Ambiguity Function Sidelobes Research Articles

Ambiguity function analysis of iridium burst transmissions for opportunistic navigation

AbstractThe objective of this work is to investigate the Ambiguity Function (AF) characterization of the Iridium L‐band downlink burst transmissions under single burst and multiband multi‐burst mode to demonstrate its suitability and capability as Signal of OPportunity (SoOP) for navigation. The Iridium bursts are collected and examined by demodulating without any prior knowledge for frame verification. The comprehensive analysis and theoretical model of the two mode AFs are presented and verified to evaluate the waveform properties with resolution and sidelobes in both the Doppler and delay domains. Degradation in AF resulting from signal model and multiband channel combination is characterized to exploit the trade‐offs for selection and utilization of the Iridium burst. It has been found that the single burst even with maximum length of 20.32 ms appears available but far from excellent for navigation, while the multiband mode produces significant improvements over the time delay and Doppler resolution as well as a certain degradation on the AF sidelobes. Issues relating to the Iridium bursts utilization have been identified.

Improved Information Embedding for Frequency Hopping-Based MIMO DFRC System

Dual function radar communication (DFRC) system, which treats the radar as the primary modality and embeds information into the transmitted waveforms, is proposed recently to solve the problem of spectrum congestion. In this letter, we propose an improved information embedding scheme for a frequency hopping (FH) based multiple-input multiple-output (MIMO) DFRC system. First, we develop an FH matrix construction method by taking the radar ambiguity function (AF) into consideration. The constructed FH matrix is able to generate FH waveforms with superior radar detection performance. Then, an offset quadrature phase-shift keying (OQPSK) modulated communication waveform is presented to alleviate the spectral leakage issue caused by canonical modulation schemes, which together with the FH waveform, forms the transmit waveform of the considered DFRC system. Simulation results verify that the proposed scheme achieves lower AF sidelobe levels (SLLs) and better spectral containment as compared with the state-of-the-art.

Generalized MBI Algorithm for Designing Sequence Set and Mismatched Filter Bank With Ambiguity Function Constraints

A sequence set with ambiguity function (AF) specifications is frequently required in multi-transmit active sensing systems which exploit waveform diversity. This paper formulates a new model to jointly design sequence set and mismatched filter bank with AF requirements, which is a generalization of the auto-AF and cross-AF adopted in the matched filter scheme to attain lower AF sidelobe levels with an increased degree-of-freedom. The aforementioned designs result in nonconvex and nonlinear high-order polynomial (HOP) optimization problems with HOP constraints. Although the maximum block improvement (MBI) method has exhibited the powerful HOP optimization ability to design a short sequence with slow-time AF, it cannot tackle HOP constraints and involves high-complexity tensor operations. To address these issues, we develop a generalized MBI method for the HOP constrained optimization formulations. In addition, the proposed algorithm significantly reduces the computational complexity via designing an equivalent polynomial function for the original multi-linear tensor function. Numerical results demonstrate the excellent performance of our design solutions.

Code Optimization for Fast Chirp FMCW Automotive MIMO Radar

Fast chirp FMCW MIMO radar with inter-chirp coding provides high emission power by utilizing simultaneous antennas transmissions. However, the coding produces high side-lobes in the Doppler and angle dimensions of the radar's ambiguity function. The high side-lobes may cause miss-detection due to masking between targets that are at similar range and have large received power difference, as is often the case in automotive scenarios. In this paper, we develop a novel code optimization method that attenuates the side-lobes of the radar's ambiguity function and hence improves the probability of detection in the case of multiple targets. We formulate an analytical expression for the ambiguity function side-lobes, which takes into account that the targets range difference migrates during the detection interval, and that the migration is proportional to the targets Doppler frequency difference. We then develop an optimization algorithm that finds the code that minimizes the ambiguity function side-lobes average energy. The optimized code attenuates the ambiguity function side-lobes at the Doppler frequencies that are near the main lobe frequency. These frequencies correspond to targets with small speed difference, for which the range difference between the targets does not change significantly during the detection interval, and hence overlapping in range can cause severe interference. We demonstrate by simulation that the optimized code achieves an improvement in the ambiguity function side-lobes attenuation and an improvement in the probability of detection compared to reference codes.

