.
• Report Manipulation: FSUs can arbitrarily manipulate their local soft energy reports E_j before transmitting them to the FC. They are not limited to simple binary decisions but can generate continuous-valued false energy statistics that conform to expected distributions (e.g., Gaussian with manipulated mean/variance), making their reports appear statistically believable.
  The primary objective of the FSUs is to disrupt the FC’s global decision. The specific goals vary by attack type:
• NFS Goal: Maximize the probability of missed detection (P_m). By consistently reporting low energy, the attacker aims to deceive the FC to declare the channel free (H₀) even when the PU is active (H₁), causing harmful interference to the PU.
• YFS Goal: The attacker’s goal is to maximize the probability of false alarm (P_f). They do this by consistently reporting high energy to deceive the Fusion Center (FC) into declaring a busy channel (H₁) when it is actually free (H₀). This illegally monopolizes the spectrum and reduces SU throughput.
• OFS Goal: Maximize the total probability of error (P_e). By always reporting the opposite of the true state, the attacker seeks to make the FC’s decision uniformly unreliable, maximizing both P_m and P_f regardless of the actual PU activity.
• YNFS Goal: The attacker’s objectives are to create uncertainty and avoid detection. By randomly switching strategies, they become less predictable than a pure NFS or YFS attacker. This randomness helps them evade simple outlier detection schemes, while still degrading overall sensing performance.

This comprehensive attacker model establishes a strong foundation for evaluating the ECDAE framework in a stringent and realistic threat environment, ensuring that the demonstrated robustness is credible and meaningful.

To address the dual challenges of sensing efficiency and robustness against the FSU attacks described in this model, we propose a hybrid ECDAE framework that operates sequentially in two distinct phases. The first phase is called the Sensing-Time Configuration. In it, an EC dynamically finds the optimal sensing time k_j for each user j. This ensures that the user meets its target P_d and P_f requirements based on the current SNR conditions . In the second phase, data denoising and fusion, users sense the channel using their assigned k_j and report soft energy statistics E_j to the FC. A DAE then processes the aggregated report vector . Its purpose is to mitigate distortions from both AWGN and FSUs. The output is a cleaned vector , which is used for a reliable final decision fusion. The specific details of each phase and their interface are elaborated in the following section.

3.1 Dataset for reconfigurable sensing time

This section describes the construction of a dataset to estimate the optimal number of samples for the ML classifier. Sensing samples used in energy reports (3) are determined for a target false alarm, SNR, and detection probability requirements as

(4)

where is the threshold for the energy detector, P_f is the false alarm probability, while and are the mean and variance. The expression of the detection probability P_d in the possibility of the PU presence hypothesis H₁ is as follows:

(5)

Eqs (4) and (5) are standard expressions for the false alarm probability (P_f) and the detection probability (P_d) in energy detection, as derived in [34]. Likewise, the expression of the detection probability is expressed as SNRs, the number of samples, and the false alarm probability as follows [35]:

(6)

Eq (6) expresses the detection probability (P_d) in terms of the false alarm probability (P_f), SNR and sensing samples (k). This formulation is based on the complementary and inverse complementary Gaussian distribution functions, as described in [36]. and are the complementary and inverse complementary Gaussian distribution functions. Eq (6) needs a non-convex function solution to find optimal sensing samples for a given detection, false alarm, and SNR conditions, which is difficult to obtain in real time. The nonconvexity of (6) arises from the inverse complementary Gaussian distribution function (), which does not have a closed form solution. Solving this equation analytically is computationally expensive and impractical for real-time applications. To address this challenge, we construct a dataset that maps the input parameters (, P_f, P_d) to the optimal sensing samples (k). This dataset is generated by solving (6) numerically for various combinations of , P_f, and P_d. The EC is then trained on this dataset to predict sensing samples, eliminating the need to solve the non-convex equation in real time.

These estimated samples will lead to minimum error probabilities and higher-throughput interpretation in the FC. A feature vector of the dataset is represented as

(7)

This allows the EC to be trained with the input and k_j output labels.

