Len T. Bruton

Design of 3-D planar and beam recursive digital filters using spectral transformation

A spectral transformation technique is proposed for the design of three-dimensional (3-D) recursive digital filters having planar and beam frequency responses. Circuit-theoretic concepts are used to generate stable 3-D continuous domain networks from a corresponding one-dimensional (1-D) prototype network. Implementation schemes are developed in the discrete domain that convert the 3-D analog network into a 3-D wave digital filter (WDF). The proposed 3-D discrete beam and planar filters offer significant advantages over direct-form realizations including the low-sensitivity properties of the WDF and simplicity of the structure. >

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.

On the attenuation of interference and mutual coupling in antenna arrays using 3D space-time filters

A 3D space-time filtering method is proposed for attenuating undesirable electromagnetic signals that propagate at or close to light speed across the surface of the plane that contains an array of antennas. Such signals may include the so-called radio frequency interference (RFI) that emanate from sources that lie well outside the directions of arrival (DOAs) of the signals of interest (SOIs). They may also include the intra-plane inter-antenna signals that result from the undesirable electromagnetic mutual coupling that exists between rectangularly-spaced antennas in aperture arrays (AAs) and in the focal plane arrays (FPAs) of paraboloidal dishes. Such signals have 3D space-time spectra possessing regions of support (ROSs) that are close to the surface of the 3D spectral light cone. They can therefore be attenuated by means of 3D space-time filters having 3D stopbands that include and encompass the surface of this light cone. Such a 3D space-time filter is described here and used to evaluate the validity of the proposed approach. Numerical results confirm that the proposed method significantly attenuates broadband RFI signals and moderately suppresses mutual coupling.

A Systolic-Array Architecture for First-Order 3-D IIR Frequency-Planar Filters

A massively parallel systolic-array architecture is proposed for the implementation of real-time VLSI spatio-temporal 3-D IIR frequency-planar filters at a throughput of one-frame-per-clock-cycle (OFPCC). The architecture is based on a differential-form transfer function and is of low circuit complexity compared with the direct-form architecture. A 3-D look-ahead (LA) form of the transfer function is proposed for maximizing the speed of the implementation, which has a nonseparable 3-D transfer function. The systolic array enables real-time implementation of 3-D IIR frequency-planar filters at radio-frequency (RF) frame-rates and is therefore a suitable building block for 3-D IIR digital filters having beam- and cone-shaped passbands as required for smart-antenna-array beam-forming applications involving the broadband spatio-temporal filtering of plane-waves. The fixed-point systolic-array implementation have a throughput of OFPCC and the tested real-time prototype achieves frame (clock) sample frequencies of up to 90 MHz using one Xilinx Virtex-4 sx35-10ff668 FPGA device.

Selective filtering of spatio-temporal plane waves using 3D cone filter banks

A 3D cone-shaped pass band is ideally required for the selective filtering of spatio-temporal plane waves on the basis of their directions of arrival. A method is proposed for approximating 3D cone-shaped pass bands using a 3D cone filter bank structure in which the bands consist of band limited 3D beam filters having 3D bandwidths that are approximately proportional to their distance from the origin in the 3D frequency space. The individual 3D beam filters way be realized from a cascade of stable 3D frequency planar filters, each of which corresponds to a passive stable 3D continuous-domain frequency-planar prototype filter.

Five-Dimensional Depth-Velocity Filtering for Enhancing Moving Objects in Light Field Videos

Five-dimensional (5-D) light field video (LFV) (also known as plenoptic video) is a more powerful form of representing information of dynamic scenes compared to conventional three-dimensional (3-D) video. In this paper, the 5-D spectrum of an object in an LFV is derived for the important practical case of objects moving with constant velocity and at constant depth. In particular, it is shown that the region of support (ROS) of the 5-D spectrum is a skewed 3-D hyperfan in the 5-D frequency domain, with the degree of skew depending on the velocity and depth of the moving object. Based on this analysis, a 5-D depth-velocity digital filter to enhance moving objects in LFVs is proposed, described and implemented. Further, by means of the commercially available Lytro light-field camera, LFVs of real scenes are generated and used to test and confirm the performance of the 5-D depth-velocity filters for enhancing such objects.

