Overview of Constrained PARAFAC Models

In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between different modes of the tensor which are captured by the equivalent core tensor. Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first introduced. This Kronecker product based approach is also formulated in terms of the index notation, which provides an original and concise formalism for both matricizing tensors and writing tensor models. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for $N^{th}$ order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models

Semi-blind channel estimation for multiuser OFDM-IDMA systems.

M. Sc. Eng. University of KwaZulu-Natal, Durban 2014.Over the last decade, the data rate and spectral efficiency of wireless mobile communications have been significantly enhanced. OFDM technology has been used in the development of advanced systems such as 3GPP LTE and terrestrial digital TV broadcasting. In general, bits of information in mobile communication systems are conveyed through radio links to receivers. The radio channels in mobile radio systems are usually multipath fading channels, which cause inter-symbol interference (ISI) in the received signal. The ability to know the channel impulse response (CIR) and Channel State Information (CSI) helps to remove the ISI from the signal and make coherent detection of the transmitted signal at the receiver end of the system easy and simple. The information about CIR and CSI are primarily provided by channel estimation. This thesis is focused on the development of multiple access communication technique, Multicarrier Interleave Division Multiple Access (MC-IDMA) and the corresponding estimation of the system channel. It compares various efficient channel estimation algorithms. Channel estimation of OFDM-IDMA scheme is important because the emphasis from previous studies assumed the implementation of MC-IDMA in a perfect scenario, where Channel State Information (CSI) is known. MC-IDMA technique incorporates three key features that will be common to the next generation communication systems; multiple access capability, resistance to multipath fading and high bandwidth efficiency. OFDM is almost completely immune to multipath fading effects and IDMA has a recently proposed multiuser capability scheme which employs random interleavers as the only method for user separation. MC-IDMA combines the features of OFDM and IDMA to produce a system that is Inter Symbol Interference (ISI) free and has higher data rate capabilities for multiple users simultaneously. The interleaver property of IDMA is used by MC-IDMA as the only means by which users are separated at the receiver and also its entire bandwidth expansion is devoted to low rate Forward Error Correction (FEC). This provides additional coding gain which is not present in conventional Multicarrier Multiuser systems, (MC-MU) such as Code Division Multiple Access (CDMA), Multicarrier-Code Division Multiple Access (MC-CDMA) systems, and others. The effect of channel fading and both cross-cell and intra-cell Multiple Access Interference (MAI) in MC-IDMA is suppressed efficiently by its low-cost turbo-type Chip-by-Chip (CBC) multiuser detection algorithm. We present the basic principles of OFDM-IDMA transmitter and receiver. Comparative studies between Multiple Access Scheme such as Frequency Division Multiple Access (FDMA), Time Division Multiple Access (TDMA), CDMA and IDMA are carried out. A linear Minimum Mean Square Error (MMSE)-based estimation algorithm is adopted and implemented. This proposed algorithm is a non-data aided method that focuses on obtaining the CSI, remove ISI and reduce the complexity of the MMSE algorithm. However, to obtain a better and improved system performance, an improved MMSE algorithm and simplified MMSE using the structured correlation and reduced auto-covariance matrix are developed in this thesis and proposed for implementation of semi-blind channel estimation in OFDM-IDMA communication systems. The effectiveness of the adopted and proposed algorithms are implemented in a Rayleigh fading multipath channel with varying mobile speeds thus demonstrating the performance of the system in a practical scenario. Also, the implemented algorithms are compared to ascertain which of these algorithms offers a better and more efficient system performance, and with less complexity. The performance of the channel estimation algorithm is presented in terms of the mean square error (MSE) and bit error rate (BER) in both slow fading and fast fading multipath scenarios and the results are documented as well

Approximate Rank-Detecting Factorization of Low-Rank Tensors

We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the gold standard PARAFAC over which it has the advantages that it can intrinsically detect the true rank, avoids spurious components, and is stable with respect to outliers and non-Gaussian noise

Multiuser MIMO-OFDM for Next-Generation Wireless Systems

This overview portrays the 40-year evolution of orthogonal frequency division multiplexing (OFDM) research. The amelioration of powerful multicarrier OFDM arrangements with multiple-input multiple-output (MIMO) systems has numerous benefits, which are detailed in this treatise. We continue by highlighting the limitations of conventional detection and channel estimation techniques designed for multiuser MIMO OFDM systems in the so-called rank-deficient scenarios, where the number of users supported or the number of transmit antennas employed exceeds the number of receiver antennas. This is often encountered in practice, unless we limit the number of users granted access in the base station’s or radio port’s coverage area. Following a historical perspective on the associated design problems and their state-of-the-art solutions, the second half of this treatise details a range of classic multiuser detectors (MUDs) designed for MIMO-OFDM systems and characterizes their achievable performance. A further section aims for identifying novel cutting-edge genetic algorithm (GA)-aided detector solutions, which have found numerous applications in wireless communications in recent years. In an effort to stimulate the cross pollination of ideas across the machine learning, optimization, signal processing, and wireless communications research communities, we will review the broadly applicable principles of various GA-assisted optimization techniques, which were recently proposed also for employment inmultiuser MIMO OFDM. In order to stimulate new research, we demonstrate that the family of GA-aided MUDs is capable of achieving a near-optimum performance at the cost of a significantly lower computational complexity than that imposed by their optimum maximum-likelihood (ML) MUD aided counterparts. The paper is concluded by outlining a range of future research options that may find their way into next-generation wireless systems