Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms

This paper considers three problems in sparse filter design, the first involving a weighted least-squares constraint on the frequency response, the second a constraint on mean squared error in estimation, and the third a constraint on signal-to-noise ratio in detection. The three problems are unified under a single framework based on sparsity maximization under a quadratic performance constraint. Efficient and exact solutions are developed for specific cases in which the matrix in the quadratic constraint is diagonal, block-diagonal, banded, or has low condition number. For the more difficult general case, a low-complexity algorithm based on backward greedy selection is described with emphasis on its efficient implementation. Examples in wireless channel equalization and minimum-variance distortionless-response beamforming show that the backward selection algorithm yields optimally sparse designs in many instances while also highlighting the benefits of sparse design.Texas Instruments Leadership University Consortium Progra

A fast-initializing digital equalizer with on-line tracking for data communications

A theory is developed for a digital equalizer for use in reducing intersymbol interference (ISI) on high speed data communications channels. The equalizer is initialized with a single isolated transmitter pulse, provided the signal-to-noise ratio (SNR) is not unusually low, then switches to a decision directed, on-line mode of operation that allows tracking of channel variations. Conditions for optimal tap-gain settings are obtained first for a transversal equalizer structure by using a mean squared error (MSE) criterion, a first order gradient algorithm to determine the adjustable equalizer tap-gains, and a sequence of isolated initializing pulses. Since the rate of tap-gain convergence depends on the eigenvalues of a channel output correlation matrix, convergence can be improved by making a linear transformation on to obtain a new correlation matrix

Channel equalization to achieve high bit rates in discrete multitone systems

textMulticarrier modulation (MCM) techniques such as orthogonal frequency division multiplexing (OFDM) and discrete multi-tone (DMT) modulation are attractive for high-speed data communications due to the ease with which MCM can combat channel dispersion. With all the benefits MCM could give, DMT modulation has an extra ability to perform dynamic bit loading, which has the potential to exploit fully the available bandwidth in a slowly time-varying channel. In broadband wireline communications, DMT modulation is standardized for asymmetric digital subscribe line (ADSL) and very-high-bit-rate digital subscriber line (VDSL) modems. ADSL and VDSL standards are used by telephone companies to provide high speed data service to residences and offices. In an ADSL receiver, an equalizer is required to compensate for the channel’s dispersion in the time domain and the channel’s distortion in the frequency domain of the transmitted waveform. This dissertation proposes design methods for linear equalizers to increase the bit rate of the connection. The methods are amenable to implementation on programmable fixed-point digital signal processors, which are employed in ADSL/VDSL transceivers. A conventional ADSL equalizer consists of a time-domain equalizer, a fast Fourier transform, and a frequency domain equalizer. The time domain equalizer (TEQ) is a finite impulse response filter that when coupled with a discretized channel produces an equivalent channel whose impulse response is shorter than that of the discretized channel. This channel shortening is required by the ADSL standards. In this dissertation, I first propose a linear phase TEQ design that exploits symmetry in existing eigen-filter approaches such as minimum mean square error(MMSE), maximum shortening signal to noise ratio (MSSNR) and minimum intersymbol interference (Min-ISI) equalizers. TEQs with symmetric coefficients can reach the same performance as non-symmetric ones with much lower training complexity. Second, I improve Min-ISI design. I reformulate the cost function to make long TEQs design feasible. I remove the dependency of transmission delay in order to reduce the complexity associated with delay optimization. The quantized weighting is introduced to further lower the complexity. I also propose an iterative optimization procedure of Min-ISI that completely avoids Cholesky decomposition hence is better suited for a fixed-point implementation. Finally I propose a dual-path TEQ structure, which designs a standard singleFIR TEQ to achieve good bit rate over the entire transmission bandwidth, and designs another FIR TEQ to improve the bit rate over a subset of subcarriers. Dualpath TEQ can be viewed as a special case of a complex valued filter bank structure that delivers the best bit rate of existing DMT equalizers. However, dual-path TEQ provides a very good tradeoff between achievable bit rate vs. implementation complexity on a programmable digital signal processor.Electrical and Computer Engineerin

Digital processing of signals in the presence of inter-symbol interference and additive noise

Imperial Users onl

Machine learning for optical fiber communication systems: An introduction and overview

Optical networks generate a vast amount of diagnostic, control and performance monitoring data. When information is extracted from this data, reconfigurable network elements and reconfigurable transceivers allow the network to adapt both to changes in the physical infrastructure but also changing traffic conditions. Machine learning is emerging as a disruptive technology for extracting useful information from this raw data to enable enhanced planning, monitoring and dynamic control. We provide a survey of the recent literature and highlight numerous promising avenues for machine learning applied to optical networks, including explainable machine learning, digital twins and approaches in which we embed our knowledge into the machine learning such as physics-informed machine learning for the physical layer and graph-based machine learning for the networking layer