Broadband beamforming of dense aperture array (DAA) and focal plane array (FPA) signals using 3D spatio-temporal filters for applications in aperture synthesis radio astronomy

It is shown that 3D spatio-temporal filters have potential applications in aperture synthesis radio astronomy for the broadband-beamforming of the array of signals that is received from dense aperture arrays (DAAs) and also from focal plane arrays (FPAs). In particular, we consider possible applications for the planned Square Kilometer Array (SKA) project where broadband beamforming is required at the front-end of the signal processing system for some experiments such as pulsar timing. In the case of a synthesized aperture that is composed of DAAs, the required 3D magnitude frequency response has a non-separable narrow-cone-shaped (or narrow-frustum-shaped) passband whereas, for FPAs, the required 3D magnitude frequency response has a non-separable wide-cone-shaped (or wide-frustum-shaped) passband. The corresponding 3D passbands are designed to faithfully transmit the celestial signals of interest (SOIs), whereas the 3D stopbands are designed to significantly attenuate such undesired signal components such as natural and artificial sources of radio frequency interference (RFI) and the dominant part of the 3D electronic broadband noise that is contributed by millions of low noise amplifiers (LNAs), each of which amplifies the signal received in each elemental antenna of the DAAs or FPAs. The criteria for designing both narrow- and wide-cone/frustal filters, in order to achieve optimal sensitivity, are presented in terms of the power of the recovered signal and the power of the contaminating noise.

All-Pass Filter-Based 2-D IIR Filter-Enhanced Beamformers for AESA Receivers

An active electronically scanned array (AESA) beamforming method that provides enhanced selectivity (interference rejection) for the same number of antennas compared to conventional delay-and-sum (DAS) beamforming is proposed. Conventional DAS 2-D transfer function is modified by introducing complex pole-manifolds based on recently proposed 2-D infinite impulse response (IIR) beam filters, at guaranteed stability. A continuous-time domain signal flow graph is proposed based on first order all-pass filters that eliminate the need of transmission line-based delays used in conventional DAS beamformers. Improved interference rejection is verified using closed-form signal processing models. For an array of 64 antennas, with desired signal direction of arrival (DOA) 10 ° and interference DOA -60° from array broadside, the proposed scheme shows an improvement in the signal-to-interference ratio (SIR) around 7 dB for the same number of antennas, compared to DAS beamforming. The improvement in interference rejection is observed for both uniform and non-uniform aperture weights in terms of side lobe performance. A feasibility study is presented on potential CMOS circuit implementation of the proposed AESA for a linear array of eight antennas and maximum operational frequency of 1 GHz.

A low-complexity scanned-array 3D IIR frequency-planar filter

We extend a 3D differential-operator-based filter architecture to a 3D IIR FPGA filter circuit implementation employing a recently proposed scanned-array method, which uses a single time-multiplexed A/D converter, resulting in the proposed low-complexity elemental predistorted scanned-array filter FPGA circuit. Test results confirm the low hardware complexity and the capability of operating in real-time over rectangular sensor arrays consisting of up to thousands of band-limited analog sensors. Cascaded connections of two frequency-planar filters are useful for implementing highly-selective 3D IIR beam plane-wave filters.

Space-Time Spectral White Spaces in Cognitive Radio: Theory, Algorithms, and Circuits

Space-time spectral white spaces in a cognitive radio environment are defined based on multidimensional spatio-temporal spectral properties of radio waves received by a planar array of antennas. Spectral occupancy of a given carrier frequency pertaining to a particular direction in space is expressed by the volume of a semi-cone shaped geometrical region in the 3-D spatio-temporal frequency space ω. A combined approach employing low complexity array processing and conventional time-frequency spectrum sensing is proposed towards the detection of space-time white spaces in ω. The detection scheme employs four subsystems; antenna array, front-end processing, 3-D spatio-temporal array processing, and 1-D spectrum sensing. Key components in the antenna array and front-end processing subsystems are described including an example of a broadband Vivaldi antenna simulated in the frequency range 1.25-2 GHz. The array processing subsystem employs 3-D infinite impulse response digital beam filters, as a low complexity alternative to conventional phased arrays. One potential realization of the 1-D spectrum sensing subsystem is described by using a tunable bandpass filter followed by an energy detector. Simulation examples are provided by considering different directions of arrival, effect of multi-path replicas, signal to noise ratio changes and both narrow band and wideband signals in the normalized temporal frequency range (0,π).