Complementary Waveforms Research Articles

Delay-Doppler Map Shaping through Oversampled Complementary Sets for High-Speed Target Detection

Advanced waveform design schemes have been widely employed for radar and sonar remote sensing analysis such as target detection and separation, where significant range sidelobe is a main factor that limits the improvement of analysis performance. As an extensional type of Golay complementary waveforms, complementary sets are a waveform design scenario of concern that shows more diversity in the design of transmission order, and results in a different distribution of range sidelobes. This work proposes an oversampled generalized Prouhet–Thue–Morse (OGPTM) method for the transmitted signal design of complementary sets, with comprehensive analysis to the influence on the sidelobe distribution. Based on this idea and our previous work, we further put forward a pointwise multiplication processor (PMuP) to integrate two delay-Doppler maps of oversampled complementary sets, which achieve much better sidelobe suppression performance on high-speed target detection with range migration.

Target-Oriented SAR Complementary Waveform Optimization for SCR Improvement

Target-Oriented SAR Complementary Waveform Optimization for SCR Improvement

Enhanced Doppler Resolution and Sidelobe Suppression Performance for Golay Complementary Waveforms

An enhanced Doppler resolution and sidelobe suppression have long been practical issues for moving target detection using Golay complementary waveforms. In this paper, Golay complementary waveform radar returns are combined with a proposed processor, the pointwise thresholding processor (PTP). Compared to the pointwise minimization processor (PMP) illustrated in a previous work, which could only achieve a Doppler resolution comparable to existing methods, this approach essentially increases the Doppler resolution to a very high level in theory. This study also introduced a further filtering process for the delay-Doppler map of the PTP, and simulations verified that the method results in a delay-Doppler map virtually free of range sidelobes.

Complementary waveforms for range sidelobe suppression based on a singular value decomposition approach

AbstractWhile Doppler resilient complementary waveforms (DRCWs) have previously been considered to suppress range sidelobes within a Doppler interval of interest in radar systems, their ability to provide Doppler resilience can be further improved. A new singular value decomposition (SVD)‐based DRCW construction is proposed, in which both transmit pulse trains (made up of complementary pairs) and receive pulse weights are jointly considered. Besides, using the proposed SVD‐based method, a theoretical bound is derived for the range sidelobes within the Doppler interval of interest. Moreover, based on the SVD solutions, a challenging non‐convex optimization problem is formulated and solved to maximise the signal‐to‐noise ratio (SNR) with the constraint of low range sidelobes. It is shown that, compared with existing DRCWs, the proposed SVD‐based DRCW has better Doppler resilience. Further, the new optimised SVD‐based DRCW has a higher SNR while maintaining the same Doppler resilience.

Joint Radar and Communications Waveform Design Based on Complementary Sequence Sets

The joint radar and communications (JRC) waveform often has a high range sidelobe, which will degrade the target detection performance of an automotive JRC system. To solve this problem, a joint radar and communications complementary waveform group (JRC-CWG) design method is proposed in this paper by exploiting the philosophy of the complementary sequence. In the JRC-CWG, the traditional unimodular communications waveforms, such as the binary phase shift keying (BPSK) waveform, are used to perform the communications function. The sum of the autocorrelation function (SACF) of JRC-CWG is optimized to minimize the sidelobe level. Furthermore, considering that the JRC-CWG has poor Doppler resilience, a Doppler-resilient joint radar and communications complementary waveform (DR-JRC-CWG) design method is proposed to improve the Doppler resilience. Finally, the simulation results show that the proposed JRC-CWG and DR-JRC-CWG have superior radar performances without the degradation in communications performance in terms of the bit error rate (BER).

