Plane-wave Filters Research Articles

A convolutional plane wave model for sound field reconstruction

Spatial sound field interpolation relies on suitable models to conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest is large compared to the wavelength or when spherical and planar wavefronts are present or the sound field is complex, as in the near-field. To span such complex sound fields, the global reconstruction task can be partitioned into local subdomain problems. Previous studies have shown that partitioning approaches rely on sufficient measurements within each domain due to the higher number of model coefficients. This study proposes a joint analysis of all of the local subdomains while enforcing self-similarity between neighbouring partitions. More specifically, the coefficients of local plane wave representations are sought to have spatially smooth magnitudes. A convolutional model of the sound field in terms of plane wave filters is formulated and the inverse reconstruction problem is solved via the alternating direction method of multipliers. The experiments on simulated and measured sound fields suggest that the proposed method retains the flexibility of local models to conform to complex sound fields and also preserves the global structure to reconstruct from fewer measurements.

A 16-Element 2.4-GHz Multibeam Array Receiver Using 2-D Spatially Bandpass Digital Filters

This paper presents the design, implementation, and the experimental verifications of a 2.4-GHz multibeam array receiver based on two-dimensional (2-D) spatially bandpass (SBP) digital plane wave (PW) filters. The digital array receiver consists of 2.4-GHz 16-element uniform linear array, and quadrature sampling is employed to process the broadband PWs at the baseband. Both 2-D finite impulse response (FIR) and infinite impulse response (IIR) digital filters having multiple trapezoidal-shaped passbands are employed as the 2-D SBP digital PW filters. Both 2-D FIR and IIR trapezoidal filters are implemented on a Xilinx Virtex 6 sx475t field programmable gate array chip that comes with the reconfigurable open architecture computing hardware version-2 (ROACH-2) platform. The 16 in-phase and quadrature-phase downconverted signals are sampled using the ROACH-2 platform and are processed using the digital architectures to form multiple beams. Example radio-frequency beam patterns corresponding to each filter architecture are measured and reported. The main lobes of the measured multibeam patterns are well aligned with the simulated multibeam patterns.

Investigation into use of double‐layer grid structures as frequency selective surfaces for buildings

A simple double-layer grid plane wave filter structure is proposed that can provide multiple transmission bands for cellular phone frequencies but with a reflection band for wireless local area network signals. The approach offers ease of construction making it applicable to building applications. A parametric study using simulation supported by simple experimental data investigates the proposed, novel design.

Electronically scanned RF-to-bits beam aperture arrays using 2-D IIR spatially bandpass digital filters

A beamforming system based on two-dimensional (2-D) spatially bandpass infinite impulse response (IIR) plane wave filtering is presented in a multi-dimensional signal processing perspective and the implementation details are discussed. Real-time implementation of such beamforming systems requires modeling of computational electromagnetics for the antennas, radio frequency (RF) analog design aspects for low-noise amplifiers (LNAs), mixed-signal aspects for signal quantization and sampling and finally, digital architectures for the spatially bandpass plane wave filters proposed in Joshi et al. (IEEE Trans Very Large Scale Integr Syst 20(12):2241---2254, 2012). Multi-dimensional spatio-temporal spectral properties of down-converted RF plane wave signals are reviewed and derivation of the spatially bandpass filter transfer function is presented. An example of a wideband antipodal Vivaldi antenna is simulated at 1 GHz. Potential RF receiver chains are identified including a design of a tunable combline microstrip bandpass filter with tuning range 0.8---1.1 GHz. The 1st-order sensitivity analysis of the beam filter 2-D $$\mathbf z $$ z -domain transfer function shows that for a 12-bits of fixed-point precision, the maximum percentage error in the 2-D magnitude frequency response due to quantization is as low as $$0.3\,\%$$ 0.3 % . Monte-Carlo simulations are used to study the effect of quantization on the bit error rate (BER) performance of the beamforming system. 5-bit analog to digital converter (ADC) precision with 8-bit internal arithmetic precision provides a gain of approximately 16 dB for a BER of $$10^{-3}$$ 10 - 3 with respect to the no beamforming case. ASIC Synthesis results of the beam filter in 45 nm CMOS verifies a real time operating frequency of 429 MHz.

Accelerated plane-wave destruction

When plane-wave destruction (PWD) is implemented by implicit finite differences, the local slope is estimated by an iterative algorithm. We propose an analytical estimator of the local slope that is based on convergence analysis of the iterative algorithm. Using the analytical estimator, we design a noniterative method to estimate slopes by a three-point PWD filter. Compared with the iterative estimation, the proposed method needs only one regularization step, which reduces computation time significantly. With directional decoupling of the plane-wave filter, the proposed algorithm is also applicable to 3D slope estimation. We present synthetic and field experiments to demonstrate that the proposed algorithm can yield a correct estimation result with shorter computational time.

