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The rapid expansion of 5G networks and Internet-connected wireless devices (such as IoT) has led to intensified spectrum congestion in the Fifth Generation New Radio Frequency Range 1 (5G NR FR1). Efficient spectrum utilization through effective spectrum-sharing solutions is crucial for seamless 5G and Next-Generation (Next-Gen) wireless networks. The statistical/signal processing based sensing methods that allow new wireless devices for spectrum sharing are facing challenges such as uncertain thresholds and degraded performance under high noise levels relative to the signal. Alternatively, machine and deep learning-based spectrum sensing models demonstrate better performance which is independent of detection threshold, but requires large datasets for model training. This paper investigates the applications of frequency-domain auto-correlation coefficients to develop novel sensing methods, namely Auto-Correlation Integral-based Sensing (ACIS) and Logistic Regression Model-based Sensing (LRMS). The work also compares their detection performance and computational complexity against other prominent techniques in the literature. Results and analysis show that ACIS achieves the recommended detector performance
Article highlights
New methods (ACIS & LRMS) help detect weak wireless signals even in very noisy environments.
LRMS reliably detects signals as low as − 30 dB, using simpler computations than many existing tools.
These advances support better sharing of crowded 5G frequencies, helping future wireless networks.
Introduction
The fast growth of wireless communication, especially with the rise of fifth-generation (5G) networks, Internet-connected wireless devices, as well as data-hungry devices, has caused more congestion in the radio spectrum [1]. Efficient spectrum sensing is essential for enabling dynamic spectrum access (DSA) and reducing interference in the shared 5G FR1 frequency bands [2]. These frequency bands are widely used for key 5G applications, including low-latency communication, enhanced mobile broadband, and large-scale machine-type communication, among others [3]. Technologies such as NB-IoT (Narrowband IoT), which operate within these FR1 bands, require reliable spectrum management to work efficiently and avoid interference with other important 5G services, particularly in environments where noise is far greater than signal levels [4]. 5G, NB-IoT, and other wireless systems can coexist better by detecting spectrum holes. This emphasizes the need for advanced sensing methods to ensure interference-free communication in 5G and beyond-5G (B5G) wireless networks.
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Fig. 1
Mind map of proposed sensing methods addressing challenges in Next-Gen wireless networks
Figure 1 presents a mind map of proposed sensing methods and potential sensing challenges in Next-Gen wireless networks. This paper focuses on narrow-band sensing using a single sensor (NBSS).
In literature, numerous statistical/signal and machine learning-based detection methods have been suggested for NBSS [5]. Among signal processing-based detectors, the primary method is the energy detector, which relies on the energy of the signal, equivalent to the autocorrelation of the received signal at zero lag. Though the energy detector has low computational complexity of , it is not a reliable detector due to high random noise energy at zero lag and uncertainty in the detection threshold. In [6], the authors observed that the energy detector performs poorly at low signal-to-noise ratio (SNR), especially in non-Gaussian noise, highlighting the need for alternative methods. In [7], a cooperative sensing method using correlation sum and equalization techniques in a multi-transceiver environment was introduced. However, the complexity and detection accuracy of a single node using the correlation-sum metric were not analyzed. The second method is matched filtering, which uses the correlation concept with prior knowledge of the communication signal. This is unsuitable for wideband sensing due to the required prior information. In contrast, the authors in [8] proposed a blind matched filtering algorithm that does not require prior knowledge. However, its detection performance at low SNR is suboptimal. The third method is based on the cyclostationary properties of the signal—an extension of autocorrelation-based sensing. It can detect hidden periodicities such as modulation patterns but is computationally intensive, with a complexity of , where M is the number of cyclic frequency bins. The authors in [9] proposed a cyclostationary feature detection method with short sensing time to reduce complexity. Although this reduces complexity, its performance is still suboptimal in low-SNR environments. Another signal processing method that has gained popularity is the eigenvalue-based detector, which utilizes the sample covariance matrix of the received signal. It is robust under