Group Delay Deviation Research Articles

A Nonlinear Optimization Design Algorithm for Nearly Linear-Phase 2D IIR Digital Filters

In this paper, a new optimization method for the design of nearly linear-phase two-dimensional infinite impulse (2D IIR) digital filters with a separable denominator is proposed. A design framework for 2D IIR digital filters is formulated as a nonlinear constrained optimization problem where the group delay deviation in the passband is minimized under prescribed soft magnitude constraints and hard stability requirements. To achieve this goal, sub-level sets of the group delay deviations are utilized to generate a sequence of filters, from which the one with the best performance is selected. The quality of the obtained filter is evaluated using three quality factors, namely, the passband magnitude quality factor Qh and the group delay deviation quality factor Qτ, while the third one is a new quality factor Qs that assesses the performance in the stopband relative to the minimum filter gain in the passband. The proposed framework is implemented using the interior-point (IP) method in a MATLAB environment, and the experimental results show that filters designed using the proposed method have good magnitude response and low group delay deviation. The performance of the resulting filters is compared with the results of other methods.

Improved Design Method for Nearly Linear-Phase IIR Filters Using Constrained Optimization

In this paper, the design of nearly linear-phase recursive digital filters using a constrained optimization method is investigated. The method is based on existing constrained optimization techniques for nearly linear-phase IIR digital filters, and it is expected to be useful in applications where both magnitude and phase response specifications are required to be satisfied. Starting from an initial filter, the proposed method minimizes the group delay deviation under a set of linear constraints in terms of the magnitude response and filter stability. Improved sampling functions are introduced to the optimization problem, which are used to control the sampling points that are used for approximating the group delay and the rest of the constraints in various frequency bands. By using the proposed sampling functions we get an improved IIR filter response.

A Compact Ka-Band 4-bit Phase Shifter With Low Group Delay Deviation

This letter presents a compact $Ka$ -band 4-bit switch-type phase shifter with low group delay deviation (GDD) using 28-nm CMOS technology. A magnetically coupled all-pass network (APN) configuration is employed to achieve both equal and flat group delay characteristics versus frequency at each phase state. The measured rms phase error is 1.2°, and the gain error is 1.1 dB at 33 GHz. The average measured insertion loss is 12.8 dB at 33 GHz, and the input and output return losses are both lower than −10 dB from 29 to 37 GHz. The fabricated phase shifter has a compact size of 0.08 mm2 excluding pads, low GDD of ±4 ps, and rms group delay error of $Ka$ -band phase shifter has the lowest GDD per bandwidth (GDD/BW) compared with other reported passive phase shifters.

Area- and Power-Efficient Nearly-Linear Phase Response IIR Filter by Iterative Convex Optimization

Low complexity infinite impulse response (IIR) filter design with nearly-linear phase response has attracted considerable attention in recent years due to the substantially high area and power consumption of linear phase finite impulse response (FIR) filter. Compared with the FIR filter, designing an IIR filter with the minimized group delay deviation and low power cost is a challenging topic. In this paper, the non-convex group delay deviation minimization problem for IIR filter design is reformulated into an iterative optimization problem to achieve lower group delay deviation. The hardware complexity of the solution is iteratively reduced by approximating the IIR filter coefficients to maximize the number of eliminable common subexpressions. The headroom for the coefficient adjustment is governed by the gradient of group delay deviation between iterations. Using our proposed design algorithm, a high-order lowpass filter with a minimum stopband attenuation of 60dB can be implemented by a 13-tap IIR filter with a group delay deviation of 0.002 only, as opposed to two linear-phase FIR filters designed by two recent and competitive FIR filter design algorithms with tap number of 51 and 57, respectively. Logic synthesis shows that the proposed IIR design saves 39.4% of the area and 41.8% of power consumption over the FIR solutions. Comparing with the latest nearly-linear phase IIR filter design algorithms, the group delay deviation of the solutions generated by our proposed algorithm are on average 25.5% lower, along with an average area and power savings of 20.5% and 18.4%, respectively, from the logic synthesis results.

