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

Sparse equalizer filter design for multi-path channels

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 81-82).In this thesis, sparse Finite Impulse Response (FIR) equalizers are designed for sparse multi-path channels under a pre-defined Mean Squared Error (MSE) constraint. We start by examining the intrinsic sparsity of the Zero Forcing equalizers and the FIR Minimum MSE (MMSE) equalizers. Next the equalization MSE is formulated as a quadratic function of the equalizer coefficients. Both the Linear Equalizer (LE) and the Decision Feedback Equalizer (DFE) are analyzed. Utilizing the quadratic form, designing a sparse equalizer under a single MSE constraint becomes an 10-norm minimization problem under a quadratic constraint, as described in [2]. Three previously developed methods for solving this problem are applied, namely the successive thinning algorithm, the branch-and-bound algorithm, and the simple linear programming algorithm. Simulations under various channel specifications, equalizer specifications and algorithm specifications are conducted to show the dependency of the sparsity on these factors. The channels include the ideal discrete multipath channels and the Vehicular A multi-path channels in both the Single-Input-Single- Output (SISO) and the Multiple-Input-Multiple-Output scenarios. Additionally, the sparse FIR equalizer is designed for MIMO channels under two MSE constraints. This is formulated as an 10-norm minimization problem under two quadratic constraints. A sub-optimal solution by decoupling the two constraints is proposed.by Xue Feng.S.M

A Branch-and-Bound Algorithm for Quadratically-Constrained Sparse Filter Design

This paper presents an exact algorithm for sparse filter design under a quadratic constraint on filter performance. The algorithm is based on branch-and-bound, a combinatorial optimization procedure that can either guarantee an optimal solution or produce a sparse solution with a bound on its deviation from optimality. To reduce the complexity of branch-and-bound, several methods are developed for bounding the optimal filter cost. Bounds based on infeasibility yield incrementally accumulating improvements with minimal computation, while two convex relaxations, referred to as linear and diagonal relaxations, are derived to provide stronger bounds. The approximation properties of the two relaxations are characterized analytically as well as numerically. Design examples involving wireless channel equalization and minimum-variance distortionless-response beamforming show that the complexity of obtaining certifiably optimal solutions can often be significantly reduced by incorporating diagonal relaxations, especially in more difficult instances. In the case of early termination due to computational constraints, diagonal relaxations strengthen the bound on the proximity of the final solution to the optimum.Texas Instruments Leadership University Consortium Progra

Design of discrete-time filters for efficient implementation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 325-333).The cost of implementation of discrete-time filters is often strongly dependent on the number of non-zero filter coefficients or the precision with which the coefficients are represented. This thesis addresses the design of sparse and bit-efficient filters under different constraints on filter performance in the context of frequency response approximation, signal estimation, and signal detection. The results have applications in several areas, including the equalization of communication channels, frequency-selective and frequency-shaping filtering, and minimum-variance distortionless-response beamforming. The design problems considered admit efficient and exact solutions in special cases. For the more difficult general case, two approaches are pursued. The first develops low-complexity algorithms that are shown to yield optimal or near-optimal designs in many instances, but without guarantees. The second focuses on optimal algorithms based on the branch-and-bound procedure. The complexity of branch-and-bound is reduced through the use of bounds that are good approximations to the true optimal cost. Several bounding methods are developed, many involving relaxations of the original problem. The approximation quality of the bounds is characterized and efficient computational methods are discussed. Numerical experiments show that the bounds can result in substantial reductions in computational complexity.by Dennis Wei.Ph.D

