Dissertation•
On Linear Transmission Systems
01 Jan 2012-
TL;DR: The object in Part I is to study the impact of both the signaling rate and the pulse shape on the information rate of single antenna, single carrier linear modulation systems, and a iterative optimization method is developed, which produces precoders improving upon the best known ones in the literature.
Abstract: This thesis is divided into two parts. Part I analyzes the information rate of single antenna, single carrier linear modulation systems. The information rate of a system is the maximum number of bits that can be transmitted during a channel usage, and is achieved by Gaussian symbols. It depends on the underlying pulse shape in a linear modulated signal and also the signaling rate, the rate at which the Gaussian symbols are transmitted. The object in Part I is to study the impact of both the signaling rate and the pulse shape on the information rate.
Part II of the thesis is devoted to multiple antenna systems (MIMO), and more specifically to linear precoders for MIMO channels. Linear precoding is a practical scheme for improving the performance of a MIMO system, and has been studied intensively during the last four decades. In practical applications, the symbols to be transmitted are taken from a discrete alphabet, such as quadrature amplitude modulation (QAM), and it is of interest to find the optimal linear precoder for a certain performance measure of the MIMO channel. The design problem depends on the particular performance measure and the receiver structure. The main difficulty in finding the optimal precoders is the discrete nature of the problem, and mostly suboptimal solutions are proposed. The problem has been well investigated when linear receivers are employed, for which optimal precoders were found for many different performance measures. However, in the case of the optimal maximum likelihood (ML) receiver, only suboptimal constructions have been possible so far. Part II starts by proposing new novel, low complexity, suboptimal precoders, which provide a low bit error rate (BER) at the receiver. Later, an iterative optimization method is developed, which produces precoders improving upon the best known ones in the literature. The resulting precoders turn out to exhibit a certain structure, which is then analyzed and proved to be optimal for large alphabets.
Citations
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Dissertation•
01 Jan 2013
TL;DR: A framework to design reduced-complexity receivers for FTN and general linear channels that achieve optimal or near-optimal performance and an improvement of the minimum phase conversion that sharpens the focus of the ISI model energy is proposed.
Abstract: Fast and reliable data transmission together with high bandwidth efficiency are important design aspects in a modern digital communication system. Many different approaches exist but in this thesis bandwidth efficiency is obtained by increasing the data transmission rate with the faster-than-Nyquist (FTN) framework while keeping a fixed power spectral density (PSD). In FTN consecutive information carrying symbols can overlap in time and in that way
introduce a controlled amount of intentional intersymbol interference (ISI). This technique was introduced already in 1975 by Mazo and has since then been extended in many directions.
Since the ISI stemming from practical FTN signaling can be of significant duration, optimum detection with traditional methods is often prohibitively complex, and alternative equalization methods with acceptable complexity-performance tradeoffs are needed. The key objective of this thesis is therefore to design reduced-complexity receivers for FTN and general linear channels that achieve optimal or near-optimal performance. Although the performance of a detector can be measured by several means, this thesis is restricted to bit error rate (BER) and mutual information results. FTN signaling is applied in two ways: As a separate uncoded narrowband communication system or in a coded scenario consisting of a convolutional encoder, interleaver and the inner ISI mechanism in serial concatenation. Turbo equalization where soft information in the form of log likelihood ratios (LLRs) is exchanged between the equalizer and the decoder is a commonly used decoding technique for coded FTN signals.
The first part of the thesis considers receivers and arising stability problems when working within the white noise constraint. New M-BCJR algorithms for turbo equalization are proposed and compared to reduced-trellis VA and BCJR benchmarks based on an offset label idea. By adding a third low-complexity M-BCJR recursion, LLR quality is improved for practical values of M. M here measures the reduced number of BCJR computations for each data symbol. An improvement of the minimum phase conversion that sharpens the focus of the ISI model energy is proposed. When combined with a delayed and slightly mismatched receiver, the decoding allows a smaller M without significant loss in BER.