uncertain noise conditions but computationally expensive at . The authors in [10, 11] proposed using circular matrices to develop low-complexity eigenvalue-based detectors. However, detection in the low SNR regime remains challenging. Recently, machine and deep learning models (MDLMs) have demonstrated better classification performance and are threshold-independent [12, 13]. However, they require large labeled datasets, incur high computational costs, and lack interpretability [14]. Among MDLM techniques, logistic regression is the least complex with , where d is the feature vector size [15]. Support Vector Machines (SVMs) using kernel tricks classify in-band signals with complexity [16]. Random Forests, an ensemble method using energy features, have high complexity of , where T is the number of trees [17], and both SVMs and Random Forests show lower accuracy in some cases. Deep learning techniques such as ANNs, RNNs, and CNNs with complexities and respectively are used for band sensing [5, 18, 19–20]. In [21], DL-based sensing under low-SNR conditions using features like signal energy, cyclic features, power spectrum magnitudes, and I/Q components achieves 90% accuracy down to dB. Hybrid models are also explored [22, 23], and a low-complexity hybrid DL sensing model was proposed in [24], though its detection probability drops as SNR increases. Despite their drawbacks, DL models remain popular due to their robustness and threshold independence. Therefore, this work focuses on low-complexity models that utilize autocorrelation coefficients across multiple lags: a signal processing model computes the Auto-Correlation Integral (ACI) as the test statistic, and a machine learning model trains a logistic regression classifier using autocorrelation coefficients as features. The ACI is chosen because it differs significantly between pure noise and in-band signal cases. Table 1 summarizes the related works, highlighting their methods, strengths and limitations.
Table 1. Summary of existing signal detection methods for narrowband spectrum sensing (NBSS)
Author (Year) | Method description (technique, features/inputs, complexity) | Remarks |
|---|---|---|
Abdelbaset et al. (2024) [5] | Energy detection using autocorrelation at lag 0; Feature: signal energy; Complexity: | Unreliable at low SNR due to noise dominance |
Gao et al. (2021) [6] | Energy detection using signal power; Complexity: | Poor performance in non-Gaussian noise |
Zhang et al. (2023) [8] | Blind matched filtering; Feature: signal signature; Complexity: Moderate | Suboptimal detection at low SNR |
Shrestha et al. (2020) [9] | Cyclostationary detection using cyclic features; Complexity: | Reduced sensing time; weak at low SNR |
Du et al. (2021) [10]; Chaurasiya et al. (2019) [11] | Eigenvalue-based detection using sample covariance; Complexity: | Weak in low-SNR regime |
Alsharif et al. (2018) [12] | kNN classifier using energy features; Complexity: High | Needs large training data |
Xu et al. (2024) [14] | Review on ML-based sensing; Complexity: Not defined | High computational cost; low explainability |
Srinu et al. (2023) [15] | Logistic regression on energy and eigenvalue features; Complexity: | Poor accuracy in low-SNR |
Reddy et al. (2023) [16] | SVM with kernels on energy and eigenvalue features; Complexity: | Ineffective in low SNR |
Mishra et al. (2020) [25]; Solanki et al. (2022) [19] | Random Forest on energy features; Complexity: | Accuracy depends on trees; resource-heavy |
Zhang et al. (2024) [21] | Deep learning using energy, cyclic, spectrum and I/Q features; Complexity: High | 90% accuracy at −13 dB SNR |
Kumar et al. (2023) [18]; Alsharif et al. (2021) [20] | ANN/CNN on signal features; Complexity: High | Accurate but resource intensive |
Yang et al. (2023) [23] | Hybrid of heuristics and DL; Complexity: High | Performance degrades with SNR |
Mohanakurup et al. (2022) [24] | Lightweight DL with selected features; Complexity: Moderate | Accuracy drops in low SNR |
Proposed work | Both signal processing and ML methods using autocorrelation features; Complexity: Very low | Efficient in low SNR with fewer samples |
This work aims to improve spectrum sensing for 5G and beyond applications by leveraging frequency-domain auto-correlation features.Two models, namely Auto-Correlation Integral-based Sensing (ACIS) and Logistic Regression Model-based Sensing (LRMS) are developed to improve detection performance in low-SNR conditions. The study also compares these model’s performance using extensive Python simulations.
The following sections outline the structure of this paper: Section 2 presents the problem statement and mathematical modelling of proposed ACIS and LRMS including detection threshold. Section 3 details the simulation set-up to evaluate ACIS and LRMS models detection accuracy on Python. Section 4 summarizes the work and suggests avenues for future research. Finally, Section 5 (Appendix) provides materials and additional results supporting the main algorithm.
