Nonuniform Spacings Research Articles

Optimal Design of Nonuniform Linear Arrays in Cellular Systems by Out-of-Cell Interference Minimization

Optimal design of a linear antenna array with nonuniform interelement spacings is investigated for the uplink of a cellular system. The optimization criterion considered is based on the minimization of the average interference power at the output of a conventional beamformer (matched filter) and it is compared to the maximization of the ergodic capacity (throughput). Out-of-cell interference is modelled as spatially correlated Gaussian noise. The more analytically tractable problem of minimizing the interference power is considered first, and a closed-form expression for this criterion is derived as a function of the antenna spacings. This analysis allows to get insight into the structure of the optimal array for different propagation conditions and cellular layouts. The optimal array deployments obtained according to this criterion are then shown, via numerical optimization, to maximize the ergodic capacity for the scenarios considered here. More importantly, it is verified that substantial performance gain with respect to conventionally designed linear antenna arrays (i.e., uniform λ/2 interelement spacing) can be harnessed by a nonuniform optimized linear array.

Low-frequency noise from a bubble plume formed by a plunging water jet

Wind-driven, low-frequency ambient noise in the ocean may be due to bubble clouds created by wave breaking. To investigate this idea, a laboratory experiment was performed in which a vertical jet of fresh water plunged into a fresh water pool, to form a conical plume of bubbles beneath the surface. Both the jet speed, uj, and the air entrainment ratio, q, were carefully controlled and monitored. The power spectra of the sound from the plume, measured with an adjacent hydrophone, exhibit a sequence of nonuniformly spaced peaks below 1 kHz, which are associated with the resonances of the bubble-plume cavity. Each eigenfrequency scales accurately as (1/uj)1/2 and approximately as (1/q)1/4. A theoretical analysis of these scalings, based on a momentum-flux argument, shows that the sound speed profile within the plume varies as the square-root of depth down the axis. Using this square-root profile in the wave equation, an analytical solution for the pressure field within the plume is obtained, from which an explicit expression for the eigenfrequencies is derived. These theoretical eigenfrequencies, predicted from the conical geometry and square-root sound speed profile, exhibit the same nonuniform spacing and inverse-fractional power-law scalings as seen in the data. [Research supported by ONR.]

Compact analytical model for room-temperature-operating silicon single-electron transistors with discrete quantum energy levels

A compact and analytical model for silicon single-electron transistors (SETs) considering the discrete quantum energy levels and the parabolic tunneling barriers is proposed. The model is based on a steady-state master equation that considers only the three most probable states derived from ground level and the first excited level for each number of electrons in the dot to reduce the complexity while accounting for the quantum-level spacing and multiple peaks in Coulomb oscillation. Negative differential conductance (NDC) characteristics and aperiodic Coulomb oscillations due to nonuniform quantum-level spacings can be reproduced in this model. The model was compared with measurements, and good agreement was obtained. Simulations of some basic circuits that utilize NDC are successfully carried out by applying our model to the HSPICE circuit simulation. Our model can provide suitable environments for designing CMOS-combined room-temperature-operating highly functional SET circuits.

Design of Steerable Linear and Planar Array Geometry with Non-uniform Spacing for Side-Lobe Reduction

In this paper, we present a noble pattern synthesis method of linear and planar array antennas, with non-uniform spacing, for simultaneous reduction of their side-lobe level and pattern distortion during beam steering. In the case of linear array, the Gauss-Newton method is applied to adjust the positions of elements, providing an optimal linear array in the sense of side-lobe level and pattern distortion. In the case of planar array, the concept of thinned array combined with non-uniformly spaced array is applied to obtain an optimal two dimensional (2-D) planar array structure under some constraints. The optimized non-uniformly spaced linear array is extended to the 2-D planar array structure, and it is used as an initial planar array geometry. Next, we further modify the initial 2-D planar array geometry with the aid of thinned array theory in order to reduce the maximum side-lobe level. This is implemented by a genetic algorithm under some constraints, minimizing the maximum side-lobe level of the 2-D planar array. It is shown that the proposed method can significantly reduce the pattern distortion as well as the side-lobe level, although the beam direction is scanned.

