Transceiver designs and analysis for LTI, LTV and broadcast channels - new matrix decompositions and majorization theory

Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multiple-input multiple-output (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrix-vector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the point-to-point MIMO transceiver design problems.

In this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear time-varying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmit-receive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.

The first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.

In the second part of the thesis, we focus on MIMO transceiver design for slowly time-varying MIMO channels with zero-forcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly time-varying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the time-varying channels is not exploited. Based on the GTD, we develop space-time GTD (ST-GTD) for the decomposition of linear time-varying flat MIMO channels. Under the assumption that CSIT, CSIR and channel prediction are available, by using the proposed ST-GTD, we develop space-time geometric mean decomposition (ST-GMD) DFE transceivers under the zero-forcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each space-time (ST) block (which consists of several coherence blocks), and the average per ST-block BER in the moderate high SNR region. Moreover, the ST-GMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each ST-block. In general, the newly proposed transceivers perform better than the GGMD-based systems since the super-imposed temporal precoder is able to exploit the temporal diversity of time-varying channels. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD DFE transceiver is also proposed.

The third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (min-power) with a total bitrate constraint and per-stream BER constraints. The second problem is the rate maximization problem (max-rate) with a total transmit power constraint and per-stream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the min-power and max-rate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.

Finally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFT-FBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFT-FBT such that the SINR at the receiver is maximized. Also, a novel pilot-aided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasi-stationary multi-path Rayleigh fading channels. Using the concept of a difference co-array, the new technique can construct M^2 co-pilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.

Quasi -symmetric designs with good blocks and intersection number one

Mavron, Vassili; McDonough, T.P.; Schrikhande, M.S., (2003) 'Quasi -symmetric designs with good blocks and intersection number one', Designs Codes and Cryptography 28(2) pp.147-162 RAE2008

Researching and designing GREAT; the extremely condensed hybrid urban block

The fact that the hybrid building is an extremely condensed urban block which increases the city’s density and contributes to the public realm of the city – horizontally as well vertically - forms one of the key interests of this documentation, research and master studio work. The “ground scraper” is not only public because of the character of its plinth facing surrounding streets, but also in regard to its interior space that is partly accessible to public. As such the European hybrid building potentially extends the city’s public domain horizontally and vertically into the building’s interior and links the public domain inside and outside. Notwithstanding, the hybrid building due to its specific and unconventional character represents a truly urban architecture that was unfortunately often rejected in the name of ‘purity’ of form and function during the twentieth century. Or with other words, its rejection demonstrates the domination of the building’s plan opposed to the section. Today, new frameworks for the city, like the “compact city,” ask for innovative interpretations and designs of building types, worthy to be investigated and proposed. The architectural type of the hybrid building, (re)defines and expresses the relation between architecture and the city in a specific manner. To begin with, the city of Rotterdam forms the first test-case of the Hybrid’s project to document and discuss statements, such as “the hybrid building has a long- standing tradition within this ‘modern city”, “it is a machine for urbanity,” “it enlarges the city,” “it innovates because of its ambitiousness but also because of necessity,” “it combines to activate,” “it asks for extraordinary design intelligence and craftsmanship.” A special way of drawing is developed to document, analyse and compare historical and contemporary representatives of the species. The method includes panoply of scales ranging from the morphological arrangement on the scale of the city, the typologies of stacking diverse programs to the architectural features that establish the mutual relationship between the public space of the city and the interior of the building. Basically the features analysed within the series of drawings are also constitutional for (the success of) every future hybrid building.

Multistratum response surface designs

Response surface designs are usually described as if the treatments have been completely randomized to the experimental units. However, in practice there is often a structure to the units, implying the need for blocking. If, in addition, some factors are more difficult to vary between units than others, a multistratum structure arises naturally. We present a general strategy for constructing response surface designs in multistratum unit structures. Designs are constructed stratum by stratum, starting in the highest stratum. In each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata, allowing-for all the effects that have to be estimated. Three examples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment set. Finally, some practical considerations in randomization are discussed.

