Suchergebnisse

This paper revisits the linear model with noisy inputs, in which the performance of the total least squares (TLS) method is far from acceptable. Under the assumption of Gaussian noises, the maximum likelihood (ML) estimation of the system response is reformulated as a general balanced least squares (BLS) problem. Unlike TLS, which minimizes the trace of the product between the empirical and inverse theoretical covariance matrices, BLS promotes solutions with similar values of both the empirical and theoretical error covariance matrices. The general BLS problem is reformulated as a semidefinite program with a rank constraint, which can be relaxed in order to obtain polynomial time algorithms. Moreover, we provide new theoretical results regarding the scenarios in which the relaxation is tight, as well as additional insights on the performance and interpretation of BLS. Finally, some simulation results illustrate the satisfactory performance of the proposed method. ; This work has been supported by the Spanish Government, Ministerio de Ciencia e Innovación, under project RACHEL (TEC2013-47141-C4-3-R)

This paper focuses on a linear model with noisy inputs in which the performance of the conventional Total Least Squares (TLS) approach is (maybe surprisingly) far from satisfactory. Under the typical Gaussian assumption, we obtain the maximum likelihood (ML) estimator of the system response. This estimator promotes a reasonable balance between the empirical and theoretical variances of the residual errors, which suggests the name of Balanced Least Squares (BLS). The solution of the associated optimization problem is based on its reformulation as a rank constrained semidefinite program (SDP), for which we show that the relaxation is tight with probability one. Both TLS and BLS can be seen as regularized LS estimators, but the (possibly negative) regularization in BLS is softer than its TLS counterpart, which avoids the inconsistency of TLS in our particular model. ; This work has been supported by the Spanish Government, Ministerio de Ciencia e Innovación, under project RACHEL (TEC2013-47141-C4-3-R).

In this paper, we propose a cooperative distributed framework to optimize a variety of rate and energy-efficiency (EE) utility functions, such as the minimum-weighted rate or the global EE, for the K-user interference channel. We focus on the single-input multiple-output (SIMO) case, where each user, based solely on local channel state information (CSI) and limited exchange information from other users, optimizes its transmit power and receive beamformer, although the framework can also be extended to the multiple-output multiple-input (MIMO) case. The distributed framework combines an alternating optimization approach with majorization-minimization (MM) techniques, thus ensuring convergence to a stationary point of the centralized cost function. Closed-form power update rules are obtained for some utility functions, thus obtaining very fast convergence algorithms. The receivers treat interference as noise (TIN) and apply the beamformers that maximize the signal-to-interference-plus-noise (SINR). The proposed cooperative distributed algorithms are robust against channel variations and network topology changes and, as our simulation results suggest, they perform close to the centralized solution that requires global CSI. As a benchmark, we also study a non-cooperative distributed framework based on the so-called "signal-to-leakage-plus-noise ratio" (SNLR) that further reduces the overhead of the cooperative version. ; The work of Ignacio Santamaria was supported in part by the Ministerio de Ciencia e Innovación (Gobierno de España) / Agencia Española de Investigación (AEI) / FEDER funds of the European Union (EU) under Grant PID2019-104958RB-C43 (ADELE).

Interference temperature (IT) is a widely-used approach for protecting primary users (PUs) from the secondary users (SUs) in underlay cognitive radio. H owever, when multiple antennas are available at the transmitters and receivers, the spatial structure of the interference comes into play, strongly affecting the performance of the primary network. In this work, we propose interference shaping constraints as an alternative to IT-based approaches. Spatial shaping constraints take account of the structure of interference and exploit it in benefit of the secondary network. Moreover, they can be designed dynamically based on the channel conditions and performance requirements of the PUs. We first show that spatial shaping constraints generalize IT, in that the latter can be expressed as a set of isotropic shaping constraints on each interference dimension. Then, we exemplary consider a PU that has a rate requirement, and propose an algorithm for obtaining suitable shaping matrices, which can be easily modified to include primary transmitter cooperation. This algorithm is performed at the primary receiver using only local channel state information. Afterwards, we address the transceiver optimization of the SU, modeled as a multiple-input multiple-output point-to-point link, and provide optimal and suboptimal transmit covariance designs under the proposed shaping constraints. ; C. Lameiro and I. Santamaría have received funding from the Spanish Government (MICINN) under projects TEC2013-47141-C4-3- R (RACHEL), TEC2016-75067-C4-4-R (CARMEN) and FPU Grant AP2010-2189. W. Utschick receives financial support from the Deutsche Forschungsgemeinschaft (DFG) under the grant Ut36/15-1.