Improved spectral observations of equatorial spread F echoes at Jicamarca using aperiodic transmitter coding

We present preliminary radar results obtained with a new method of spectrum estimation of moderately overspread equatorial spread F (ESF) echoes over Jicamarca. This new method is similar to the classical pulse-to-pulse methods but with nonuniform pulse spacings, i.e., using aperiodic transmitter pulses, allowing us to avoid range and frequency aliasing, at the cost of extra clutter at some ranges. We also present different ways of dealing with the extra clutter, depending on the spectral characteristics of the clutter. We have identified two kinds of clutter: ground clutter (due to mountains and transmitter pulses) and ionospheric clutter (due to ESF and equatorial electrojet echoes). Preliminary radar results are very encouraging, and ways of improving them are proposed based on Monte Carlo simulations. Particularly, we propose alternating the phases of the uncoded aperiodic pulses using random binary phase codes to flatten the spectrum of the ionospheric clutter. The theoretical implications of the newly estimated spectra, particularly from topside echoes, are presented and discussed in a companion paper.

Design of Nonuniformly Spaced Tapped-Delay-Line Equalizers for Sparse Multipath Channels

Analytical expressions that explicitly indicate the tap values and tap positions of infinite-length, T-spaced tapped-delay-line (TDL) equalizers for sparse multipath channels are derived. Simple design rules for allocating taps to finite-length, minimum mean-square error, nonuniformly spaced TDL equalizers (NU-Es) are formulated based on the derived results. The design-rule-based methodology demonstrates a better tradeoff between accuracy and efficiency than existing tap-allocation schemes. The resultant NU-Es also achieve a lower overall computational complexity than conventional, uniformly spaced TDL equalizers (U-Es) of the same span for both directly adaptive and channel-estimate-based implementations. Moreover, a square-root raised cosine (SRRC) receive filter matched to a SRRC transmit filter is better than a matched filter when used to precede a NU-E.

Comparisons of multi-source localization and spatial filtering techniques

Localization of moving sources in a multiple source environment has been investigated with simulated annealing algorithms. Results obtained, both by classical annealing and by fast simulated annealing using a rotated coordinate basis, are presented. The fast annealing method varies from the classical method in that each parameter is varied only once per temperature reduction, resulting in many fewer iteration calls per inversion. Accuracy and efficiency for these methods as a function of signal-to-noise ratio are examined using simulated data containing a weak source in the presence of a loud interferer. A method for filtering element level data prior to inversion is compared to subarray processing for effectiveness in localizing the source of interest. The effect of varying the level of the weak source relative to the level of the interferer, as well as the sources azimuthal separation, is also presented. Comparisons between an equally spaced horizontal line array (HLA) and an HLA with nonuniform sensor spacing are made. Finally, comparisons of the inversion techniques for a real data set from a nonuniformly spaced HLA at a Gulf of Mexico site, where ground truth bottom properties have been established, are discussed. [Work sponsored by ONR.]

Predicting the effect of non-uniform ply cracking on the thermoelastic properties of cross-ply laminates

When damage in the form of ply cracks in laminated composites arises during loading, the cracks are in general non-uniformly spaced due to property and geometrical inhomogeneities in the laminate. The objective of this paper is to establish the validity of an approximation that can be made when analysing the stress and displacement distributions in multiple-ply cross-ply laminates having arrays of non-uniformly spaced ply cracks. The approximation assumes that the stress and displacement distributions in the region between the planes containing neighbouring ply cracks are the same as those arising in an identical laminate having uniformly spaced ply cracks of the same separation. The validity of this approach is established by comparing predictions of the thermo-elastic constants of the cracked laminates generated by two distinct stress-transfer models. The first model, that generates the approximations for non-uniform ply crack spacings, is based on a stress-transfer analysis that was specifically developed for uniformly spaced ply cracks while the second model accurately takes account of the effects of the non-uniformity of ply crack spacing on the stress distribution. It is shown, following a comprehensive analysis of various laminate types and crack patterns for both carbon fibre and glass fibre systems, that the approximation suggested provides highly accurate predictions of effective thermo-elastic constants over a wide range of laminate parameter variations.

Pairing Correlation Effect on the Zero-Bias Tunneling Spectra of Ultrasmall Superconducting Grains

We study the superconducting pairing correlation (SPC) effect on the resonant tunneling through an ultrasmall metallic grain with a gate electrode. The resonant conductance peaks appearing with an increase or decrease of the gate voltage are accompanied by the transition of the total electron number N on the grain, such as N ↔ N ±1. We focus our attention on the tunneling resonance associated with an odd- N state. In the absence of the SPC effect, the structure of the zero-bias resonant conductance peak for N ↔ N - 1 is equivalent to that for N ↔ N + 1. It is shown that due to the interplay between the SPC effect and the nonuniform spacings of single-particle energy levels, we expect a notable difference between the two peak structures.