An algorithm for arranging response surface designs in small blocks

We consider the problem of blocking response surface designs when the block sizes are prespecified to control variation efficiently and the treatment set is chosen independently of the block structure. We show how the loss of information due to blocking is related to scores defined by Mead and present an interchange algorithm based on scores to improve a given blocked design. Examples illustrating the performance of the algorithm are given and some comparisons with other designs are made. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Some practical advice on polynomial regression analysis from blocked response surface designs

It is often necessary to run response surface designs in blocks. In this paper the analysis of data from such experiments, using polynomial regression models, is discussed. The definition and estimation of pure error in blocked designs are considered. It is recommended that pure error is estimated by assuming additive block and treatment effects, as this is more consistent with designs without blocking. The recovery of inter-block information using REML analysis is discussed, although it is shown that it has very little impact if thc design is nearly orthogonally blocked. Finally prediction from blocked designs is considered and it is shown that prediction of many quantities of interest is much simpler than prediction of the response itself.

Fixed block configuration GDDs with block size 6 and (3, r)-regular graphs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis. In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; λ1; λ2). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s points from one of the two groups and t points from the other. Chapter 2 begins with an overview of previous results and constructions for small group size and block sizes 3, 4 and 5. Chapter 2 is largely devoted to presenting constructions and results about GDDs with two groups and block size 6. We show the necessary conditions are sufficient for the existence of GDD(n, 2, 6; λ1, λ2) with fixed block configuration (3; 3). For configuration (1; 5), we give minimal or nearminimal index constructions for all group sizes n ≥ 5 except n = 10, 15, 160, or 190. For configuration (2, 4), we provide constructions for several families ofGDD(n, 2, 6; λ1, λ2)s. Chapter 3 addresses characterizing (3, r)-regular graphs. We begin with providing previous results on the well studied class of (2, r)-regular graphs and some results on the structure of large (t; r)-regular graphs. In Chapter 3, we completely characterize all (3, 1)-regular and (3, 2)-regular graphs, as well has sharpen existing bounds on the order of large (3, r)- regular graphs of a certain form for r ≥ 3. Finally, the appendix gives computational data resulting from Sage and C programs used to generate (3, 3)-regular graphs on less than 10 vertices.

Existence of complementary pairs of proportionally balanced designs

Proportionally balanced designs (pi BDs) were introduced by Gray and Matters in response to a need for the allocation of markers of the Queensland Core Skills Test to have a certain property. Subsequent papers extended the theoretical results relating to such designs and provided further instances and general constructions. This work focused on designs comprising blocks of precisely two sizes, and when each variety occurs with one of precisely two possible frequencies. Two designs based on the set V of varieties are complementary if, whenever B is a block of one, then its complement with regard to the set V is a block of the other. Here we present necessary conditions for the existence of complementary pairs of such pi BDs and provide lists of some restricted parameter sets satisfying these necessary conditions. The lists are arranged according to the number of blocks. We demonstrate that not all of these parameter sets give rise to designs. However we establish by construction of the sets of blocks that, for every feasible number of blocks less than or equal to 100, with the possible exception of 63, there exists at least one pair of complementary pi BDs. We also investigate the conditions under which the complementary design can be isomorphic to the original design, and again provide a list of feasible parameters for pairs of such designs with at most 400 blocks.

Embedding a restricted class of partial K-4-designs

Given a partial K-4-design (X, P), if x is an element of X is a vertex which occurs in exactly one block of P, then call x a free vertex. In this paper, a technique is described for obtaining a cubic embedding of any partial K-4-design with the property that every block in the partial design contains at least two free vertices.

Interface adaptor logic: A new model for interfacing peripherals in IP based designs

The introduction of standard on-chip buses has eased integration and boosted the production of IP functional cores. However, once an IP is bus specific retargeting to a different bus is time-consuming and tedious, and this reduces the reusability of the bus-specific IP. As new bus standards are introduced and different interconnection methods are proposed, this problem increases. Many solutions have been proposed, however these solutions either limit the IP block performance or are restricted to a particular platform. A new concept is presented that can connect IP blocks to a wide variety of interface architectures with low overhead. This is achieved through the use a special interface adaptor logic layer.

