Signal-to-noise Ratio Wall Research Articles

On the Signal-to-Noise Ratio Wall of Energy Detection in Spectrum Sensing

In this paper, a comprehensive analysis of the signal-to-noise ratio wall (SNRw) of cognitive radio (CR)-based non-cooperative spectrum sensing (nCSS) and cooperative spectrum sensing (CSS) using energy detection (ED) is presented. The analysis considers a novel realistic noise uncertainty (NU) model in which it is assumed that the estimated noise variance used to determine the decision threshold is unbiased and follows a truncated-Gaussian random distribution with configurable limits. Expressions are derived for the individual detection performances at CRs and global detection performances at the fusion center in terms of probability of false alarm and probability of detection and the SNRw of ED in nCSS and CSS in hard-decision fusion under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k $ </tex-math></inline-formula> -out-of- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M $ </tex-math></inline-formula> rule, and soft-decision fusion, considering the proposed NU model, respectively. Empirical SNRw algorithms are also proposed, allowing for the SNRw computation of any detector, including the ED, in nCSS and CSS. All theoretical findings are verified through computer simulations or empirical results.

An Adaptive Energy Detection Scheme with Real-Time Noise Variance Estimation

Energy detection-based spectrum sensing techniques are ideally suited for power-constrained cognitive radio applications because of their lower computational complexity compared to feature detection techniques. However, their detection performance is dependent on multiple factors like accuracy of noise variance estimation and signal-to-noise ratio (SNR). Many variations of energy detection techniques have been proposed to address these challenges; however, they achieve the desired detection accuracy at the cost of increased computational complexity. This restricts the use of enhanced energy detection schemes in power-constrained applications such as aeronautical communication. In this paper, an adaptive low-complexity energy detection scheme is proposed for spectrum sensing in an L-band Digital Aeronautical Communication System (LDACS) at lower SNR levels. Our scheme uses a real-time noise variance estimation technique using autocorrelation which is induced by the cyclic prefix property in LDACS signals. The proposed technique does not incur dedicated hardware blocks for noise variance estimation, leading to an efficient hardware implementation of the scheme without significant resource overheads. The simulation studies of the proposed scheme show that the desired accuracy (90% detection accuracy with only 10% of false alarms) can be achieved even at $$-16.5$$ dB SNR, significantly lowering the SNR wall over existing energy detection schemes.

Improvement of Noise Uncertainty and Signal-To-Noise Ratio Wall in Spectrum Sensing Based on Optimal Stochastic Resonance.

Noise uncertainty and signal-to-noise ratio (SNR) wall are two very serious problems in spectrum sensing of cognitive radio (CR) networks, which restrict the applications of some conventional spectrum sensing methods especially under low SNR circumstances. In this study, an optimal dynamic stochastic resonance (SR) processing method is introduced to improve the SNR of the receiving signal under certain conditions. By using the proposed method, the SNR wall can be enhanced and the sampling complexity can be reduced, accordingly the noise uncertainty of the received signal can also be decreased. Based on the well-studied overdamped bistable SR system, the theoretical analyses and the computer simulations verify the effectiveness of the proposed approach. It can extend the application scenes of the conventional energy detection especially under some serious wireless conditions especially low SNR circumstances such as deep wireless signal fading, signal shadowing and multipath fading.

Adaptive Technique with Cross Correlation for Lowering Signal-to-Noise Ratio Wall in Sensor Networks

Energy detection is considered as most popular spectrum sensing technique. However, the impact of noise uncertainty in wireless environment limits the sensitivity of energy-based detector. It generally suffers from Signal-to-Noise Ratio (SNR) wall, which is defined as the minimum SNR in which robust detection is not possible. This paper presents an adaptive technique to improve SNR wall in sensor networks that combines cross-correlation scheme and dynamic threshold method to improve performance. An analytical expression of SNR wall is derived to show improved performance over traditional energy detector. Theoretical analyses and simulations validate effectiveness of the proposed method under noise uncertainty environment.

SNR wall for generalized energy detector in the presence of noise uncertainty and fading

The performance of energy detection (ED) degrades under low SNR, noise uncertainty (NU) and fading. The generalized energy detector (GED) is obtained by changing the squaring operation in ED by an arbitrary positive number p. In this paper, we investigate the signal to noise ratio (SNR) wall for GED under diversity considering NU as well as fading by considering p-Law combining (pLC) and p−law selection (pLS) diversity. First, the SNR walls considering AWGN channel are derived. It is shown that for pLC diversity, increasing p results in lower SNR wall. It is also shown that under no diversity and pLS diversity, the SNR wall is independent of p. The analysis is then extended to the channel with Nakagami fading where it is shown that the SNR wall increases significantly. As a byproduct of this work, we also study the effect of NU and fading on the detection performance and show that above certain value, the effect of NU is more severe when compared to the fading. The effect of p on the performance is analyzed and it is shown that the performance is the best for values of p close to 2. The performance of pLC and pLS is also compared.

