Approximate Linear Phase Research Articles

Design and Implementation of a Low-Complexity Multi-h CPM Receiver with Linear Phase Approximation Synchronization Algorithm.

Multi-h continuous phase modulation (CPM), with extremely high spectral efficiency, involves the plague of high demodulation complexity with a large number of matched filters and a complex trellis. In this paper, an efficient all-digital demodulator for multi-h continuous phase modulation (CPM) is proposed based on a low-complexity decision-directed synchronization algorithm. Based on the maximum-likelihood estimation of the carrier phase and timing errors, we propose a reduced-complexity timing error detector with linear phase approximation (LPA) to the phase of the multi-h CPM. Compared with the traditional synchronization methods, it avoids derivative matched filtering and reduces about 2/3 of matched filters. The estimated accuracy and bit error rate (BER) performance of the LPA-based synchronization algorithm have no loss, as shown by the numerical simulation. Its stability is verified by the derived S-curve. Then, the receivers with the LPA-based synchronization for the three kinds of promising multi-h CPM are implemented on a Xilinx Kintex-7 FPGA platform. The experimental results show that the onboard tested BER of the proposed design has an ignorable loss in the numerical simulation. The implementation overhead on FPGA is significantly reduced by about 27% slices, 64% DSPs, and 70% block RAMs compared with the conventional method.

The Phase Response of a Rough Rectangular Facet for Radar Sounder Simulations of Both Coherent and Incoherent Scattering

AbstractWith radar sounders, coherent backscattering simulations from global planetary digital elevation models (DEMs) typically display a deficit in diffuse clutter, which is mainly due to the implicit assumption that roughness at scales below the resolution of the DEM is absent. Indeed, while polynomial approximations of the phase evolution across the facet allow for fast and mathematically rigorous simulators, the coarse resolution of these planetary DEMs leads to a potentially significant portion of the backscattering response being neglected. In this paper, we derive the analytical phase response of a rough rectangular facet characterized by Gaussian roughness and a Gaussian isotropic correlation function under the linear phase approximation. Formulae for the coherent and incoherent power scattered by such an object are obtained for arbitrary bistatic scattering angles. Validation is done both in isolation and after inclusion in different Stratton‐Chu simulators. In order to illustrate the different uses of such a formulation, we reproduce two lunar radargrams acquired by the Lunar Radar Sounder instrument with a Stratton‐Chu simulator incorporating the proposed rough facet phase integral, and we show that the original radargrams are significantly better‐reproduced than with state‐of‐the‐art methods, at a similar computational cost. We also show how the rough facet integral formulation can be used in isolation to better characterize subglacial water bodies on Earth.

Unique-Solution Single-Sample Complex Dielectric Characterization Through Linear Phase Approximation

Unique-Solution Single-Sample Complex Dielectric Characterization Through Linear Phase Approximation

A Coherent Method for Simulating Active and Passive Radar Sounding of the Jovian Icy Moons

The possibility to apply passive radar sounding techniques to the Jovian icy moons, making use of Jupiter's strong decametric emissions (DAMs), has recently garnered large research interest. In this article, we propose a radar sounding simulation approach being able to simulate and compare passive and active acquisitions for a given scenario. The proposed simulator is based on the Stratton-Chu integral used with the linear phase approximation on triangular facets. The external field is modeled with plane waves, the direction, polarization, and amplitude of which can be freely chosen. The time-domain dependence can be either synthetically generated (e.g., Gaussian white noise) or taken from experimental measurements (e.g., waveforms recorded by a radio telescope observing Jupiter). For passive sounding, both autocorrelation and cross-correlation processing are considered. Validation tests were conducted on a series of ideal digital elevation models (DEMs), such as flat surfaces and subsurfaces, or Gaussian rough surfaces, and a good agreement with the existing literature was obtained. To illustrate the capabilities of the proposed simulator, we conducted additional more realistic experiments of radar sounding simulations, where we use both white noise and Jovian waveforms recorded by the LWA1 radio telescope.

A Simplified Direct-Decision Synchronization Algorithm for Coherent CPM Receiver Using Linear Phase Approximation

We propose a simplified decision-directed synchronization algorithm for continuous phase modulation (CPM) based on the linear approximation to the phase of the CPM signal. It yields simple and practical synchronization algorithm with closed-loop architecture, in which the derivative matched filters are not required. Numerical results demonstrate that this novel synchronizer achieves improved timing estimation performance while requiring lower complexity when compared with the well-known method based on pulse amplitude modulation approximation. The demodulation architecture with the proposed algorithm is presented, and its bit-error-rate approaches the theoretical bound.