3.2 Classification with the AdaBoost

The EC creates a more reliable classifier by ensembling the contents of multiple weak classifiers and mixing their results with more promising prediction results. The ensembling method allows weak classifiers to update and eliminate retraining requirements. As individual classifiers result in prejudiced predictions, ensembling the categories of different classifiers is a more admissible choice. The execution of the EC test is compared with the DT, GNB, NN, KNN, RUSBoost, and XGBoost algorithms to select optimal sensing as required.

The users reporting energies form a history matrix at the FC as

(8)

where t₁,t₂ and t_n denote the n feature vectors that have the detection, false alarm and SNR requirements as the input and sensing samples as the response or output. The AdaBoost constructs stronger classifiers with an ensemble of weak classifiers. The training set T is a matrix in the space as

(9)

where x_i denotes the input feature vectors to be classified with the ensembling method. The input training data to the EC in matrix form T has X and Y submatrices. Here, X is the n feature matrix, and Y is the n 1 output label matrix that constructs the sensing samples.

Thus, a reduction in the sensing duration leads to a higher throughput since more time is allocated for data transmission. As depends on the sensing samples k_j (with f_s fixed), reducing k_j directly shortens and improves throughput. However, this reduction comes at a cost: fewer sensing samples degrade detection reliability, increasing the probability of missed detections (P_m) and false alarms (P_f).

In conventional non-configurable CRNs, k is fixed without accounting for dynamic sensing conditions, often leading to excessive sensing (reducing throughput) or insufficient sensing (compromising detection). In contrast, the proposed reconfigurable network optimizes k_j adaptively using EC, balancing throughput and detection accuracy based on real-time SNR, P_f requirements, and P_d constraints. For example, under favorable SNR conditions, k_j can be safely reduced to boost throughput without violating the thresholds of P_d, whereas in low-SNR regimes, k_j is increased to maintain reliable detection.

The energy consumed during sensing, given by

(10)

further underscores this trade-off: while lower k_j reduces s(i), it risks higher sensing errors. Thus, the proposed scheme dynamically optimizes k_j to ensure that throughput gains do not come at the expense of unacceptable sensing performance, adhering to predefined P_f and P_d targets.

3.3 Data denoising through autoencoder

A DAE is used that reduces the dimensionality of the reported sensing data and reconstructs the data from anomalies due to noisy channel behavior and false reporting by NFS, YFS, OFS and YNFS. This work examined DAE as a variant of the simple autoencoder for better results. However, DAE offers more features than the simple autoencoder in reconstructing the sensing reports from the attacked or corrupted sensing information. Fig 5 shows the architecture of the DAE, which consists of three main components: The encoder, decoder, and compressed latent space. The encoder section transforms the corrupted and attacked input s into the hidden and latent space representation h using the non-linear transformation.

(11)

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. DAE.

https://doi.org/10.1371/journal.pone.0338915.g005

This f is a nonlinear activation function, such as a logistic sigmoid (logsig) and rectified linear unit (ReLU) function. is the weight matrix and is optimized in an encoder with n nodes in latent space. Then, the decoder evolves the latent space into a reconstructed vector, , at the output layer, employing nonlinear adaptation as follows:

(12)

where g denotes the pure linear activation function (purelin). To improve learning efficiency, . The reconstruction error is calculated for a given input training set as . The DAE training objective is to find the optimal parameters that minimize the reconstruction error, as shown below:

(13)

It is evident from (13) that the reconstruction error is the dissimilarity between the actual sensing data and the reconstructed output.

3.4 Channel state final decision

Here, the system makes its final decision on channel availability using various combination schemes as in Fig 6. The identical gain combination (IGS) allocates equal weightage to the individual user reports and deals with the users similarly in constructing its decision. Similarly, the highest-gain scheme (HGS) assigns high weight to the user with high channel gain. The cumulative decision of the system using the IGS combination is as follows:

(14)

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 6. Sample estimation and report cleaning using a DAE.

https://doi.org/10.1371/journal.pone.0338915.g006

The detection and false alarm probabilities and of the IGS according to the cumulative decision C_IGS(i) are given by

(15)

The HGS combination multiplies each user-received report by its branch gain. Therefore, a higher weight is assigned to the user sensing with a high SNR regime and a lower weight to the user sensing with a low SNR regime. The cumulative decision C_HGS(i) at the FC using the HGS technique is written as

