A.L.F. de Almeida

A Constrained Factor Decomposition With Application to MIMO Antenna Systems

In this paper, we formulate a new tensor decomposition herein called constrained factor (CONFAC) decomposition. It consists in decomposing a third-order tensor into a triple sum of rank-one tensor factors, where interactions involving the components of different tensor factors are allowed. The interaction pattern is controlled by three constraint matrices the columns of which are canonical vectors. Each constraint matrix is associated with a given dimension, or mode, of the tensor. The explicit use of these constraint matrices provides degrees of freedom to the CONFAC decomposition for modeling tensor signals with constrained structures which cannot be handled with the standard parallel factor (PARAFAC) decomposition. The uniqueness of this decomposition is discussed and an application to multiple-input multiple-output (MIMO) antenna systems is presented. A new transmission structure is proposed, the core of which consists of a precoder tensor decomposed as a function of the CONFAC constraint matrices. By adjusting the precoder constraint matrices, we can control the allocation of data streams and spreading codes to transmit antennas. Based on a CONFAC model of the received signal, blind symbol/code/channel recovery is possible using the alternating least squares algorithm. For illustrating this application, we evaluate the bit-error-rate (BER) performance for some configurations of the precoder constraint matrices.

Space-Time Multiplexing Codes: A Tensor Modeling Approach

In this paper, we present new space-time multiplexing codes (STMC) for multiple-antenna transmissions, which rely on a three-dimensional tensor modeling of the transmitted/received signals. The proposed codes combine spatial multiplexing and space-time coding by spreading a linear combination of different sub-streams of data over the space and time dimensions. We show the STMC induces a tensor structure on the transmitted/received signal that can be modeled using a trilinear tensor decomposition. Tensor modeling is exploited at the receiver for a blind decoding of the transmitted sub-streams based on linear processing and without any ambiguity. The proposed approach also provides full diversity while benefiting from the maximum multiplexing gain offered by the multiple antennas. Simulation results show that the tensor-based STMC offer remarkable performance with good diversity-multiplexing trade-off

Blind Identification of Underdetermined Mixtures Based on the Characteristic Function: The Complex Case

Blind identification of underdetermined mixtures can be addressed efficiently by using the second ChAracteristic Function (CAF) of the observations. Our contribution is twofold. First, we propose the use of a Levenberg-Marquardt algorithm, herein called LEMACAF, as an alternative to an Alternating Least Squares algorithm known as ALESCAF, which has been used recently in the case of real mixtures of real sources. Second, we extend the CAF approach to the case of complex sources for which the previous algorithms are not suitable. We show that the complex case involves an appropriate tensor stowage, which is linked to a particular tensor decomposition. An extension of the LEMACAF algorithm, called then proposed to blindly estimate the mixing matrix by exploiting this tensor decomposition. In our simulation results, we first provide performance comparisons between third- and fourth-order versions of ALESCAF and LEMACAF in various situations involving BPSK sources. Then, a performance study of is carried out considering 4-QAM sources. These results show that the proposed algorithm provides satisfying estimations especially in the case of a large underdeterminacy level.

Unified Tensor Modeling for Blind Receivers in Multiuser Uplink Cooperative Systems

In this letter, we present new blind receivers for uplink multiuser cooperative diversity systems. Considering amplify-and-forward (AF), fixed decode-and-forward (FDF), and selective decode-and-forward (SDF) relaying protocols, the proposed receivers exploits a unified formulation of the received signal as a CANDECOMP/PARAFAC (CP) model with dimensions receive antenna ×cooperative branch × symbol period. Under the assumption that channel state information (CSI) is not available neither at the relays nor at the base station, the proposed receiver jointly and blindly estimates the transmitted symbols and channel parameters. In addition to avoiding the use of pilots symbols, the CP-based receiver can operate with less base station antennas than users or, alternatively, with a single relay per user.

Tensor-Based Space-Time Multiplexing Codes for MIMO-OFDM Systems with Blind Detection

A new approach to space-time-frequency coding for multiple-input multiple-output (MIMO) systems based on orthogonal frequency division multiplexing (OFDM) is presented. Tensor-based space-time-multiplexing (TSTM) codes combine multi-stream spatial multiplexing and transmit diversity, and are based on a tensor modeling of the transmitted/received signals. The proposed codes are designed to offer some transmission flexibility by allowing a simple multiplexing-diversity-rate control as well as to achieve full space and multipath diversities in a frequency-selective channel. We show that the received signal has a tensor structure and this tensor modeling is exploited for blind separation/decoding of the transmitted information. Simulation results illustrate the performance of some TSTM codes with blind detection

Double Khatri–Rao Space-Time-Frequency Coding Using Semi-Blind PARAFAC Based Receiver

We first introduce a new class of tensor models for fourth-order tensors, referred to as “nested PARAFAC models.” Then, we present a space-time-frequency (STF) coding scheme for multiple antenna orthogonal frequency division multiplexing systems. This scheme, called double Khatri-Rao STF (D-KRSTF) coding, combines time-domain spreading with space-frequency precoding and provides an extension of Khatri-Rao space-time (KRST) coding . We show that the received signals define a fourth-order tensor satisfying two nested PARAFAC models, and a semi-blind receiver is then derived using a two-step alternating least squares algorithm for joint channel and symbol estimation. Simulation results show that our receiver offers superior performance compared with previously proposed tensor-based solutions and operates close to the zero forcing receiver with perfect channel state information.