Problem statement and methodology
The signal detection in 5G NR FR1 bands can be formulated as hypothesis testing, as presented below:
1
where is the discrete-time received signal at the radio receiver, is the deterministic/modulated in-band signal, is the additive noise, modelled as a Gaussian random process. The matrix represents the channel gain and is assumed to be ideal.[See PDF for image]
Fig. 2
Framework of proposed sensing using auto-correlation coefficients
The proposed framework to scan 5G FR1 bands is shown in the block diagram of Fig. 2. The process starts by capturing the received RF signal from the 5G FR1 band. The signal preprocessing includes bandpass filtering, downconversion to baseband, and sampling to extract the signal r(n). Then the Auto-Correlation Integral (ACI) unit calculates correlation values at different lags using Wiener–Khinchin theorem (WKT). Then, the ACI is computed and used as a test statistic to scan the spectrum bands. The decision logic/unit compares the ACI value with a predefined threshold (). If the computed ACI of r(n) exceeds , indicating band is occupied, then the output block supports else it supports . In case of LRMS, auto-correlation values are used as input features to train the proposed data driven model and sigmoid function is used to classify the input data/sample (either or ).
Autocorrelation integral based sensing (ACIS)
The autocorrelation in time domain of a signal is defined as [7],
2
where, is a lag parameter. Using the WKT, the above autocorrelation can be computed as:3
where, is the power spectral density (PSD), and is the fast Fourier transform of . The vector will have elements, corresponding to lags .The autocorrelation integral (ACI) is computed over a finite window 2N, given as,
4
The characteristics (behaviour) of ACI differs under the two hypotheses. Under (noise-only), it can be shown that the autocorrelation of noise is,5
Then, the estimated ACI under can be expressed as,6
Under (signal + noise), the received signal contains a correlated component due to the presence of deterministic signal s(t). Then, it can be shown that the autocorrelation of r(n) is,7
which leads to a larger ACI value when compared to noise alone, expressed as8
Under , autocorrelation has higher magnitude correlations, which gives, .Hence, the decision rule can be derived as follows: Under , the received signal is white Gaussian noise . Its autocorrelation is given by: .
Therefore, the ACI under is approximately:
9
Assuming the use of N independent realizations for averaging, the distribution of can be modelled as Gaussian: with10
Let be the detection threshold using fixed . Then, the threshold () can be defined as,11
The probability of false alarm under is given by the Gaussian tail probability:12
To determine the threshold for a given false alarm probability , we invert the Q-function:13
14
15
where, .Logistic regression model-based sensing (LRMS)
Let the training dataset , where is a feature vector contains values, with to L and is the binary-class label corresponding to the or . Then, the hypothesis function for predicting the probability, given the input feature vector () is,
16
Where, the input vector = contains correlation features. The vector and b are the weight vector and bias of the LRMS model, respectively.The decision logic to discriminate the hypothesis based on the Logit function is given as,
17
Where, the symbols 1 and 0 represent the hypotheses and for a given input feature vector, respectively.To compute optimal parameters () for the Logit function, we minimize the cost function using batch gradient descent (BGD) optimization, expressed as:
18
Where, M is the total number of records in training dataset, is regularization term to create generalized model.Optimal values of weight and bias b are obtained using the following update criterion for each iteration during training:
19
where m is the total number of training samples, and is the learning rate.20
Simulation results
The simulation set-up to evaluate the proposed ACIS and LRMS methods are as follows: The test statistic for ACIS method is an autocorrelation coefficients sum (or ACI), whereas for LRMS the model is trained using autocorrelation values at different lags ranging from to L. The synthetic dataset is generated by emulating 5G FRI mid-band range at a carrier frequency of 3.5 GHz with additive Gaussian noise. Captured datasets from DeepSig can also be utilized for real-time spectrum sensing [26]. The signal SNR is varied by keeping noise constant and increasing signal strength from to 0 dB. False alarm rate of 10% is considered. Different sample sizes N = 256, 512, 1024 are taken, with the goal of identifying the robustness of the technique in low SNR conditions. The results are plotted to compare the detection performance across different sample sizes, varying values, and SNR of the signal. The simulation is implemented in Python. To train the model, a balanced dataset is created using random sampling from two SNR ranges by varying threshold SNR. For instance, the dataset by assuming a threshold at −25 dB is: to dB (Low SNR represents noise alone in the band) and to 0 dB (in-band communication signal presence), with equal representation to avoid bias. The dataset size is varied from 100 to 20,000 samples, and for three sample sizes are considered for the auto-correlation computation. The dataset that contains M number of records is partitioned into training and testing/validation subsets in a 3:2 ratio, followed by correlation feature normalization. The Logistic Regression model is trained and evaluated on the test set, with accuracy as the performance metric. During the training process, 5-fold cross-validation (K = 5) is used to improve model accuracy and reduce the over-fitting problem. Gradient descent optimization is used to update the weights of the LRMS model, with a learning rate of . The implementation is carried out using scikit-learn’s built-in solver in a Python environment. regularization is applied to prevent overfitting and ensure better generalization. The entire simulation and model training process is executed in a Python script on the Google Colab platform, which provides a cloud-based environment with CPU/GPU support for reproducibility and efficient experimentation.