Digital Architectures for UWB Beamforming Using 2D IIR Spatio-Temporal Frequency-Planar Filters

A design method and an FPGA-based prototype implementation of massively parallel systolic-array VLSI architectures for 2nd-order and 3rd-order frequency-planar beam plane-wave filters are proposed. Frequency-planar beamforming enables highly-directional UWB RF beams at low computational complexity compared to digital phased-array feed techniques. The array factors of the proposed realizations are simulated and both high-directional selectivity and UWB performance are demonstrated. The proposed architectures operate using 2's complement finite precision digital arithmetic. The real-time throughput is maximized using look-ahead optimization applied locally to each processor in the proposed massively-parallel realization of the filter. From sensitivity theory, it is shown that 15 and 19-bit precision for filter coefficients results in better than 3% error for 2nd- and 3rd-order beam filters. Folding together with Ktimes multiplexing is applied to the proposed beam architectures such that throughput can be traded forK-fold lower complexity for realizing the 2-D fan filter banks. Prototype FPGA circuit implementations of these filters are proposed using a Virtex 6 xc6vsx475t-2ff1759 device. The FPGA-prototyped architectures are evaluated using area (A), critical path delay (T), and metricsATandAT2. TheL2error energy is used as a metric for evaluating fixed-point noise levels and the accuracy of the finite precision digital arithmetic circuits.

Effects of Quantization in Systolic 2D IIR Beam Filters on UWB Wireless Communications

Ultra-wideband (UWB) wireless beamforming systems may potentially be implemented digitally at multi-gigahertz clock frequencies using low-precision systolic array realizations of two-dimensional (2D) infinite impulse response (IIR) beam plane-wave filters. The finite precision performance of such filters is analyzed in terms of quantization noise. Extensive Monte Carlo simulations are performed using test vectors that are derived from 2D finite-difference time-domain (FDTD) computational electromagnetic models of the UWB channels. The bit error rate (BER) is determined as a function of signal-to-interference ratio (SIR), with and without beamforming, and for various practical combinations of finite internal wordlengths and A/D converter precisions. It is established that 3-bit A/D converters with 3- to 6-bit internal wordlengths are adequate for good performance and that 4-bit A/D converters with 4- to 7-bit internal wordlengths achieve excellent performance.

UWB Beamforming Using 2-D Beam Digital Filters

Ultrawideband (UWB) communication systems can benefit from the spatial selectivity provided by adaptive antenna arrays. This communication presents a new spatio-temporal digital filtering technique for realizing a UWB beamformer. Through the use of an infinite impulse response 2D frequency-planar beam space-time plane wave filter, the complexity of the underlying structure can be made to be extremely simple and implementable in real time. Simulations of a UWB system equipped with this technique, utilizing realistic channel conditions computed using a full-wave electromagnetic solver, are presented in this communication and demonstrate a dramatic improvement in communication system performance in multiuser scenarios.

A Speed-Optimized Systolic Array Processor Architecture for Spatio-Temporal 2-D IIR Broadband Beam Filters

For high-speed plane-wave filtering applications, real-time 2-D spatio-temporal linear-array broadband beam filters are required, operating at temporal frame rates in excess of hundreds of megahertz. The corresponding application specific VLSI circuits must have low critical-path latencies. A novel high-speed systolic array architecture for a first-order 2-D broadband frequency-planar spatio-temporal beam filter is proposed for this purpose and employs a field-programmable gate array (FPGA) circuit where the critical path latency is minimized by timing optimization of inter- and intra-parallel processor pipelines, together with 3-D look-ahead techniques. The method facilitates single-chip VLSI circuit implementations operating at real-time frame rates of several hundred megahertz.

Low-complexity distributed parallel processor for 2D IIR broadband beam plane-wave filters

Real-time systolic-array-based implementations of VLSI two-dimensional (2D) infinite-impulse-response (IIR) frequency-planar beam plane-wave filters have potentially wide applications in the filtering of spatio-temporal RF broadband plane waves based on their directions of arrival (DOAs). Distributed-parallel-processor (DPP) implementations of the systolic arrays allow synchronous sampling of the 2D input signal array, but because of the direct-form structure they have high circuit complexity. To address the high-complexity problem, the differential-form 2D z-domain transfer function is employed here to obtain a novel DPP systolic-array-based filter architecture. Differential operators are obtained by applying elemental predistortion to the passive LR prototype filter network using series-connected negative-resistance elements. The proposed systolic 2D IIR architecture is implemented on a single Xilinx Virtex-4 Xc4v Sx35-10ff668 FPGA chip. Two examples of broadband plane-wave filtering supporting N = 32 and N = 64 sensors are reported. On-chip test results are achieved using stable real-time tests at frame sample frequencies of up to 90MHz as well as stepped hardware cosimulation in conjunction with a parallel-operating MATLAB/Simulink simulation.