(16)

where . The cooperative detection and false alarm probabilities of the HGS scheme are measured based on the individual sensing reports as

(17)

Unlike the IGS and HGS combinations, this scheme forms its cumulative determination using IGS through reconstructed data at the output. The cumulative decision of the ECDAE at the FC is as follows:

(18)

where C_ECDAE is the cumulative response of the ECDAE. The detection and false alarm probabilities of the ECDAE are expressed as

(19)

4.1 Dataset creation

To train and evaluate the proposed framework, synthetic datasets were generated for classifier selection and DAE to emulate realistic CRN conditions under both normal operation and false attacks. The dataset for classifier selection is generated by solving (6) numerically for various combinations of , P_f, and P_d. This allows us to create a lookup table that the EC can use to predict sensing samples for target detection probability, false alarm, and SNR conditions. The dataset for the ML classifiers to predict sensing samples consists of ten levels of false alarm probability ranging from 0.01 to 0.11 (step size 0.01) with a target detection probability ranging from 0.01 to 0.99 (step size 0.1). In the formation of the dataset, the SNRs change from –15 dB to 4 dB (step size 1 dB) in the presence of ten sensing users. The corresponding number of samples is determined by a combination of these values. Hence, the sensing samples are collected for 50 sensing iterations to obtain 100,000 examples in the dataset. The classifiers are trained through the dataset with the detection probability, the false alarm probability, and the SNRs as input and the number of samples as output features. The signal bandwidth and sampling frequency values are selected at 40 kHz with a frame duration of 100 ms.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 4. Dataset schema for classifier training.

https://doi.org/10.1371/journal.pone.0338915.t004

Similarly, the dataset for DAE consists of 20,000 feature vectors, each containing energy readings from 10 cooperative SUs (columns 1-10) and a binary PU state label (column 11). PU states (H₀: absent, H₁: present) were generated with perfect ground-truth knowledge using a balanced distribution (). The energy values were simulated according to Gaussian distributions: under H₀ and under H₁, with SNRs varying from -15dB to 4dB between users to ensure diversity.

The dataset incorporates two attack configurations: (1) fixed position attacks where specific columns (e.g., 5-7) consistently contained FSUs and (2) random position attacks where FSUs were dynamically assigned per sensing interval. Three attack types were modeled: NFS users consistently report H₀ energies (), YFS users always transmit H₁ energies (), and YNFS attackers randomly switch between both strategies. The input data was split into 80% training sets and 20% test sets. To improve DAE robustness, Gaussian noise (noise level = 0.15) was added to the training data. Table 5 summarizes the complete structure of the DAE dataset. The complete dataset used for DAE training is available in S4 File.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 5. Dataset schema for DAE.

https://doi.org/10.1371/journal.pone.0338915.t005

4.2 Classifier selection

We first evaluate the performance of multiple candidate classifiers to identify the most accurate and reliable model. In this section, multiple classifiers are evaluated to verify their ability to classify sensing samples. The accuracy results in Fig 7 demonstrate the superiority of the EC, achieving an accuracy of 100% training and an accuracy of 99.78% in the testing, closely followed by XGBoost (100% training, 99.6% testing). Among traditional classifiers, DT performs well (96% training, 95% testing), while NN and KNN also show competitive results (95% training, 94.56% testing and 95% training, 90% testing, respectively). In contrast, GNB and RUSBoost exhibit significantly poorer performance (16.5%/14.5% and 21%/20.33%, respectively), highlighting their unsuitability for this task.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 7. Classifier accuracy performance.

https://doi.org/10.1371/journal.pone.0338915.g007

The results of the F1 score in Fig 8 further validate the dominance of the EC, with a training of 98.6% and 99.23% testing, outperforming XGBoost (98.7% training, 97.45% testing) and other baselines. DT (96.14% training, 95.45% testing) and NN (95% training, 93% testing) maintain robust performance, while KNN shows a notable drop in the F1 test score (88.32% vs. 95.71% training). GNB and RUSBoost again under-perform, reinforcing their limitations in this context.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 8. Classifier F1-score performance.

