Source enumeration in non-white noise and small sample size via subspace averaging

This paper addresses the problem of source enumeration by an array of sensors in the challenging conditions of: i) large uniform arrays with few snapshots, and ii) non-white or spatially correlated noises with arbitrary correlation. To solve this problem, we combine a subspace averaging (SA) technique, recently proposed for the case of independent and identically distributed (i.i.d.) noises, with a majority vote approach. The number of sources is detected for increasing dimensions of the SA technique and then a majority vote is applied to determine the final estimate. As illustrated by some simulation examples, this simple modification makes SA a very robust method of enumerating sources in these challenging scenarios.This work was supported by the Ministerio de Economía y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grants TEC2016-75067-C4-4-R (CARMEN) and BES-2017-080542

Multi-output kernel adaptive filtering with reduced complexity

In this paper, two new multi-output kernel adaptive filtering algorithms are developed that exploit the temporal and spatial correlations among the input-output multivariate time series. They are multi-output versions of the popular kernel least mean squares (KLMS) algorithm with two different sparsification criteria. The first one, denoted as MO-QKLMS, uses the coherence criterion in order to limit the dictionary size. The second one, denoted as MO-RFF-KLMS, uses random Fourier features (RFF) to approximate the kernel functions by linear inner products. Simulation results with synthetic and real data are presented to assess convergence speed, steady-state performance and complexities of the proposed algorithms.This work was supported by the Ministerio de Ciencia, Innovación y Universidades and AEI/FEDER funds of the E.U., under grant PID2019-104958RB-C43 (ADELE)

Flexible duplexing for maximum downlink rate in multi-tier MIMO networks

In this paper, we propose an algorithm to maximize downlink rate performance in the context of multiple-input multiple-output (MIMO) Heterogeneous Networks (HetNets). Specifically, we evaluate the benefits of flexible duplexing, a promising strategy that consists in combining uplink and downlink cells within the same channel use. In order to handle intercell interference, we rely on the interference alignment (IA) technique, taking into account the impact of the channel estimation errors on the inter-cell interference leakage. Determining the best uplink/downlink configuration is a combinatorial problem, and therefore we consider several approaches to reduce the computational demands of the problem. First, we use a statistical characterization for the average rates achieved by IA in order to avoid the calculation of alignment solutions for all possible settings in the network. Additionally, we propose two hierarchical switching (HS) strategies so that only a subset among the total number of combinations is explored. As a performance baseline, we include in the comparison the conventional time division duplex (TDD) approach and the well-known minimum mean square error (MMSE) decoder. The obtained results show that downlink rates achieved by implementing flexible duplexing and applying inter-cell IA significantly outperform conventional TDD transmissions. Finally, the proposed hierarchical schemes are shown to obtain almost the same rates as exhaustive search with much lower computational cost.This work has been supported by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain under grant TEC2016-75067-C4-4-R (CARMEN), and FPI grant BES-2014-069786

On the spatial degrees of freedom benefits of reverse TDD in multicell MIMO networks

In this paper we study the degrees of freedom (DoF) achieved by interference alignment (IA) for cellular networks in reverse time division duplex (R-TDD) mode, a new configuration associated to heterogeneous networks. We derive a necessary feasibility condition for interference alignment in the multi-cell R-TDD scenario, which is then specialized to the particular case of symmetric demands and antenna distribution. We show that, for those symmetric networks for which the properness condition holds with equality, R-TDD does not improve the DoF performance of conventional synchronous TDD systems. Nevertheless, our simulation results indicate that, in more asymmetric scenarios, significant DoF benefits can be achieved by applying the R-TDD approach.This work has been supported by the Ministerio de Economía y Competitividad (MINECO) of Spain under grant TEC2013-47141- C4-R (RACHEL project) and FPI grant BES-2014-069786

Balanced Least Squares: Linear model estimation with noisy inputs

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)

Balanced least squares: estimation in linear systems with noisy inputs and multiple outputs

