An observer-based dynamic output feedback H∞ controller is proposed for a class of two-dimensional (2D) uncertain discrete systems described by the Roesser model with actuator saturation, time-varying state delay and external disturbances. First, a delay-dependent Lyapunov stability condition is derived in linear matrix inequality (LMI) form which uses the reciprocal convex approach and H∞ disturbance attenuation performance is also analysed. Secondly, a convex hull is adopted to represent the saturation nonlinearity. The H∞ control synthesis for uncertain 2D discrete systems is described by a Roesser model subjected to actuator saturation and external disturbances using an observer-based dynamic output feedback approach. Some practical examples are provided to highlight the usefulness of the presented results.

Robust output feedback control of 2D discrete systems with actuator saturation and time-varying delay

An analog all-pass filter based transfer function synthesis method is proposed for realizing multifunctional microwave active circuits. An analog realization is obtained by replacing unit sample delays in an existing digital prototype with a second-order all-pass analog filter. A novel space time array processor (STAP) and a frequency and bandwidth agile multi-band filter have been simulated using the proposed transfer function synthesis method using measured S- parameters of a fabricated 130 nm second-order CMOS all- pass filter. Simulated array patterns of the STAP beamformer show improved side-lobe performance for better interference suppression and noise rejection. The tunability of the multi-band analog filter, in terms of the center frequency and the quality factor, is verified up to 8 GHz, which has potential applications in analog microwave front-ends.

All-Pass Filter Based Synthesis of Multifunctional Microwave Active Circuits

The presented work explores novel methods for synthesizing approximately frequency independent array factors at lower hardware complexity for wideband beamforming applications. The proposed approach employs 2-D infinite impulse response (IIR) digital beam filters together with nested uniform linear arrays (ULAs). The array is designed to have multiple levels of nesting. Each level of nesting consists of a ULA covering a temporal subband of the incident wideband signal. The use of nested arrays provides the required aperture size using a smaller number of elements compared to using a single ULA to capture the entire wideband signal. The use of different levels of nesting allows the operation of the digital processor for each sub-band at different clock rates. This is a hierarchical approach that saves both digital VLSI hardware and power consumption. The 2-D IIR digital beam filters that process each subband signal from each of the nested subarray achieves wideband beamforming. Simulations illustrate approximately frequency independent passbands as required in wideband beamforming.

Mixed microwave-digital and multi-rate approach for wideband beamforming applications using 2-D IIR beam filters and nested uniform linear arrays

In this review paper, recent advancements in multidimensional (MD) spatio-temporal signal processing for highly-directional radio frequency (RF) antenna array based receivers are discussed. MD network-resonant beamforming filters having infinite impulse response (IIR) and recursive spatio-temporal signal flow graphs are reviewed. The concept of MD network-resonant pre-filtering is described as a modification to existing phased/timed array beamforming back-ends to achieve improved side-lobe performance in the array pattern, leading to better interference rejection capabilities. Both digital and analog signal processing models are described in terms of their system transfer functions and signal flow graphs. Example MD frequency response and RF antenna array pattern simulations are presented.

An overview of multi-dimensional RF signal processing for array receivers

Beam-enhanced digital aperture arrays employ 2-D infinite-impulse-response (IIR) filters as a preprocessing stage for phased/timed-array beamformers to obtain lower side-lobe levels without compromising the array size or the main-lobe selectivity. A digital very-large-scale integration architecture is proposed for beam-enhanced linear aperture arrays. The proposed architecture consists of four subsystems: 2-D IIR prefiltering, beam steering via fast computation of filter coefficients, compensation for nonlinear phase, and phased/timed-array beamforming. Systolic-array architectures are used for first- and second-order 2-D IIR prefiltering subsystems, including fast computation of filter coefficients. The trade-off due to the nonlinear phase response of the 2-D IIR prefilter is partially compensated via fast Fourier transform-based complex phase rotations. Designs are implemented on a Xilinx Virtex-6 XC6VLX240T field-programmable gate-array device and verified using on-chip hardware cosimulation. Field-programmable gate-array designs for both 2-D IIR prefiltering and filter coefficient computation are mapped to standard-cell application-specific integrated circuits in 45 nm complementary metal-oxide semiconductor technology up to the synthesis level with supply VDC = 1.1 V. For a simulation having 64 antennas with binary phase-shift keying modulation, the beam-enhanced aperture array provides better than 10 dB improvement in bit error rate versus signal-to-interference ratio performance compared to phased/timed-array beamforming.