Design and FPGA implementation of 11th order Efficient IIR Wavelet Filter Banks with Approximate Linear-phase

In this paper. Bireciprocal Lattice Wave Digital Filters (BLWDFs) are utilized in an approximate linear-phase in pass-band design of order IIR wavelet filter banks (FBs). These filter banks are efficiently designed by replacement one of branches for (BLWDFs) by only a unit delay. The coefficients of the designed filter are achieved by simulating the IIR response suggested in [1]. The design is first simulated using Matlab programming in order to investigate the resulting wavelet filter properties and to find the suitable wordlength for the BLWDFs coefficients. FPGA implemtation of the proposed IIR wavelet filter bank is also achived for three levels with less complexity and high operating frequency.

Design and FPGA implementation of 11th order Efficient IIR Wavelet Filter Banks with Approximate Linear-phase

In this paper. Bireciprocal Lattice Wave Digital Filters (BLWDFs) are utilized in an approximate linear-phase in pass-band design of order IIR wavelet filter banks (FBs). These filter banks are efficiently designed by replacement one of branches for (BLWDFs) by only a unit delay. The coefficients of the designed filter are achieved by simulating the IIR response suggested in [1]. The design is first simulated using Matlab programming in order to investigate the resulting wavelet filter properties and to find the suitable wordlength for the BLWDFs coefficients. FPGA implemtation of the proposed IIR wavelet filter bank is also achived for three levels with less complexity and high operating frequency.

A Coherent Multilayer Simulator of Radargrams Acquired by Radar Sounder Instruments

Reliable electromagnetic simulators are of prime importance for the design of radar sounder instruments and for supporting the subsequent analysis of their data. In this paper, we present a coherent, facet method-based simulator that can compute radar echoes from the subsurface of a target area with an arbitrary number of geological layers, thus going beyond the surface-only or the two-layer descriptions so far implemented in coherent ray-tracing radar sounder simulators. Propagation of fields throughout the subsurface is computed according to Snell’s law following a ray-tracing approach. For each ray interacting with the surface, be it a direct reflection or a refracted ray coming from the subsurface, the phase contribution of each facet is calculated through the linear phase approximation, while the total field received at the antenna is computed using Huygen’s principle. Validation simulations have been performed against the radar data of lunar and martian areas characterized by a multilayer nature and collected by the Lunar Radar Sounder instrument of JAXA’s Kaguya lunar probe and the Shallow Radar instrument onboard NASA’s Mars Reconnaissance Orbiter, respectively. Results confirm the effectiveness of the proposed simulator.

Estimation of Modulation Index for Partial Response CPM Signal

Continuous phase modulation (CPM) is a power and bandwidth efficient modulation scheme used in cellular, personal, and satellite communications among other applications. If the modulation index of the CPM waveform used by the transmitter is unavailable at the receiver, serious performance degradation may occur. This paper investigates the problem of modulation index estimation for partial response continuous phase modulation schemes. Specifically, we propose two novel estimators for the CPM signal observed in an additive white Gaussian noise channel. A non-data aided method of moments (MoM) estimator based upon the fourth-order cumulants and a data-aided best linear unbiased estimator (BLUE) based upon an approximate linear phase model of the received CPM signal have been proposed. Modified Cramer-Rao lower bound is derived for the partial response CPM schemes to assess the performance of the estimators. We also perform numerical simulations to compare the mean-squared error (MSE) performance of the proposed MoM and BLUE estimators with previously proposed estimators in the literature. It is shown that the MoM estimator exhibits good MSE performance at low signal-to-noise ratio (SNR) while the BLUE estimator performs very well at high SNRs. Moreover, the proposed estimators have lower complexity than existing methods and are based upon non-iterative algorithms.

Study of phase estimation methods to analyse cardiorespiratory synchronization in OSA patients.

Obstructive Sleep Apnea (OSA) is a sleep disorder highly prevalent in the general population. Cardiorespiratory Phase Synchronization (CRPS) is a form of non-linear interaction between respiratory and cardiovascular systems that was found to be reduced in severe OSA patients. The Hilbert Transform (HT) method was the recommended choice for estimating the respiratory phase in CRPS studies. But we have noticed that HT provides a phase that is aligned to the transition between the exhalation and the inhalation parts of different breathing cycles, instead of being aligned to the breathing onsets. In this work we proposed a Realigned HT phase estimation method (RHT) and we compared it to the conventional HT and to the Linear Phase (LP) approximation for estimating CRPS in a database of 28 patients with different OSA severity levels. RHT provided similar synchronization percentages (%Sync) as HT, and it enhanced the significant differences in %Sync between mild and severe OSA patients. %Sync showed the highest negative correlation with the Apnea-Hypopnea Index (AHI) when using RHT (rAHI=-0.692, p<;0.001), which only had an 10% extra computational cost. On the other hand, LP method significantly overestimated %Sync especially in the more severe patients, because it was unable to track the phase non-linearities that can be observed during sleep disordered breathing. Therefore, the newly proposed RHT can be the preferred alternative over the conventional HT or the LP approximation for estimating CRPS in OSA patients.