Programmable dual-electric-field immunosensor using MXene-Au-based competitive signal probe for natural parathion-methyl detection

Immunosensor is a promising tool for natural parathion-methyl (PTM) detection, and its analytical advantages can be magnified by introducing flexibly-fabricating technique. Herein, we present a dual-electric-field PTM immunosensor on highly-compatible screen-printed electrode (SPE). MXene-Au, the product of in-situ gold nanoparticle growth on MXene, provides considerable binding sites for PTM antigen (ATG) and methylene blue (MB). During sensing, the MXene-Au-MB-ATG probe competitively binds antibody against PTM, composing a ratiometric immune-system. With DC-biased sine excitations from complementary waveforms, on-chip electric field couple improves immunoreactions among PTM, probe, and antibody. Electric field distribution is programmed by trimming bypass resistors to pursue optimal performance. Probe synthesis is solidly proven with morphological examinations, and competition mechanism between the probe and target PTM is clarified in electrochemical analyses. Remarkably, this method brings less consumption of immune time than electric-field-free or solo-electric-field setup (50 s vs. 900 or 70 s), and simultaneously provides more powerful ratiometric signal than the rivals. Log-linear relationship, between PTM level and sensor readout, is established in 0.02–38 ng/mL, and limit of detection is found as 0.01 ng/mL. This method is applied in laboratorial and natural PTM analyses, and the readouts are consistent with high performance liquid chromatography and recovery test.

Coordination of Complementary Sets for Low Doppler-Induced Sidelobes

Golay complementary waveforms are, by definition, able to generate narrow pulses with low sidelobes via coherent signal processing. However, while an ideal impulse can be obtained for target returns at zero-Doppler, significant sidelobes are observed at nonzero Doppler shifts. In this paper, a Generalized Binominal Design (GBD) procedure is proposed for the waveforms consisting of complementary sets in an attempt to reduce the Doppler-induced sidelobes. Our theoretical analysis as well as simulation results show that the proposed approach performs as good as existing Binominal Design method used for sidelobe suppression with Golay complementary waveforms and can also achieve around 28% enhancement on the Doppler resolution, with an acceptable loss in peak to peak-sidelobe ratio (PPSR).

Multiple target detection by using Golay complementary waveforms in Reed–Muller sequences

Multiple target detection by using Golay complementary waveforms in Reed–Muller sequences

Quasi-Orthogonal Z-Complementary Pairs and Their Applications in Fully Polarimetric Radar Systems

One objective of this paper is to propose a novel class of sequence pairs, called “quasi-orthogonal Z-complementary pairs (QOZCPs)”, each depicting Z-complementary property for their aperiodic auto-correlation sums and also having a low correlation zone when their aperiodic cross-correlation is considered. Construction of QOZCPs based on Successively Distributed Algorithms under Majorization Minimization (SDAMM) is presented. Another objective of this paper is to apply the proposed QOZCPs in fully polarimetric radar systems and analyse the corresponding ambiguity functions. It turns out that QOZCP waveforms are much more Doppler resilient than the known Golay complementary waveforms.

Doppler Resilient Complementary Waveform Design for Active Sensing

Active sensing systems prefer probing waveforms with good auto-correlation properties. Faced with the difficulty in getting individual sequences with impulse-like aperiodic auto-correlation functions, we resort to the temporal waveform diversity based on complementary sets of sequences (CSS). It seems an ideal solution, but has rarely been used due to the extreme sensitivity of CSS to Doppler shifts. This paper is devoted to applying numerical methods to the design of Doppler resilient complementary waveforms (DRCW) whose ambiguity functions are almost free of range sidelobes along modest Doppler shifts. We formulate the problem as minimizing the worst-case peak sidelobe level (PSL) with low peak-to-average power ratio (PAR) constraints, and then approximate the min-max problem by a ${l}_{p}$ -norm minimization problem. A hierarchical strategy is developed to tackle the phase optimization and the amplitude-phase optimization respectively. Correspondingly, two algorithms based on phase-gradient and Majorization-Minimization are proposed, both of which can be efficiently computed via FFT. Numerical experiments show our method is effective and superior to existing ones. The DRCWs thus obtained have their range sidelobes at all lags suppressed below −60dB, and are expected to bring significant performance improvements in active sensing. Two application examples, detecting weak targets in heavy clutter and estimating the high-resolution range profile of an extended target by active radars, are given.