Transition between flat magnitude and flat group delay low pass recursive digital filters

Many a paper has been written on the characteristics of the continuous-time and discrete-time low-pass filters which are designed to have either maximally flat magnitude characteristics or maximally flat group delay responses. The polynomial (all pole) low pass recursive digital filters which are characterised by characterise the transition between a flat magnitude and flat group delay characteristics, named Transitional Butterworth Thiran (TBTh) recursive digital filters, is considered. The characteristics of the resulting filter change gradually from the characteristics of the well known Butterwort's filter to the characteristics of the Thiran's filter with the maximally flat group delay characteristic. Poles of the TBTh filter are obtained by interpolating between poles Butterworth and Thiran's filters by varying a parametar which controls the pole positions that enables a tradeoff between the steepness magnitude characteristic at passband edge and group delay deviation.

A 128-Tap Highly Tunable CMOS IF Finite Impulse Response Filter for Pulsed Radar Applications

A configurable-bandwidth (BW) filter is presented in this paper for pulsed radar applications. To eliminate dispersion effects in the received waveform, a finite impulse response (FIR) topology is proposed, which has a measured standard deviation of an in-band group delay of 11 ns that is primarily dominated by the inherent, fully predictable delay introduced by the sample-and-hold. The filter operates at an IF of 20 MHz, and is tunable in BW from 1.5 to 15 MHz, which makes it optimal to be used with varying pulse widths in the radar. Employing a total of 128 taps, the FIR filter provides greater than 50-dB sharp attenuation in the stopband in order to minimize all out-of-band noise in the low signal-to-noise received radar signal. Fabricated in a 0.18- $\mu \text{m}$ silicon on insulator CMOS process, the proposed filter consumes approximately 3.5 mW/tap with a 1.8-V supply. A 20-MHz two-tone measurement with 200-kHz tone separation shows IIP3 greater than 8.5 dBm.

외팔 보를 이용한 Location Template Matching 방법을 적용함에 있어서 격자간격의 영향 분석

Measuring similarity between two signals is a key element of the location template matching (LTM) method which is one of impact source localization technique. As a measure of similarity, the correlation coefficient is most widely used, and the group delay based method is recently proposed to improve the accuracy of finding the impact source. In practice, the LTM method assumes that the similarity between two signals decreases as the distance between two corresponding impact points increases, where the distance between two neighboring impact points defines the grid spacing. In this paper, it is shown that this assumption is not always true but the correlation coefficients fluctuate forming a main robe and many side robes as the distance between two neighboring impact points increases. On the other hand, the standard deviation of group delay sharply increases with a small increase of the grid spacing. These are demonstrated by using a simple cantilever beam. Based on these findings, an optimal way of implementing the LTM method may be suggested by combining the correlation coefficient and the group delay based approaches.

Analysis and design of miniaturized multisection crossover with open stubs

ABSTRACTA compact branch‐line crossover using open stubs structure is proposed. Even and odd mode analysis is adopted to derive the analytical formulas for a crossover with wide bandwidth and a compact size. The proposed crossover operating at 2.5 GHz has a fractional bandwidth of 23% (from 2.2 to 2.78 GHz) with high isolation, a high return loss, and low insertion loss. It also has a low group delay deviation of about 0.38 ns. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2673–2677, 2015

Iterative Closed-Loop Phase-Aware Single-Channel Speech Enhancement

Many short-time Fourier transform (STFT) based single-channel speech enhancement algorithms are focused on estimating the clean speech spectral amplitude from the noisy observed signal in order to suppress the additive noise. To this end, they utilize the noisy amplitude information and the corresponding a priori and a posteriori SNRs while they employ the observed noisy phase when reconstructing enhanced speech signal. This paper presents two contributions: i) reconsidering the relation between the phase group delay deviation and phase deviation, and ii) proposing a closed-loop single-channel speech enhancement approach to estimate both amplitude and phase spectra of the speech signal. To this end, we combine a group-delay based phase estimator with a phase-aware amplitude estimator in a closed loop design. Our experimental results on various noise scenarios show considerable improvement in the objective perceived signal quality obtained by the proposed iterative phase-aware approach compared to conventional Wiener filtering which uses the noisy phase in signal reconstruction.