In this paper, a cognitive radio (CR) scenario comprised of a secondary interference channel (IC) and a primary point-to-point link (PPL) is studied, when the former interferes the latter. In order to satisfy a given rate requirement at the PPL, typical approaches impose an interference temperature constraint (IT).When the PPL transmits multiple streams, however, the spatial structure of the interference comes into play. In such cases, we show that spatial interference shaping constraints can provide higher sum-rate performance to the IC while ensuring the required rate at the PPL. Then, we extend the interference leakage minimization algorithm (MinIL) to incorporate such constraints. An additional power control step is included in the optimization procedure to improve the sum-rate when the interference alignment (IA) problem becomes infeasible due to the additional constraint. Numerical examples are provided to illustrate the effectiveness of the spatial shaping constraint in comparison to IT when the PPL transmits multiple data streams. ; The research leading to these results has received funding from the Spanish Government (MICINN) under projects TEC2010-19545-C04-03 (COSIMA), CONSOLIDER-INGENIO 2010 CSD2008-00010 (COMONSENS), and FPU Grant AP2010-2189. This research has been funded by the Deutsche Forschungsgemeinschaft (DFG) under the grant Ut36/15-1.

This paper derives the interference-temperature (IT) limit for a multi-antenna primary user (PU) with a rate constraint. While in the case of a single-antenna PU there is a one-to-one mapping between IT and achievable rate, this correspondence does not hold anymore when a multiple-input multiple-output (MIMO) system is considered. In such cases, the spatial distribution of the interference must be taken into account, since it strongly affects the PU performance. To this end, we derive a closed-form expression for the maximum IT that can be tolerated by identifying the worst-case interference covariance matrix, which results in a multilevel waterfilling problem. ; C. Lameiro and I. Santamaría have received funding from the Spanish Government (MICINN) under projects CONSOLIDER-INGENIO 2010 CSD2008-00010 (COMONSENS), TEC2013-47141-C4-3-R (RACHEL) and FPU Grant AP2010-2189. W. Utschick receives financial support from the Deutsche Forschungsgemeinschaft (DFG) under the grant Ut36/15-1.

In this letter we study the potential benefits of improper signaling for a secondary user (SU) in underlay cognitive radio networks. We consider a basic yet illustrative scenario in which the primary user (PU) always transmit proper Gaussian signals and has a minimum rate constraint. After parameterizing the SU transmit signal in terms of its power and circularity coefficient (which measures the degree of impropriety), we prove that the SU improves its rate by transmitting improper signals only when the ratio of the squared modulus between the SU-PU interference link and the SU direct link exceeds a given threshold. As a by-product of this analysis, we obtain the optimal circularity coefficient that must be used by the SU depending on its power budget. Some simulation results show that the SU benefits from the transmission of improper signals especially when the PU is not highly loaded. ; C. Lameiro and I. Santamaría have received funding from the Spanish Government (MICINN) under projects CONSOLIDER-INGENIO 2010 CSD2008-00010 (COMONSENS), TEC2013-47141-C4-3-R (RACHEL) and FPU Grant AP2010-2189; and also from the Deutscher Akademischer Austauschdienst (DAAD) under its programm "Research grants for doctoral candidates and young academics and scientists". P. Schreier receives financial support from the Alfried Krupp von Bohlen und Halbach foundation, under its program "Return of German scientists from abroad".