Digital VLSI architectures for beam-enhanced RF aperture arrays

A uniform linear array (ULA) digital beamformer with enhanced selectivity (interference rejection) over conventional true-time delay-sum (TTDS) beamforming is proposed for scanned aperture applications. Conventional TTDS transfer function, which contains only zero-manifolds, is modified by introducing complex pole-manifolds based on 2-D infinite impulse response (IIR) digital beam filters, thereby achieving enhanced selectivity for the same number of antennas in the ULA. For a ULA of 64 antennas, desired direction of arrival (DOA) 30° and interference DOA -60° from array broadside, a relative improvement in signal-to-interference ratio (SIR) of 7 dB is verified. For 128-element ULA, interference DOA -10°, a relative improvement in SIR of 5-10 dB is obtained for the desired DOA in the range 10°-90°. The projected improvements are independent of the weights of the conventional phased-array, TTDS, or filter-sum beamformer used because the method does not change the zero-manifolds of the original array pattern.

2-D-IIR Time-Delay-Sum Linear Aperture Arrays

Radio-frequency (RF) two-dimensional (2-D) infinite impulse response (IIR) space-time plane-wave frequency-planar beam digital filters have potential applications in ultra-wideband (UWB) directional filtering of propagating electromagnetic far-field plane-waves. Such plane-wave filters achieve highly directional digital RF beamforming for aperture array applications. The phase response of emerging 2-D beam filters which are designed using the concept of frequency-planar resonant network prototypes is studied in this paper. The high frequency phase non-linearities are quantified and compensated using a real-time FFT-based multirate phase rotator architecture.

FFT-based phase compensation of 2-D beam digital filters for electronically steerable RF arrays

A linear antenna array beamforming method which significantly improves the spatial selectivity of conventional phased/timed arrays is presented. A two-dimensional (2-D) infinite impulse response (IIR) digital beam filter is employed as a pre-processing stage to existing phased/timed arrays, thereby mathematically modifying the array transfer function. Introduction of a pre-filter is possible due to multi-input multi-output signal flow structure of the 2-D IIR beam filters, and the improvement in spatial selectivity is presented using closed-form frequency response and array pattern simulations. An example wireless communication scenario shows that the proposed beamformer leads to additional gain of more than 10 dB in terms of the BER vs. SIR performance.

Combined time-delay FIR and 2-D IIR filters for EARS, radar, and imaging applications

Radio-frequency (RF) digital phased array antennas are highly-useful for achieving electronically-scanned smart antenna apertures with applications in radar, signal intelligence, microwave and mm-wave imaging and wireless communication systems. However, digital phased array algorithms are of high computational complexity, which leads to correspondingly high circuit complexity in a VLSI implementation. A 2-D IIR beam space-time plane-wave digital filter can achieve the required electronically-scanned RF beams albeit at an order of magnitude lower circuit complexity compared to phased arrays at the cost of non-linear phase response. The proposed method approximately rectifies the non-linearity in the phase response using an FFT-based phase compensation method which linearises the response at higher frequencies close to the Nyquist limit where the phase non-linearity is worst in the beam filter response. FPGA prototypes using a Xilinx Virtex-4 Sx35-10ff668 device on an XtremeDSP Kit-4 are provided, which show real-time operation at up to 315 MHz.

Sewwandi Wijayaratna

Papers

2-D-IIR Time-Delay-Sum Linear Aperture Arrays

Digital VLSI architectures for beam-enhanced RF aperture arrays

FFT-based phase compensation of 2-D beam digital filters for electronically steerable RF arrays

Combined time-delay FIR and 2-D IIR filters for EARS, radar, and imaging applications

Reconfigurable phase-linearizer for 2-D IIR RF-to-bits antenna-array digital beam filters