L -infinity norm design of linear-phase robust broadband beamformers using constrained optimization

A new method for the design of linear-phase robust far-field broadband beamformers using constrained optimization is proposed. In the method, the maximum passband ripple and minimum stopband attenuation are ensured to be within prescribed levels, while at the same time maintaining a good linear-phase characteristic at a prescribed group delay in the passband. Since the beamformer is intended primarily for small-sized microphone arrays where the microphone spacing is small relative to the wavelength at low frequencies, the beamformer can become highly sensitive to spatial white noise and array imperfections if a direct minimization of the error is performed. Therefore, to limit the sensitivity of the beamformer the optimization is carried out by constraining a sensitivity parameter, namely, the white noise gain (WNG) to be above prescribed levels across the frequency band. Two novel design variants have been developed. The first variant is formulated as a convex optimization problem where the maximum error in the passband is minimized, while the second variant is formulated as an iterative optimization problem and has the advantage of significantly improving the linear-phase characteristics of the beamformer under any prescribed group delay or linear-array configuration. In the second variant, the passband group-delay deviation is minimized while ensuring that the maximum passband ripple and stopband attenuation are within prescribed levels. To reduce the computational effort in carrying out the optimization, a nonuniform variable sampling approach over the frequency and angular dimensions is used to compute the required parameters. Experiment results show that beamformers designed using the proposed methods have much smaller passband group-delay deviation for similar passband ripple and stopband attenuation than a modified version of an existing method.

60-GHz 5-bit Phase Shifter With Integrated VGA Phase-Error Compensation

A 57-64-GHz low phase-error 5-bit switch-type phase shifter integrated with a low phase-variation variable gain amplifier (VGA) is implemented through TSMC 90-nm CMOS low-power technology. Using the phase compensation technique, the proposed VGA can provide appropriate gain tuning with almost constant phase characteristics, thus greatly reducing the phase-tuning complexity in a phased-array system. The measured root mean square (rms) phase error of the 5-bit phase shifter is 2° at 62 GHz. The phase shifter has a low group-delay deviation (phase distortion) of +/- 8.5 ps and an excellent insertion loss flatness of ±0.8 dB for a specific phase-shifting state, across 57-64 GHz. For all 32 states, the insertion loss is 14.6 ± 3 dB, including pad loss at 60 GHz. For the integrated phase shifter and VGA, the VGA can provide 6.2-dB gain tuning range, which is wide enough to cover the loss variation of the phase shifter, with only 1.86° phase variation. The measured rms phase error of the 5-bit phase shifter and VGA is 3.8° at 63 GHz. The insertion loss of all 32 states is 5.4 dB, including pad loss at 60 GHz, and the loss flatness is ±0.8 dB over 57-64 GHz. To the best of our knowledge, the 5-bit phase shifter presents the best rms phase error at center frequency among the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> -band switch-type phase shifter.

Improved Design Method for Nearly Linear-Phase IIR Filters Using Constrained Optimization

A new optimization method for the design of nearly linear-phase IIR digital filters that satisfy prescribed specifications is proposed. The group-delay deviation is minimized under the constraint that the passband ripple and stopband attenuation are within the prescribed specifications and either a prescribed or an optimized group delay can be achieved. By representing the filter in terms of a cascade of second-order sections, a non-restrictive stability constraint characterized by a set of linear inequality constraints can be incorporated in the optimization algorithm. An additional feature of the method, which is very useful in certain applications, is that it provides the capability of constraining the maximum gain in transition bands to be below a prescribed level. Experimental results show that filters designed using the proposed method have much lower group-delay deviation for the same passband ripple and stopband attenuation when compared with corresponding filters designed with several state-of-the-art competing methods.