遺伝的アルゴリズムを用いた不等間隔リニアアレーアンテナの給電方法の簡略化

遺伝的アルゴリズムを用いた不等間隔リニアアレーアンテナの給電方法の簡略化

A propagation model for urban microcellular systems at the UHF band

This paper presents a new propagation model for urban environments, which takes into account propagation over buildings and inside streets. The formulation for multiple diffraction loss over rooftops results from a combination of the Vogler (1982) and Xia and Bertoni (1992) models, which enables its application to profiles of buildings with nonuniform heights and spacings, keeping the calculation time low. A ray-tracing tool based on the image method and on the uniform theory of diffraction (UTD) has been developed to estimate the attenuation inside streets; loss introduced by vegetation is also accounted for. The results obtained with the application of the model to two areas of Lisbon show the importance of rays conducted by transversal streets and diffracted by vertical edges when predicting the signal near crossroads. Average values of 3.5 dB, -0.07 dB, and 2.6 dB were obtained for the mean absolute and relative errors and for the standard deviation error, respectively.

Modulo conversion method for estimating the direction of arrival

A modulo conversion method for resolving phase ambiguity and consequently estimating the direction of arrival (DOA) of an electromagnetic wave incident on a multielement interferometer with nonuniform spacings is presented. The technique involves a step-by-step reduction of the number of ambiguities in the measured phase difference of the longest interelement spacing. A major advantage of this method is that even the shortest interelement spacing can be larger than half-wavelength.

Nonselective Fading Channel Estimation with Nonuniformly Spaced Pilot Symbols

Recently, there has been great demand for multimedia and data communications in mobile communication systems. In order to enhance voice quality and increase packet data throughput rate for the existing mobile systems and the next generation mobile systems, a number of new standards are being developed. 8-PSK/QPSK modulation has been adopted by most of these standards as one of the modulation schemes, and nonuniformly spaced pilot symbols are employed in slot structures to have successful demodulation. In this paper, an accurate and computationally efficient method is presented for estimating nondispersive channel fading with non-uniformly spaced pilot symbols. By employing a least-squares method with time-variant complex-valued coefficient polynomials, it is proven that nonselective channel fading of each slot can be estimated by the product of a constant matrix and the fading at pilot symbol locations of the slot. The constant matrix is further optimized by least-squares off-line training method provided by this paper. Using the estimated fading process, the fading on the data symbols can be removed by using the estimated amplitude and phase of the fading as the reference, greatly improving the BER. Closed form results for the BER of coherent 8-PSK are included in this paper as well. Simulation results indicate that our method provides BER performance very close to the analytic BER result.

Quadrature integration for orthogonal wavelet systems

Wavelet systems can be used as bases in quantum mechanical applications where localization and scale are both important. General quadrature formulas are developed for accurate evaluation of integrals involving compact support wavelet families, and their use is demonstrated in examples of spectral analysis and integrals over anharmonic potentials. In contrast to usual expectations for these uniformly spaced basis functions, it is shown that nonuniform spacings of sample points are readily allowed. Adaptive wavelet quadrature schemes are also presented for the purpose of meeting specific accuracy criteria without excessive oversampling.

Finite-Difference Method for Convective Terms using Non-Uniform Grid.

To improve the numerical simulation of incompressible fluid flow using rectangular grids of non-uniform spacings, a fully consistent and conservative finite-difference method is proposed for the convection term of Navier-Stokes equation of motion. When the mass continuity is satisfied numerically, the present schemes have complete conpatibility between the divergence form and the gradient form. In addition, the kinetic energy is conserved numerically according to the condition. These properties are evaluated by the numerical examples for laminar flow in a square cavity.

A Rugged and Reliable System for Measuring Engine Crankshaft Speed Fluctuations

A measurement system and the associated signal processing algorithm for accurately determining engine crankshaft speed fluctuations are presented in this work. The main features of the system include ruggedness, simple sensor installation, and high accuracy and resolution. The ruggedness and simplicity of the system are characterized by the use of highly reliable Hall-Effect Transducers (HETs) mounted on the engine flywheel bell housing to sense the passing of flywheel gear teeth. A relatively significant noise component is introduced to the HET measurements by the nonuniform flywheel gear tooth spacings. The high measurement accuracy is achieved by a very computationally efficient signal processing algorithm based on two HET inputs. The advantages of the current system over the single HET systems commonly used in practice are clearly demonstrated through experiments on a Detroit Diesel Corporation 6V-92TA engine.

