Roberto López-Valcarce

Detection of Rank-

Spectrum sensing is a key component of the cognitive radio paradigm. Primary signals are typically detected with uncalibrated receivers at signal-to-noise ratios (SNRs) well below decodability levels. Multiantenna detectors exploit spatial independence of receiver thermal noise to boost detection performance and robustness. We study the problem of detecting a Gaussian signal with rank-P unknown spatial covariance matrix in spatially uncorrelated Gaussian noise with unknown covariance using multiple antennas. The generalized likelihood ratio test (GLRT) is derived for two scenarios. In the first one, the noises at all antennas are assumed to have the same (unknown) variance, whereas in the second, a generic diagonal noise covariance matrix is allowed in order to accommodate calibration uncertainties in the different antenna frontends. In the latter case, the GLRT statistic must be obtained numerically, for which an efficient method is presented. Furthermore, for asymptotically low SNR, it is shown that the GLRT does admit a closed form, and the resulting detector performs well in practice. Extensions are presented in order to account for unknown temporal correlation in both signal and noise, as well as frequency-selective channels.

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Spectrum sensing is a key ingredient of the dynamic spectrum access paradigm, but it needs powerful detectors operating at SNRs well below the decodability levels of primary signals. Noise uncertainty poses a significant challenge to the development of such schemes, requiring some degree of diversity (spatial, temporal, or in distribution) for identifiability of the noise level. Multiantenna detectors exploit spatial independence of receiver thermal noise. We review this class of schemes and propose a novel detector trading off performance and complexity. However, most of these methods assume that the noise power, though unknown, is the same at all antennas. As it turns out, calibration errors have a substantial impact on these detectors. Another novel detector is proposed, based on an approximation to the Generalized Likelihood Ratio, outperforming previous schemes for uncalibrated multiantenna receivers.

Signals in Cognitive Radio Networks With Uncalibrated Multiple Antennas

Signal-to-noise ratio (SNR) estimation is an important task in many digital communication systems. With nonconstant modulus constellations, the performance of the classical second- and fourth-order moments estimate is known to degrade with increasing SNR. A new non-data-aided estimate is proposed, which makes use of the sixth-order moment of the received data, and which can be tuned for a particular constellation in order to extend the usable range of SNR values. The advantage of the new method is especially significant for constellations with two different amplitude levels, e.g. 16-amplitude-and-phase-shift keying (16-APSK)

Multiantenna spectrum sensing for Cognitive Radio: overcoming noise uncertainty

The performance of existing moments-based non-data-aided (NDA) estimators of signal-to-noise ratio (SNR) in digital communication systems substantially degrades with multilevel constellations. We propose a novel moments-based approach that is amenable to practical implementation and significantly improves on previous estimators of this class. This approach is based on a linear combination of ratios of certain even-order moments, which allow the derivation of NDA SNR estimators without requiring memory-costly lookup tables. The weights of the linear combination can be tuned according to the constellation and the SNR operation range. As particular case we develop an eighth-order statistics (EOS)-based estimator, showing in detail the statistical analysis that leads to the weight optimization procedure. The EOS-based estimators yield improved performance for multilevel constellations, especially for those with two and three amplitude levels. Monte Carlo simulations validate the new approach in a wide SNR range.

Sixth-Order Statistics-Based Non-Data-Aided SNR Estimation

Abstract: To know the location of nodes plays an important role in many current and envisioned wireless sensor network applications. In this framework, we consider the problem of estimating the locations of all the nodes of a network, based on noisy distance measurements for those pairs of nodes in range of each other, and on a small fraction of anchor nodes whose actual positions are known a priori. The methods proposed so far in the literature for tackling this non-convex problem do not generally provide accurate estimates. The difficulty of the localization task is exacerbated by the fact that the network is not generally uniquely localizable when its connectivity is not sufficiently high. In order to alleviate this drawback, we propose a two-objective evolutionary algorithm which takes concurrently into account during the evolutionary process both the localization accuracy and certain topological constraints induced by connectivity considerations. The proposed method is tested with different network configurations and sensor setups, and compared in terms of normalized localization error with another metaheuristic approach, namely SAL, based on simulated annealing. The results show that, in all the experiments, our approach achieves considerable accuracies and significantly outperforms SAL, thus manifesting its effectiveness and stability.