In this paper, the impact of improper Gaussian signaling is studied for an underlay cognitive radio (CR) scenario comprised of a primary user (PU), which has a rate constraint, and a secondary user (SU), both single-antenna. We first derive expressions for the achievable rate of the SU when it transmits proper and maximally improper Gaussian signals (assuming that the SU is solely limited by the CR constraint). These expressions depend on the channel gains to and from the SU through a single variable. Thereby, we observe that improper signaling is beneficial whenever the SU rate is below a threshold, which depends on the signal-to-noise ratio (SNR) and rate requirement of the PU. Furthermore, we provide bounds on the achievable gain that also depend only on the PU parameters. Then, the achievable rate is studied from a statistical viewpoint by deriving its cumulative distribution function considering a constant received SNR at the PU. In addition, we specialize this expression for the Z interference channel, for which the expected achievable rate is also derived. Numerical examples illustrate our claims and show that the SU may significantly benefit from using improper signaling. ; C. Lameiro and I. Santamaría have received funding from the Spanish Government (MICINN) under projects CONSOLIDER-INGENIO 2010 CSD2008-00010 (COMONSENS), TEC2013-47141-C4-3-R (RACHEL) and FPU Grant AP2010-2189; and also from the Deutscher Akademischer Austauschdienst (DAAD) under its programm "Research grants for doctoral candidates and young academics and scientists". Peter Schreier receives financial support from the Alfried Krupp von Bohlen und Halbach foundation, under its program "Return of German scientists from abroad".

Alternating minimization and steepest descent are commonly used strategies to obtain interference alignment (IA) solutions in the K-user multiple-input multiple-output (MIMO) interference channel (IC). Although these algorithms are shown to converge monotonically, they experience a poor convergence rate, requiring an enormous amount of iterations which substantially increases with the size of the scenario. To alleviate this drawback, in this letter we resort to the Gauss-Newton (GN) method, which is well-known to experience quadratic convergence when the iterates are sufficiently close to the optimum. We discuss the convergence properties of the proposed GN algorithm and provide several numerical examples showing that it always converges to the optimum with quadratic rate, reducing dramatically the required computation time in comparison to other algorithms, hence paving a new way for the design of IA algorithms. ; The authors were supported by the Spanish Government (MICINN) under projects TEC2010-19545-C04-03 (COSIMA), CONSOLIDER-INGENIO 2010 CSD2008-00010 (COMONSENS) and FPU grants AP2009-1105 and AP2010-2189.

In this paper we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for MIMO X networks (XN). The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the known solutions of a start system which can be trivially solved. The key observation leading to a simple start system is realizing that the inverse IA problem, i.e., finding the channels that satisfy the IA conditions given a set of precoders and decoders, is linear and, therefore, a convenient trivial system. Once the start system has been solved, standard prediction and correction techniques are applied to track the solution all the way to the target system. Our results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom (DoF) whereas alternating minimization techniques, which typically work well for the interference channel (IC), repeatedly fail for the XN. Further, the algorithm provides insights into the feasibility of alignment in MIMO X networks for which theoretical results are scarce. ; This work was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project COSIMA (TEC2010-19545-C04-03), project COMONSENS (CSD2008-00010, CONSOLIDER-INGENIO 2010 Program) and FPU grant AP2009-1105.

In this work we consider a two-channel passive detection problem, in which there is a surveillance array where the presence/absence of a target signal is to be detected, and a reference array that provides a noise-contaminated version of the target signal. We assume that the transmitted signal is an unknown rank-one signal, and that the noises are uncorrelated between the two channels, but each one having an unknown and arbitrary spatial covariance matrix. We show that the generalized likelihood ratio test (GLRT) for this problem rejects the null hypothesis when the largest canonical correlation of the sample coherence matrix between the surveillance and the reference channels exceeds a threshold. Further, based on recent results from random matrix theory, we provide an approximation for the null distribution of the test statistic. ; The work of I. Santamaría was supported by the Spanish Government through grants PRX14/0028 (Estancias de Movilidad de Profesores, Ministerio de Educación) and by project RACHEL (TEC2013-47141-C4-3-R) funded by the Ministerio de Economía y Competitividad (MINECO). The work of L. Scharf and D. Cochran was supported in part by a sub-contract with Matrix Research for research sponsored by the Air Force Research Laboratory under contract FA8650-14-D-1722.