POINT TRANSECT ESTIMATES OF RESIDUE COVER OR CROP CANOPY IN ROWS

Linear, evenly spaced point transects are typically used to measure percent of the soil surface covered by cropresidue or canopy. As few as five 100-point count transects provide relatively precise measures of uniformly distributedcover, but such transects can provide very poor precision if used to measure cover lying in parallel rows. Highly variablecounts can be expected if the target occupies evenly spaced parallel stripes with alternating high (80% or more) and low(20% or less) cover. Precise means (S.D. < 5%) of cover on striped surfaces can be obtained with equally spaced pointtransects if both point spacing and transect angle relative to tillage or planting rows are custom-selected for each rowspacing. However, no single equal point spacing or transect angle will provide precise cover estimates at all planter andtillage tool row spacings used in agricultural fields. It is hypothesized that nonuniform point spacings will allow estimatesof cover that are independent of transect angle on striped surfaces.<br><br>The hypothesis was tested using the variance in counts of intersections between the point distributions and regularlystriped geometric patterns. The standard deviation of intersection counts from randomly spaced point transects rangedbetween 5 and 10% cover, but was independent of transect angle and row spacing. A sinewave-like point spacing alsoproduced cover estimates that were independent of transect angle and row spacing. The advantages of a sinewave patternare the following: it is unique in contrast to the large number of possible random spacings, it can be used on any rowspacing, and it usually provides a lower standard deviation than that obtained from randomly spaced points. Thesinewave pattern shares with evenly spaced points the disadvantage that non-random points do not meet the strictrequirements for statistical sampling. Randomly spaced point transects are recommended for percent cover estimates onfields with visible striping.

Preliminary results on environmentally robust vertical array design for shallow water mode filtering

Many shallow water acoustics techniques require accurate estimates of the propagating modes from pressure observations at a vertical array. The noise in these estimates is a function of the conditioning of the vertical modes as sampled by the hydrophone array. However, the sound-speed profile and thus vertical mode shapes are usually not known when the array is designed. In addition, economic considerations often dictate the same array be used in a wide range of environments. Consequently, optimizing the array for a specific environment risks a degradation in performance if the experimental environment differs from the environment assumed by the array design. Conventional wisdom holds that in the absence of precise environmental knowledge, the safest approach is to space the hydrophones evenly throughout the water column. This work presents several simplified mode filtering scenarios demonstrating that nonuniform hydrophone spacings exist which are more robust in the minimax sense than uniform spacing, if it is possible to specify a range of operating environments for the array. This means that their worst case performance is better than the worst case performance of the uniformly spaced array over the range of environments.

Receptances and Natural Frequencies of Finite Beams on Non-Uniformly Spaced Supports

Receptance functions for multi-supported finite beams have been derived in terms of the end receptances of individual beam elements. Receptances of some multi-supported beams have been studied as they vary with frequency over the range fully covering the lowest group of natural frequencies. Effect of variation of support spacing on the receptances and natural frequencies of the beam has also been studied. The results have been compared to a beam on equally spaced (periodic) simple supports. The receptances of undamped systems, as considered in this paper are real functions, and the frequencies at which they can be spring-like or mass-like, have been discussed. The receptances of finite beams have been found to be very useful in determining the resonance frequencies of finite systems having ideal or any other end conditions.

An adaptive filter with adaptation to nonuniformly spaced samples

AbstractA novel adaptive filter is proposed that adapts to the sample spacing as well as to the tap weights. Although in adaptive digital processing, the tapped‐delay line usually has uniformly spaced taps, with the spacing equal to symbol period or a fraction of symbol period, an adaptive filter with a few taps should be adaptively arranged for nonuniform spacing for better convergence as the sampling timing varies. The conventional nonuniformly spaced filters are not adaptively changed or not arranged under the constraint of the acceptable meansquare error. In this paper, a least‐mean square (LMS)‐type algorithm is derived in which an adaptive filter adaptively changes the amount of delay, as well as the filter coefficients. The performance of the proposed algorithm is investigated by computer simulation.