Space time transceiver design over multipath fading channels

Imperial Users onl

Robust leakage-based distributed precoder for cooperative multicell systems

Coordinated multipoint (CoMP) from long term evolution (LTE)-advanced is a promising technique to enhance the system spectral efficiency. Among the CoMP techniques, joint transmission has high communication requirements, because of the data sharing phase through the backhaul network, and coordinated scheduling and beamforming reduces the backhaul requirements, since no data sharing is necessary. Most of the available CoMP techniques consider perfect channel knowledge at the transmitters. Nevertheless for practical systems this is unrealistic. Therefore in this study the authors address this limitation by proposing a robust precoder for a multicell-based systems, where each base station (BS) has only access to an imperfect local channel estimate. They consider both the case with and without data sharing. The proposed precoder is designed in a distributed manner at each BS by maximising the signal-to-leakage-and-noise ratio of all jointly processed users. By considering the channel estimation error in the design of the precoder, they are able to reduce considerably the impact of these errors in the system's performance. The results show that the proposed scheme has improved performance especially for the high signal-to-noise ratio regime, where the impact of the channel estimation error may be more pronounced

Polynomial matrix algebra with applications

[Abstract unavailable

MVDR broadband beamforming using polynomial matrix techniques

This thesis addresses the formulation of and solution to broadband minimum variance distortionless response (MVDR) beamforming. Two approaches to this problem are considered, namely, generalised sidelobe canceller (GSC) and Capon beamformers. These are examined based on a novel technique which relies on polynomial matrix formulations. The new scheme is based on the second order statistics of the array sensor measurements in order to estimate a space-time covariance matrix. The beamforming problem can be formulated based on this space-time covariance matrix. Akin to the narrowband problem, where an optimum solution can be derived from the eigenvalue decomposition (EVD) of a constant covariance matrix, this utility is here extended to the broadband case. The decoupling of the space-time covariance matrix in this case is provided by means of a polynomial matrix EVD. The proposed approach is initially exploited to design a GSC beamformer for a uniform linear array, and then extended to the constrained MVDR, or Capon, beamformer and also the GSC with an arbitrary array structure. The uniqueness of the designed GSC comes from utilising the polynomial matrix technique, and its ability to steer the array beam towards an off-broadside direction without the pre-steering stage that is associated with conventional approaches to broadband beamformers. To solve the broadband beamforming problem, this thesis addresses a number of additional tools. A first one is the accurate construction of both the steering vectors based on fractional delay filters, which are required for the broadband constraint formulation of a beamformer, as for the construction of the quiescent beamformer. In the GSC case, we also discuss how a block matrix can be obtained, and introduce a novel paraunitary matrix completion algorithm. For the Capon beamformer, the polynomial extension requires the inversion of a polynomial matrix, for which a residue-based method is proposed that offers better accuracy compared to previously utilised approaches. These proposed polynomial matrix techniques are evaluated in a number of simulations. The results show that the polynomial broadband beamformer (PBBF) steersthe main beam towards the direction of the signal of interest (SoI) and protects the signal over the specified bandwidth, and at the same time suppresses unwanted signals by placing nulls in their directions. In addition to that, the PBBF is compared to the standard time domain broadband beamformer in terms of their mean square error performance, beam-pattern, and computation complexity. This comparison shows that the PBBF can offer a significant reduction in computation complexity compared to its standard counterpart. Overall, the main benefits of this approach include beam steering towards an arbitrary look direction with no need for pre-steering step, and a potentially significant reduction in computational complexity due to the decoupling of dependencies of the quiescent beamformer, blocking matrix, and the adaptive filter compared to a standard broadband beamformer implementation.This thesis addresses the formulation of and solution to broadband minimum variance distortionless response (MVDR) beamforming. Two approaches to this problem are considered, namely, generalised sidelobe canceller (GSC) and Capon beamformers. These are examined based on a novel technique which relies on polynomial matrix formulations. The new scheme is based on the second order statistics of the array sensor measurements in order to estimate a space-time covariance matrix. The beamforming problem can be formulated based on this space-time covariance matrix. Akin to the narrowband problem, where an optimum solution can be derived from the eigenvalue decomposition (EVD) of a constant covariance matrix, this utility is here extended to the broadband case. The decoupling of the space-time covariance matrix in this case is provided by means of a polynomial matrix EVD. The proposed approach is initially exploited to design a GSC beamformer for a uniform linear array, and then extended to the constrained MVDR, or Capon, beamformer and also the GSC with an arbitrary array structure. The uniqueness of the designed GSC comes from utilising the polynomial matrix technique, and its ability to steer the array beam towards an off-broadside direction without the pre-steering stage that is associated with conventional approaches to broadband beamformers. To solve the broadband beamforming problem, this thesis addresses a number of additional tools. A first one is the accurate construction of both the steering vectors based on fractional delay filters, which are required for the broadband constraint formulation of a beamformer, as for the construction of the quiescent beamformer. In the GSC case, we also discuss how a block matrix can be obtained, and introduce a novel paraunitary matrix completion algorithm. For the Capon beamformer, the polynomial extension requires the inversion of a polynomial matrix, for which a residue-based method is proposed that offers better accuracy compared to previously utilised approaches. These proposed polynomial matrix techniques are evaluated in a number of simulations. The results show that the polynomial broadband beamformer (PBBF) steersthe main beam towards the direction of the signal of interest (SoI) and protects the signal over the specified bandwidth, and at the same time suppresses unwanted signals by placing nulls in their directions. In addition to that, the PBBF is compared to the standard time domain broadband beamformer in terms of their mean square error performance, beam-pattern, and computation complexity. This comparison shows that the PBBF can offer a significant reduction in computation complexity compared to its standard counterpart. Overall, the main benefits of this approach include beam steering towards an arbitrary look direction with no need for pre-steering step, and a potentially significant reduction in computational complexity due to the decoupling of dependencies of the quiescent beamformer, blocking matrix, and the adaptive filter compared to a standard broadband beamformer implementation