Optimizing Pulse Shaping Filter for DOCSIS Systems

This paper proposes a cost efficient nearly linear phase approximation to an square root raised cosine (SRRC) pulse shaping filter that satisfies the out-of-band spectral constraints of DOCSIS down-stream channels. A nearly linear phase filter structure is converted to an SRRC filter using a weighted and sampled least-squares criterion to fit the magnitude and phase responses. To ensure stability, the search for optimum coefficients is constrained using the Steigliz–McBride (SM) and Gauss–Newton (GN) methods, which unfortunately also eliminates sets of stable coefficients, one of which could be and probably is the optimum. To expand the sets of coefficients that produce stable filters in the SM and GN methods, the transfer function is parameterized in a special way. The effectiveness of the proposed filter is verified and compared with other approaches.

Subspace-based DOA with linear phase approximation and frequency bin selection preprocessing for interactive robots in noisy environments

This work develops a method of estimating subspace-based direction of arrival (DOA) that uses two proposed preprocesses. The method can be used in applications that involve interactive robots to calculate the direction to a noise-contaminated signal in noisy environments. The proposed method can be divided into two parts, which are linear phase approximation and frequency bin selection. Linear phase approximation rectifies the phases of the two-channel signals that are affected by noise, and reconstructs the covariance matrix of the received signals according to the compensative phases using phase line regression. To increase the accuracy of DOA result, a method of frequency bin selection that is based on eigenvalue decomposition (EVD) is utilized to detect and filter out the noisy frequency bins of the microphone signals. The proposed techniques are adopted in a method of subspace-based DOA estimation that is called multiple signal classification (MUSIC). Experimental results reveal that the mean estimation error obtained using proposed method can be reduced by 7.61° from the conventional MUSIC method. The proposed method is compared with the covariance-based DOA method that is called the minimum variance distortionless response (MVDR). The DOA improves the mean estimation accuracy by 4.98° relative to the conventional MVDR method. The experimental results demonstrate that both subspace-based and covariance-based DOA algorithms with the proposed preprocessing method outperform the DOA estimation in detecting the direction of signal in a noisy environment.

Design and Implementation of DWMT Transmission Systems using IIR Wavelet Filter Banks

Multicarrier modulation using orthogonal frequency division multiplexing (OFDM) is often recognized as an efficient solution for wireless communications. However, waveform bases other than sinusoidal functions can similarly be used for multicarrier systems in order to provide an alternative to OFDM. In this context, DWMT transmission systems are suggested. It is known that such systems suffer obviously from the two main problems of Inter Symbol Interference (ISI) and Inter-Carrier Interference (ICI). ISI may be considerably reduced via channel equalization. The effect of ICI can be reduced using high order Finite Impulse Response(FIR)wavelet filter banks, but at the expense of increased system complexity. Those FIR banks which are required to reduce effect the ICI should have autocorrelation functions approaching an impulse. On other hand, Infinite Impulse Response(IIR) filter banks can be used to replace those FIR counterparts to increase sub-band discrimination while reducing the required filter order, i.e., decreasing the complexity of system. In this paper, a special type of IIR filter banks is designed and implemented for such purpose. Bi- reciprocal lattice wave digital filters (BLWDFs) are utilized in an approximate linear phase design of 11th order IIR wavelet filter bank (FB) for discrete wavelet multi-tone (DWMT) transmission systems. The performances of the proposed DWMT for transmission over simulated wireless channels with additive white Gaussian noise (AWGN) are examined and compared with one of the recent FIR designs. Significant improvements over the classical DWMT approach are observed.