The problem of estimating a low-dimensional subspace from a collection of experimentally measured subspaces arises in many applications of statistical signal processing. In this paper we address this problem, and give a solution for the average subspace that minimizes an extrinsic mean-squared error, defined by the squared Frobenius norm between projection matrices. The solution automatically returns the dimension of the optimal average subspace, which is the novel result of the paper. The proposed order fitting rule is based on thresholding the eigenvalues of the average projection matrix, and thus it is free of penalty terms or other tuning parameters commonly used by other rank estimation techniques. Several numerical examples demonstrate the usefulness and applicability of the proposed criterion, showing how the dimension of the average subspace captures the variability of the measured subspaces. ; The work of I. Santamaría was supported by the Spanish Government through grants PRX14/0028 (Estancias de Movilidad de Profesores, Ministerio de Educación) and by project RACHEL (TEC2013-47141-C4-3-R) funded by the Ministerio de Economía y Competitividad (MINECO). The work of L. L. Scharf was supported by the National Science Foundation (NSF) under grant CCF-1018472.

The spectrum sensing accuracy has been improved by the introduction of cooperative spectrum sensing (CSS) strategies where the spatial diversity is exploited among nonlegacy users. However, these CSS strategies also bring new impairments, such as the interference from other sources that severely degrade the sensing performance. In this paper, we evaluate experimentally our recent proposal for CSS based on kernel canonical correlation analysis (KCCA), where the effect of an interferer is also modeled. The experiments are conducted on a cognitive radio platform composed of several Universal Radio Peripheral (USRP) nodes, and the measurements show that our scheme is able of implicitly learning the surrounding environment by only exploiting the non-linear correlation among the receiver signals of each SU. Eventually, we provide comparative results where a considerable gain over a conventional energy detector is obtained in spite of the impairments provoked by external interferers. ; The research leading to these results has received funding from the Spanish Government (MICINN) under projects TEC2010-19545-C04-03 (COSIMA) and CONSOLIDERINGENIO 2010 CSD2008-00010 (COMONSENS).

In this paper, a new technique for the blind estimation of frequency and/or time-selective multiple-input multiple-output (MIMO) channels under space-time block coding (STBC) transmissions is presented. The proposed method relies on a basis expansion model (BEM) of the MIMO channel, which reduces the number of parameters to be estimated, and includes many practical STBC-based transmission scenarios, such as STBC-orthogonal frequency division multiplexing (OFDM), space-frequency block coding (SFBC), time-reversal STBC, and time-varying STBC encoded systems. Inspired by the unconstrained blind maximum likelihood (UML) decoder, the proposed criterion is a subspace method that efficiently exploits all the information provided by the STBC structure, as well as by the reduced-rank representation of the MIMO channel. The method, which is independent of the specific signal constellation, is able to blindly recover the MIMO channel within a small number of available blocks at the receiver side. In fact, for some particular cases of interest such as orthogonal STBC-OFDM schemes, the proposed technique blindly identifies the channel using just one data block. The complexity of the proposed approach reduces to the solution of a generalized eigenvalue (GEV) problem and its computational cost is linear in the number of sub-channels. An identifiability analysis and some numerical examples illustrating the performance of the proposed algorithm are also provided ; This work was supported by the Spanish Government under projects TEC2007-68020-C04-02/TCM (MultiMIMO) and CONSOLIDER-INGENIO 2010 CSD2008-00010 (COMONSENS).

This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector-valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover, using Wijsman's theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Loe`ve spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic GLRT and LMPIT. This goes beyond the state-of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra. ; The work of P. Schreier was supported by the Alfried Krupp von Bohlen und Halbach Foundation, under its program "Return of German scientists from abroad". The work of I. Santamaría and J. Vía was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project RACHEL (TEC2013-47141-C4-3-R). The work of L. Scharf was supported by the Airforce Office of Scientific Research under contract FA9550-10-1-0241.