A Fully Multiplexed First-Order Frequency-Planar Module for Fan, Beam, and Cone Plane-Wave Filters

A VLSI architecture for the on-chip realization of a first-order two-dimensional (2-D) or three-dimensional (3-D) infinte impulse response (IIR) fully multiplexed frequency-planar filter module (FMFPM) is proposed. Such filter modules may be used in 3-D video processing and 2-D/3-D plane-wave filtering using sensor arrays. The proposed FMFPM can potentially be used as a 2-D/3-D IIR building block circuit for the on-chip realization of second- (or higher) order frequency-planar filters, 3-D IIR beam filters, 2-D IIR fan filter banks and 3-D IIR cone filter banks

Near-field calibration arrays for acoustic wavefield determination

The use of near-field calibration array (NFCA) to determine the far-field properties of acoustic receivers and projectors by measurements made in their near-field is described. When used as a projector to evaluate receivers, the NFCA produces a nearly uniform plane wave over a large volume in its near-field and over a large frequency range. When used as a receiver to evaluate projectors, the NFCA becomes a plane-wave filter for acoustic radiation (or target scattering) originating from within the plane-wave volume. The basis of the NFCA is a reciprocity principle. Numerical implementation of this principle provides the complex weighting factors to be used as shading coefficients for the individual elements in the NFCA. The original Trott NFCAs, given by W.J. Trott (see J. Acoust. Soc. Am., vol.36, p.1557-68, Aug. 1964), were planar. Subsequent extensions of the concept to a cylindrical NFCA suitable for determining the azimuthal far-field pattern and to a spherical NFCA that allows a determination of the entire three-dimensional far-field pattern are described.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Near-field transmitting and receiving properties of planar near-field calibration arrays

The planar near-field calibration array (NFCA) was developed by Trott [W. J. Trott, Underwater Sound Ref. Rep. No. 55 (1961); also J. Acoust. Soc. Am. 36, 1557–1568 (1964)] for use in determining the far-field acoustic radiation from underwater transducers by measurements in the near field. As a projector, the NFCA produces a nearly uniform plane wave over a large volume in its near field and over a large frequency range. As a receiver the NFCA acts like a plane-wave filter for acoustic radiation (or target scattering) originating from within the plane-wave volume. Thus the NFCA can be used to determine the far-field performance of both receiving and projecting transducers. In addition, it can be used to insonify nearby targets with plane waves and determine the resulting scattered far-field pressure. Earlier papers concentrated on the geometrical design of NFCA’s and the computation of their relative element responses (or sensitivities) for a specified array configuration, near-field volume, and frequency range. This paper provides analytical expressions for the near-field transmitting voltage and current responses and near-field receiving voltage and current sensitivities of a planar NFCA. The paper also provides information to aid in the NFCA element selection process, especially with regard to shading of the NFCA.

Spherical nearfield calibration array for three-dimensional scanning

Nearfield calibration arrays (NFCAs) are used to determine the farfield acoustic radiation from a transducer by measurements made in the nearfield. The original Trott NFCAs were planar arrays. More recently, cylindrical NFCAs have been developed. This paper describes a spherical NFCA for determining the full three-dimensional radiation pattern of an enclosed transducer. In theory, the NFCA consists of a large number of discrete hydrophone elements arranged over a spherical surface in N equi-spaced constant latitude bands. In practice, the array can be synthesized by use of a single semicircular are containing relatively few elements and by either rotation of the transducer or revolution of the are about the polar axis. Individual hydrophone sensitivities (both amplitude and phase) are selected so that the NFCA serves as a plane-wave filter for acoustic radiation from inside the sphere. The relative sensitivities, called shading coefficients, are computed using the NFCA reciprocity principle and a least-squares procedure. Only a few sets of N/2 shading coefficients are required for full three-dimensional operation of the NFCA over a frequency range of three octaves or more. Design criteria are discussed and sample numerical results are presented.

Spherical nearfield calibration array for three-dimensional scanning

Nearfield calibration arrays (NFCAs) are used to determine the farfield acoustic radiation from a transducer by measurements made in the nearfield. The original Trott NFCAs [W. J. Trott, Underwater Sound Ref. Lab. Rep. No. 55 (1961); also J. Acoust. Soc. Am. 36, 1557–1568 (1964)] were planar arrays. More recently, cylindrical NFCAs have been developed for determining the azimuthal radiation pattern of an enclosed transducer. This paper describes a spherical NFCA for determining the full three-dimensional radiation pattern of an enclosed transducer. In theory, the NFCA consists of a large number of discrete hydrophone elements arranged over a spherical surface in N equispaced constant latitude bands. In practice, the array can be synthesized by use of a single semicircular arc containing relatively few elements and by either rotation of the transducer or revolution of the arc about the polar axis. Individual hydrophone sensitivities (both amplitude and phase) are adjusted so that the NFCA serves as a plane-wave filter for acoustic radiation originating from inside the sphere. The relative sensitivities, called shading coefficients, are computed using the NFCA reciprocity principle and a least-squares procedure. Only a few sets of N/2 [or (N+1)/2, if N is odd] shading coefficients are required for full three-dimensional operation of the NFCA over a frequency range of 3 oct or more. Design criteria are discussed and example numerical results are presented.