https://doi.org/10.1371/journal.pone.0338915.g008

The MCC results in Fig 9 assess the authenticity of the classifier, with the EC method achieving near perfect scores (99.74% training, 99.6% testing), marginally surpassed by XGBoost in training (99.8%) but superior in testing. DT and NN exhibit strong consistency (DT: 96.2%/94.61%; NN: 95.33%/95.12%), while KNN’s MCC aligns with its accuracy (89.5%). GNB and RUSBoost produce the lowest MCC values (16% and 20%), corroborating their unreliability.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 9. Classifier MCC performance.

https://doi.org/10.1371/journal.pone.0338915.g009

The EC consistently outperforms others in all metrics (accuracy, F1 score, MCC), with XGBoost as a close competitor. DT and NN are viable alternatives, whereas GNB and RUSBoost are not. Although XGBoost demonstrates competitive performance (99.6% accuracy, 97.45% F1 score), our proposed EC (99.78% accuracy, 99.23% F1 score) is preferred for deployment in CRNs due to three key advantages: (1) lower computational complexity during both training and inference, making it suitable for resource-constrained edge devices; (2) simpler hyperparameter tuning compared to XGBoost’s extensive parameter space; and (3) inherently more interpretable decision-making through its linear combination of weak learners with explicit weights, facilitating better model transparency and debugging in practical CRN deployments.

The high accuracy of the EC reflects its success in learning the deterministic mapping from the input parameters to the optimal sensing samples k, a well-defined regression task for which near-perfect performance is achievable. Furthermore, the DAE’s performance was rigorously evaluated on a separate, unseen test set, and we employed L2 and sparsity regularization (as described in Sect 4.3) specifically to mitigate overfitting.

Having identified the EC as the optimal model for predicting samples, these samples are now used by the SUs to perform sensing. The resulting reports, which may be corrupted by noise and FSUs, form the input for the next stage of our denoising framework. The completenumerical results for classifier performance (Figs 7–9) are available in S2 File.

4.3 DAE architecture and performance

The raw energy reports collected in the FC are purified using a DAE. This section evaluates the DAE architecture and its ability to reconstruct clean data from inputs corrupted by channel noise and false sensing attacks. The cooperative user uses the estimated sensing samples through the EC for sensing. The DAE architecture employs a 2-neuron hidden layer, optimized for generalization, with logsig (encoder) and purelin (decoder) transfer functions to handle bounded energy values and linear reconstruction, respectively. Training spans 1500 epochs using a combined MSE-sparse loss function (msesparse), strengthened by regularization of L2 (0.01) and sparsity constraints (proportion = 0.1, regularization = 1) to prevent overfitting. Reconstruction performance is evaluated under adversarial conditions, where NFS users (always reporting low energy) and YFS users (always reporting high energy) attack at rates of 10%–100%. Figs 10–13 demonstrate that the DAE achieves stable convergence, with loss values decreasing monotonically as the epochs increase. Fig 10 shows MSE results in the presence of 1, 2, and 3 NFS users with 100% attacks that always report false low energy reports in both hypotheses. The results in the figure show a decrease in MSE as the number of epochs increases from 1 to 1500. Similarly, the MSE results for DAE are collected in the presence of YFS users in Fig 11, which shows a reduction in the loss function as the number of epochs increases and less impact when the YFS increases from 1 to 3. The DAE MSE results are collected in Fig 12 in the presence of OFS users that report opposite information on channel availability compared to actual states. In the final check to confirm the denoising effect of DAE, a probabilistic attack from the YNFS users is tested in Fig 13. In this kind of attack, the attacker switched between the NFS and the YFS attacker probabilistically. The figure shows a slight increase in the loss results when the number of FSU attackers increases from 1 to 3 attacking at a rate of 100%. The results of the loss function show that the system can reconstruct the data with a minimum error in the presence of NFS, YFS, OFS, and YNFS users.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 10. MSE vs. epoch in the presence of NFS.

https://doi.org/10.1371/journal.pone.0338915.g010

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 11. MSE vs. epoch in the presence of YFS.

https://doi.org/10.1371/journal.pone.0338915.g011

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 12. MSE vs. epoch in the presence of OFS.

https://doi.org/10.1371/journal.pone.0338915.g012

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 13. MSE vs. epoch in the presence of YNFS.

https://doi.org/10.1371/journal.pone.0338915.g013

The stable convergence and low reconstruction error demonstrate the proficiency of the DAE in cleaning the sensing data. This cleaned data is subsequently used for the final decision fusion at the FC.

