Eigenvalue Dynamics of a Central Wishart Matrix with Application to MIMO Systems

We investigate the dynamic behavior of the stationary random process defined by a central complex Wishart (CW) matrix ${\bf{W}}(t)$ as it varies along a certain dimension $t$. We characterize the second-order joint cdf of the largest eigenvalue, and the second-order joint cdf of the smallest eigenvalue of this matrix. We show that both cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order joint cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit ($N_T$) and receive ($N_R$) antennas is similar. However, as $N_T$ is increased while keeping $N_R$ fixed, we see how the best and worst channels tend to have a similar rate of change.Comment: 15 pages, 9 figures and 1 table. This work has been accepted for publication at IEEE Trans. Inf. Theory. Copyright (c) 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]

Characterisation and Modelling of Indoor and Short-Range MIMO Communications

Over the last decade, we have witnessed the rapid evolution of Multiple-Input Multiple-Output (MIMO) systems which promise to break the frontiers of conventional architectures and deliver high throughput by employing more than one element at the transmitter (Tx) and receiver (Rx) in order to exploit the spatial domain. This is achieved by transmitting simultaneous data streams from different elements which impinge on the Rx with ideally unique spatial signatures as a result of the propagation paths’ interactions with the surrounding environment. This thesis is oriented to the statistical characterisation and modelling of MIMO systems and particularly of indoor and short-range channels which lend themselves a plethora of modern applications, such as wireless local networks (WLANs), peer-to-peer and vehicular communications. The contributions of the thesis are detailed below. Firstly, an indoor channel model is proposed which decorrelates the full spatial correlation matrix of a 5.2 GHzmeasuredMIMO channel and thereafter assigns the Nakagami-m distribution on the resulting uncorrelated eigenmodes. The choice of the flexible Nakagami-m density was found to better fit the measured data compared to the commonly used Rayleigh and Ricean distributions. In fact, the proposed scheme captures the spatial variations of the measured channel reasonably well and systematically outperforms two known analytical models in terms of information theory and link-level performance. The second contribution introduces an array processing scheme, namely the three-dimensional (3D) frequency domain Space Alternating Generalised Expectation Maximisation (FD-SAGE) algorithm for jointly extracting the dominant paths’ parameters. The scheme exhibits a satisfactory robustness in a synthetic environment even for closely separated sources and is applicable to any array geometry as long as its manifold is known. The algorithm is further applied to the same set of raw data so that different global spatial parameters of interest are determined; these are the multipath clustering, azimuth spreads and inter-dependency of the spatial domains. The third contribution covers the case of short-range communications which have nowadays emerged as a hot topic in the area of wireless networks. The main focus is on dual-branch MIMO Ricean systems for which a design methodology to achieve maximum capacities in the presence of Line-of-Sight (LoS) components is proposed. Moreover, a statistical eigenanalysis of these configurations is performed and novel closed-formulae for the marginal eigenvalue and condition number statistics are derived. These formulae are further used to develop an adaptive detector (AD) whose aim is to reduce the feasibility cost and complexity of Maximum Likelihood (ML)-based MIMO receivers. Finally, a tractable novel upper bound on the ergodic capacity of the above mentioned MIMO systems is presented which relies on a fundamental power constraint. The bound is sufficiently tight and applicable for arbitrary rank of the mean channel matrix, Signal-to-Noise ratio (SNR) and takes the effects of spatial correlation at both ends into account. More importantly, it includes previously reported capacity bounds as special cases

