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Spectrum Sensing in Cognitive Radios Based on Multiple Cyclic Frequencies
Jarmo Lundén, Visa Koivunen, Anu Huttunen, H. Vincent Poor
TL;DR
Cognitive radios need reliable primary-user detection at low SNR and under shadowing and fading. This paper develops a GLRT using multiple cyclic frequencies and combines quantized local statistics from cooperating secondary users. Simulations report improved low-SNR detector reliability and significant gains from collaborative decision making.
Problem
Reliable primary-user detection is needed at low SNR and in the presence of shadowing and fading, while single-frequency tests use only part of signals’ cyclostationary information.
Method
The paper proposes a GLRT for simultaneous detection over multiple cyclic frequencies and combines quantized local likelihood ratios from multiple secondary users under conditional independence.
Results
Multiple-cyclic-frequency detectors outperform single-frequency detection in the low-SNR regime, while the sum-based detector performs best among the tested multi-frequency statistics.
Takeaways & Limitations
Cooperative detection improves reliability and mitigates sensitivity to shadowing and fading in cognitive-radio spectrum sensing.
Abstract
from arXiv · showhide
Cognitive radios sense the radio spectrum in order to find unused frequency bands and use them in an agile manner. Transmission by the primary user must be detected reliably even in the low signal-to-noise ratio (SNR) regime and in the face of shadowing and fading. Communication signals are typically cyclostationary, and have many periodic statistical properties related to the symbol rate, the coding and modulation schemes as well as the guard periods, for example. These properties can be exploited in designing a detector, and for distinguishing between the primary and secondary users' signals. In this paper, a generalized likelihood ratio test (GLRT) for detecting the presence of cyclostationarity using multiple cyclic frequencies is proposed. Distributed decision making is employed by combining the quantized local test statistics from many secondary users. User cooperation allows for mitigating the effects of shadowing and provides a larger footprint for the cognitive radio system. Simulation examples demonstrate the resulting performance gains in the low SNR regime and the benefits of cooperative detection.
I. INTRODUCTION
Cognitive radios use spectrum sensing to identify transmission opportunities while limiting interference to primary users. The paper exploits cyclostationary signal properties and distributed cooperation to improve detection under difficult propagation conditions.
- Motivation: Spectrum sensing identifies opportunities for agile spectrum use and helps control interference to primary users.Sensing provides awareness that supports dynamic adaptation of carrier frequency, power, and waveforms.
- Cyclostationary detection: Signal knowledge about modulation, rates, coding, guard periods, and correlation can support low-SNR, low-complexity detectors.Without such knowledge, energy detection may require long data collection and face difficulty controlling false alarms under time-varying conditions.
- Cyclostationary detection: Cyclostationarity describes periodic changes in statistical properties such as the mean and autocorrelation, often arising from modulation or coding.These properties have been used in several wireless sensing and estimation applications.
- Contribution: The proposed detector tests multiple cyclic frequencies simultaneously rather than using only one frequency, incorporating information from symbol, coding, and related signal structures.The paper states that this improves detector performance and supports distinguishing primary and secondary signals and different waveforms.
- Contribution: Distributed secondary users combine quantized local decision statistics to enlarge coverage and reduce sensitivity to shadowing and fading.The approach can operate with or without a fusion center and may also reduce communication bandwidth and power consumption.
- Paper scope: The paper derives a multiple-cyclic-frequency detector, analyzes collaborative primary-user detection, and evaluates reliability and cooperation gains through simulations.The organization follows these topics across the detector, collaboration, simulation, and conclusion sections.
II. CYCLOSTATIONARITY: A RECAP
The section introduces cyclostationarity through periodic second-order statistics and their Fourier representation. It defines cyclic autocorrelation and explains that cyclic frequencies may form harmonic or more general countable sets.
- Definition: A wide-sense second-order cyclostationary process has statistical properties that repeat with a period T0.T0 is called the period of the cyclostationary process.
- Fourier representation: Periodicity in the autocorrelation function permits a Fourier-series representation indexed by cyclic frequencies.The representation uses a time-centered pair of arguments, t1 = t + τ/2 and t2 = t − τ/2.
- Cyclic autocorrelation: The Fourier coefficients define the cyclic autocorrelation function, which is also the cyclic autocovariance function for zero-mean processes.The cyclic autocorrelation captures the second-order periodic structure used by the detector.
- Cyclic frequencies: With one period, cyclic frequencies form harmonics of a fundamental frequency; multiple periods produce a broader set of cyclic frequencies.The set is denoted A in the paper.
- Generalization: Almost cyclostationary processes can have a countable set A of cyclic frequencies that need not be harmonics.The paper generally identifies cyclostationarity through a nonzero cyclic autocorrelation at some nonzero cyclic frequency.
