We consider the problem of detecting an unknown signal that lies in a union of subspaces (UoS) and that is observed in additive white Gaussian noise with unknown variance. The main contribution of this letter is the derivation of a detector that can accommodate a union made of nested subspaces. This detector includes the generalized likelihood ratio test (GLRT) as a special case when the subspace dimensions are all identical. It relies on the framework of multifamily likelihood ratio tests (MFLRT) and is shown by numerical examples to achieve better performance than existing detectors.

In this paper, we consider a network of sensors in which a fusion center applies a clustering method over the sensor measurements. In order to limit their energy consumption, the sensors transmit their measurements in a compressed form. This paper proposes a novel clustering algorithm that applies directly over compressed data, and that does not require the knowledge of the number of clusters. The proposed algorithm is based on a new cost function for centroid estimation, and a theoretical analysis shows that the cluster centroids are the only minimizers of this cost function. The clustering algorithm then estimates the cluster centroids by looking for the minimizers of the cost function, even when their number is unknown. The proposed algorithm shows performance close to that of the K-means algorithm over compressed data, without need to know the number of clusters.

Matched-field estimation is known to be sensitive to mismatch between the assumed replica of the acoustic field and the actual field. An interval error-based method (MIE) is proposed to predict the mean-squared error (MSE) performance for multisnapshot and multifrequency maximum-likelihood matched-field estimation under model mismatch. The source signal is assumed deterministic unknown. Global errors are predicted by deriving exact expressions of pairwise error probabilities with model mismatch in conjunction with the use of the Union bound. Local errors are approximated using a Taylor expansion of the MSE. Numerical examples show the accuracy of the method.

We consider the problem of testing whether the energy of a random signal projected onto a known subspace exceeds some specified value$\tau \geq 0$. The probability distribution of the signal is assumed to be unknown and this signal is observed in additive and independent white Gaussian noise with known variance. The proposed theoretical framework relies on the invariance of the problem and the resulting test is shown to be uniformly most powerful invariant in an extended sense suitable for random signals. This work extends Scharf and Friedlander’s matched subspace detector.

Statistical properties of real-valued symmetric -stable noise after short-time Fourier transformation are derived. Circularity, stationarity and dependence between the real and imaginary components are studied as a function of the STFT parameters and the stability index .

We derive a lower bound on the capacity of discrete-time Rician-fading channels that are selective both in time and frequency. The noncoherent setting is considered, where neither the transmitter nor the receiver knows a priori the actual channel realization. Single-input single-output communications subject to both average and peak power constraints are investigated. The lower bound assumes independent and identically distributed input data and is expressed as a difference between two terms. The first term is the information rate of the coherent channel with a weighted signal-to-noise ratio that results from the peak-power limitation. The second term is a penalty term, explicit in the Doppler spectrum of the channel, that captures the effect of the channel uncertainty induced by the noncoherent setting. The impact of channel selectivity and power constraints are discussed, and numerical applications on an experimental Rician channel surveyed in an underwater acoustic environment are also provided.

In order to provide a concise time-varying SISO channel model, the principle of maximum entropy is applied to scattering function derivation. The resulting model is driven by few parameters that are expressed as moments such as the channel average power or the Doppler spread. Physical interpretations of the model outputs are discussed. In particular, it is shown that common Doppler spectra such as the flat or the Jakes spectrum fit well into the maximum entropy framework. The Matlab code corresponding to the proposed model is available at http://perso.telecom-bretagne.eu/fxsocheleau/software.

We present two new noise variance estimation methods for OFDMA signals transmitted through an unknown multipath fading channel. We focus on blind estimation as it does not require any pilot sequences and is therefore applicable to contexts, such as cognitive radio for instance, where little prior signal knowledge is available. The two estimators are respectively based on the time-frequency sparsity of OFDMA signals and on the redundancy induced by the cyclic prefix. Numerical simulations compare the performance of the two algorithms and highlight their complementarity.

In the context of cognitive radio, this paper addresses the challenge of OFDM system identification. We show that it is possible to take advantage of pilot tone structures to perform identification. Pilot subcarrier usage is of great interest since it enables to discriminate OFDM systems that have the same modulation parameters (subcarrier spacing, cyclic prefix duration, etc.). The proposed method relies on the periodic redundancy often induced between pilot symbols. We demonstrate that most OFDM systems (Wifi, WiMAX, DVB-T, etc.) can be identified thanks to this redundancy by conducting a hypothesis test based on second order statistics. Detailed numerical examples demonstrate the efficiency of the proposed identification criterion in various kinds of environments.

In the context of cognitive radio, system identification is a crucial step towards radio environment awareness. In this paper, we present a new OFDM system identification method based on m-sequence (MS) specific characteristics. Thanks to their good random properties, m-sequences are commonly used in existing standards (such as Wifi or WiMAX) to modulate pilot tones for channel estimation and/or for synchronization purposes. We demonstrate that such sequences show extra-properties relevant to distinguish systems from each other and therefore advocate to generalize their use in a cognitive context. MS signatures are indeed of interest since they are able to discriminate OFDM based systems that have the same modulation parameters (intercarrier spacing, cyclic prefix duration, etc.). In order to detect these signatures, we conduct a hypothesis test based on the MS high order statistics. Detailed numerical examples demonstrate the efficiency of the proposed identification criterion and especially show its benefits compared to classical correlation based methods.