Richard K. Martin

A blind adaptive TEQ for multicarrier systems

This letter exploits the cyclic prefix to create a blind adaptive globally convergent channel-shortening algorithm, with a complexity like least mean squares. The cost function is related to that of the shortening signal-to-noise solution of Melsa et al. (see IEEE Trans. Commun., vol.44, p.1662-72, Dec. 1996), and simulations are provided to demonstrate the performance of the algorithm.

Unification and evaluation of equalization structures and design algorithms for discrete multitone modulation systems

To ease equalization in a multicarrier system, a cyclic prefix (CP) is typically inserted between successive symbols. When the channel order exceeds the CP length, equalization can be accomplished via a time-domain equalizer (TEQ), which is a finite impulse response (FIR) filter. The TEQ is placed in cascade with the channel to produce an effective shortened impulse response. Alternatively, a bank of equalizers can remove the interference tone-by-tone. This paper presents a unified treatment of equalizer designs for multicarrier receivers, with an emphasis on discrete multitone systems. It is shown that almost all equalizer designs share a common mathematical framework based on the maximization of a product of generalized Rayleigh quotients. This framework is used to give an overview of existing designs (including an extensive literature survey), to apply a unified notation, and to present various common strategies to obtain a solution. Moreover, the unification emphasizes the differences between the methods, enabling a comparison of their advantages and disadvantages. In addition, 16 different equalizer structures and design procedures are compared in terms of computational complexity and achievable bit rate using synthetic and measured data.

Exploiting sparsity in adaptive filters

This paper studies a class of algorithms called natural gradient (NG) algorithms. The least mean square (LMS) algorithm is derived within the NG framework, and a family of LMS variants that exploit sparsity is derived. This procedure is repeated for other algorithm families, such as the constant modulus algorithm (CMA) and decision-directed (DD) LMS. Mean squared error analysis, stability analysis, and convergence analysis of the family of sparse LMS algorithms are provided, and it is shown that if the system is sparse, then the new algorithms will converge faster for a given total asymptotic MSE. Simulations are provided to confirm the analysis. In addition, Bayesian priors matching the statistics of a database of real channels are given, and algorithms are derived that exploit these priors. Simulations using measured channels are used to show a realistic application of these algorithms.

Self-collimation in photonic crystal structures: a new paradigm for applications and device development

In this paper, we report on the development of the self-collimation phenomenon in photonic crystal structures for integrated optics applications. In addition, detailed numerical analysis, design procedures, fabrication and characterization techniques are included. Applications presented in this paper include: channelless waveguiding, orthogonal bending of light, tunable beam splitter, all-optical analog-to-digital converter, reconfigurable optical switch, chemical/gas sensor and a three-dimensional optical interconnect bus.

Low-complexity MIMO blind, adaptive channel shortening

Channel shortening is often employed as a means of mitigating intersymbol and intercarrier interference (ISI and ICI) in systems using multicarrier modulation. The Multicarrier Equalization by Restoration of RedundancY (MERRY) algorithm has previously been shown to blindly and adaptively shorten a channel to the length of the guard interval in a multicarrier system. This paper addresses synchronization and complexity reduction issues that were not dealt with in previous work and provides extensions to and generalizations of the MERRY algorithm. A modification is presented that removes the square root and division needed at each iteration without introducing additional complexity, with the added benefit of allowing the use of constraints other than a unit norm equalizer; an extension is proposed that allows for the use of more data in the MERRY update; the algorithm is generalized to the multiple-input multiple output (MIMO) and fractionally spaced cases; a low-complexity, blind symbol synchronization technique is proposed, and a method is proposed for blind initialization of the algorithm to avoid slow modes of convergence. Each extension to the basic MERRY algorithm is accompanied by an illustrative simulation example.