The results are plotted to compare the accuracy of the model across different dataset sizes (M number of entries) and sample sizes (N - length of each entry).
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Fig. 3
Auto-correlation coefficients of received signal at different SNR signals ( to L)
Figure 3 presents the auto-correlation coefficients of received signal at different lags from to L, where with different sample sizes () and SNR levels ( dB). As N increases, the resolution of the auto-correlation improves, revealing a more defined periodic structure corresponding to the received signal r(n). The curves with higher SNR levels shows a stronger periodic peaks, while lower SNR values are distorted due to relatively stronger noise strength. The central peak at lag ( zero remains dominant across all sample sizes, representing the similarity of the received signal with itself. Increasing the sample size reduces fluctuations in correlation values, enhancing the reliability of the estimation. Figure 3 clearly shows that the impact of noise and sample size of signal effect the decision metric (ACI).
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Fig. 4
Auto-correlation coefficients of received signal at different SNR levels (N = 1024, to L)
Figure 4 presents the auto-correlation coefficients of received signal at different lags from to L, where with constant sample size of 1024 and varying SNR levels set to 0 dB, −5 dB, −10 dB, as well as a noise-only scenario. The curves (red and green) with higher SNR (0 dB and −5 dB) levels shows a stronger periodic peaks, while lower SNR values are distorted due to relatively stronger noise strength. The central peak at zero lag ( remains dominant across all sample sizes, representing the similarity of the received signal with itself (termed as energy of the signal). The red stem plot corresponds to the noise alone auto-correlation values, which appears random/uncorrelated at all the lags except for a dominant peak at zero lag. Figure 4 reveals that the impact of noise in the in-band signal effects the decision statistic.
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Fig. 5
Detection probability of proposed ACIS method against false alarm probability across four low SNR levels
Figure 5 depicts the variation of detection probability () with false alarm probability () across four low SNR levels (−24 dB, −22 dB, −20 dB, −18 dB) at a constant sample size of . The curves show a non-linear relationship, with rising sharply at moderate values, especially for better SNR conditions. As increases from 0.001 to 1, the also rises since the change in threshold allows more signals to be detected, with a higher risk of false alarms/positives. Among considered SNR range, ACIS exhibit better detection performance at dB across all values, while it achieves low detection accuracy at dB.
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Fig. 6
Detection probability of ACIS method against SNR (, )
The impact of different sample sizes (N = 256, 512, 1024) on the versus SNR is depicted in Fig. 6, considering a constant of 0.1. As the received SNR level of the signal increases from dB to 0 dB, the performance () improves significantly which indicates that the stronger signals can be distinguishable from random noise easily. In addition, larger sample sizes () exhibit higher across all SNR values, as more data points improves the magnitudes of auto-correlation coefficients signal but not for random noise and hence corresponding ACI values. The detection probability for small sample sizes () remains low at negative SNRs and is increasing gradually with increasing SNR. This result highlights the impact of both SNR and sample sizes on in-band signal detection for 5G FR1 bands. Table 1 provides the of the proposed ACIS technique for different sample sizes at varying SNR levels. The results indicate that for N = 256, the exceeds 90% when the SNR is −15 dB, as highlighted in bold. Similarly, for N = 512, the detection probability reaches 90% at an SNR of −18 dB. Furthermore, for N = 1024 the achieves above 90% at an SNR of −21 dB. This indicates that increasing the N can improve the detection accuracy even at lower SNR levels. Most importantly, the proposed ACIS model can perform better than many other statistical detection techniques proposed in the literature. The bold values in Table 2 indicate the SNR at which the detection probability exceeds 90%.