4.4 Ablation study: Component-wise performance

To quantitatively isolate and evaluate the contribution of each component of the proposed ECDAE framework, an ablation study was conducted. This analysis compares the performance of the EC-only model, the DAE-only model, the full hybrid ECDAE model, and a baseline PCA denoising method. The goal is to demonstrate that the synergy between dynamic sensing-time optimization and data denoising is crucial to achieving better performance and that neither component alone is sufficient.

The results, summarized in Table 6, were obtained under a challenging scenario with 3 FSUs attacking at a 100% rate and an SNR of -5 dB. The key metrics are the final decision error probability (P_e) for each type of attack and the computational latency.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 6. Performance comparison of individual components versus the full ECDAE framework.

https://doi.org/10.1371/journal.pone.0338915.t006

The results lead to several critical insights:

• EC-Only Limitations: The EC-Only scheme, which only adapts the sensing time but does not apply denoising, struggles against FSUs. Although it improves reliability, it has no mechanism to cleanse the corrupted data reports, resulting in the highest error probabilities across all types of attack (e.g., P_e = 0.004 for NFS).
• PCA-Only Baseline: The PCA-only scheme, a linear dimensionality reduction technique, serves as our denoising baseline. It reduces error compared to the raw data (e.g., see IGS/HGS results in Figs 14–17) but is significantly outperformed by all other learning-based components. Its linear transformation is insufficient to capture the complex, non-linear distortions introduced by both the channel and malicious FSU attacks, resulting in the highest error probabilities among the compared components (e.g., P_e = 0.0051 for NFS).
• DAE-Only Limitations: The DAE-Only scheme, which denoises the data but uses a fixed, non-optimized sensing time, performs better than EC-Only. It effectively mitigates the impact of FSUs, as seen in the lower error rates (e.g., P_e = 0.0012 for NFS). However, its performance is limited by the suboptimal quality of the input data; without an optimized sensing time, the energy reports consume more sensing time, making the DAE’s reconstruction task difficult.
• DAE-Only vs. PCA: The DAE-Only scheme, which employs a non-linear denoising autoencoder, significantly outperforms the linear PCA baseline (e.g., a 76% reduction in error for NFS attacks). This performance gap highlights the advantage of the DAE’s non-linear activation functions and learned representations in effectively isolating false data patterns and noise.
• ECDAE performance: The full ECDAE framework delivers the best performance, reducing the error rate by 5 to 10 more compared to the best standalone component. This shows a powerful sequential integration: the EC front-end provides optimally clean data by configuring the sensing duration, which in turn makes the DAE back-end significantly more effective at purification and reconstruction. The resulting error probabilities are near zero across all attack types.
• Latency Overhead: The added computational latency of the full ECDAE pipeline (1.4 ms) is the sum of its parts but remains well within the budget of a typical 100 ms sensing frame (see Table 3). This minimal overhead is a worthwhile trade-off for the improvement in sensing reliability and security.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 14. Error probability (Pe) vs. SNRs (dB) for (a) one NFS attack (b) three NFS attack.

https://doi.org/10.1371/journal.pone.0338915.g014

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 15. Error probability (Pe) vs. SNRs (dB) for (a) one YFS attack (b) three YFS attack.

https://doi.org/10.1371/journal.pone.0338915.g015

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 16. Error probability (Pe) vs. SNRs (dB) for (a) one OFS (b) three OFS attack.

https://doi.org/10.1371/journal.pone.0338915.g016

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 17. Error probability (Pe) vs. SNRs (dB) for (a) one YNFS attack (b) three YNFS attack.

https://doi.org/10.1371/journal.pone.0338915.g017

The ablation study confirms that both EC and DAE components are essential, with their sequential integration creating a synergistic relationship rather than merely additive performance gains. This synergy—where the EC front-end provides optimally configured sensing data that enhances the DAE back-end’s purification effectiveness—enables robust cross-generalization across diverse attack scenarios, a key advantage over standalone components.