SNR Estimation for Multilevel Constellations Using Higher-Order Moments

We consider the blind equalization and estimation of single-user, multichannel models from the second-order statistics of the channel output when the channel input statistics are colored but known. By exploiting certain results from linear prediction theory, we generalize the algorithm of Tong et al. (1994), which was derived under the assumption of a white transmitted sequence. In particular, we show that all one needs to estimate the channel to within an unitary scaling constant, and thus to find its equalizers, is (a) that a standard channel matrix have full column rank, and (b) a vector of the input signal and its delays have positive definite lag zero autocorrelation. An algorithm is provided to determine the equalizer under these conditions. We argue that because this algorithm makes explicit use of the input statistics, the equalizers thus obtained should outperform those obtained by other methods that neither require, nor exploit, the knowledge of the input statistics. Simulation results are provided to verify this fact.

A two-objective evolutionary approach based on topological constraints for node localization in wireless sensor networks

We address the problem of distributed estimation of a parameter from a set of noisy observations collected by a sensor network, assuming that some sensors may be subject to data failures and report only noise. In such scenario, simple schemes such as the Best Linear Unbiased Estimator result in an error floor in moderate and high signal-to-noise ratio (SNR), whereas previously proposed methods based on hard decisions on data failure events degrade as the SNR decreases. Aiming at optimal performance within the whole range of SNRs, we adopt a Maximum Likelihood framework based on the Expectation-Maximization (EM) algorithm. The statistical model and the iterative nature of the EM method allow for a diffusion-based distributed implementation, whereby the information propagation is embedded in the iterative update of the parameters. Numerical examples show that the proposed algorithm practically attains the Cramer-Rao Lower Bound at all SNR values and compares favorably with other approaches.

Blind channel equalization with colored sources based on second-order statistics: a linear prediction approach

Signal-to-noise ratio (SNR) estimation for linearly modulated signals is addressed in this letter, focusing on envelope-based estimators, which are robust to carrier offsets and phase jitter, and on the challenging case of nonconstant modulus constellations. For comparison purposes, the true Cramer-Rao lower bound is numerically evaluated, obtaining an analytical expression in closed form for the asymptotic case of high SNR values, which quantifies the performance loss with respect to coherent estimation. As the maximum-likelihood algorithm is too complex for practical implementation, an expectation-maximization (EM) approach is proposed, achieving a good tradeoff between complexity and performance for medium-to-high SNRs. Finally, a hybrid scheme based on EM and moments-based estimates is suggested, which performs close to the theoretical limit over a wide SNR range.

A Diffusion-Based EM Algorithm for Distributed Estimation in Unreliable Sensor Networks

The estimation of the symbol rate of a linearly modulated signal is addressed, with special focus on low signal-to-noise ratio (SNR) scenarios. This problem finds application in automatic modulation classification and signal monitoring. A maximum-likelihood (ML) approach is adopted to derive practical estimators, exploiting information on the cyclostationarity of the modulated signal as well as knowledge of the received signaling pulse shape. The structure of the ML estimator suggests a two-step estimation procedure, whereby an initial coarse search determines first a neighborhood from which a subsequent fine search yields the final symbol rate estimate. Links between the ML approach and previous results from the literature in symbol rate estimation are established as well. The proposed scheme is applicable even for small excess bandwidths, at the cost of a higher complexity with respect to simpler estimators known to fail under such conditions.

Cramer-Rao lower bound and EM algorithm for envelope-based SNR estimation of nonconstant modulus constellations

Recently, there has been renewed interest in the use of infinite impulse response (IIR) linear equalizers (LEs) for digital communication channels as a means for both improving performance and blindly initializing decision feedback structures (DFEs). Theoretical justification for such an approach is usually given assuming unconstrained filters, which are not causal and therefore not implementable in practice. We present an analysis of realizable (i.e., causal, stable, and of finite degree) minimum mean square error (MMSE) equalizers for single-input multiple-output channels, both in the LE and DFE cases, focusing on their structures and filter orders, as well as the connections between them. The DFE resulting from rearranging the MMSE LE within a decision feedback loop is given special attention. It is shown that although this DFE does not in general coincide with the MMSE DFE, it still enjoys certain optimality conditions. The main tools employed are the Wiener theory of minimum variance estimation and Kalman filtering theory, which show interesting properties of the MMSE equalizers not revealed by previous polynomial approaches.