Hybrid Joint Diagonalization Algorithms

This paper deals with a hybrid joint diagonalization (JD) problem considering both Hermitian and transpose congruences. Such problem can be encountered in certain non-circular signal analysis applications including blind source separation. We introduce new Jacobi-like algorithms using Givens or a combination of Givens and hyperbolic rotations. These algorithms are compared with state-of-the-art methods and their performance gain, especially in the high dimensional case, is assessed through simulation experiments including examples related to blind separation of non-circular sources.Comment: Supplementary material (ref. [18]) is included in this fil

Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization

Here we focus on the measurement induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement induced nonlocality and has analytic expressions for many quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost analytic expressions for any quantum state, which can also shed light on other aspects in physics

FastFCA-AS: Joint Diagonalization Based Acceleration of Full-Rank Spatial Covariance Analysis for Separating Any Number of Sources

Here we propose FastFCA-AS, an accelerated algorithm for Full-rank spatial Covariance Analysis (FCA), which is a robust audio source separation method proposed by Duong et al. ["Under-determined reverberant audio source separation using a full-rank spatial covariance model," IEEE Trans. ASLP, vol. 18, no. 7, pp. 1830-1840, Sept. 2010]. In the conventional FCA, matrix inversion and matrix multiplication are required at each time-frequency point in each iteration of an iterative parameter estimation algorithm. This causes a heavy computational load, thereby rendering the FCA infeasible in many applications. To overcome this drawback, we take a joint diagonalization approach, whereby matrix inversion and matrix multiplication are reduced to mere inversion and multiplication of diagonal entries. This makes the FastFCA-AS significantly faster than the FCA and even applicable to observed data of long duration or a situation with restricted computational resources. Although we have already proposed another acceleration of the FCA for two sources, the proposed FastFCA-AS is applicable to an arbitrary number of sources. In an experiment with three sources and three microphones, the FastFCA-AS was over 420 times faster than the FCA with a slightly better source separation performance.Comment: Submitted to IWAENC201

Sliced Average Variance Estimation for Multivariate Time Series

Supervised dimension reduction for time series is challenging as there may be temporal dependence between the response $y$ and the predictors $\boldsymbol x$. Recently a time series version of sliced inverse regression, TSIR, was suggested, which applies approximate joint diagonalization of several supervised lagged covariance matrices to consider the temporal nature of the data. In this paper we develop this concept further and propose a time series version of sliced average variance estimation, TSAVE. As both TSIR and TSAVE have their own advantages and disadvantages, we consider furthermore a hybrid version of TSIR and TSAVE. Based on examples and simulations we demonstrate and evaluate the differences between the three methods and show also that they are superior to apply their iid counterparts to when also using lagged values of the explaining variables as predictors

Prescient Precoding in Heterogeneous DSA Networks with Both Underlay and Interweave MIMO Cognitive Radios

This work examines a novel heterogeneous dynamic spectrum access network where the primary users (PUs) coexist with both underlay and interweave cognitive radios (ICRs); all terminals being potentially equipped with multiple antennas. Underlay cognitive transmitters (UCTs) are allowed to transmit concurrently with PUs subject to interference constraints, while the ICRs employ spectrum sensing and are permitted to access the shared spectrum only when both PUs and UCTs are absent. We investigate the design of MIMO precoding algorithms for the UCT that increase the detection probability at the ICRs, while simultaneously meeting a desired Quality-of-Service target to the underlay cognitive receivers (UCRs) and constraining interference leaked to PUs. The objective of such a proactive approach, referred to as prescient precoding, is to minimize the probability of interference from ICRs to the UCRs and primary receivers due to imperfect spectrum sensing. We begin with downlink prescient precoding algorithms for multiple single-antenna UCRs and multi-antenna PUs/ICRs. We then present prescient block-diagonalization algorithms for the MIMO underlay downlink where spatial multiplexing is performed for a plurality of multi-antenna UCRs. Numerical experiments demonstrate that prescient precoding by UCTs provides a pronounced performance gain compared to conventional underlay precoding strategies.Comment: 23 pages; Submitted to IEEE Trans. Wireless Commu

Beamforming for Multiuser Massive MIMO Systems: Digital versus Hybrid Analog-Digital

This paper designs a novel hybrid (a mixture of analog and digital) beamforming and examines the relation between the hybrid and digital beamformings for downlink multiuser massive multiple input multiple output (MIMO) systems. We assume that perfect channel state information is available only at the transmitter and we consider the total sum rate maximization problem. For this problem, the hybrid beamforming is designed indirectly by considering a weighed sum mean square error (WSMSE) minimization problem incorporating the solution of digital beamforming which is obtained from the block diagonalization technique. The resulting WSMSE problem is solved by applying the theory of compressed sensing. The relation between the hybrid and digital beamformings is studied numerically by varying different parameters, such as the number of radio frequency (RF) chains, analog to digital converters (ADCs) and multiplexed symbols. Computer simulations reveal that for the given number of RF chains and ADCs, the performance gap between digital and hybrid beamformings can be decreased by decreasing the number of multiplexed symbols. Moreover, for the given number of multiplexed symbols, increasing the number of RF chains and ADCs will increase the total sum rate of the hybrid beamforming which is expected.Comment: Accepted for publication in GLOBECOM 2014, Texas,USA See my personal web page for matlab code (via google scholar