III. DETECTION USING MULTIPLE CYCLIC FREQUENCIES
The paper extends single-frequency cyclostationarity testing to simultaneous testing over multiple cyclic frequencies. It proposes maximum- and sum-based statistics and derives their null distributions for thresholding.
- Motivation: Existing tests can detect cyclostationarity at one cyclic frequency but do not fully exploit information distributed across frequencies.Communication signals may contain cyclic frequencies tied to carrier, symbol, chip, coding, guard-period, and scrambling structures.
- Application: The detector targets unoccupied-band identification, where missed opportunities can result when a band is unnecessarily classified as occupied.This motivates reliable multi-frequency detection in cognitive-radio applications.
- Construction: The method extends second-order cyclic-statistics testing to a set A of cyclic frequencies and multiple lags.It defines estimated cyclic autocorrelations, covariance matrices, and spectral estimates for constructing the test.
- Asymptotic model: Cyclic autocorrelation estimates are modeled as an asymptotically normal estimate plus an estimation error that vanishes as the sample size grows.This asymptotic model supports the generalized likelihood-ratio construction.
- Test statistics: The proposed statistics take either the maximum or the sum of the cyclostationary GLRT statistic across the frequencies of interest.Under independence, the sum-based statistic is itself the GLRT statistic, while performance can depend on the signal and tested-frequency set.
- Null distributions: The null distributions of the sum and maximum statistics are derived from chi-square distributions and the distribution of maxima of independent variables.The resulting false-alarm threshold uses the tested-frequency count Nα.
IV. COOPERATIVE DETECTION
Cooperative detection combines quantized local statistics from geographically distributed secondary users at a fusion center to decide whether the primary user is active. Under conditional sensor independence, generalized likelihood-ratio statistics can be combined, although the GLRT has no claimed optimality properties.
- A fusion center collects quantized local decision statistics from K secondary users and decides whether the spectrum is available.The local information may be likelihood ratios or, under very coarse quantization, binary decisions.
- Under conditional independence, the fusion rule is a likelihood-ratio test over the received local likelihood ratios.
- Binary local decisions can be fused by summing the ones and comparing the result with a threshold.
- The proposed cooperative test uses sums of generalized log-likelihood ratios rather than products of generalized likelihood ratios.
- The GLRT has no claimed optimality properties, although it performs highly reliably in many applications.
- The cooperative test statistics have asymptotic chi-square distributions under conditional independence, with degrees of freedom determined by the number of users and tested cyclic frequencies.For Dm,K, the null distribution uses 2NK degrees of freedom and Nα tested cyclic frequencies.
- Reducing transmitted data and handling communication-rate constraints are left for future work.
V. SIMULATION EXAMPLES
Simulations with OFDM signals compare single- and multicycle detectors in AWGN and cooperative settings. Multiple cyclic frequencies, sum statistics, and cooperation improve detection, including under shadowing.
- Experimental setup: The OFDM simulations use cyclic frequencies 1/Ts and 2/Ts, with two time lags ±Td, and compare one- versus two-frequency detectors in AWGN.The signal has 32 subcarriers, a cyclic prefix one-fourth the useful symbol data, 16-QAM modulation, and 100 OFDM symbols.
- Single-user detection: Multiple cyclic-frequency detectors outperform the single-frequency detector at low SNR, with the sum detector of Ds performing best.The comparison uses a constant false alarm rate of 0.05 and averages 10,000 experiments.
- Single-user detection: The detectors exhibit desirable receiver operating characteristics at an SNR of -7 dB: detection probability increases with the false alarm rate.
- Cooperative detection: With cooperation, using multiple cyclic frequencies further improves detection, and the multicycle sum statistic Ds,K performs best.The probability-of-detection comparison is shown as a function of SNR and false alarm rate.
- Cooperative detection: Cooperation among 5 secondary users provides a performance gain of roughly 3 dB compared with a single secondary user.Using two cyclic frequencies provides similar improvement in the cooperative and single-user cases.
- Shadowing: Under shadowing, cooperation reduces sensitivity to shadowing effects significantly.Each user's SNR was independently drawn from a normal distribution with mean -9 dB and standard deviation 10 dB.
VI. CONCLUSION
The paper proposes a GLRT for detecting primary transmissions through multiple cyclic frequencies and derives the asymptotic distribution of its test statistic. Simulations report improved low-SNR reliability and significant gains from collaborative decision making.
- A generalized likelihood ratio test detects primary transmissions using multiple cyclic frequencies, with an asymptotic distribution derived for its test statistic.
- The proposed test combines quantized local likelihood ratios from multiple secondary users under a conditional independence assumption to mitigate shadowing and fading.
- Simulation examples demonstrate improved detector reliability in the low-SNR regime and significant gains from collaborative decision making.