Table 2. Detection probability of the proposed ACIS method at different SNR levels for varying sample sizes
SNR (dB) | |||
|---|---|---|---|
−30 | 0.1865 | 0.2130 | 0.3185 |
−28 | 0.2045 | 0.2845 | 0.4030 |
−26 | 0.2460 | 0.3605 | 0.5440 |
−24 | 0.3140 | 0.4510 | 0.6950 |
−22 | 0.3975 | 0.6090 | 0.8485 |
−21 | 0.4560 | 0.7005 | 0.9070 |
−20 | 0.5425 | 0.7765 | 0.9490 |
−19 | 0.6160 | 0.8545 | 0.9770 |
−18 | 0.6620 | 0.9045 | 0.9955 |
−17 | 0.7635 | 0.9525 | 0.9990 |
−16 | 0.8435 | 0.9810 | 1.0000 |
−15 | 0.9130 | 0.9945 | 1.0000 |
−14 | 0.9470 | 0.9990 | 1.0000 |
−12 | 0.9915 | 1.0000 | 1.0000 |
−10 | 1.0000 | 1.0000 | 1.0000 |
−8 | 1.0000 | 1.0000 | 1.0000 |
−6 | 1.0000 | 1.0000 | 1.0000 |
−4 | 1.0000 | 1.0000 | 1.0000 |
−2 | 1.0000 | 1.0000 | 1.0000 |
0 | 1.0000 | 1.0000 | 1.0000 |
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Fig. 7
Confusion matrix of LRMS model using a dataset of 20,000 records/entries
The confusion matrix results for LRMS are displayed in Fig. 7. It discloses the model performance in classifying the and using auto-correlation coefficient data as input feature vector. The matrix cells/elements indicate the model performance in terms of correct classifications and false alarms. The cell values for true positives and true negatives, together 7802 (4014 + 3788) instances, indicate that the LRMS model is making correct predictions. Whereas, the cell values for false positives and false negatives, totalling 198, suggest the instances where the LRMS model is incorrectly predicting the in-band signal. This demonstrates that the model achieves an accuracy of 97%. A balanced confusion matrix with fewer false alarms indicates a well-performing model. However, achieving this accuracy requires a large training dataset, can be seen in Table 2.
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Fig. 8
Prediction accuracy of LRMS against different sizes of dataset and sample sizes (N)
Figure 8 evaluates the accuracy of LRMS in classifying signals based on different dataset and sample sizes. The dataset is generated with varying SNR values, where auto-correlation features are extracted and used to train the model along with their target values. Three sample sizes () are considered, while the dataset size (number of entries) varies from 100 to 20,000 samples. The results indicate that accuracy improves as the dataset size increases, demonstrating that the proposed LRMS model learns better with more data. Additionally, larger sample sizes (N) lead to higher accuracy due to the greater amount of information extracted from the auto-correlation function. The plotted results are summarized in Table 3, which quantifies accuracy across different sample and dataset sizes, showing improved model performance with larger datasets. Bold values in Table 3 indicate the dataset size corresponding to the maximum detection probability.