Study of Opportunistic Cooperation Techniques using Jamming and Relays for Physical-Layer Security in Buffer-aided Relay Networks

In this paper, we investigate opportunistic relay and jammer cooperation schemes in multiple-input multiple-output (MIMO) buffer-aided relay networks. The network consists of one source, an arbitrary number of relay nodes, legitimate users and eavesdroppers, with the constraints of physical layer security. We propose an algorithm to select a set of relay nodes to enhance the legitimate users' transmission and another set of relay nodes to perform jamming of the eavesdroppers. With Inter-Relay interference (IRI) taken into account, interference cancellation can be implemented to assist the transmission of the legitimate users. Secondly, IRI can also be used to further increase the level of harm of the jamming signal to the eavesdroppers. By exploiting the fact that the jamming signal can be stored at the relay nodes, we also propose a hybrid algorithm to set a signal-to-interference and noise ratio (SINR) threshold at the node to determine the type of signal stored at the relay node. With this separation, the signals with high SINR are delivered to the users as conventional relay systems and the low SINR performance signals are stored as potential jamming signals. Simulation results show that the proposed techniques obtain a significant improvement in secrecy rate over previously reported algorithms.Comment: 8 pages, 3 figure

Spectral Learning for Supervised Topic Models

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte Carlo sampling, which often suffers from the local minimum defect. Spectral methods have been applied to learn unsupervised topic models, such as latent Dirichlet allocation (LDA), with provable guarantees. This paper investigates the possibility of applying spectral methods to recover the parameters of supervised LDA (sLDA). We first present a two-stage spectral method, which recovers the parameters of LDA followed by a power update method to recover the regression model parameters. Then, we further present a single-phase spectral algorithm to jointly recover the topic distribution matrix as well as the regression weights. Our spectral algorithms are provably correct and computationally efficient. We prove a sample complexity bound for each algorithm and subsequently derive a sufficient condition for the identifiability of sLDA. Thorough experiments on synthetic and real-world datasets verify the theory and demonstrate the practical effectiveness of the spectral algorithms. In fact, our results on a large-scale review rating dataset demonstrate that our single-phase spectral algorithm alone gets comparable or even better performance than state-of-the-art methods, while previous work on spectral methods has rarely reported such promising performance

Spectral Efficiency Optimization For Millimeter Wave Multi-User MIMO Systems

As a key enabling technology for 5G wireless, millimeter wave (mmWave) communication motivates the utilization of large-scale antenna arrays for achieving highly directional beamforming. However, the high cost and power consumption of RF chains stands in the way of adoption of the optimal fullydigital precoding in large-array systems. To reduce the number of RF chains while still maintaining the spatial multiplexing gain of large-array, hybrid precoding architecture has been proposed for mmWave systems and received considerable interest in both industry and academia. However, the optimal hybrid precoding design has not been fully understood, especially for the multi-user MIMO case. This paper is the first work that directly addresses the nonconvex hybrid precoding problem of mmWave multi-user MIMO systems (without any approximation) by using penalty dual decomposition (PDD) method. The proposed PDD method have a guaranteed convergence to KKT solutions of the hybrid precoding problem under a mild assumption. Simulation results show that, even when both the transmitter and the receivers are equipped with the fewest RF chains that are required to support multi-stream transmission, hybrid precoding can still approach the performance of fully-digital precoding in both the infinite resolution phase shifter case and the finite resolution phase shifter case with several bits quantization.Comment: The first draft of this paper was finished when I was at Iowa in 201

Dynamical Deformation of Toroidal Matrix Varieties

In this document we study the local connectivity of the sets whose elements are $m$-tuples of pairwise commuting normal matrix contractions. Given $\varepsilon>0$, we prove that there is $\delta>0$ such that for any two $m$-tuples of pairwise commuting normal matrix contractions $\mathbf{X}:=(X_1,\ldots,X_m)$ and $\tilde{\mathbf{X}}:=(\tilde{X}_1,\ldots,\tilde{X}_m)$ that are $\delta$-close with respect to some suitable distance $\eth$ in $(\mathbb{C}^{n\times n})^m$, we can find a $m$-tuple of matrix paths (homotopies) connecting $\mathbf{X}$ to $\mathbf{\tilde{X}}$ relative to the intersection of some $\varepsilon,\eth$-neighborhood of $\mathbf{X}$ with the set of $m$-tuples of pairwise commuting normal matrix contractions. One of the key features of these matrix homotopies is that $\delta$ can be chosen independent of $n$. Some connections with topology and numerical matrix analysis will be outlined as well