The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

Unsupervised texture segmentation using Gabor filters

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

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Fading channels: information-theoretic and communications aspects

Digital processing of speech signals

This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for obtaining this CSI is time-division duplex (TDD) operation where uplink training in conjunction with reciprocity simultaneously provides the base stations with downlink as well as uplink channel estimates. This paper mathematically characterizes the impact that uplink training has on the performance of such multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, the paper shows that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells in an undesirable manner. This paper analyzes this fundamental problem of pilot contamination in multi-cell systems. Furthermore, it develops a new multi-cell MMSE-based precoding method that mitigates this problem. In addition to being linear, this precoding method has a simple closed-form expression that results from an intuitive optimization. Numerical results show significant performance gains compared to certain popular single-cell precoding methods.

/pdf/pilot-contamination-and-precoding-in-multi-cell-tdd-systems-326zvjyo0u.pdf

Pilot Contamination and Precoding in Multi-Cell TDD Systems

A new idea for waveform coding using vector quantisation (VQ) is introduced. This idea makes it possible to deal with codevectors much larger than before for a fixed bit per sample rate. Also a solution to the matching problem (inherent in the present context) in the L∞-norm describing a measure of nearness is presented. The overall computational complexity of this solution is O(n3 log2n). Sample results are presented to demonstrate the advantage of using this technique in the context of coding of speech waveforms.

Variation of vector quantisation and speech waveform coding

In this work we propose to design a minimum phase FIR digital filter transfer function from a given linear phase FIR transfer function which has identical amplitude. We are concentrating on very high degree polynomials for which factorisation procedures for root extraction are unreliable. We also assume that the polynomials have roots on the unit circle. The approach taken involves the use of the Cauchy Residue Theorem applied to the logarithmic derivative of the transfer function. This leads into a set of parameters derivable directly from the polynomial coefficients that facilitate the factorisation problem. The concept is developed in a way that leads naturally to the celebrated Newton Identities. In addition to solving the above problem, the results of the proposed design scheme are very encouraging as far as robustness and computational complexity are concerned.

/pdf/root-moments-a-nonlinear-signal-transformation-for-minimum-4dxgvmul0t.pdf

Root moments: a nonlinear signal transformation for minimum FIR filter design.

A novel object oriented motion estimation algorithm is presented. The algorithm provides the means for highly efficient moving image encoding by fully exploiting the temporal redundancy among the objects of successive frames. Two-dimensional segmentation is performed on a composite image synthesised from two consecutive frames. The object correspondence problem is removed implicitly by virtue of the fact that the generated composite segments correspond to successive versions of the same objects. The scheme guarantees well matched segments by reducing the effects of noise and varying illumination. While preserving motion or deformation information. Progressive motion estimation is achieved within the segmentation process which adapts to the assumed translational or affine model. Motion compensated extrapolation is performed on uncovered background and overlapping regions of the predicted frame. Simulation results show clearly the efficiency of the predictive scheme even in the case when only motion and deformation parameters need to be transmitted.

Object oriented motion and deformation estimation using composite segmentation

This paper deals with the wireless transfer of real-time high update rate supermedia data over the Internet of Things. It presents the related work on supermedia data transferring and QoE requirements. It proposes a high-level architectural design for the transport of wireless multiple supermedia streams over IoT. The most known compression techniques and flow controls for wireless sensory data transferring are analyzed. Based on these compression techniques, a new network adaptive flow control algorithm is proposed. Measurements for multihop wireless transferring of high update rate supermedia packets over IoT are presented.

Transferring Wireless High Update Rate Supermedia Streams Over IoT

A method for finding the state distribution in a physical system, on the basis of a detailed analysis of the experimental response of the system to an external probe, is presented. The concomitant algorithm, based upon the maximum entropy principle, is specifically devised so as to take into account the presence of noise due to experimental errors in the response signal. The formalism is illustrated by recourse to two numerical problems and is applied to a realistic situation involving X-ray diffraction.

Anthony G. Constantinides

Papers

Variation of vector quantisation and speech waveform coding

Root moments: a nonlinear signal transformation for minimum FIR filter design.

Object oriented motion and deformation estimation using composite segmentation

Transferring Wireless High Update Rate Supermedia Streams Over IoT

Statistical inference, state distribution, and noisy data