4.5 Final sensing performance

This section presents the overall P_e after processing the cleansed data using the soft combination rule, comparing our method against the state-of-the-art techniques for all types of attack. Performance is evaluated using the total probability of error (P_e), which provides a balanced measure of the overall decision of the FC accuracy by combining the probabilities of false alarms and missed detections. For a given combination scheme, P_e is defined as:

(20)

where and are the prior probabilities of the PU being absent or present, respectively (assumed to be in our simulations), P_f is the false alarm probability from Eqs (15), (17), or (19), and P_m = 1 − P_d is the missed detection probability, with P_d being the detection probability. This metric P_e is plotted against the SNR in Figs 14–17 for all the evaluated schemes. ECDAE consistently demonstrates superior robustness across all scenarios, achieving substantially higher error probability reduction than competing methods, particularly at improved SNR conditions. The subsequent analysis quantifies these performance gains.

In the NFS attacks in Fig 14, the proposed ECDAE scheme demonstrates unparalleled robustness against varying numbers of FSUs. With three attackers (ECDAE-3-NFS), it achieves 0% error at SNR dB, while its closest competitors, PSO-3-NFS [31] and DE-ML-3-NFS [32], plateau at 0.003 and 0.0023, respectively. The CNN-3-NFS [19] approach, although better than traditional schemes, remains inadequate with three attackers, stagnating at 0.006 (6 higher than ECDAE) even at SNR  = 4 dB. In stark contrast, non-learning schemes fail catastrophically under coordinated attacks: IGS-3-NFS maintains a 0.057 error in the SNR  = 4 dB, which is worse than ECDAE 0%, while HGS-3-NFS marginally improves to 0.026.

Critically, the superiority of ECDAE holds even with fewer attackers: for a single MU (ECDAE-1-NFS), the error drops to 0.0005 at SNR  = 4 dB, outperforming HGS-1-NFS (0.002) and IGS-1-NFS (0.003). These results underscore ECDAE scalability, maintaining dominance under both low (1 attacker) Fig 14(a) and high (3 attackers) Fig 14(b) adversarial loads, while traditional schemes degrade catastrophically with increasing attackers.

For YFS attacks in Fig 15, where FSUs consistently report high energy signals regardless of actual spectrum conditions, the proposed ECDAE demonstrates definitive enhancement. With one attacker (ECDAE-1-YFS) Fig 15(a), perfect detection (0% error) is achieved at SNR dB, whereas DE-ML-1-YFS requires SNR dB to achieve zero error. At SNR  = −10 dB, ECDAE-1-YFS exhibits an error of 0.0048, compared to 0.0137 for DE-ML-1-YFS and 0.0291 for PSO-1-YFS.

In coordinated attacks with three FSUs Fig 15(b), conventional learning approaches fail catastrophically, sustaining 0.147 error even at favorable SNR (4 dB). Traditional schemes show fundamental limitations: HGS-1-YFS achieves zero error only when SNR is dB, while IGS-3-YFS cannot suppress errors below 0.0159 at SNR  = −10 dB, more than three times higher than ECDAE-1-YFS’s 0.0048 under identical conditions.

In the OFS attack scenarios in Fig 16, ECDAE maintains its lead, reaching a 0% error at SNR –4 dB with single attacker Fig 16(a), 33% more SNR efficient than DE-ML-1-OFS, which achieves this only at SNR –3 dB. For three attackers Fig 16(b), ECDAE-3-OFS achieves a 0% error at SNR –3 dB, while DE-ML-3-OFS lags at SNR –1 dB. PSO-3-OFS shows moderate resilience but still exhibits a 0.0007 error in the SNR equal to 3 dB, which is worse than ECDAE 0%. The CNN-3-OFS scheme performs poorly, with an error that lingers at 0.21 (higher than ECDAE) at SNR equal to 4 dB. Meanwhile, traditional IGS and HGS schemes collapse under pressure: IGS-3-OFS error remains 0.056 higher than ECDAE at SNR = 4 dB, and HGS-3-OFS improves only to 0.012. Even with one attacker, HGS-1-OFS (0.011) and IGS-1-OFS (0.018) are worse, respectively, than ECDAE-1-OFS (0.0005). This confirms ECDAE’s unmatched capability to mitigate opportunistic attacks, where both learning and non-learning alternatives fall short.

