Source-linked AI summary
Matched filter detection with dynamic threshold for cognitive radio networks
Fatima Salahdine, Naima Kaabouch, Hassan El Ghazi
TL;DR
Cognitive-radio sensing must identify unused licensed channels, but static thresholds are unreliable because noise is random. The paper uses estimated dynamic thresholds with matched-filter and other sensing methods, finding that matched filtering performs well at low SNR and with few samples, while each method has different strengths and limitations.
Problem
Static sensing thresholds are unreliable under random noise, motivating dynamic threshold estimation for cognitive-radio spectrum sensing.
Method
The paper evaluates estimated dynamic thresholds for energy detection, matched-filter detection, and autocorrelation-based sensing through simulations.
Results
Matched-filter detection works under low SNR and with a small number of samples, reaching nearly 100% detection for N=1000 samples.
Takeaways & Limitations
Choosing a sensing technique depends on SNR, noise uncertainty, and the available primary-user signal information.
Abstract
from arXiv · showhide
-In cognitive radio networks, spectrum sensing aims to detect the unused spectrum channels in order to use the radio spectrum more efficiently. Various methods have been proposed in the past, such as energy, feature detection, and matched filter. These methods are characterized by a sensing threshold, which plays an important role in the sensing performance. Most of the existing techniques used a static threshold. However, the noise is random, and, thus the threshold should be dynamic. In this paper, we suggest an approach with an estimated and dynamic sensing threshold to increase the efficiency of the sensing detection. The matched filter method with dynamic threshold is simulated and its results are compared to those of other existing techniques. Keywords-cognitive radio networks; spectrum sensing; energy detection; matched filter detection; autocorrelation based sensing; estimated dynamic threshold
I. INTRODUCTION
Cognitive radio spectrum sensing identifies whether licensed channels are occupied so secondary users can use temporarily unused spectrum. The paper focuses on improving sensing reliability by replacing static thresholds with estimated dynamic thresholds.
- Cognitive radio enables secondary users to detect and use licensed channels when primary users are not transmitting.
- Non-cooperative sensing includes energy detection, feature detection, and matched filter-based sensing.
- Matched filter sensing maximizes output SNR for known primary-user signals but requires prior knowledge of the signal or pilot stream.
- Improper threshold adjustment degrades sensing performance, while noise-power estimation errors strongly affect detection.
- The paper proposes estimated dynamic thresholds for energy, matched-filter, and correlation-based detection to improve detection probability and decision reliability.
- Detection probability and false-alarm probability measure primary-user protection and idle-spectrum identification, respectively.
II. SPECTRUM SENSING TECHNIQUES
The sensing model represents primary-user absence or presence at the secondary receiver and compares a detector output with a threshold. The same model is reused across techniques by changing the sensing-method block.
- Spectrum sensing detects primary-user transmission so a secondary user can decide whether to transmit in a frequency band.
- The received signal y(n), primary-user signal s(n), channel gain h, and noise w(n) define the sensing model over N samples.
- The detector output T is compared with a threshold; if T is below it, the primary-user signal is declared absent.
- If the primary-user signal is absent, the secondary user may transmit; otherwise, it does not transmit or stops transmission.
- The general sensing model is applied to all techniques by replacing the spectrum-sensing method block.
A. Energy detection method
Energy detection forms a received-energy test statistic and evaluates detection and false-alarm probabilities from it. Its implementation is simple but sensitive to noise uncertainty.
- The energy detector calculates its decision statistic from the squared-magnitude FFT averaged over N samples.
- The resulting received signal energy is the test statistic T_ED used for detection.
- For N > 250, the central limit theorem approximates the test statistic as Gaussian to evaluate P_d and P_f.
- The sensing threshold depends on noise power and is expressed for a target P_f.
- Energy detection is simple to implement but sensitive to noise uncertainty.
B. Matched filter detection with an estimated threshold
Matched filter detection projects the received signal onto a known pilot and compares the resulting test statistic with a threshold. The paper frames threshold selection through Neyman–Pearson detection probabilities and notes practical limitations when the signal is not fully known.
- The matched filter is an optimal filter that projects the received signal in the direction of the pilot x_p.
- The matched-filter test statistic T_MFD is compared with a threshold to make the sensing decision.T_MFD is described as a Gaussian random variable formed from a linear combination of Gaussian random variables.