Techniques to Improve the Efficiency of Data Transmission in Cable Networks

The cable television (CATV) networks, since their introduction in the late 1940s, have now become a crucial part of the broadcasting industry. To keep up with growing demands from the subscribers, cable networks nowadays not only provide television programs but also deliver two-way interactive services such as telephone, high-speed Internet and social TV features. A new standard for CATV networks is released every five to six years to satisfy the growing demands from the mass market. From this perspective, this thesis is concerned with three main aspects for the continuing development of cable networks: (i) efficient implementations of backward-compatibility functions from the old standard, (ii) addressing and providing solutions for technically-challenging issues in the current standard and, (iii) looking for prospective features that can be implemented in the future standard. Since 1997, five different versions of the digital CATV standard had been released in North America. A new standard often contains major improvements over the previous one. The latest version of the standard, namely DOCSIS 3.1 (released in late 2013), is packed with state-of-the-art technologies and allows approximately ten times the amount of traffic as compared to the previous standard, DOCSIS 3.0 (released in 2008). Backward-compatibility is a must-have function for cable networks. In particular, to facilitate the system migration from older standards to a newer one, the backward compatible functions in the old standards must remain in the newer-standard products. More importantly, to keep the implementation cost low, the inherited backward compatible functions must be redesigned by taking advantage of the latest technology and algorithms. To improve the backward-compatibility functions, the first contribution of the thesis focuses on redesigning the pulse shaping filter by exploiting infinite impulse response (IIR) filter structures as an alternative to the conventional finite impulse response (FIR) structures. Comprehensive comparisons show that more economical filters with better performance can be obtained by the proposed design algorithm, which considers a hybrid parameterization of the filter's transfer function in combination with a constraint on the pole radius to be less than 1. The second contribution of the thesis is a new fractional timing estimation algorithm based on peak detection by log-domain interpolation. When compared with the commonly-used timing detection method, which is based on parabolic interpolation, the proposed algorithm yields more accurate estimation with a comparable implementation cost. The third contribution of the thesis is a technique to estimate the multipath channel for DOCSIS 3.1 cable networks. DOCSIS 3.1 is markedly different from prior generations of CATV networks in that OFDM/OFDMA is employed to create a spectrally-efficient signal. In order to effectively demodulate such a signal, it is necessary to employ a demodulation circuit which involves estimation and tracking of the multipath channel. The estimation and tracking must be highly accurate because extremely dense constellations such as 4096-QAM and possibly 16384-QAM can be used in DOCSIS 3.1. The conventional OFDM channel estimators available in the literature either do not perform satisfactorily or are not suitable for the DOCSIS 3.1 channel. The novel channel estimation technique proposed in this thesis iteratively searches for parameters of the channel paths. The proposed technique not only substantially enhances the channel estimation accuracy, but also can, at no cost, accurately identify the delay of each echo in the system. The echo delay information is valuable for proactive maintenance of the network. The fourth contribution of this thesis is a novel scheme that allows OFDM transmission without the use of a cyclic prefix (CP). The structure of OFDM in the current DOCSIS 3.1 does not achieve the maximum throughput if the channel has multipath components. The multipath channel causes inter-symbol-interference (ISI), which is commonly mitigated by employing CP. The CP acts as a guard interval that, while successfully protecting the signal from ISI, reduces the transmission throughput. The problem becomes more severe for downstream direction, where the throughput of the entire system is determined by the user with the worst channel. To solve the problem, this thesis proposes major alterations to the current DOCSIS 3.1 OFDM/OFDMA structure. The alterations involve using a pair of Nyquist filters at the transceivers and an efficient time-domain equalizer (TEQ) at the receiver to reduce ISI down to a negligible level without the need of CP. Simulation results demonstrate that, by incorporating the proposed alterations to the DOCSIS 3.1 down-link channel, the system can achieve the maximum throughput over a wide range of multipath channel conditions

Multi-user linear equalizer and precoder scheme for hybrid sub-connected wideband systems

Millimeter waves and massive multiple-input multiple output (MIMO) are two promising key technologies to achieve the high demands of data rate for the future mobile communication generation. Due to hardware limitations, these systems employ hybrid analog–digital architectures. Nonetheless, most of the works developed for hybrid architectures focus on narrowband channels, and it is expected that millimeter waves be wideband. Moreover, it is more feasible to have a sub-connected architecture than a fully connected one, due to the hardware constraints. Therefore, the aim of this paper is to design a sub-connected hybrid analog–digital multi-user linear equalizer combined with an analog precoder to efficiently remove the multi-user interference. We consider low complexity user terminals employing pure analog precoders, computed with the knowledge of a quantized version of the average angles of departure of each cluster. At the base station, the hybrid multi-user linear equalizer is optimized by using the bit-error-rate (BER) as a metric over all the subcarriers. The analog domain hardware constraints, together with the assumption of a flat analog equalizer over the subcarriers, considerably increase the complexity of the corresponding optimization problem. To simplify the problem at hand, the merit function is first upper bounded, and by leveraging the specific properties of the resulting problem, we show that the analog equalizer may be computed iteratively over the radio frequency (RF) chains by assigning the users in an interleaved fashion to the RF chains. The proposed hybrid sub-connected scheme is compared with a fully connected counterpart.publishe

Hybrid Transceiver Optimization for Multi-Hop Communications

Multi-hop communication with the aid of large-scale antenna arrays will play a vital role in future emergence communication systems. In this paper, we investigate amplify-and-forward based and multiple-input multiple-output assisted multi-hop communication, in which all nodes employ hybrid transceivers. Moreover, channel errors are taken into account in our hybrid transceiver design. Based on the matrix-monotonic optimization framework, the optimal structures of the robust hybrid transceivers are derived. By utilizing these optimal structures, the optimizations of analog transceivers and digital transceivers can be separated without loss of optimality. This fact greatly simplifies the joint optimization of analog and digital transceivers. Since the optimization of analog transceivers under unit-modulus constraints is non-convex, a projection type algorithm is proposed for analog transceiver optimization to overcome this difficulty. Based on the derived analog transceivers, the optimal digital transceivers can then be derived using matrix-monotonic optimization. Numeral results obtained demonstrate the performance advantages of the proposed hybrid transceiver designs over other existing solutions.Comment: 32 pages, 6 figures. This manuscript has been submitted to IEEE Journal on Selected Areas in Communications (special issue on Multiple Antenna Technologies for Beyond 5G