Source separation and beamforming

As part of the last day of the UDRC 2021 summer school, this presentation provides an overview over polynomial matrix methods. The use of polynomial matrices is motivated through a number of broadband multichannel problems, involving space-time covariance matrices, filter banks, or wideband MIMO systems. We extend the utility of EVD from narrowband to broadband solutions via a number of factorisation algorithms belonging to the second order sequential rotation or sequential matrix diagonalisation families of algorithms. In a second part of this presentation, a number of application areas are explored, ranging from precoder and equaliser design for broadband MIMO communications systems, to broadband angle of arrival estimation, broadband beamforming, and the problem of identifying source-sensor transfer paths from the second order statistics of the sensor signals

Relevance of polynomial matrix decompositions to broadband blind signal separation

The polynomial matrix EVD (PEVD) is an extension of the conventional eigenvalue decomposition (EVD) to polynomial matrices. The purpose of this article is to provide a review of the theoretical foundations of the PEVD and to highlight practical applications in the area of broadband blind source separation (BSS). Based on basic definitions of polynomial matrix terminology such as parahermitian and paraunitary matrices, strong decorrelation and spectral majorization, the PEVD and its theoretical foundations will be briefly outlined. The paper then focuses on the applicability of the PEVD and broadband subspace techniques — enabled by the diagonalization and spectral majorization capabilities of PEVD algorithms—to define broadband BSS solutions that generalise well-known narrowband techniques based on the EVD. This is achieved through the analysis of new results from three exemplar broadband BSS applications — underwater acoustics, radar clutter suppression, and domain-weighted broadband beamforming — and their comparison with classical broadband methods

Enhanced multi-user DMT spectrum management using polynomial matrix decomposition techniques