Adaptive equalization: transitioning from single-carrier to multicarrier systems

This article discusses the creation of adaptive algorithms for channel shortening, with particular attention to blind algorithms. The context is multicarrier modulation, through other applications of channel shortening are discussed. It is shown that the algorithms used for adaptive equalization are not easily applied to adaptive channel shortening. In a return to first principles, a property restoral design philosophy is put forth and several recent property-restoral-based approaches to adaptive channel shortening are reviewed. The authors conclude with a discussion of the limitations of the current approaches and a list of open problems in the area of adaptive channel shortening.

Algorithms and bounds for estimating location, directionality, and environmental parameters of primary spectrum users

Most existing work on dynamic spectrum access deals with creating a spectral and temporal map of spectrum white space, and then filling it. The spectrum can be better utilized by increasing the spatial awareness of secondary users to include knowledge of the locations of all primary and secondary users, as well as the orientations and parameters of their directional or omni-directional antennas. This paper derives a maximum likelihood (ML) algorithm, an approximate ML algorithm, and associated performance bounds for jointly estimating a transmitters position, orientation, beam width, and transmit power, as well as the environments path loss exponent, using received signal strength measurements. The methods can be used for either a primary or secondary user. Simulations are used to determine what types of sensor geometries lead to good estimates of each parameter, to evaluate the performance of the estimators, and to determine spectrum availability as a function of spatial coordinates.

Bandwidth Efficient Cooperative TDOA Computation for Multicarrier Signals of Opportunity

Source localization, the problem of determining the physical location of an acoustic or wireless emitter, is commonly encountered in sensor networks which are attempting to locate and track an emitter. Similarly, in navigation systems that do not rely on the global positioning system (GPS), ldquosignals of opportunityrdquo (existing wireless infrastructure) can be used as ad hoc navigation beacons, and the goal is to determine their location relative to a receiver and thus deduce the receivers position. These two research problems have a very similar mathematical structure. Specifically, in either the source localization or navigation problem, one common approach relies on time difference of arrival (TDOA) measurements to multiple sensors. In this paper, we investigate a bandwidth efficient method of TDOA computation when the signals of opportunity use multicarrier modulation. By exploiting the structure of the multicarrier transmission, much less information needs to be exchanged between sensors compared to the standard cross correlation approach. Analytic and simulation results quantify the performance of the proposed algorithm as a function of the signal-to-noise ratio (SNR) and the bandwidth between the sensors.

Blind, adaptive channel shortening by sum-squared auto-correlation minimization (SAM)

We propose a new blind, adaptive channel shortening algorithm for updating a time-domain equalizer (TEQ) in a system employing multicarrier modulation. The technique attempts to minimize the sum-squared auto-correlation of the combined channel-TEQ impulse response outside a window of desired length. The proposed algorithm, sum-squared auto-correlation minimization (SAM), assumes the source sequence to be white and wide-sense stationary, and it is implemented as a stochastic gradient descent algorithm. Simulation results demonstrating the success of the SAM algorithm are provided.

Fast-Converging Blind Adaptive Channel-Shortening and Frequency-Domain Equalization

Orthogonal frequency-division multiplexing (OFDM) is a popular transmission format for emerging wireless communication systems, including satellite radio, various wireless local area network (LAN) standards, and digital broadcast television. Single-carrier cyclic-prefixed (SCCP) modulation is similar to OFDM, but with all frequency-domain operations performed at the receiver. Systems employing OFDM and SCCP perform well in the presence of multipath provided that the channel delay spread is shorter than the guard interval between transmitted blocks. If this condition is not met, a channel-shortening equalizer can be used to shorten the channel to the desired length. In modestly time-varying environments, an adaptive channel shortener is of interest. All existing adaptive channel shorteners require renormalization to restrain the channel shortener away from zero. In this paper, we study the use of a unit-tap constraint rather than a unit-norm constraint on the adaptive channel shortener. We use this constraint to manipulate existing algorithms into a framework analogous to the recursive least squares algorithm, and we develop adaptation rules for blind and semiblind frequency domain equalizers for SCCP receivers. Simulations of the proposed algorithms show an order of magnitude improvement in convergence speed, as well as a reduced asymptotic bit error rate