Cooperative Energy Detection With Heterogeneous Sensors Under Noise Uncertainty: SNR Wall and Use of Evidence Theory

The analyzed system model in this paper is a distributed parallel detection network in which each secondary user (SU) evaluates the energy-based test statistic from the received observations and sends it to a fusion center (FC), which makes the final decision. Uncertainty in the noise variance at each SU is modeled as an unknown constant in a certain interval around the nominal noise variance. It is assumed that the SUs are heterogeneous in that the nominal noise variances and the uncertainty intervals can be different for different SUs. Moreover, the received signal power at each SU may be different. For the considered system model, the paper presents important results for two inter-related themes on cooperative energy detection (CED) in the presence of noise uncertainty (NU). First, the expressions for generalized signal-to-noise ratio (SNR) walls are derived for the classical CED fusion rule, i.e., sum of energies from all SUs. Second, a Dempster–Shafer theory based CED is proposed in the presence of NU with heterogeneous sensors. In the proposed scheme, the test statistic from each SU is the energy-based basic mass assignment values, which are first discounted depending on the uncertainty level associated with the SU and then fused at the FC using the Dempster rule of combination to arrive at the global decision. It is shown that the proposed scheme outperforms the traditional sum fusion rule in terms of detection performance as well as the location of SNR wall.

Parzen window entropy based spectrum sensing in cognitive radio

In this paper, we propose a Parzen window entropy based spectrum sensing algorithm for enhancing the signal-to-noise ratio (SNR) wall of cognitive radio primary user detection. We compute the information entropy using a non-parametric Kernel Density Estimation (KDE) method. Single node sensing is extended to cooperative sensing using the weighted gain combining (WGC) fusion method. The weights of WGC technique are computed using a Differential Evolution(DE) algorithm and compared with the log-likelihood ratio (LLR) method. In addition, the detection performance of the proposed Parzen window entropy is compared with Shannon entropy and energy detection techniques. We consider a DVB-T signal with Additive White Gaussian Noise (AWGN) subjected to Rayleigh fading under noise uncertainty as a primary user signal for simulation. The simulation result reveals that in the case of a single node and cooperative sensing, the proposed method achieves SNR wall of −19 dB and −24 dB respectively at the probability of false alarm 0.1.

SNR Wall Effect Alleviation by Generalized Detector Employed in Cognitive Radio Networks.

The most commonly used spectrum sensing techniques in cognitive radio (CR) networks, such as the energy detector (ED), matched filter (MF), and others, suffer from the noise uncertainty and signal-to-noise ratio (SNR) wall phenomenon. These detectors cannot achieve the required signal detection performance regardless of the sensing time. In this paper, we explore a signal processing scheme, namely, the generalized detector (GD) constructed based on the generalized approach to signal processing (GASP) in noise, in spectrum sensing of CR network based on antenna array with the purpose to alleviate the SNR wall problem and improve the signal detection robustness under the low SNR. The simulation results confirm our theoretical issues and effectiveness of GD implementation in CR networks based on antenna array.

Lowering the signal‐to‐noise ratio wall for energy detection using parameter‐induced stochastic resonator

Energy detection is the most frequently used spectrum sensing technique, however, in uncertain low signal-to-noise ratio (SNR) conditions, it generally suffers from the `SNR wall', that is, a minimum SNR below which it is impossible to reliably detect a signal. To address this issue, an improved energy detection (IED) algorithm based on non-linear parameter-induced stochastic resonator (PSR) is proposed in this study. By adopting the method which combines classic adiabatic approximation stochastic resonance (SR) theory and non-classic parameter-induced SR theory, an analytical expression of SR system parameters is derived. On this basis, a PSR is proposed which is mathematically testified to have the ability to improve the SNR of the received signal. Further, an IED algorithm is proposed by introducing the PSR as the preprocessor of energy detection. Theoretical analyses and simulation results prove that a significantly detection performance and SNR wall improvement can be achieved using the proposed IED algorithm.

Pulse signal detection in cognitive UWB system

According to the problem of cognitive ultra wide-band (UWB) spectrum sensing, a novel UWB pulse signal detection algorithm based on cumulative sum (CUSUM) test is proposed in this paper. Based on the analysis of the existing spectrum sensing schemes for cognitive UWB system, some obvious facts are obtained that it is difficult to detect UWB pulse signal with conventional spectrum sensing schemes, due to its low average signal to noise ratio (SNR), large bandwidth, and low duty ratio. In this paper the detection algorithm of signal distribution change, which is application of CUSUM test, is considered to be applied to cognitive UWB spectrum sensing. But CUSUM test request that the pre-change and the post-change distributions are i.i.d, which cannot be satisfied in the detection process of UWB pulse signal. Since there are two time domain descriptions on UWB pulse signal, namely one contains only noise and the other one contains pulse signal plus noise, the existing detection algorithm of signal distribution change cannot be directly applied to detect UWB pulse signal. Hence the uniform probability density function expression of UWB pulse signal is first deduced, then CUSUM test is applied to cognitive UWB spectrum sensing. The proposed algorithm is a time sequential detection algorithm, with low complexity and minimal detection delay, which is suitable to detect the low duty ratio signal. Its performance is evaluated through theoretical analysis and numerical simulations. It is shown that this algorithm outperforms the conventional energy detection algorithm and conquers SNR wall phenomenon.