Matched field source localization with Gaussian processes.

For a sparsely observed acoustic field, Gaussian processes can predict a densely sampled field on the array. The prediction quality depends on the choice of a kernel and a set of hyperparameters. Gaussian processes are applied to source localization in the ocean in combination with matched-field processing. Compared to conventional processing, the denser sampling of the predicted field across the array reduces the ambiguity function sidelobes. As the noise level increases, the Gaussian process-based processor has a distinctly higher probability of correct localization than conventional processing, due to both denoising and denser field prediction.

Costas‐code‐based radar waveform design using adaptive weights with target scattering coefficients and optimal variable time spacing with improved ambiguity function

Costas signals are widely used in modern radar systems as frequency coded. The Costas-code-based waveform can achieve a nearly thumbtack shape of the ambiguity function (AF). However, the highest AF's sidelobe levels (SLLs) of Costas waveform equals just 1/ N times of its main lobe level height, where N is the length of the Costas code. In this study, the authors suggest a generalised Costas waveform as a ‘burst’ of weighted pulses having variable time spacing between them, calling it as weighted variable time spacing Costas (WVTSC). They computed the AF analytical formulas of the designed WVTSC. They developed an adaptation model to adapt the WVTSC to target scattering coefficients, using the interior-point algorithm. The adaptive WVTSC yields much better Doppler cut and improved delay cut in the main lobe area of the AF, in the sense of SLL reduction. Moreover, they constructed an optimisation model resulting in optimal variable time spacing between the sub-pulses. The optimised WVTSC also yields considerable improvement in the AF's recurrent SLLs, using the genetic algorithm. The adapted optimised WVTSC design is proven, through simulation, to have better sidelobe performance than that of the initial waveform, without influencing the original delay-Doppler resolution, and without need to increase N .

Optimization of a new Golay sequences shaping for low sidelobe radar ambiguity function

This work addresses the radar waveform design problem using phase-coded waveforms especially Golay complementary pair (GCP). Thus, a new shaping of GCP is proposed and the good performance of this shaping in terms of ambiguity function sidelobe (SL) rejection is shown. With the new shaping, a gain of at least 10 dB is easily obtained in comparison with the standard GCP. In order to improve the performance of the proposed waveform, two optimization algorithms are proposed to deal with low sidelobe ambiguity function problem, a very hard combinatorial optimization problem. The first one is the simulated annealing algorithm, a local search algorithm. The second represents the genetic algorithm-based global search strategy. Simulation results are provided and demonstrate that both types of algorithms decrease the SL rejection of the ambiguity function for all tested instances.

Design and performances evaluation of new Costas‐based radar waveforms with pulse coding diversity

Costas codes are a variant of pulse compression waveforms, largely studied for their attractive time-frequency properties. Their 'thumbtack-like' ambiguity function (AF) makes them highly suitable for delay and Doppler estimation, in radar and sonar applications. However, this behaviour depends heavily on the length of the code: the improvement in delay-Doppler resolutions and AF sidelobes level needs an increase in the size of the code. In this study, designs that allow good performance without increasing the size of the code are proposed. They are based on a modification of Costas codes by widening frequency separation between hops and replacing rectangular pulses by other waveforms. This will lead to a removal of autocorrelation function grating lobes that normally appear when frequency separation is increased. The originality of the work lies in the proposal of diversified pulse waveforms, such as phase codes, Slepian sequences, and other Costas codes, to encode main Costas pulses. A performance comparison of the proposed approaches is supplied. Such waveforms could also be of interest for applications where waveform diversity is desired.