Spatial modulation schemes and modem architectures for millimeter wave radio systems

The rapid growth of wireless industry opens the door to several use cases such as internet of things and device-to-device communications, which require boosting the reliability and the spectral efficiency of the wireless access network, while reducing the energy consumption at the terminals. The vast spectrum available in millimeter-wave (mmWave) frequency band is one of the most promising candidates to achieve high-speed communications. However, the propagation of the radio signals at high carrier frequencies suffers from severe path-loss which reduces the coverage area. Fortunately, the small wavelengths of the mmWave signals allow packing a large number of antennas not only at the base station (BS) but also at the user terminal (UT). These massive antenna arrays can be exploited to attain high beamforming and combining gains and overcome the path-loss associated with the mmWave propagation. In conventional (fully digital) multiple-input-multiple-output (MIMO) transceivers, each antenna is connected to a specific radio-frequency (RF) chain and high resolution analog-to-digital-converter. Unfortunately, these devices are expensive and power hungry especially at mmWave frequency band and when operating in large bandwidths. Having this in mind, several MIMO transceiver architectures have been proposed with the purpose of reducing the hardware cost and the energy consumption. Fully connected hybrid analog and digital precoding schemes were proposed in with the aim of replacing some of the conventional RF chains by energy efficient analog devices. These fully connected mapping requires many analog devices that leads to non-negligible energy consumption. Partially connected hybrid architectures have been proposed to improve the energy efficiency of the fully connected transceivers by reducing the number of analog devices. Simplifying the transceiver’s architecture to reduce the power consumption results in a degradation of the attained spectral efficiency. In this PhD dissertation, we propose novel modulation schemes and massive MIMO transceiver design to combat the challenges at the mmWave cellular systems. The structure of the doctoral manuscript can be expressed as In Chapter 1, we introduce the transceiver design challenges at mmWave cellular communications. Then, we illustrate several state of the art architectures and highlight their limitations. After that, we propose scheme that attains high-energy efficiency and spectrum efficiency. In chapter 2, first, we mathematically describe the state of the art of the SM and highlight the main challenges with these schemes when applied at mmWave frequency band. In order to combat these challenges (for example, high cost and high power consumption), we propose novel SM schemes specifically designed for mmWave massive MIMO systems. After that, we explain how these schemes can be exploited in attaining energy efficient UT architecture. Finally, we present the channel model, systems assumptions and the transceiver devices power consumption models. In chapter 3, we consider single user SM system. First, we propose downlink (DL) receive SM (RSM) scheme where the UT can be implemented with single or multiple radio-frequency chains and the BS can be fully digital or hybrid architecture. Moreover, we consider different precoders at the BS and propose low complexity and efficient antenna selection schemes for narrowband and wideband transmissions. After that, we propose joint uplink-downlink SM scheme where we consider RSM in the DL and transmit SM (TSM) in the UL based on energy efficient hybrid UT architecture. In chapter 4, we extend the SM system to the multi-user case. Specifically, we develop joint multi-user power allocation, user selection and antenna selection algorithms for the broadcast and the multiple access channels. Chapter 5 is presented for concluding the thesis and proposing future research directions.Considerando los altos requerimientos de los servicios de nueva generación, las infraestructuras de red actual se han visto obligadas a evolucionar en la forma de manejar los diferentes recursos de red y computación. Con este fin, nuevas tecnologías han surgido para soportar las funcionalidades necesarias para esta evolución, significando también un gran cambio de paradigma en el diseño de arquitecturas para la futura implementación de redes.En este sentido, este documento de tesis doctoral presenta un análisis sobre estas tecnologías, enfocado en el caso de redes inter/intra Data Centre. Por consiguiente, la introducción de tecnologías basadas en redes ópticas ha sido estudiada, con el fin de identificar problemas actuales que puedan llegar a ser solucionados mediante el diseño y aplicación de nuevas técnicas, asimismo como a través del desarrollo o la extensión de los componentes de arquitectura de red.Con este propósito, se han definido una serie de propuestas relacionadas con aspectos cruciales, así como el control de dispositivos ópticos por SDN para habilitar el manejo de redes híbridas, la necesidad de definir un mecanismo de descubrimiento de topologías ópticas capaz de exponer información precisa, y el analizar las brechas existentes para la definición de una arquitectura común en fin de soportar las comunicaciones 5G.Para validar estas propuestas, se han presentado una serie de validaciones experimentales por medio de escenarios de prueba específicos, demostrando los avances en control, orquestación, virtualización y manejo de recursos con el fin de optimizar su utilización. Los resultados expuestos, además de corroborar la correcta operación de los métodos y componentes propuestos, abre el camino hacia nuevas formas de adaptar los actuales despliegues de red respecto a los desafíos definidos en el inicio de una nueva era de las telecomunicaciones.Postprint (published version