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

Efficient SER estimation for MIMO detectors via importance sampling schemes

In this paper we propose two importance sampling methods for the efficient symbol error rate (SER) estimation of maximum likelihood (ML) multiple-input multiple-output (MIMO) detectors. Conditioned to a given transmitted symbol, computing the SER requires the evaluation of an integral outside a given polytope in a high-dimensional space, for which a closed-form solution does not exist. Therefore, Monte Carlo (MC) simulation is typically used to estimate the SER, although a naive or raw MC implementation can be very inefficient at high signal-to-noise-ratios or for systems with stringent SER requirements. A reduced variance estimator is provided by the Truncated Hypersphere Importance Sampling (THIS) method, which samples from a proposal density that excludes the largest hypersphere circumscribed within the Voronoi region of the transmitted vector. A much more efficient estimator is provided by the existing ALOE (which stands for "At Least One rare Event") method, which samples conditionally on an error taking place. The paper describes in detail these two IS methods, discussing their advantages and limitations, and comparing their performances.The work of V. Elvira was partially supported by Agence Nationale de la Recherche of France under PISCES project (ANR-17-CE40-0031-01) and the French-American Fulbright Commission. The work of I. Santamaria was partly supported by the Ministerio de Econom´ıa y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grant TEC2016-75067-C4-4-R (CARMEN)

An efficient sampling scheme for the eigenvalues of dual wishart matrices

Despite the numerous results in the literature about the eigenvalue distributions of Wishart matrices, the existing closed-form probability density function (pdf) expressions do not allow for efficient sampling schemes from such densities. In this letter, we present a stochastic representation for the eigenvalues of 2×2 complex central uncorrelated Wishart matrices with an arbitrary number of degrees of freedom (referred to as dual Wishart matrices). The draws from the joint pdf of the eigenvalues are generated by means of a simple transformation of a chi-squared random variable and an independent beta random variable. Moreover, this stochastic representation allows a simple derivation, alternative to those already existing in the literature, of some eigenvalue function distributions such as the condition number or the ratio of the maximum eigenvalue to the trace of the matrix. The proposed sampling scheme may be of interest in wireless communications and multivariate statistical analysis, where Wishart matrices play a central role.The work of Ignacio Santamaria was supported in part by the Ministerio de Ciencia e Innovación and AEI/10.13039/501100011033, under Grant PID2019-104958RB-C43 (ADELE). The work of Víctor Elvira was supported in part by the Agence Nationale de la Recherche of France PISCES under Grant ANR-17-CE40-0031-01, and in part by the ARL/ARO under Grant W911NF-20-1-0126

Adaptive clustering algorithm for cooperative spectrum sensing in mobile environments

In this work we propose a new adaptive algorithm for cooperative spectrum sensing in dynamic environments where the channels are time varying. We assume a centralized spectrum sensing procedure based on the soft fusion of the signal energy levels measured at the sensors. The detection problem is posed as a composite hypothesis testing problem. The unknown parameters are estimated by means of an adaptive clustering algorithm that operates over the most recent energy estimates reported by the sensors to the fusion center. The algorithm does not require all sensors to report their energy estimates, which makes it suited to be used with any sensor selection strategy (active sensing). Simulation results show the feasibility and efficiency of the method in realistic slow-fading environments.This work has been funded by SODERCAN and Programa Operativo FEDER under grant CAIMAN - 12.JU01.64661, and by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grants TEC2017-86921-C2-1-R (CAIMAN), TEC2013-47141-C4-R (RACHEL) and TEC2016-75067- C4-4-R (CARMEN)

Statistical analysis of single-beam interference alignment schemes

In this work, we derive analytical approximate expressions for the user rates achievable by interference alignment (IA) algorithms in single-beam multiple-input multiple-output (MIMO) networks for a fixed channel realization. Unlike previous works that perform a large-system analysis in which the number of users, antennas, or streams is required to tend to infinity, in this paper we only require that the number of different IA solutions (precoders and decoders) for the given scenario is sufficiently high, which typically happens even for moderate-size feasible networks. Based on the assumption that the IA beamformers for a given channel realization are random vectors isotropically distributed on the complex unit sphere, we characterize the user rates by averaging over the (possible finite) set of IA solutions. Some simulation results show the accuracy of the proposed rate expressions.This work was supported by the Ministerio de Economía y Competitividad (MINECO), Spain, under project RACHEL (TEC2013-47141-C4-3-R) and FPI grant BES-2014-069786