A Multiplier-less Implementation of Two-Dimensional Circular-Support Wavelet Transform on FPGA

In this paper, a two-dimensional (2-D) circular-support wavelet transform (2-D CSWT) is presented. 2-D CSWT is a new geometrical image transform, which can efficiently represent images using 2-D circular spectral split schemes (circularlydecomposed frequency subspaces). 2-D all-pass functions and lattice structure are used to produce 1-level circular symmetric 2-D discrete wavelet transform with approximate linear phase 2-D filters. The classical one-dimensional (1-D) analysis Haar filter bank branches H0(z) and H1(z) which work as low-pass and high-pass filters, respectively are transformed into their 2-D counterparts H0(z1,z2) and H1(z1,z2) by applying a circular-support version of the digital spectral transformation (DST). The designed 2-D wavelet filter bank is realized in a separable architecture. The proposed architecture is simulated using Matlab program to measure the deflection ratio (DR) of the high frequency coefficient to evaluate its performance and compare it with the performance of the classical 2-D wavelet architecture. The correlation factor between the input and reconstructed images is also calculated for both architectures. The FPGA (Spartan-3E) Kit is used to implement the resulting architecture in a multiplier-less manner and to calculate the die area and the critical path or maximum frequency of operation. The achieved multiplier-less implementation takes a very small area from FPGA Kit (the die area in 3-level wavelet decomposition takes 300 slices with 7% occupation ratio only at a maximum frequency of 198.447 MHz).

Allpass-Based Design, Multiplierless Realization and Implementation of IIR Wavelet Filter Banks with Approximate Linear Phase (English)

Allpass-Based Design, Multiplierless Realization and Implementation of IIR Wavelet Filter Banks with Approximate Linear Phase (English)

Energy transfer rate in double-layer graphene systems: Linear regime

We theoretically investigate the energy transfer phenomenon in a double-layer graphene (DLG) system. We use the balance equation approach in linear regime and random phase approximation screening function to obtain energy transfer rates at different electron temperatures, densities and interlayer spacings. We find that the rate of energy transfer in the DLG is qualitatively similar to that obtained in the double-layer two-dimensional electron gas but its values are an order of magnitude greater. Also, at large electron temperature differences between two graphene layers, the electron density dependence of energy transfer is significantly different, particularly in case of unequal electron densities.

Analysis of Non-Linear Probabilistic Hybrid Systems

This paper shows how to compute, for probabilistic hybrid systems, the clock approximation and linear phase-portrait approximation that have been proposed for non probabilistic processes by Henzinger et al. The techniques permit to define a rectangular probabilistic process from a non rectangular one, hence allowing the model-checking of any class of systems. Clock approximation, which applies under some restrictions, aims at replacing a non rectangular variable by a clock variable. Linear phase-approximation applies without restriction and yields an approximation that simulates the original process. The conditions that we need for probabilistic processes are the same as those for the classic case.

Dynamic electron transport theory for multiprobe mesoscopic structures

Using the linear response theory and random phase approximation, we develop a general dynamic electron transport theory for multiprobe mesoscopic structures in an arbitrarily time-dependent external field. In this case, the responses of the dynamic current, charge and internal potential to the external fields can be determined self-consistently. Without loss of generality, charge (current) conservation and gauge invariance under a potential shift are satisfied. As an example, we employ a quantum wire with a single barrier to discuss the response of the internal potential.

A Signal Processing Approach to Fourier Analysis of Ranking Data: The Importance of Phase

Ranking data is a type of data obtained in some elections, in customer surveys, as well as from web search results. Such data may be considered as a type of signal defined on the group of permutations of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> objects, denoted <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Sn</i> . There exists a Fourier transform for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Sn</i> obtained from group representation theory, which is well known in the mathematics literature. However, previous work has not approached the transform from a signal processing perspective: in particular, there is no discussion of what constitutes “magnitude” and “phase,” nor any analysis of what phase information might tell us beyond a well-known connection to group translation. This paper explores the properties of the phase spectrum of ranking data; in particular, a novel contribution is the formulation of the bispectrum for ranking data, which may be used for studying phase linearity. Analysis of two well-known ranking data sets shows that they are surprisingly well fit by linear phase approximations.

Cross-Spectral Analysis of Midfrequency Acoustic Waves Reflected by the Seafloor

Direct path measurements of a single-bottom interacting path on a vertical array are used to probe the seabed structure. The phase of the cross-spectrum, commonly used in engineering acoustics, permits examination of the importance of subbottom paths. When the cross-spectral phase is linear with frequency it implies that source to receiver propagation is dominated by a single path. A linear cross-spectral phase would also satisfy the linear seabed reflection coefficient phase approximation sometimes employed in forward modeling and geoacoustic inversion approaches. Shallow water measurements of the cross-spectrum, however, evidence a strongly nonlinear phase, below about 1500 Hz at one site, and 600 Hz at another site, implying that: 1) the subbottom structure plays an important role (i.e., a seabed half-space approximation would be inappropriate); and 2) the linear reflection phase approximation would be violated at those frequencies.