Novel Quasi-Hermetic Photodiode Module Featuring an E-Band Rectangular Waveguide (WR-12) Output

A quasi-hermetic photodiode module featuring a WR-12 rectangular waveguide (RW) output has been developed for operation in the E-band. The module makes use of a grounded coplanar-waveguide-to-rectangular-waveguide transition implemented on a Rogers RT/duroid 5880 laminate that does not require any mechanical modifications of the RW. Simulations show that the transition has excellent radio frequency (RF) characteristics (return loss larger than 30 dB, insertion loss smaller than 2 dB, maximum group delay deviation smaller than 1 ps). Measurements confirm the simulated results and highlight the importance of via-holes to reduce the overall loss. The maximum output power delivered by the module, at a DC photocurrent of 10 mA, is -12.5dBm. At 73 GHz, the 1-dB compression point is found to be at a photocurrent of ~ 9mA, with an RF output power of ~ -13.5dBm . The measured output power has less than 1 dB ripple in the frequency range of interest.

Design of compact planar crossover using Sierpinski carpet microstrip patch

The design of a planar four-port microstrip crossover is presented. The design starts by using a half-wavelength square patch and two sets of orthogonal feeding lines. Based on the cavity theory, operation of the patch crossover is analysed. Full-wave simulations and measurements are used to support the analysis. By etching the patch as a Sierpinski carpet, resonant frequency can be lowered significantly, and this property can be employed to reduce the size of the conventional patch crossover. It is shown that the size of the crossover can be reduced by 23% with even a better performance when a second-order Sierpinski carpet microstrip patch is used. Full-wave simulations and measurements are used to validate the proposed design method. The measured data show less than 1 dB insertion loss, more than 10 dB return loss, more than 17 dB isolation and about 0.1 ns group delay deviation across 10% fractional bandwidth centred at 2.4 GHz.

Wideband planar microstrip crossover with high power handling capability and low distortion

The design of a planar four-port microstrip crossover is presented. The design starts by using a half-wavelength square patch and two sets of orthogonal feeding lines. To achieve a wideband performance, four circular slots are introduced in the square patch. A parametric analysis is used to investigate the effect of the utilized slots. Full-wave simulations and measurements are used to validate the proposed design. The simulated and measured data show less than 1 dB insertion loss, more than 10 dB return loss, more than 19 dB isolation, and about 0.2 ns group delay deviation across the band from 2.1 to 2.75 GHz. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:439–443, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27335

Delay-Spread Distribution for Multimode Fiber With Strong Mode Coupling

In the strong mode coupling regime, the delay spread of multimode fiber is statistically the same as the difference between the maximum and minimum eigenvalues of a Gaussian unitary ensemble. We study the delay-spread distribution using three methods: 1) numerical evaluation of the Fredholm determinant; 2) numerical integration based on the Andréief identity; and 3) approximation based on the Tracy-Widom distribution. Results obtained using the Fredholm determinant and the Andréief identity are virtually indistinguishable. The approximation based on the Tracy-Widom distribution is sufficiently accurate for most engineering purposes when the number of modes is at least 12. In a digital equalizer, a memory length of four to five times the group-delay standard deviation is sufficient to ensure that the delay spread will exceed the equalizer memory length with a probability of less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> -10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> .