Distributed parafac based DS-CDMA blind receiver for wireless sensor networks

In this paper, we consider a collaborative scheme in wireless sensor networks where the multiple access protocol is a DS-CDMA one. When the receiver is equipped with an antenna array, it has been shown that efficient blind receivers can be derived using the PARAFAC tensor model. In general, the parameters of the PARAFAC model are fitted using an alternating least squares algorithm. Herein, we consider the case where each receiver has a single antenna. Therefore, by allowing collaboration in a predefined neighborhood, we derive a distributed alternating least squares algorithm including some average consensus steps.

CONFAC Decomposition Approach to Blind Identification of Underdetermined Mixtures Based on Generating Function Derivatives

This work proposes a new tensor-based approach to solve the problem of blind identification of underdetermined mixtures of complex-valued sources exploiting the cumulant generating function (CGF) of the observations. We show that a collection of second-order derivatives of the CGF of the observations can be stored in a third-order tensor following a constrained factor (CONFAC) decomposition with known constrained structure. In order to increase the diversity, we combine three derivative types into an extended third-order CONFAC decomposition. A detailed uniqueness study of this decomposition is provided, from which easy-to-check sufficient conditions ensuring the essential uniqueness of the mixing matrix are obtained. From an algorithmic viewpoint, we develop a CONFAC-based enhanced line search (CONFAC-ELS) method to be used with an alternating least squares estimation procedure for accelerated convergence, and also analyze the numerical complexities of two CONFAC-based algorithms (namely, CONFAC-ALS and CONFAC-ELS) in comparison with the Levenberg-Marquardt (LM)-based algorithm recently derived to solve the same problem. Simulation results compare the proposed approach with some higher-order methods. Our results also corroborate the advantages of the CONFAC-based approach over the competing LM-based approach in terms of performance and computational complexity.

Improved Data-Aided Channel Estimation in LTE PUCCH Using a Tensor Modeling Approach

NA In 3rd. Generation Partnership Project (3GPP) Long Term Evolution (LTE) systems, when no resources has been assigned in the uplink to a given user, the control information associated with Layers 1 and 2 in the protocol stack is conveyed back to the LTE base station (also known as eNodeB) through the so-called Physical Uplink Control Channel (PUCCH). In this work we consider the Format 2 of LTE PUCCH which conveys information about the channel status. At the eNodeB, conventional receivers generally resort to reference signals (RS), or pilot symbols, to perform channel estimation prior to symbol detection. In this paper, we propose a tensor modeling approach for a Data-Aided (DA) channel estimation in PUCCH. First, we formulate the practical channel estimation problem in PUCCH using the Parallel Factor (PARAFAC) tensor model. Based in this model, we resort to the Alternating Least Squares (ALS) algorithm as a DA-based channel estimator. Contrary to conventional RS-based channel estimation operating only on reference signals, the proposed algorithm also simultaneously exploits the energy of the data symbols of all the users, which is contained in PUCCH slots in order to iteratively estimate the user channel coefficients. As will be shown in our simulation results, improved channel estimation accuracy is obtained.

Generalized PARAFAC Model for Multidimensional Wireless Communications with Application to Blind Multiuser Equalization

In this work we develop a new tensor modeling approach for multiuser wireless communication systems where the received signal has a multidimensional nature. The proposed tensor model follows from a third-order (3D) Block-Parallel Factor (Block-PARAFAC) decomposition with factor interactions, which can be viewed as a more general model than the standard model (1), (2). The proposed tensor decomposition aims at unifying the received signal modeling for i) Temporally-Oversampled, ii) Direct-Sequence Code Division Multiple Access (DS-CDMA) and iii) Orthogonal Frequency Division Multiplexing (OFDM) systems. This modeling approach assumes a receiver antenna array, specular multipath propagation and frequency-selectivity. We show that the model for each of the considered systems can be derived from the Block-PARAFAC model by making appropriate choices in its dimensions and/or structure. As an application of the proposed tensor model to blind multiuser separation/equalization, a new receiver algorithm is derived. I. INTRODUCTION