A VSLMS Style Tap-length Learning Algorithm for Structure Adaptation

Compared with the ordinary adaptive filter, the variable-length adaptive filter is more efficient (including smaller., lower power consumption and higher computational complexity output SNR) because of its tap-length learning algorithm, which is able to dynamically adapt its tap-length to the optimal tap-length that best balances the complexity and the performance of the adaptive filter. Among existing tap-length algorithms, the LMS-style Variable Tap-Length Algorithm (also called Fractional Tap-Length Algorithm or FT Algorithm) proposed by Y.Gong has the best performance because it has the fastest convergence rates and best stability. However, in some cases its performance deteriorates dramatically. To solve this problem, we first analyze the FT algorithm and point out some of its defects. Second, we propose a new FT algorithm called 'VSLMS' (Variable Step-size LMS) Style Tap-Length Learning Algorithm, which not only uses the concept of FT but also introduces a new concept of adaptive convergence slope. With this improvement the new FT algorithm has even faster convergence rates and better stability. Finally, we offer computer simulations to verify this improvement.

An LMS style variable tap-length algorithm for structure adaptation

Searching for the optimum tap-length that best balances the complexity and steady-state performance of an adaptive filter has attracted attention recently. Among existing algorithms that can be found in the literature, two of which, namely the segmented filter (SF) and gradient descent (GD) algorithms, are of particular interest as they can search for the optimum tap-length quickly. In this paper, at first, we carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvantages relative to the other. Then, we propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length (FT). Updating the tap-length with instantaneous errors in a style similar to that used in the stochastic gradient [or least mean squares (LMS)] algorithm, the proposed FT algorithm not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms. Both performance analysis and numerical simulations are given to verify the new proposed algorithm.

Structure adaptation of linear MMSE adaptive filters

The tap-length, or the number of the taps, is an important structural parameter of the linear MMSE adaptive filter. Although the optimum tap-length that balances performance and complexity varies with scenarios, most current adaptive filters fix the tap-length at some compromise value, making them inefficient to implement especially in time-varying scenarios. A novel gradient search based variable tap-length algorithm is proposed, using the concept of the pseudo-fractional tap-length, and it is shown that the new algorithm can converge to the optimum tap-length in the mean. Results of computer simulations are also provided to verify the analysis.

Optimum decision delay of the finite-length DFE

This letter investigates the optimum decision delay and tap-length of the finite-length decision feedback equalizer. First we show that, if the feedback filter (FBF) length N-b is equal to or larger than the channel memory upsilon and the decision delay Delta is smaller than the feedforward filter (FFF) length N-f, then only the first Delta + 1 elements of the FFF can be nonzero. Based on this result we prove that the maximum effective FBF length is equal to the channel memory upsilon, and if N-b greater than or equal to upsilon and N-f is long enough, the optimum decision delay that minimizes the MMSE is N-f - 1.

Optimum decision delay of the finite-length DFE

This work investigates the optimum decision delay and tap-length of the finite-length decision feedback equalizer. First we show that, if the feedback filter (FBF) length Nb is equal to or larger than the channel memory v and the decision delay Δ is smaller than the feedforward filter (FFF) length Nf, then only the first Δ+1 elements of the FFF can be nonzero. Based on this result we prove that the maximum effective FBF length is equal to the channel memory v, and if Nb ≥ v and Nf is long enough, the optimum decision delay that minimizes the MMSE is Nf-1.

An adaptive linear equalizer with optimum filter length and decision delay

The power of an adaptive equalizer is maximized when the structural parameters including the tap-length and decision delay can be optimally chosen. Although the method for adjusting either the tap-length or decision delay has been proposed, adjusting both simultaneously becomes much more involved as they interact with each other. In this paper, this problem is solved by putting a linear prewhitener before the equalizer, with which the equivalent channel becomes maximum-phase. This implies that the optimum decision delay can be simply ¯xed at the tap-length minus one, while the tap-length can then be chosen using a similar approach as that proposed in our previous work.

Flexible MMSE DFE using length and LAG adaptation

This paper investigates how to choose the optimum tap-length and decision delay for the decision feedback equalizer (DFE). Although the feedback filter length can be set as the channel memory, there is no closed-form expression for the feedforward filter length and decision delay. In this paper, first we analytically show that the two dimensional search for the optimum feedforward filter length and decision delay can be simplified to a one dimensional search, and then describe a new adaptive DFE where the optimum structural parameters can be self-adapted.

Pentagonal parch-excited sectorized antenna for localization systems

A pentagonal patch-excited sectorized antenna (SA) suitable for 2.4-2.5 GHz localization systems was studied and developed. The integration of six patch-excited structures converges into a sectorized antenna called Hive5 that provides gain improvement compared to a patch antenna, maximum variation of 3 dB beam width over the radiation pattern and circular polarization (CP). This antenna is presented and analyzed taking into account the tap length and the flare angle. The proposed antenna in combination with a RF-Switch provides a cost effective solution for localization based on Wireless Sensor Networks (WSN) and will be used for implementing angle of arrival (AoA) techniques combined with RF fingerprinting techniques.

Fractional order modelling of zero length column desorption response for adsorbents with variable particle sizes

This manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena resembles those of fractional order systems, namely those with a fast initial transient followed by long and slow tails. The experimental measurements are best fitted with the Harris model revealing a power law behavior.

Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous PBT's and complex FRT's are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the Function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy. (C) 1997 Optical Society of America.