Table 3. Prediction accuracy of LRMS for different sample sizes by varying dataset sizes (M)
Dataset size (M) | |||
|---|---|---|---|
100 | 0.9000 | 0.9000 | 0.9500 |
2311 | 0.9091 | 0.9286 | 0.9329 |
4522 | 0.9204 | 0.9525 | 0.9381 |
6733 | 0.9258 | 0.9517 | 0.9607 |
8944 | 0.9385 | 0.9486 | 0.9525 |
11155 | 0.9390 | 0.9556 | 0.9718 |
13366 | 0.9465 | 0.9540 | 0.9645 |
15577 | 0.9506 | 0.9573 | 0.9657 |
17788 | 0.9500 | 0.9559 | 0.9629 |
20000 | 0.9545 | 0.9590 | 0.9702 |
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Fig. 9
Prediction accuracy of LRMS against different sizes of dataset and sample sizes (N)
Figure 9 illustrates the variation in classification accuracy of LRMS as a function of different SNR thresholds (dB), ranging from 0 dB to −30 dB. It includes three distinct curves corresponding to different sample sizes (N = 256, 512, and 1024) used during signal and noise generation. As the SNR threshold decreases, the classification accuracy also decreases due to the dominance of noise, which makes it harder for a model to distinguish signal features. In addition, the accuracy declines across all sample sizes as the SNR threshold moves lower. However, larger sample sizes, with N = 1024, consistently achieved higher accuracy. To highlight the underlying trend, the accuracy curves are smoothed using a Gaussian filter. Overall, the results clearly demonstrates that for both cases of higher SNR thresholds and larger sample sizes enhance classification accuracy in noisy signal conditions. Table 4 provides the classification accuracy across different SNR thresholds (0 dB to −30 dB) and sample sizes (N = 256, 512, 1024). Accuracy improves as the sample size increases for a given SNR threshold. For instance, the accuracy of the LRMS classifier is 0.9060 at −30 dB using N = 512. Based on Tables 2 and 4, the performance of LRMS (machine learning model) shows a significant difference, which is attributed to the limitations of the training data. The bold values in Table 4 indicate the minimum SNR and sample size required for the proposed model to achieve an accuracy of 90% or higher. In conclusion, Proposed ACIS method can detect −18 dB signals using a correlation vector size of 512. Whereas, the proposed LRMS can detect −30 dB signals, provided that the training data for LRMS is of high quality, indicating robust detector under low SNR conditions. In conclusion, from the literature review and simulation results, it is evident that the proposed methods outperformed the most prominent signal processing and machine learning based sensing techniques [5, 18, 20, 27, 28–29], as presented in Table 5. The bold values (-18 dB and -30 dB) in Table 5 represent the SNR wall of the proposed model. The proposed ACIS and LRMS methods differ significantly from the traditional Covariance-Based Detection (CBD) approach in several key aspects, including computational complexity, detection robustness, and the signal processing domain. While CBD relies on the time-domain covariance matrix of received signal samples to make detection decisions, ACIS operates in the frequency domain by leveraging the auto-correlation function derived using the Wiener–Khinchin Theorem (WKT). ACIS calculates the area under the absolute values of normalized autocorrelation coefficients, producing a robust detection statistic, especially effective under low SNR conditions. In contrast, the covariance method involves complex matrix operations with a computational complexity that grows quadratically with the number of samples, i.e., , making it less suitable for real-time or resource-constrained applications. ACIS, which is based on the Fast Fourier Transform (FFT), has a lower computational complexity of , and demonstrates superior detection performance. It achieves over 90% probability of detection at dB SNR with 512 samples, whereas CBD typically performs poorly below dB [27]. Additionally, the LRMS method, which also uses autocorrelation features, is less sensitive to noise uncertainty and is better suited for modern 5G and IoT applications where lightweight and reliable detection techniques are essential.