Effects of Noise Power Estimation on Energy Detection for Cognitive Radio Applications

An uncertain knowledge of the noise power level can severely limit the energy detector (ED) spectrum sensing capability. In some situations this uncertainty can cause signal-to-noise ratio (SNR) penalties or even the rise of the SNR wall phenomenon. In this paper we analyze the performance of the ED with estimated noise power (ENP), addressing the threshold design and giving the conditions for the existence of the SNR wall. We derive analytical expressions for the design curves (SNR vs. observation time for a target performance) for the ENP-ED. Then we apply our analysis to cognitive radio (CR) systems where energy detection is used for fast sensing. For example it is shown that the SNR penalty with respect to ideal ED is of 5 log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> (1+λ/λ) dB, when the time dedicated to noise power estimation is a multiple λ of the ED observation interval.

Lowering the SNR Wall for Energy Detection Using Cross-Correlation

Spectrum sensing is a key enabler of cognitive radio but generally suffers from what is called a signal-to-noise ratio (SNR) wall, i.e., a minimum SNR below which it is impossible to reliably detect a signal. For energy detection, which has the advantage of not requiring knowledge of the signal, the SNR wall is caused by uncertainty in the noise level. Cross-correlation has been suggested as a possible means to obtain higher sensitivity but has received little attention in the context of noise uncertainty. The idea of cross-correlation is to have two receive paths, where each path independently processes the signal before they are combined, such that the noise added to the input signal at the individual paths is largely uncorrelated. In this paper, we mathematically quantify the SNR wall for cross-correlation, showing that it linearly scales with the amount of noise correlation. This lower noise correlation results in higher sensitivity, which is significantly better than that for autocorrelation. Equations that can be used to estimate the benefit over autocorrelation and the measurement time for a required probability of detection and false alarm are derived.

Higher-Order Cyclostationarity Detection for Spectrum Sensing

Recent years have shown a growing interest in the concept of Cognitive Radios (CRs), able to access portions of the electromagnetic spectrum in an opportunistic operating way. Such systems require efficient detectors able to work in low Signal-to-Noise Ratio (SNR) environments, with little or no information about the signals they are trying to detect. Energy detectors are widely used to perform such blind detection tasks, but quickly reach the so-called SNR wall below which detection becomes impossible Tandra (2005). Cyclostationarity detectors are an interesting alternative to energy detectors, as they exploit hidden periodicities present in man-made signals, but absent in noise. Such detectors use quadratic transformations of the signals to extract the hidden sine-waves. While most of the literature focuses on the second-order transformations of the signals, we investigate the potential of higher-order transformations of the signals. Using the theory of Higher-Order Cyclostationarity (HOCS), we derive a fourth-order detector that performs similarly to the second-order ones to detect linearly modulated signals, at SNR around 0 dB, which may be used if the signals of interest do not exhibit second-order cyclostationarity. More generally this paper reviews the relevant aspects of the cyclostationary and HOCS theory, and shows their potential for spectrum sensing.

Entropy-based robust spectrum sensing in cognitive radio

Sensitivity to noise uncertainty is a fundamental limitation of current spectrum sensing strategies in detecting the presence/absence of primary users in cognitive radio (CR). Because of noise uncertainty, the performance of traditional detectors such as matched filter, energy detector and even cyclostationary detectors deteriorates rapidly at low signal-to-noise ratio (SNR). Without accurate estimation of noise power, an absolute /SNR wall/ exists in traditional detectors below which robust detection is impossible, no matter how long the observations are. To counteract the effect of noise uncertainty in low SNR, the authors propose a blind frequency-domain entropy-based spectrum sensing scheme. The entropy of the sensed signal is estimated in the frequency domain with probability space partitioned into fixed dimensions. The authors prove that the entropy of noise is a constant and the proposed scheme is thus intrinsically robust against noise uncertainty. Monte Carlo experiments are carried out to verify the robustness and further show that the proposed scheme outperforms classical energy detector and cyclostationary detector in low SNR region with 6 and 4/dB performance improvement, respectively. In addition, the sensing time is reduced to about 75/ by the proposed scheme compared to energy detector under the same detection performance.