Range-Doppler Sidelobe Suppression for Pulsed Radar Based on Golay Complementary Codes

To relieve the interference caused by range-Doppler sidelobes in pulsed radars, we propose a new method to construct Doppler resilient complementary waveforms based on Golay codes. We design both the transmit pulse train and the receive pulse weights, so that the similarity between the pulse weights and a given window function is maximized and the constraints on Doppler null points and energy are met. That is summarized as a two-way partitioning problem, and then solved by semidefinite programming and randomization techniques. The novel waveform thus obtained has its range sidelobe outright suppressed in multiple and flexibly-adjustable Doppler zones, and performs well in Doppler sidelobe suppression, Doppler resolution and SNR. It shows great promise in detecting slightly-moving weak targets with the existence of dense interference.

Implementable phase‐coded radar waveforms featuring extra‐low range sidelobes and Doppler resilience

Golay binary complementary sequences are used to code quadriphase waveforms. The Gaussian minimum shift keying coding scheme is used to produce waveforms with constant amplitude, and continuous and differentiable phase. To satisfy spectral requirements, the waveforms are further spectrally optimised by a spectrum-optimisation process, making the final waveforms implementable. The extra-low sidelobe level is achieved by the use of an extended mismatched filter on receive of pulse compression. To improve Doppler tolerance, Doppler-resilient complementary waveforms are derived that provide first-order suppression to the raised range sidelobes introduced by the Doppler frequency shift in returned signals. This study is an expanded version of a conference paper presented at 2018 International Radar Conference held in Brisbane, Australia.

Alternative signal processing of complementary waveform returns for range sidelobe suppression

It has been an important technique to reduce sidelobes for processing nonzero Doppler target returns under Golay complementary waveforms. While the pointwise minimization processor in our early work shows an enhanced performance on the suppression of range sidelobes compared with existing approaches, it has a reduced detection probability to target with location uncertainties. In this paper, we present an alternative processing method which combines the radar returns in two separated pairs of Golay complementary waveforms through a pointwise addition processor. Our simulation result shows that this alternative method has a similar performance to that of the pointwise minimum processor for range sidelobes suppression and computational complexity but results in an improved target detection probability, with an acceptable decrease on the peak to peak-sidelobe ratio.

Golay Complementary Waveforms in Reed-Müller Sequences for Radar Detection of Nonzero Doppler Targets.

Golay complementary waveforms can, in theory, yield radar returns of high range resolution with essentially zero sidelobes. In practice, when deployed conventionally, while high signal-to-noise ratios can be achieved for static target detection, significant range sidelobes are generated by target returns of nonzero Doppler causing unreliable detection. We consider signal processing techniques using Golay complementary waveforms to improve radar detection performance in scenarios involving multiple nonzero Doppler targets. A signal processing procedure based on an existing, so called, Binomial Design algorithm that alters the transmission order of Golay complementary waveforms and weights the returns is proposed in an attempt to achieve an enhanced illumination performance. The procedure applies one of three proposed waveform transmission ordering algorithms, followed by a pointwise nonlinear processor combining the outputs of the Binomial Design algorithm and one of the ordering algorithms. The computational complexity of the Binomial Design algorithm and the three ordering algorithms are compared, and a statistical analysis of the performance of the pointwise nonlinear processing is given. Estimation of the areas in the Delay–Doppler map occupied by significant range sidelobes for given targets are also discussed. Numerical simulations for the comparison of the performances of the Binomial Design algorithm and the three ordering algorithms are presented for both fixed and randomized target locations. The simulation results demonstrate that the proposed signal processing procedure has a better detection performance in terms of lower sidelobes and higher Doppler resolution in the presence of multiple nonzero Doppler targets compared to existing methods.

Detection of moving targets in sea clutter using complementary waveforms

Work of Pezeshki, Calderbank and others [1, 2] has shown that choice of transmission order of Golay complementary waveforms in radar pulse trains can significantly improve Doppler resilience in detecting nonzero Doppler targets. For multiple targets a Weighted average Doppler (WD) algorithm [3] based on our earlier work has been shown to provide improvements. In this paper, we demonstrate that the Weighted Sidelobe Minimization procedure, developed in our recent work that combines the outputs of WD and the existing Binominal Design algorithms for ordering transmitted complementary waveform sequences using a point-wise minimization process (PMP), is also effective for the elimination of false target returns arising from sea clutter. A detailed analysis based on a Swerling II target model in terms of target detection probability is presented to validate the use of PMP. Our validation is strengthened by numerical simulations for both fixed and randomized scenarios.