A comparative study of block scheduling and traditional scheduling on academic achievement

The purpose of this study was to evaluate the effectiveness of an alternate day block schedule design (n = 419) versus a traditional six-period schedule design (n = 623) on the academic achievement of the graduating classes in two schools in which the design was used respectively. Academic achievement was measured by (a) two standardized tests: the Florida Comprehensive Assessment Test Sunshine State Standards (FCAT-SSS) in mathematics and reading for 9th and 10th grade and the Scholastic Reading Inventory Test (SRI) for 9 th, 10th, and 11th grade; (b) three school grades: the mathematics final course grades for 9th, 10th, and 11th grade, the English final course grades for 9th, 10th, 11th, and 12th grade and the graduating GPA. A total of five repeated measure analyses of variance (ANOVAs) were conducted to analyze the difference between the two schools (representing the two designs) with respect to five achievement indicators (FCAT-SSS mathematics scores, FCAT-SSS reading scores, SRI scores, mathematics final course grades, and English final course grades). The between-subject factor for the five ANOVAs was the schedule design and the within-subject factor was the time the tests were taken or the time the course grades were issued. T-tests were performed on all eighth grade achievement indicators to ensure there were no significant differences in achievement between the two cohorts prior to entering high school. An independent samples t-test was conducted to analyze the difference between the two schedule designs with respect to graduating GPA. Achievement in the alternate day block schedule design was significantly higher than in the traditional six-period schedule design for some of the locally assigned school grades. The difference between the two types of schedule designs was not significant for the standardized measures (the FCAT-SSS in reading and mathematics and the SRI). This study concludes that the use of an alternate day block schedule design can be considered an educational tool that can help improve the academic achievement of students as measured by local indicators of achievement; but, apparently the design is not an important factor in achievement as measured by state examinations such as the FCAT-SSS or the SRI.

Conceptual designs of multi-degree of freedom compliant parallel manipulators composed of wire-beam based compliant mechanisms

This paper proposes conceptual designs of multi-degree(s) of freedom (DOF) compliant parallel manipulators (CPMs) including 3-DOF translational CPMs and 6-DOF CPMs using a building block based pseudo-rigid-body-model (PRBM) approach. The proposed multi-DOF CPMs are composed of wire-beam based compliant mechanisms (WBBCMs) as distributed-compliance compliant building blocks (CBBs). Firstly, a comprehensive literature review for the design approaches of compliant mechanisms is conducted, and a building block based PRBM is then presented, which replaces the traditional kinematic sub-chain with an appropriate multi-DOF CBB. In order to obtain the decoupled 3-DOF translational CPMs (XYZ CPMs), two classes of kinematically decoupled 3-PPPR (P: prismatic joint, R: revolute joint) translational parallel mechanisms (TPMs) and 3-PPPRR TPMs are identified based on the type synthesis of rigid-body parallel mechanisms, and WBBCMs as the associated CBBs are further designed. Via replacing the traditional actuated P joint and the traditional passive PPR/PPRR sub-chain in each leg of the 3-DOF TPM with the counterpart CBBs (i.e. WBBCMs), a number of decoupled XYZ CPMs are obtained by appropriate arrangements. In order to obtain the decoupled 6-DOF CPMs, an orthogonally-arranged decoupled 6-PSS (S: spherical joint) parallel mechanism is first identified, and then two example 6-DOF CPMs are proposed by the building block based PRBM method. It is shown that, among these designs, two types of monolithic XYZ CPM designs with extended life have been presented.

Security metrics for object-oriented class designs

Measuring quality attributes of object-oriented designs (e.g. maintainability and performance) has been covered by a number of studies. However, these studies have not considered security as much as other quality attributes. Also, most security studies focus at the level of individual program statements. This approach makes it hard and expensive to discover and fix vulnerabilities caused by design errors. In this work, we focus on the security design of an object oriented application and define a number of security metrics. These metrics allow designers to discover and fix security vulnerabilities at an early stage, and help compare the security of various alternative designs. In particular, we propose seven security metrics to measure Data Encapsulation (accessibility) and Cohesion (interactions) of a given object-oriented class from the point of view of potential information flow.