Jacob D. Griesbach

Non-uniform filterbank bandwidth allocation for system modeling subband adaptive filters

Subband adaptive filters have been used extensively in system modeling configurations to model unknown systems with large impulse responses. This paper illustrates the advantages of a non-uniform subband adaptive filter over a uniform subband adaptive filter while giving insight to subband bandwidth allocations for system modeling configurations. By implementing small subbands which isolate the transition regions in the unknown system, while using larger subbands for other, more spectrally flat regions, one can minimize convergence time and lower misadjustment.

Subband adaptive filtering decimation constraints for oversampled nonuniform filterbanks

To avoid significant inband aliasing, the decimation factors for a real filterbank must satisfy strict constraints. These decimation constraints decrease the real filterbanks computational efficiency by requiring higher subband data rates. To combat this, a set of modified pseudo-quadrature mirror filter equations are proposed which easily construct complex near-perfect reconstruction filterbanks that can be utilized to build both uniform and nonuniform filterbanks with no significant inband aliasing. With a properly designed real or complex filterbank, subband adaptive filters illustrate low m.s.e. after convergence. However, the computational complexity and convergence time associated with the complex filterbank is significantly less. Several numerical simulations are included to illustrate the conclusions.

Mean square error analysis of nonuniform subband adaptive filters for system modeling

Nonuniform filterbanks have recently been proposed for subband adaptive filters (SAFs). However, nonuniform SAFs have not yet been given a thorough performance analysis. This paper gives a comprehensive mean square error (MSE) analysis of system modeling, nonuniform (and, degeneratively, uniform) SAFs after convergence for a specified filterbank. Using the equivalent polyphase representation suggested by Ono et al., minimum MSE (MMSE) estimates for the individual subband errors are presented with respect to a given filterbank for finite length (FIR), infinite length causal (IIR), and infinite noncausal adaptive filters. Using these subband MMSE estimators, an MMSE estimator is derived for the overall fullband error. Finally, the derived MMSE estimators are verified by a numerical simulation. The intent of this paper is not to compare nonuniform and uniform SAF performance but merely to present a unified mathematical methodology to predict their MMSEs.

Constituent subband allocation for system modeling nonuniform subband adaptive filters

Subband adaptive filters (SAFs) have gained widespread use in key applications such as echo cancellation, system identification, and equalization. SAFs are normally constrained to utilize uniform filterbanks. However, it has been recently proposed that nonuniform filterbanks can give additional flexibility to SAFs that may be used to increase performance. A rigorous mean square error (MSE) analysis has also been completed for standard system modeling nonuniform SAF configurations. This paper completes the next step by theoretically deriving an adaptive algorithm to control the nonuniform filterbank for a system modeling SAF. The algorithm is constructed so that MSE, convergence time, and computational complexity are minimized. Two numerical simulations compare the nonuniform SAF adaptive filterbank algorithm to standard, equivalent uniform SAF performance.

Optimal Taper Design for Overlapped Subarray Formation

Subarray formation is common in radar and sonar beamforming applications. Overlapped subarrays are of special interest, since they can provide additional control towards minimizing grating lobes. This paper proposes a methodology towards computing subarray tapers that optimally minimize sidelobe and grating lobe levels while providing a uniform weighting over the array. This also allows maximum flexibility for subsequent digital beamforming with multiple beams within the subarray beam mainlobe. Finally, resulting beampatterns are presented and compared with other design techniques.

Spectral domain MMSE estimators for non-uniform system modeling subband adaptive filters

Non-uniform subband adaptive filters have been suggested for system modeling/echo cancellation applications due to their increased flexibility. This research derives spectral domain minimum mean square (MMSE) subband error estimators for system modeling non-uniform adaptive filters. With respect to a given filterbank, MMSE estimators are presented for infinite length causal (IIR), and infinite non-causal adaptive filters which can be used as a lower bound for finite length (FIR) adaptive filters. These error estimates can be utilized to estimate and compare the performance of non-uniform subband adaptive filters.

Fitness-based exponential probabilities for genetic algorithms applied to adaptive IIR filtering

This research evaluates a new genetic algorithm for searching multimodal error surfaces. This new technique allows the genetic algorithm to search locally with chromosomes that perform relatively well, while searching globally with the other chromosomes, as opposed to using fixed rates for local and global searches. When only the best solution is important, as in adaptive IIR filtering, the fitness-based exponential genetic algorithm is shown to, on average, outperform the fixed-rate genetic algorithm as well as the fitness-based linear genetic algorithm.

Two-parameter power-variable-training STAP

Airborne ground moving target indicator (GMTI) radars must employ a method of radar clutter mitigation to separate moving objects from stationary ground clutter. Two-parameter, power variable training STAP effectively combines two distinct STAP methods to improve clutter suppression, target detection, and angle estimation. Power variable training STAP utilizes a clutter covariance scaling factor to prevent clutter overnulling and undernulling that can degrade radar performance. Two-parameter STAP augments power variable training STAP by implementing an adaptive clutter projection null for the highest power clutter, thus limiting breakthrough clutter discretes while preserving MDV. Results are illustrated with radar data collected from the Tuxedo airborne radar.

Subband MMSE bounds for filterbank adaptation in system modeling non-uniform subband adaptive filters

Minimum mean square error estimators have been developed for non-uniform subband adaptive filters (SAF) in system modeling configurations. The next step towards practical implementation of non-uniform SAF involves developing an adaptive algorithm to control the non-uniform filterbanks bandwidths and decimation factors. This paper constructs such an algorithm using subband minimum mean square error (MMSE) bounds to suggest decimation factors. A numerical simulation shows that a non-uniform SAF can achieve lower MSE with lower complexity than an equivalent uniform SAF.

Rationally decimated constituent-based filterbanks for subband adaptive filters

Subband adaptive filters (SAFs) are commonly used in high-order adaptive systems. Typically, integer decimated filterbanks are implemented with SAFs due to their ease of design. However, integer subband rates constrain SAFs to perform suboptimally. This research outlines ideas for implementing rationally decimated filterbanks in uniform and non-uniform SAFs while allowing real-time bandwidth adaptation. Rational decimation rates can increase SAF performance and efficiency.