- The sensing probabilities P_d and P_f are expressed according to the Neyman–Pearson criteria.
- The sensing threshold is given as a function of PU signal energy and noise variance.The passage identifies E as the PU signal energy.
- Assuming a completely known signal is impractical, so communication systems may instead use pilot streams or synchronization codes for sensing.Prior work also addresses frequency-offset and phase-noise effects on matched-filter performance.
C. Autocorrelation based sensing
Autocorrelation-based sensing uses the statistical behavior of autocorrelation to distinguish signal presence from noise. Its decision compares lag0 and lag1, with a correlation threshold defining the decision margin.
- The autocorrelation function is defined for a signal s(t) by integrating its product with a delayed conjugate copy.
- For random noise, the first-lag autocorrelation is very small or negative, whereas a signal produces a significant first-lag value.
- The sensing decision compares lag0 and lag1 of the received signal’s autocorrelation.
- A correlation threshold defines the margin between the two lag values, such as lag0 exceeding a percentage of lag1.The percentage λ represents the decision margin.
III. SIMULATION METHODOLOGY
The simulation generates QPSK signals, adds AWGN, applies each sensing method, and compares its test statistic with an estimated dynamic threshold. Performance is evaluated over repeated experiments while varying SNR, threshold factor, and sample number.
- The general simulation model generates a QPSK PU signal, adds AWGN, applies a sensing method, and compares its test statistic with an estimated dynamic threshold.The sensing decision is made from this comparison.
- The threshold is estimated dynamically at each iteration and multiplied by a factor to examine its impact on detection performance.The estimated threshold is also used to simulate P_d and P_f across SNR and sample-number settings.
- The simulation evaluates probability of detection P_d and probability of false alarm P_f across repeated experiments.P_d and P_f are obtained from detection and false-alarm counts over the total number of experiments.
- The experiments use 1000 cycles, an SNR range of -20dB to +20dB, and threshold factors 1, 2, 3, and 4.The sample number is selected to give the maximum P_d.
- For each parameter setting, P_d and P_f are calculated while varying SNR, threshold, or the number of samples.
- Matched-filter detection convolves the received signal with a PU pilot stream and averages the output over N samples to obtain the test statistic T.
IV. RESULTS AND DISCUSSION
The simulations compare energy, matched-filter, and autocorrelation sensing across SNR, sample count, and threshold settings. Matched-filter sensing performs well at low SNR and with few samples, while threshold changes trade detection and false-alarm probabilities.
- Methods comparison: Under N=1000 and threshold factor=1, Pd increases with SNR; above 0 dB, Pd exceeds 90%.At high SNR, matched-filter detection reaches 100% detection with a small number of samples, while energy detection also has high Pd but very high false alarm.
- Methods comparison: Matched-filter sensing achieves high performance with few samples and can operate at low SNR, whereas autocorrelation sensing has lower Pd at low SNR.For matched-filter detection, Pd reaches 100% at N=1000, and for SNR below -20 dB, Pd increases when N exceeds 400 samples.
- Threshold effects: For matched-filter detection with N=1000, Pd increases with SNR but decreases as the threshold factor increases.The experiment varied SNR from -20 dB to +20 dB across threshold factors.
- Threshold effects: For matched-filter detection, Pf decreases as threshold and SNR increase, while Pf remains high at low SNR for a fixed threshold factor.At threshold factor 4, Pf decreases at SNR values below -10 dB; lowering the threshold factor increases Pf.
- Overall findings: The simulations indicate that matched-filter sensing can work under low SNR and with a small number of samples.The comparison used common simulation parameters while varying SNR, threshold, and sample number.
V. CONCLUSION
The conclusion emphasizes that sensing methods have different strengths and weaknesses, so selection depends on SNR, noise uncertainty, and available primary-user information. It also reports better sensing performance with a dynamic rather than static threshold.
- Energy detection is easy to implement and needs no primary-user signal information, but cannot distinguish signal from noise and has high false alarm.
- Matched-filter sensing requires perfect knowledge of the primary-user signal, which is impractical, but performs well under low SNR.
- Autocorrelation-based sensing is robust against noise uncertainty, and method choice depends on SNR, channel noise uncertainty, and available primary-user information.
- Using a dynamic threshold gives better sensing performance than using a static threshold.