Noise power estimation is a key issue in modern wireless communication systems. It allows resource allocation by detecting white spectral spaces effectively, and gives control over the communication process by adjusting transmission power. Thus far, the proposed estimation methods in the literature are based on spectral averaging, eigenvalues of sample covariance matrix, information theory, and statistical signal analysis. Each method is characterized by certain stability, accuracy and complexity. However, the existing literature does not provide an appropriate comparison. In this paper, we evaluate the performance of the existing estimation techniques intensively in terms of stability and accuracy, followed by detailed complexity analysis. The basis for comparison is signal-to-noise ratio (SNR) estimation in simulated industrial, scientific and medical (ISM) band transmission. The source of used background distortions is complex noise measurement, recorded by USRP-2932 in an industrial production area. Based on the examined solutions, we also analyze the influence of noise samples separation techniques on the estimation process. As a response to the defects in the used methods, we propose a novel noise samples separation algorithm based on the adaptation of rank order filtering (ROF). In addition to simple implementation, the proposed method has a very good 0.5 dB root-mean-squared error (RMSE) and smaller than 0.1 dB resolution, thus achieving a performance that is comparable with the methods exploiting information theory concepts.
Modern researchers have proposed a number of approaches for estimating noise power, based on various properties. Most often referred to in the literature are maximum likelihood (ML) and minimum variance unbiased (MVU) estimators @cite_14 @cite_2 @cite_0 @cite_7 @cite_21 . Both ML and MVU estimators are based on the principle of power spectrum averaging. However, the range of proposed solutions is much wider and includes, for instance, information theoretic methods as Akaike Information Criteria @cite_16 @cite_8 and correlation-based methods e.g., covariance based estimator @cite_18 @cite_24 . More specialized solutions, for example based on statistical relations, can also be found as in minimum mean squared error (MMSE) estimator @cite_17 . All of these methods, although dedicated for similar applications, differ significantly in terms of accuracy, stability and complexity.
@cite_18 @cite_14 @cite_7 @cite_8 @cite_21 @cite_0 @cite_24 @cite_2 @cite_16 @cite_17
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In this paper, a newly developed SNR estimation algorithm is presented. The new algorithm is based on the eigenvalues of the samples covariance matrix of the recieved signal. The presented algorith ... 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 log10(1+λ λ) dB, when the time dedicated to noise power estimation is a multiple λ of the ED observation interval. In this paper1, we explore the Information-Theoretic Criteria, namely, Akaikes Information Criterion (AIC) and Minimum Description Length (MDL) as a tool to sense vacant sub-band over the spectrum bandwidth. The proposed technique is motivated by the fact that an idle sub-band (Normal process) presents a number of independent eigenvectors appreciably larger than for an occupied sub-band (Non-normal process). It turns out that, based on the number of the independent eigenvectors of a given covariance matrix of the observed signal, one can conclude on the nature of the sensed sub-band. Our-theoretical result as well as the empirical results are first applied on experimental measurement campaign conducted at the Eurecom PLATON Platform. We then apply our method to an IEEE 802.11b Wireless Fidelity (Wi-Fi) signal in order to analyze the robustness of the proposed approach in presence of increased levels of noise. We argue that the proposed sub-space based techniques give interesting results in terms of sensing the white space in the spectrum. The detection and estimation of signals in noisy, limited data is a problem of interest to many scientific and engineering communities. We present a mathematically justifiable, computationally simple, sample-eigenvalue-based procedure for estimating the number of high-dimensional signals in white noise using relatively few samples. The main motivation for considering a sample-eigenvalue-based scheme is the computational simplicity and the robustness to eigenvector modelling errors which can adversely impact the performance of estimators that exploit information in the sample eigenvectors. There is, however, a price we pay by discarding the information in the sample eigenvectors; we highlight a fundamental asymptotic limit of sample-eigenvalue-based detection of weak or closely spaced high-dimensional signals from a limited sample size. This motivates our heuristic definition of the effective number of identifiable signals which is equal to the number of ldquosignalrdquo eigenvalues of the population covariance matrix which exceed the noise variance by a factor strictly greater than . The fundamental asymptotic limit brings into sharp focus why, when there are too few samples available so that the effective number of signals is less than the actual number of signals, underestimation of the model order is unavoidable (in an asymptotic sense) when using any sample-eigenvalue-based detection scheme, including the one proposed herein. The analysis reveals why adding more sensors can only exacerbate the situation. Numerical simulations are used to demonstrate that the proposed estimator, like Wax and Kailath's MDL-based estimator, consistently estimates the true number of signals in the dimension fixed, large sample size limit and the effective number of identifiable signals, unlike Wax and Kailath's MDL-based estimator, in the large dimension, (relatively) large sample size limit. In Cognitive Radio, the key to overcome the spectrum scarcity is reliable spectrum sensing, which will allow efficient opportunistic spectral reuse with minimum interference to licensed users. We consider energy detection based sensing that requires efficient noise power estimation technique in order to reliably detect the primary transmissions. We consider three algorithms, viz. Akaike Information Criterion (AIC), Minimum Description Length (MDL), and Rank Order Filtering (ROF), which estimate the noise power in the presence of the signal. The ROF key property is that it attempts to track the non-flat noise floor. Algorithm probability of missed detection is evaluated using data obtained from USRP2 devices. We illustrate that ROF may gain up to 6dB when signal to be detected is in the sub-band where the noise oor is not at (e.g., at the edges of the observed band). This paper proposes a minimum mean-square error (MMSE) filtering technique to estimate the noise power that takes into account the variation of the noise statistics across the orthogonal frequency division multiplexing (OFDM) sub-carrier index as well as across OFDM symbols. The proposed method provides many local estimates that allow tracking of the variation of the noise statistics in frequency and time. The MMSE filter coefficients are obtained from the mean-squared-error (MSE) expression, which can be calculated using the noise statistics. Evaluation of the performance with computer simulations shows that the proposed method tracks the local statistics of the noise more efficiently than conventional methods.