This thesis researches the increasingly critical roles played by intelligent resource management and interference mitigation algorithms in present-day input multiple output (MIMO) communication systems. This thesis considers the application of polynomial matrix decomposition (PMD) algorithms, an emerging broadband factorisation technology for broadband MIMO access networks. Present DSL systems’ performance is constrained by the presence of interference (crosstalk) between multiple users sharing a common physical cable bundle. Compared to the traditional static spectrum management methods that define their survival to the worst-case scenarios, DSM methods provides some degree of flexibility to both direct channel and noise parameters to improve evolvability and robustness significantly. A novel crosstalk-aware DSM algorithm is proposed for the efficient management of multi-user DSL systems. Joint power allocation procedures are considered for the proposed single-channel equalisation method in DSL access networks. This thesis then shows that DSM can also benefit overdetermined precoding-equalisation systems, when the channel state information (CSI) parameters call for a specific decision feedback criterion to achieve a perfect reconstruction. A reasonable redundancy is introduced to reformulate the original multi-user MIMO problem into the simplest case of power management problem. DSM algorithms are primarily applied to solve the power allocation problem in DSM networks with the aim of maximising the system attribute rather than meeting specific requirements. Also, a powerful PMD algorithm known as sequential matrix diagonalisation (SMD) is used for analysing the eigenvalue decomposition problem by quantifying the available system resource including the effects of the crosstalk and its parameters. This analysis is carried out through joint precoding and equalisation structures. The thesis also investigates dynamic interference mitigation strategies for improving the performance of DSL networks. Two different mitigation strategies through a decision feedback equalisation (DFE) criterion are considered, including zero-forcing (ZF) and minimum mean square error (MMSE) equalisers. The difference between ZF and MMSE equalisations is analysed. Some experimental simulation results demonstrate the performance of both ZF and MMSE equalisation under the DFE equalisation constraint settings. Model reduction on the MMSE equalisation is thus applied to balance the crosstalk interference and enhance the data-rate throughput. Finally, the thesis studies a multi-user MIMO problem under the utility maximisation framework. Simulation results illustrate that the power allocation of multi-user DSL transmission can be jointly controlled and the interference can often be mitigated optimally on a single user basis. Driven by imperfect CSI information in current DSL networks, the research presents a novel DSM method that allows not only crosstalk mitigation, but also the exploitation of crosstalk environments through the fielding of versatile, flexible and evolvable systems. The proposed DSM tool is presented to achieve a robust mitigating system in any arbitrary overdetermined multi-user MIMO environment. Numerical optimisation results show that the mitigation of crosstalk impairment using the proposed DSM strategy. The design and implementation of the proposed DSM are carried out in the environment of MATLAB

Beamforming optimization for two-way relay channel

In this thesis, we focus on the optimization of the two-way relay channel (TWRC), which can double the data rate of communications comparing to the traditional one-way relay channel (OWRC). Because of the broadcasting nature of wireless transmissions, secure transmission is an appealing research topic. We take secrecy rate consideration into the optimization of the TWRC. Overall we provide near-optimal solutions for the secrecy rate maximization problems of the TWRC with imperfect channel state information (ICSI). A much lower complexity optimal SOCP solution is provided for SNR balancing of the TWRC without secrecy consideration. We first look at a flat fading TWRC network model with a multiple-input multiple-output (MIMO) relay where perfect channel state information (CSI) is assumed available. We then formulate an optimization problem, with the objective to minimize the relay’s power usage under the constraints that the signal-to-noise ratio (SNR) of the two transceivers should exceed a preset threshold. A low-complexity optimal beamforming solution is provided to this optimization problem by reformulating it in the form of second-order cone programming (SOCP). Later in the thesis, we consider the presence of an eavesdropper and address the beamforming optimization for minimizing the relay’s power with the constraints of the secrecy rates of the two transceivers. A semi-definite programming (SDP) based searching algorithm is proposed to find a near-optimal solution. For each search of the proposed approach, the previous non-convex optimization problem is transferred into an SDP problem, which can guarantee the optimality of the beamforming matrix. Afterwards, more realistic imperfect CSI (ICSI) situations are considered for the TWRC network models. As ICSI completely changes the structure and the property of the optimization problems, we reformulate the optimization problems into two scenarios. For the first case, we consider that the relay is an untrusted eavesdropper and in this case an SDP solution is provided to maximize the joint-decoding sum-secrecy rate. For the second case, we investigate the robust beamforming problems where the relay is trusted but there is an external eavesdropper, another SDP solution is provided to maximize the sum-secrecy rate

Paraunitary oversampled filter bank design for channel coding

Oversampled filter banks (OSFBs) have been considered for channel coding, since their redundancy can be utilised to permit the detection and correction of channel errors. In this paper, we propose an OSFB-based channel coder for a correlated additive Gaussian noise channel, of which the noise covariance matrix is assumed to be known. Based on a suitable factorisation of this matrix, we develop a design for the decoder's synthesis filter bank in order to minimise the noise power in the decoded signal, subject to admitting perfect reconstruction through paraunitarity of the filter bank. We demonstrate that this approach can lead to a significant reduction of the noise interference by exploiting both the correlation of the channel and the redundancy of the filter banks. Simulation results providing some insight into these mechanisms are provided