Ambiguity Function of the Transmit Beamspace-Based MIMO Radar

In this paper, we derive an ambiguity function (AF) for the transmit beamspace (TB)-based multipleinput multiple-output (MIMO) radar for the case of far-field targets and narrow-band waveforms. The effects of transmit coherent processing gain and waveform diversity are incorporated into the AF definition. To cover all the phase information conveyed by different factors, we introduce the equivalent transmit phase centers. The newly defined AF serves as a generalized AF form for which the phased-array (PA) and traditional MIMO radar AFs are important special cases. We establish relationships among the defined TB-based MIMO radar AF and the existing AF results including the Woodward's AF, the AFs defined for the traditional colocated MIMO radar, and also the PA radar AF, respectively. Moreover, we compare the TB-based MIMO radar AF with the square-summation-form AF definition and identify two limiting cases to bound its 'clear region' in Doppler-delay domain that is free of sidelobes. Corresponding bounds for these two cases are derived, and it is shown that the bound for the worst case is inversely proportional to the number of transmitted waveforms K, whereas the bound for the best case is independent of K. The actual 'clear region' of the TB-based MIMO radar AF depends on the array configuration and is in between of the worst- and best-case bounds. We propose a TB design strategy to reduce the levels of the AF sidelobes, and show in simulations that proper design of the TB matrix leads to reduction of the relative sidelobe levels of the TB-based MIMO radar AF.

Adaptive highly localized waveform design for multiple target tracking

When tracking multiple targets, radar measurements from weak targets are often masked by the ambiguity function (AF) sidelobes of the measurements from stronger targets. This results in deteriorated tracking performance and lost tracks. In this study, we consider the design of configurable waveforms whose AF sidelobes can be positioned to unmask weak targets. Specifically, we construct multicarrier phase-coded (MCPC) waveforms based on Björck constant amplitude zero-autocorrelation (CAZAC) sequences. The MCPC CAZAC waveforms exhibit wide regions in their AF surface without sidelobes and allow for selective positioning of sidelobes. We apply these waveforms in the context of a target tracker by selecting waveform parameters that minimize the expected tracking error. We show that this is accomplished by selecting the position of AF sidelobes to unmask weak targets. The target tracker is based on an independent partitions likelihood particle filter that is capable of processing the high-resolution measurements resulting from the Björck CAZAC sequences and tracks a fixed and known number of targets. Using simulations, we demonstrate the improvement in tracking performance when we adaptively select the MCPC CAZAC waveforms over tracking using non-adaptive waveform configurations or single-carrier phase-coded CAZAC waveforms.

Adaptive High-Resolution Sensor Waveform Design for Tracking

Recent innovations in modern radar for designing transmitted waveforms, coupled with new algorithms for adaptively selecting the waveform parameters at each time step, have resulted in improvements in tracking performance. Of particular interest are waveforms that can be mathematically designed to have reduced ambiguity function sidelobes, as their use can lead to an increase in the target state estimation accuracy. Moreover, adaptively positioning the sidelobes can reveal weak target returns by reducing interference from stronger targets. The manuscript provides an overview of recent advances in the design of multicarrier phase-coded waveforms based on Bjorck constant-amplitude zero-autocorrelation (CAZAC) sequences for use in an adaptive waveform selection scheme for mutliple target tracking. The adaptive waveform design is formulated using sequential Monte Carlo techniques that need to be matched to the high resolution measurements. The work will be of interest to both practitioners and researchers in radar as well as to researchers in other applications where high resolution measurements can have significant benefits. Table of Contents: Introduction / Radar Waveform Design / Target Tracking with a Particle Filter / Single Target tracking with LFM and CAZAC Sequences / Multiple Target Tracking / Conclusions

Staggered Costas Signals

A radar signal, based on coherent processing of a train of staggered Costas bursts, is suggested and investigated. The selection of sequences of each burst is based on a minimum number of collocation of their individual ambiguity function sidelobe peaks. The resulting ambiguity function combines qualities of both "thumbtack" and "bed of nails" signals. Comparison with linear-FM, V-FM, and complementary phase coded (CPC) signals is given, as well as comparison with hybrid signals consisting of both phase and frequency coding.