The second part analyzes the effect of the internal metric calculations on the performance of Forney- and Ungerboeck-based reduced-complexity equalizers of the M-algorithm type for both ISI and multiple-input multiple-output (MIMO) channels. Even though the final output of a full-complexity equalizer is identical for both models, the internal metric calculations are in general different. Hence, suboptimum methods need not produce the same final output. Additionally, new models working in between the two extremes are proposed and evaluated. Note that the choice of observation model does not impact the detection complexity as the underlying algorithm is unaltered.
The last part of the thesis is devoted to a different complexity reducing approach. Optimal channel shortening detectors for linear channels are optimized from an information theoretical perspective. The achievable information rates of the shortened models as well as closed form expressions for all components of the optimal detector of the class are derived. The framework used in this thesis is more general than what has been previously used within the area.
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References
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TL;DR: In this article, the authors deal with the determination of suboptimal feedback laws for the control of linear time-varying systems with quadratic performance criteria, where easily implementable time functions are used to generate the required time varying gains; free constant parameters in the control law description are chosen so as to minimize an averaged control cost.
Abstract: This paper deals with the determination of suboptimal feedback laws for the control of linear time-varying systems with quadratic performance criteria. Easily implementable time functions are used to generate the required time-varying gains; free constant parameters in the control law description are chosen so as to minimize an "averaged" control cost. A simple example is included to illustrate the theory.
160 citations
159 citations
01 Nov 1991
TL;DR: A new lower bound for the capacity of the continuous-time strictly bandlimited Gaussian channel with either peak or simultaneously peak power and bandlimiting constraints imposed on the channel's input waveform is reported, an improvement on previously reported lower bounds.
Abstract: Bounds are presented on I/sub i.i.d./-the achievable information rate for a discrete Gaussian Channel with intersymbol interference (ISI) present and i.i.d. channel input symbols governed by an arbitrary predetermined distribution p/sub x/(x). The lower and upper bounds on I/sub i.i.d./ and I are formulated. The bounds on I/sub i.i.d./ are calculated for independent equiprobably binary channel symbols and for causal channels with ISI memory of degree one and two. The bounds on I/sub i.i.d./ are compared to the approximated (by Monte Carlo methods) known value of I/sub i.i.d./ and their tightness is considered. An application of the new lower bound on I/sub i.i.d./ yields an improvement on previously reported lower bounds for the capacity of the continuous-time strictly bandlimited (or bandpass) Gaussian channel with either peak or simultaneously peak power and bandlimiting constraints imposed on the channel's input waveform. >
158 citations
TL;DR: A new criterion for designing the codebook of beamforming matrices that is based on minimizing an approximation to the capacity loss resulting from the limited rate in the feedback channel is proposed and an iterative design algorithm is developed that converges to a locally optimum codebook.
Abstract: This paper investigates the problem of transmit beamforming in multiple-antenna spatial multiplexing (SM) systems employing a finite-rate feedback channel. Assuming a fixed number of spatial channels and equal power allocation, we propose a new criterion for designing the codebook of beamforming matrices that is based on minimizing an approximation to the capacity loss resulting from the limited rate in the feedback channel. Using the criterion, we develop an iterative design algorithm that converges to a locally optimum codebook. Under the independent identically distributed channel and high signal-to-noise ratio (SNR) assumption, the effect on channel capacity of the finite-bit representation of the beamforming matrix is analyzed. Central to this analysis is the complex multivariate beta distribution and tractable approximations to the Voronoi regions associated with the code points. Furthermore, to compensate for the degradation due to the equal power allocation assumption, we propose a multimode SM transmission strategy wherein the number of data streams is determined based on the average SNR. This approach is shown to allow for effective utilization of the feedback bits resulting in a practical and efficient multiple-input multiple-output system design
145 citations
TL;DR: In this article, the degree of the minimal polynomials of a linear functional on a fixed rank locus in a linear space of symmetric matrices was determined using methods from complex algebraic geometry, such as projective duality, determinantal varieties, and their Chern classes.
Abstract: Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number We study the degree of the minimal polynomials of these algebraic numbers Geometrically, this degree counts the critical points attained by a linear functional on a fixed rank locus in a linear space of symmetric matrices We determine this degree using methods from complex algebraic geometry, such as projective duality, determinantal varieties, and their Chern classes
138 citations