Range sidelobe suppression for using Golay complementary waveforms in multiple moving target detection

We describe a method for processing radar signals, combining the outputs of two – a Weighted average Doppler algorithm and an existing Binominal Design algorithm via a point-wise minimum processor. The method renders a better performance in range sidelobe suppression for the detection of multiple moving targets using Golay complementary waveforms than the existing Binominal Design algorithm. The effectiveness of the method is justified by analyzing the corresponding ambiguity functions. We also show the performance of the new signal processing method by simulations under a realistic scenario.

Doppler tolerance, complementary code sets, and generalised Thue–Morse sequences

The authors generalise the construction of Doppler-tolerant Golay complementary waveforms by Pezeshki–Calderbank–Moran–Howard to complementary code sets having more than two codes, which they call Doppler-null codes. This is accomplished by exploiting number-theoretic results involving the sum-of-digits function and a generalisation to more than two symbols of the classical two-symbol Thue–Morse sequence. Two approaches are taken to establish higher-order nulls of the composite ambiguity function: one by rewriting it in terms of equal sums of powers (ESP) and the other by factoring it in product form to reveal a higher-order zero, analogous to spectral-null codes. They conclude by describing an application of minimal ESP sets to multiple-input–multiple-output radar.

Strong ionization asymmetry in a geometrically symmetric radio frequency capacitively coupled plasma induced by sawtooth voltage waveforms.

The ionization dynamics in geometrically symmetric parallel plate capacitively coupled plasmas driven by radio frequency tailored voltage waveforms is investigated using phase resolved optical emission spectroscopy (PROES) and particle-in-cell (PIC) simulations. Temporally asymmetric waveforms induce spatial asymmetries and offer control of the spatiotemporal dynamics of electron heating and associated ionization structures. Sawtooth waveforms with different rise and fall rates are employed using truncated Fourier series approximations of an ideal sawtooth. Experimental PROES results obtained in argon plasmas are compared with PIC simulations, showing excellent agreement. With waveforms comprising a fast voltage drop followed by a slower rise, the faster sheath expansion in front of the powered electrode causes strongly enhanced ionization in this region. The complementary waveform causes an analogous effect in front of the grounded electrode.

A Novel Dead-Time Control Method for Double End Converter

In order to achieve symmetry of the drive signal and suppress the magnetic bias, a novel dead-time control method for the double end converter is put forward in this paper, which can generate two independent and complementary PWM waveforms by configuring EPWM (Enhanced Pulse Width Modulator) module. The magnetic bias problems of the double end converter, principle of EPWM module and adjustment process of the dead-time control method are analyzed. Two different dead-times can de realized by setting the rising edge delay and falling edge delay of the corresponding registers in Dead-band (DB) module in one cycle to meet the requirement of drive signals. Experimental research on the novel dead-time control method is done on the push-pull forward circuit and the experiment results verify the feasibility of the proposed method.

Doppler Resilient Golay Complementary Waveforms

We describe a method of constructing a sequence (pulse train) of phase-coded waveforms, for which the ambiguity function is free of range sidelobes along modest Doppler shifts. The constituent waveforms are Golay complementary waveforms which have ideal ambiguity along the zero Doppler axis but are sensitive to nonzero Doppler shifts. We extend this construction to multiple dimensions, in particular to radar polarimetry, where the two dimensions are realized by orthogonal polarizations. Here we determine a sequence of two-by-two Alamouti matrices where the entries involve Golay pairs and for which the range sidelobes associated with a matrix-valued ambiguity function vanish at modest Doppler shifts. The Prouhet-Thue-Morse sequence plays a key role in the construction of Doppler resilient sequences of Golay complementary waveforms.