For the complex YNFS attacks in Fig 17, ECDAE maintains its superiority, achieving 0% error at SNR dB with one attacker Fig 17(a). This is 400% more SNR efficient than DE-ML-1-YNFS, which reaches this at SNR dB. At SNR  = −10 dB, ECDAE-1-YNFS (0.0048) outperforms PSO-1-YNFS (0.0076) by 37% and CNN-1-YNFS (0.0191) by 298%. With three attackers Fig 17(b), ECDAE-3-YNFS achieves a 0% error at SNR dB, while PSO-3-YNFS requires SNR dB. CNN-3-YNFS fails entirely, with the error stuck at 0.003 (higher than ECDAE) at SNR  = 4 dB. The traditional schemes IGS and HGS show partial improvements, but remain non-competitive: IGS-3-YNFS achieves an error of 0% at SNR dB (400% behind ECDAE), while HGS-3-YNFS achieves this at SNR dB (200% behind). At SNR  = −10 dB, ECDAE-1-YNFS 0.0048 is 140% and 158% better than HGS-1-YNFS (0.0115) and IGS-1-YNFS (0.0124), respectively. These results solidify ECDAE’s position as the only scheme capable of neutralizing hybrid threats with near-perfect accuracy. The complete error probability results for all scenarios (Figs 14–17) are provided in S3 File.

4.6 Computational complexity and comparative analysis

A critical aspect of deploying any ML-based solution in resource-constrained CRN devices is its computational overhead. This section analyzes the complexity-robustness trade-off of the proposed ECDAE framework and provides a quantitative comparison with other state-of-the-art methods, including those based on DAE and deep learning.

The inference complexity of ECDAE is determined by its two core components. The EC complexity is , where 30 is the number of weak learners (decision trees) in the AdaBoost ensemble, d is the average depth of a tree (approximately for n training samples), and m is the number of users. The DAE involves a forward pass through an encoder and decoder. For our architecture with a 10-dimensional input, a 2-neuron hidden layer, and a 10-dimensional output, the complexity is O(m), specifically involving two matrix-vector multiplications. The total complexity is additive:  +  .

We benchmarked the average processing latency per sensing interval for our Python/NumPy implementation on a standard CPU. The results, alongside key comparative metrics, are summarized in Table 7.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 7. Computational and robustness trade-offs of CSS approaches.

https://doi.org/10.1371/journal.pone.0338915.t007

As evidenced in Table 7, the proposed ECDAE framework strikes a superior balance between computational cost and robustness:

• Vs. Traditional Schemes (IGS/HGS): While adding moderate latency (3.2 ms vs. 0.5 ms), ECDAE provides a monumental leap in robustness, tolerating 100% attack rates from diverse FSU types where traditional schemes fail catastrophically with just 20% malicious users.
• Vs. Optimization-based ML (PSO, DE-ML): ECDAE offers lower latency and significantly higher robustness. PSO and DE-ML lack a dedicated denoising component, making them vulnerable to higher attack rates (50-80%).
• Vs. Other DL/ML Models (CNN [25], Stacking Ensemble [13]): ECDAE is more efficient and robust. The CNN approach [25], while powerful for feature extraction, has higher complexity () and was shown in Figs 14–17 to be far less robust to FSUs. The stacking ensemble method [13] fuses hard decisions from multiple complex models, likely leading to higher latency and, as our results demonstrate, does not address the soft-data denoising challenge solved by our DAE.

The 3.2 ms latency of ECDAE is well within the budget of a typical 100 ms sensing frame, confirming its practical deployability. This analysis justifies the slightly higher computational cost as a necessary and worthwhile trade-off for achieving near-perfect sensing reliability in adversarial environments, a feat unmatched by existing alternatives.

Furthermore, as established in Sect 4.2, the EC component offers superior interpretability compared to more complex alternatives, providing an additional practical advantage for system deployment and debugging.