The coding and feedback inaccuracies of the channel state information (CSI) in limited feedback multiple-input multiple-output (MIMO) wireless systems can severely impact the achievable data rate and ...reliability. The CSI is mathematically represented as a Grassmann manifold or manifold of unitary matrices. These are non-Euclidean spaces with special constraints that makes efficient and high fidelity coding especially challenging. In addition, the CSI inaccuracies may occur due to digital representation, time variation, and delayed feedback of the CSI. To overcome these inaccuracies, the manifold structure of the CSI can be exploited. The objective of this dissertation is to develop a new signal processing techniques on the manifolds to harvest the benefits of MIMO wireless systems. First, this dissertation presents the Kerdock codebook design to represent the CSI on the Grassmann manifold. The CSI inaccuracy due to digital representation is addressed by the finite alphabet structure of the Kerdock codebook. In addition, systematic codebook construction is identified which reduces the resource requirement in MIMO wireless systems. Distance properties on the Grassmann manifold are derived showing the applicability of the Kerdock codebook to beam-forming and spatial multiplexing systems. Next, manifold-constrained algorithms to predict and encode the CSI with high fidelity are presented. Two prominent manifolds are considered; the Grassmann manifold and the manifold of unitary matrices. The Grassmann manifold is a class of manifold used to represent the CSI in MIMO wireless systems using specific transmission strategies. The manifold of unitary matrices appears as a collection of all spatial information available in the MIMO wireless systems independent of specific transmission strategies. On these manifolds, signal processing building blocks such as differencing and prediction are derived. Using the proposed signal processing tools on the manifold, this dissertation addresses the CSI coding accuracy, tracking of the CSI under time variation, and compensation techniques for delayed CSI feedback. Applications of the proposed algorithms in single-user and multiuser systems show that most of the spatial benefits of MIMO wireless systems can be harvested.
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The excised shoots of tea plants were cultivated for 1 week in (15NH4)2SO4 solution. 15N was incorporated considerably more into protein and caffeine of young than into those of mature and old ...leaves. It was proved by these results that formation of caffeine can take place in the leaves of tea plant.
From the rhizoma of Peltoboykinia tellimoides (MAXIM.) HARA, two triterpene acids were isolated. One of them, a new triterpene, named β-peltoboykinolic acid (I), mp 220-222°(decomp.), α24D+114°, has ...been established to be olean-12-ene-3β-ol-27-oic acid and another, named α-peltoboykinolic acid (II), mp 234-236°, α17D+121°, to be urs-12-ene-3β-ol-27-oic acid, which is identical with a compound derived from quinovic acid by L. Ruzicka, et al. in 1946. These are the first examples of naturally occurring triterpene acids with the only carboxyl group at C-27 of ursane and oleanane types.
A codebook based limited feedback strategy is a practical way to obtain partial channel state information at the transmitter in a precoded multiple-input multiple-output (MIMO) wireless system. ...Conventional codebook designs use Grassmannian packing, equiangular frames, vector quantization, or Fourier based constructions. While the capacity and error rate performance of conventional codebook constructions have been extensively investigated, constructing these codebooks is notoriously difficult relying on techniques such as nonlinear search or iterative algorithms. Further, the resulting codebooks may not have a systematic structure to facilitate storage of the codebook and low search complexity. In this paper, we propose a new systematic codebook design based on Kerdock codes and mutually unbiased bases. The proposed Kerdock codebook consists of multiple mutually unbiased unitary bases matrices with quaternary entries and the identity matrix. We propose to derive the beamforming and precoding codebooks from this base codebook, eliminating the requirement to store multiple codebooks. The propose structure requires little memory to store and, as we show, the quaternary structure facilitates codeword search. We derive the chordal distance for two antenna and four antenna codebooks, showing that the proposed codebooks compare favorably with prior designs. Monte Carlo simulations are used to compare achievable rates and error rates for different codebooks sizes.
By feeding tea shoots with methionine-(methyl-14C) it was proved that the methyl group of methionine served as a precursor of the methyl groups of caffeine in tea plants.
In this paper, we shall be concerned with the embedding-construction problem from a given proof-theoretic embedding and with some criterion to distinguish one embedding with another. We shall first ...point out some false argument in the second section of the paper 12 of the above title. However, thanks to certain constructions introduced in the present paper, the main results of the section, i.e. the affirmative answers to the problem posed in it (= Question 2 in 12) remain valid and so does the rest of the paper 12. Further we shall generalize the obtained results on constructions with atomic formulas to those with more general unprovable formulas. In addition, we shall show that a certain set obtained by such a construction forms a lattice isomorphic to a certain sublattice of the Nishimura-Rieger lattice of formulas of one variable p of intuitionistic propositional logic for any p. For all the logics treated in this paper, i.e. classical and intuitionistic logics and modal logics S4 and S5, some of the constructions give even an affirmative answer to Question 1 of 12: i.e., "Let X and Y be given consistent formal systems. For any embedding τ of X in Y, is there a construction 𝒞 such that by the construction 𝒞, we can obtain a set with cardinality κ ≥ ℵ₀ of mutually non-C-equivalent embeddings from τ ?". Further we shall give a necessary and sufficient condition for an affirmative answer to Question 1. We shall also show that a certain set of such constructions forms a lattice for certain formal systems. This paper is the overture to my forthcoming paper 14 (on a generalized Gödel's theorem on embedding) and our further work on the theme of this paper.
During the past 17 months from June 1976, aortic and mitral valves have been replaced with a Lillehei-Kaster pivoting disc prosthesis. The hospital mortality was 28.5%. All of the patients leaving ...the hospital showed definite improvement and were in N. Y. H. A. functional classes I and II The hemodynamic function of the prosthesis was assessed intraoperatively. The average pressure gradients across the prosthesis were minimal (4.32mmHg in AVR and 4.68mmHg in MVR) and the average calculated valve areas were satisfactory (1.86cm2 in AVR and 2.75cm2 in MVR) As the number of the operation is still small and the follow-up period is too short, we will continue to use this prosthesis to reach final conclusions.
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