Table 4. Classification accuracy of the proposed LRMS model for different sample sizes and SNR thresholds
SNR (dB) | |||
|---|---|---|---|
0 | 0.9990 | 0.9980 | 0.9990 |
−2 | 0.9974 | 0.9991 | 0.9982 |
−4 | 0.9958 | 0.9998 | 0.9974 |
−6 | 0.9970 | 1.0000 | 0.9974 |
−8 | 0.9990 | 1.0000 | 0.9982 |
−10 | 1.0000 | 1.0000 | 0.9990 |
−12 | 0.9890 | 0.9984 | 0.9958 |
−14 | 0.9790 | 0.9968 | 0.9926 |
−16 | 0.9748 | 0.9848 | 0.9884 |
−18 | 0.9664 | 0.9624 | 0.9812 |
−20 | 0.9660 | 0.9680 | 0.9820 |
−22 | 0.9332 | 0.9500 | 0.9632 |
−24 | 0.9164 | 0.9410 | 0.9534 |
−26 | 0.9027 | 0.9290 | 0.9447 |
−28 | 0.8761 | 0.9050 | 0.9281 |
−30 | 0.8760 | 0.9060 | 0.9280 |
Table 5. Typical detection SNR thresholds for single-node narrow-band sensing methods
Signal processing-based sensing methods | SNR (dB) |
|---|---|
Energy detection | −5 |
Matched filtering | −20 |
Cyclo-stationary based sensing | −15 |
Autocorrelation based detection | −7 |
Eigenvalue based sensing | −10 |
Wavelet based detection | −6 |
Proposed ACIS | −18 |
Machine learning-based methods | SNR (dB) |
|---|---|
SVM (ML-based) | −12 |
ANN/MLP | −15 |
CNN (deep learning) | −18 |
LSTM/RNN | −17 |
RBFN | −12 |
KNN | −10 |
Proposed LRMS | −30 |
Table 6. Comparison between ACIS and LRMS methods
Aspect | ACIS | LRMS |
|---|---|---|
Input | Raw signal samples | Autocorrelation features |
Feature extraction | Sum or area under curve | Automated via model training |
Computational complexity | Higher due to repeated simulations | Lower after initial training |
Training needed | Not required | Required |
Data required | Low | High to train the model |
Generalization and flexibility | Poor due to uncertain noise | Better (learns nonlinear patterns at different noise environments) |
Regularization | Not applicable | L2 regularization for generalization |
Detection ability under low SNR | Up to −18 dB | Superior (up to −30 dB) |
Table 6 compares proposed ACIS and LRMS models based on simulation results. ACIS is simpler and does not require training, but it lacks adaptability and performs poorly under low SNR conditions. In contrast, LRMS use structured features from the autocorrelation, enabling better generalization and flexibility. While ACIS has lower initial complexity, logistic regression provides higher accuracy, especially in noisy environments. The logistic model benefits from L2 regularization, which prevents overfitting and enhances robustness. Although it requires labeled training data, once trained, it offers efficient inference. Overall, logistic regression can detect signal up to dB shows superior detection performance, particularly at low SNR, where ACIS fail below dB.
Conclusions
This paper proposes Auto-Correlation Integral-based Sensing (ACIS) and Logistic Regression Model-based Sensing (LRMS) as two novel techniques that leverage frequency-domain auto-correlation coefficients to address congestion in 5G NR FR1. By computing autocorrelation in the frequency domain rather than in the time domain, the computational complexity is reduced from to , enabling real-time deployment. This frequency-domain approach plays a critical role in balancing performance and computational efficiency. ACIS demonstrated significant noise robustness, achieving a detection probability () of at least 90% at an SNR of dB with a sample size of . This makes ACIS an ideal signal processing detector under low-SNR conditions when the noise distribution is Gaussian. Furthermore, for , exceeds 90% at an SNR of dB, implying that its performance improves with increasing sample size. In contrast, LRMS, with a complexity of O(N), serves as a lightweight and threshold-independent machine learning technique for detecting in-band signals. Its prediction accuracy exceeds 90% for signals as low as dB, using a dataset size (M) of 20,000 records. Additionally, its detection performance improves as the size of the training dataset increases. Both methods outperform conventional detectors in terms of accuracy and complexity, with LRMS excelling in noise resilience without relying on a detection threshold. In conclusion, the proposed methods ACIS and LRMS identify signals as weak as dB and dB, respectively, using a correlation vector size of 512. This highlights LRMS as an optimal machine learning model that surpasses most existing models in the literature. Ultimately, LRMS is well-suited for scenarios requiring robustness under low-SNR and is ideal for dynamic IoT devices operating in the 5G-FR1 spectrum with uncertain in-band noise distributions. Future work will focus on extending this research to wideband and cooperative sensing. The proposed sensing paradigms can contribute to spectrum-sharing solutions for Next-Gen wireless networks operating under low SNR conditions.
Author contributions
Srinu Sesham: Conceptualization, sensing design, data analysis, and manuscript preparation. Nalina Suresh: Data analysis, performance validation, and manuscript review. Dickson Kanungwe Chembe: Literature survey, result validation, and manuscript proofreading.
Funding
No funding.
Data availability
Data information supporting the findings are available within the manuscript.
Declarations
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
No known competing financial interests.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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