MIMO channel modelling and simulation for cellular and mobile-to-mobile

Recently, mobile-to-mobile (M2M) communications have received much attention due to several emerging applications, such as wireless mobile ad hoc networks, relay-based cellular networks, and dedicated short range communications (DSRC) for intelligent transportation systems (e.g., IEEE 802.11p standard). Different from conventional fixed-to-mobile (F2M) cellular systems, in M2M systems both the transmitter (Tx) and receiver (Rx) are in motion and often equipped with low elevation antennas. Multiple-input-multiple-output (MIMO) technologies, employing multiple antennas at both the Tx and Rx, have widely been adopted for the third generation (3G) and beyond-3G (B3G) F2M cellular systems due to their potential benefits of improving coverage, link reliability, and overall system capacity. More recently, MIMO has been receiving more and more attention for M2M systems as well. Reliable knowledge of the propagation channel obtained from channel measurements and corresponding channel models serve as the enabling foundation for the design and analysis of MIMO F2M and M2M systems. Furthermore, the development of accurate MIMO F2M and M2M channel simulation models plays a major role in the practical simulation and performance evaluation of these systems. These form the primary motivation behind our research on MIMO channel modelling and simulation for F2M cellular and M2M communication systems. In this thesis, we first propose a new wideband theoretical multiple-ring based MIMO regular-shaped geometry-based stochastic model (RS-GBSM) for non-isotropic scattering F2M macro-cell scenarios and then derive a generic space-time-frequency (STF) correlation function (CF). The proposed theoretical reference wideband model can be reduced to a narrowband one-ring model, a new closed-form STF CF of which is derived as well. Narrowband and wideband sum-of-sinusoids (SoS) simulation models are then developed, demonstrating a good agreement with the corresponding reference models in terms of correlation functions. Secondly, based on a well-known narrowband two-ring single-input single-output (SISO) M2M channel reference model, we propose new deterministic and stochastic SoS simulation models for non-isotropic scattering environments. The proposed deterministic simulator is the first SISO M2M deterministic simulator with good performance, while the proposed stochastic simulator outperforms the existing one in terms of fitting the desired statistical properties of the corresponding reference model. Thirdly, a new adaptive narrowband MIMO M2M RS-GBSM is proposed for nonisotropic scattering environments. To the best of our knowledge, the proposed M2M model is the first RS-GBSM that has the ability to study the impact of the vehicular traffic density on channel statistics. From the proposed theoretical reference model, we comprehensively investigate some important M2M channel statistics including the STF CF, space-Doppler-frequency power spectral density, envelope level crossing rate, and average fade duration. A close agreement between some channel statistics obtained from the proposed reference model and measurement data is observed, confirming the utility of our model. Finally, we extend the above narrowband model to a new wideband MIMO M2M RSGBSM with respect to the frequency-selectivity. The proposed wideband reference model is validated by observing a good match between some statistical properties of the theoretical model and available measurement data. From the wideband reference model, we further design new wideband deterministic and stochastic SoS simulation models. The proposed wideband simulators can be easily reduced to narrowband ones. The utilities of the newly derived narrowband and wideband simulation models are validated by comparing their statistical properties with those of the corresponding reference models. The proposed channel reference models and simulators are expected to be useful for the design, testing, and performance evaluation of future MIMO cellular and M2M communication systems.Scottish Funding Counci

Multi-dimensional lattice equaliser for Q2 PSK

The aim of this dissertation was the design, implementation and performance evaluation of a Recursive Least Squares (RLS), lattice based, adaptive, multidimensional, decision feedback equaliser (DFE) for the spectrally efficient four-dimensional digital modulation technique, re¬ferred to as Quadrature-Quadrature Phase-Shift Keying, Q2pSK. Q2PSK constitutes a relatively new modulation technique, and the application of adaptive equalisation to this technique has not yet been considered in the open literature. This dissertation represents an in depth study into the Q2PSK modulation technique, as well as the optimal implementation, in simulation, of such a modem to aid the inclusion of the adap¬tive lattice DFE, for application to high speed mobile digital communication over the V /UHF channel in the presence of multi path propagation. Specific aspects of synchronization applicable to this modem platform are also addressed. An in depth study was also conducted into the realisation of a V /UHF channel simulation, capable of producing a Ricean and/or Rayleigh fad¬ing multipath propagation environment for the evaluation of the modem platform and adaptive equaliser structure. The theoretical analysis of the effect of multi path on a Q2PSK signal led to the correct design of the adaptive lattice structure, as well as the correct interfacing of the equaliser to the receiver platform. The performance of the proposed synchronisation strategies, in tandem with the equalisation technique were evaluated for several static, as well as fading multipath channels. The simulation results obtained show the equaliser operates correctly, and can give large performance gains over the static matched filter (matched to the transmitted waveform) implementation of the modem platform. Several simulations were specifically designed to highlight the performance limitations of the adaptive equalisation technique.Dissertation (MEng (Digital Communication))--University of Pretoria, 2006.Electrical, Electronic and Computer Engineeringunrestricte