Generalized Energy Detector Research Articles

Generalized Energy Detector with Iterative Processing of Narrowband Signals in Frequency Domain

The article is devoted to improvement and study of efficiency of the energy detector of narrow-band signals in background of additive noise of unknown power. Analytical expressions describing the probability density distribution of samples of the generalized energy spectrum of noise are obtained. It is shown that the obtained distributions describe well the broadband noise, which differs from the Gaussian one. For the separation of signal and noise samples in the frequency domain, was proposed the decisive statistics in the form of the standard deviation of generalized power spectral density. The threshold value of the decisive statistics for a given probability of false alarm rate in frequency domain was obtained numerically. An iterative algorithm for detecting narrow-band signals in the frequency domain was proposed. A distinctive feature of the developed algorithm is the normalization of the vector of frequency samples to the sum of its elements after each iteration of processing, which consists of recursively calculating the value of decisive statistics, comparing it with the threshold and, if the threshold is exceeded, discarding the maximum frequency sample from the vector. Each dropped sample is signal sample. This approach will allow to detect narrow-band signals in a dynamic range, which is limited only by the maximum level of side lobes of the window function. During the study of the algorithm, it was found that the highest detection quality indicators are achieved when the value of the exponent to which the frequency samples is about 3. The type of window function has little effect on the probability of detection, and this effect decreases with increasing the load on the analysis frequency band. At the same time, the proposed detector remains operable when the analysis frequency band is loaded up to 20%, and its performance is not worse than for the case of a known noise level. If the value of the exponent deviates from 3, the algorithm will be operational with a smaller bandwidth load.

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.

Generalized energy detector for weak random signals via vibrational resonance

In this paper, the generalized energy (GE) detector is investigated for detecting weak random signals via vibrational resonance (VR). By artificially injecting the high-frequency sinusoidal interferences into an array of GE statistics formed for the detector, we show that the normalized asymptotic efficacy can be maximized when the interference intensity takes an appropriate non-zero value. It is demonstrated that the normalized asymptotic efficacy of the dead-zone-limiter detector, aided by the VR mechanism, outperforms that of the GE detector without the help of high-frequency interferences. Moreover, the maximum normalized asymptotic efficacy of dead-zone-limiter detectors can approach a quarter of the second-order Fisher information for a wide range of non-Gaussian noise types.

Wide-Band Sensing and Optimization for Cognitive Radio Networks With Noise Variance Uncertainty

This paper considers wide-band spectrum sensing and optimization for cognitive radio (CR) networks with noise variance uncertainty. It is assumed that the considered wide-band contains one or more white sub-bands. Under this assumption, we consider throughput maximization of the CR network while appropriately protecting the primary network. We address this problem as follows. First, we propose novel ratio based test statistics for detecting the edges of each sub-band. Second, we employ simple energy comparison approach to choose one reference white sub-band. Third, we propose novel generalized energy detector (GED) for examining each of the remaining sub-bands by exploiting the noise information of the reference white sub-band. Finally, we optimize the sensing time (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ) to maximize the CR network throughput using the detection and false alarm probabilities of the GED. The proposed GED does not suffer from signal to noise ratio (SNR) wall and outperforms the existing signal detectors. Moreover, the relationship between the proposed GED and conventional energy detector (CED) is quantified analytically. We show that the optimal To depends on the noise variance information. In particular, with 10TV bands, SNR = -20 dB and 2s frame duration, we found that the optimal T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> is 28.5 ms (50.6 ms) with perfect (imperfect) noise variance scenario.

Signal activity detection of phase-shift keying signals

We propose computationally inexpensive and efficient solutions for signal activity detection of phase-shift keying (PSK) signals in additive white Gaussian noise. We consider the complex amplitude of the signal, as well as the information sequence, as the unknown parameters. In addition, the noise variance is assumed unknown. We derive the generalized likelihood ratio test (GLRT) and suggest a computationally efficient implementation thereof. Furthermore, we develop a new inexpensive detector for binary PSK signals, which we will refer to as the generalized energy detector. To evaluate the performance of these detectors, we attempt to derive a uniformly most powerful invariant (UMPI) test as an optimal detector. It turns out that the UMPI test exists only if the signal-to-noise ratio is known. We use this UMPI test in order to obtain an upper-bound performance for the evaluation of invariant detectors, such as the GLRT. Simulation results illustrate and compare the performance and the efficiency of the proposed signal activity detectors

Signal Activity Detection of Phase-Shift Keying Signals

We propose computationally inexpensive and efficient solutions for signal activity detection of phase-shift keying (PSK) signals in additive white Gaussian noise. We consider the complex amplitude of the signal as well as the information sequence as the unknown parameters. In addition, the noise variance is assumed unknown. We derive the generalized likelihood ratio test (GLRT) and suggest a computationally efficient implementation thereof. Furthermore, we develop a new inexpensive detector for binary PSK signals, which we will refer to as the generalized energy detector. To evaluate the performance of these detectors, we attempt to derive a uniformly most powerful invariant test (UMPI) as an optimal detector. It turns out that the UMPI test exists only if the signal-to-noise ratio is known. We use this UMPI test in order to obtain an upper-bound performance for the evaluation of invariant detectors, such as the above-mentioned GLRT. Simulation results illustrate and compare the performance and the efficiency of the proposed signal activity detectors.

Detection of weak stochastic signals in double-sided exponential noise using generalized energy detector

Many locally optimum, suboptimum, and ad hoc detectors exploit knowledge of the noise probability density function (pdf) to obtain their test statistic for the detection of stochastic signals in non-Gaussian noise. These detectors appear to offer potential for highly improved performance for very small signal to noise ratios (asymptotically approaching zero). This paper studies a locally optimum detector namely the generalized energy detector, by deriving analytical expressions for a performance measure using a double-sided exponential noise pdf. The paper concludes that the apparently large gains predicted by the asymptotic theory may not be reachable within the practical range of signal-to-noise ratios.