Planar wideband crossover with distortionless response using dual‐mode microstrip patch

AbstractA microwave crossover using a dual‐mode microstrip patch is presented. The patch is designed to operate at two orthogonal modes. Each of those modes is used to couple a pair of face‐to‐face ports. The isolation between the two orthogonal modes is enhanced by using symmetrical slits in the microstrip patch. The proposed crossover has the main features of high‐power handling capability and distortionless response due to its extremely low group delay deviation. A prototype is designed to operate at the WLAN band from 5.15 to 5.85 GHz. The simulated and measured results indicate less than 0.06 ns deviation in the group delay, less than 1 dB insertion loss, more than 13 dB return loss and more than 12 dB isolation across the whole band. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2077–2079, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27028

CMOS Passive Phase Shifter With Group-Delay Deviation of 6.3 ps at $K$-Band

This paper presents a CMOS vector-sum-based phase shifter with a flat group-delay deviation of 6.3 ps at K-band. The theoretical analyses confirm the effects of the nonideal phase-invertible variable attenuator (PIVA) on the increasing of the root-mean-square (rms) phase error and magnitude variation of the phase shifter. The design procedures, which can eliminate the effects from the voltage-dependent parasitics of the reflection load and the nonideal directional coupler, are reported to make an ideal phase reversal and reduce the attenuation-dependent phase shifting of the PIVA. The prototype of the phase shifter, which consists of one 3-dB directional coupler, two PIVAs, and one power combiner, are realized by using synthetic transmission lines for the circuit miniaturization. The circuit is fabricated in standard 0.18-μm 1P6M CMOS technology with a size of 560 μm × 560 μm excluding the testing pads. The comparisons between simulated and experimental results show that the prototype can cover full 360° phase shifting with less than 1.5° of rms phase error and 0.45 dB of magnitude variation from 22.0 to 26.0 GHz. The input P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1dB</sub> and IIP3 of the prototype with a relative phase shifting of 292.5° are 12.0 and 28.0 dBm, respectively.

Optimal Design of an RSPUDT-Based SAW Filter with Constant Group Delay

This paper describes the application of resonant single-phase unidirectional transducers (RSPUDTs) to the development of low-loss SAW filters with constant group delay in transition bands as well as in the passband. A low-loss SAW filter with constant group delay was designed and fabricated on a 128 degrees YX-LiNbO3 substrate. Experimental results were in good agreement with the design; the group delay deviation of 20 ns was realized over the range of +/-8 MHz at the center frequency of 512 MHz. The minimum insertion loss and -3 dB bandwidth were 4.3 dB and 8.5 MHz, respectively. The application of this technique is also extended to develop high-performance wideband filters employing quasi-slanted interdigital transducers.

Antenna Link Transfer Function Factorization Applied to Optimized Channel Design

A channel broadband factored model is developed and numerically verified with a method of moment (MoM) technique for design of optimized UWB links with real, dispersive antennas. In this study, two-antenna link transfer functions are decomposed into port-load and full-wave dependent components based on general linearity and reciprocity in electromagnetics. Specifically, the port-related components account for antenna termination to the transmitter generator and front-end receiver circuits as antenna loads. In turn, the wave portion, which is associated with link transmission impedance, involves all geometrical factors like antenna shapes and their positioning/pointing in space that account collectively for radiation, propagation and reception. As a result, any link of fixed geometry can be full-wave numerically simulated just once for a suitable set of reference generator/load impedances. Then, all variations in link performance caused by variable port terminations are easily predicted by manipulating the full-wave data obtained for the case of reference antenna port loads. This approach provides some useful physical insights and an optimized co-design procedure for transmitter and receiver impedances to meet several significant performance-related design objectives, such as: i) maximized link energy transmission efficiency; ii) maximum amplitude of received signals; iii) minimized time confinement for signal energy at receiver loads; iv) flatness of magnitude of link transfer functions; and v) minimized group delay deviation. The major results are numerically illustrated for a number of useful far-field line-of-sight link cases with flat and solid dipole antennas operating in up to 3:1 bands and ideally aligned in terms of their gain and polarization matching. Numerical results are given in a normalized form and scalable to any band of interest