Joint Covariance Estimation with Mutual Linear Structure

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered populations with different covariances, our aim is to determine the mutual structure of these covariance matrices and estimate them. Supposing that the covariances span a low dimensional affine subspace in the space of symmetric matrices, we develop a new efficient algorithm discovering the structure and using it to improve the estimation. Our technique is based on the application of principal component analysis in the matrix space. We also derive an upper performance bound of the proposed algorithm in the Gaussian scenario and compare it with the Cramer-Rao lower bound. Numerical simulations are presented to illustrate the performance benefits of the proposed method

Cluster-based cooperative subcarrier sensing using antenna diversity-based weighted data fusion

Cooperative spectrum sensing (CSS) is used in cognitive radio (CR) networks to improve the spectrum sensing performance in shadow fading environments. Moreover, clustering in CR networks is used to reduce reporting time and bandwidth overhead during CSS. Thus, cluster-based cooperative spectrum sensing (CBCSS) has manifested satisfactory spectrum sensing results in harsh environments under processing constraints. On the other hand, the antenna diversity of multiple input multiple output CR systems can be exploited to further improve the spectrum sensing performance. This paper presents the CBCSS performance in a CR network which is comprised of single- as well as multiple-antenna CR systems. We give theoretical analysis of CBCSS for orthogonal frequency division multiplexing signal sensing and propose a novel fusion scheme at the fusion center which takes into account the receiver antenna diversity of the CRs present in the network. We introduce the concept of weighted data fusion in which the sensing results of different CRs are weighted proportional to the number of receiving antennas they are equipped with. Thus, the receiver diversity is used to the advantage of improving spectrum sensing performance in a CR cluster. Simulation results show that the proposed scheme outperforms the conventional CBCSS scheme

Bayesian variable selection with shrinking and diffusing priors

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the well-known spike and slab Gaussian priors with a distinct feature, that is, the prior variances depend on the sample size through which appropriate shrinkage can be achieved. We show the strong selection consistency of the proposed method in the sense that the posterior probability of the true model converges to one even when the number of covariates grows nearly exponentially with the sample size. This is arguably the strongest selection consistency result that has been available in the Bayesian variable selection literature; yet the proposed method can be carried out through posterior sampling with a simple Gibbs sampler. Furthermore, we argue that the proposed method is asymptotically similar to model selection with the $L_0$ penalty. We also demonstrate through empirical work the fine performance of the proposed approach relative to some state of the art alternatives.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1207 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Modeling Heterogeneous Network Interference Using Poisson Point Processes

Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complicated, making evaluation of different communication strategies challenging in both analysis and simulation. Leveraging recent applications of stochastic geometry to analyze cellular systems, this paper proposes to analyze downlink performance in a fixed-size cell, which is inscribed within a weighted Voronoi cell in a Poisson field of interferers. A nearest out-of-cell interferer, out-of-cell interferers outside a guard region, and cross-tier interference are included in the interference calculations. Bounding the interference power as a function of distance from the cell center, the total interference is characterized through its Laplace transform. An equivalent marked process is proposed for the out-of-cell interference under additional assumptions. To facilitate simplified calculations, the interference distribution is approximated using the Gamma distribution with second order moment matching. The Gamma approximation simplifies calculation of the success probability and average rate, incorporates small-scale and large-scale fading, and works with co-tier and cross-tier interference. Simulations show that the proposed model provides a flexible way to characterize outage probability and rate as a function of the distance to the cell edge.Comment: Submitted to the IEEE Transactions on Signal Processing, July 2012, Revised December 201

A design study for an optimal non-linear receiver/demodulator Final report

Design study for optimal nonlinear receiver demodulato