Peak Sidelobe Level Research Articles

Small RCS targets detection based on pulse compression radar signal generator and processor

In the last two decades, field programmable gate arrays (FPGAs) have become the leading technology for implementing real time systems, specially radars. The most important advantage of FPGA is its parallel nature of executing complicated algorithms. As a result, the received data flow will be processed in a real time manner, which is suitable for radar applications. This paper attempts to show the design and the FPGA implementation of a binary phase-coded pulse compression radar signal generator and processor, that are intended to determine the ranges, and the speeds of targets with small radar cross-section area like drones. The system operating waveform is a bi-phase sequence, that is known to have the best known peak sidelobe level compared to compound Barker codes of the same length. In addition, the design incorporates a range sidelobes cancellation method to remove the time sidelobes in the matched filter output. Also, we are going to represent and investigate the FPGA implementing steps of the radar waveform generator and processor according to the required parameters. Finally, the implementation results of the proposed system will be represented.

Joint design of antenna selection and transmit linear array beamformer for integrated radar and communications

The design of integrated radar-communication (IRC) systems is seen as a promising solution to alleviate the congestion of spectrum resource in recent years. Additionally, with the deployment of large-scaled arrays in base stations, sparse array design via antenna selection has become prominent to reduce system overheads and alleviate mutual coupling effect. In this paper, we propose a joint design of antenna selection and transmit beamformer for IRC systems to realize the dual operations of radar and communications. Specifically, we propose a joint model that achieves a trade-off between minimizing the total number of antennas for IRC and suppressing the peak sidelobe level (PSL) of overall transmit beampattern with well-controlled mainlobe ripples. Unlike the existing schemes that focus on individual beamformer design with varying sparse array configurations, we impose a group sparsity on the beamforming matrix and jointly optimize multiple beamformers to obtain a common sparse array for the constellation of all communication symbols. To solve the resulting non-convex problem, we employ the alternating direction method of multipliers to split the original problem into parallel subproblems which are then solved iteratively. Simulation results illustrate the superiority of the proposed method over the conventional approaches in obtaining a lower PSL using fewer antennas with dual functions.

Thinned planar antenna array synthesis using a hybrid approach combining almost difference sets and weighted total least squares method

This paper introduces a hybrid approach for designing thinned planar antenna arrays with low peak sidelobe levels (PSLLs). The standard almost difference set (ADS) approach allows the analytical determination of the turned-on element positions within the array configuration, but it provides suboptimal performance in PSLL reduction. To address this limitation, a hybrid method is presented by integrating the ADS approach with the weighted total least squares (WTLS) method. Simulation results from various case studies demonstrate the effectiveness of the hybrid ADS-WTLS method in designing thinned planar antenna arrays with low PSLLs. Additionally, the performance of the synthesized designs obtained through the hybrid method is validated using electromagnetic (EM) simulations.

Pattern synthesis of distorted phased array antenna with unsteady surface deformation considering dynamic range ratio

Abstract This paper presents an optimization method for pattern synthesis of distorted phased array antenna with unsteady surface deformation considering the dynamic range ratio (DRR). In the synthesis approach, different array deformations under unsteady mechanical loads are considered, and the distorted distribution of array elements is calculated after solving the mechanical deformation model. Then, optimize the excitation coefficients of each array element including amplitude and phase with DRR control so as to recover a high-quality pattern from a deteriorated pattern caused by the unsteady deformations. The optimization objective is to minimize the peak sidelobe level, which is synthesized by using a gradient-based algorithm. The optimized excitations can be used as the initial excitation, and the corresponding phase excitations can be derived according to the different deformations.

Application of chaotic colony predation algorithm in electromagnetics

The colony predation algorithm (CPA) is a new meta-heuristic algorithm that mimics the predation of animals to improve the radiation properties of antenna arrays. To overcome CPA’s problems of low accuracy and fast convergence, we propose an improved CPA called the chaotic colony predation algorithm (CCPA). The performance of CCPA was investigated in three parts. First, CCPA was tested with four benchmark functions. Then, CCPA was applied to equally spaced linear arrays to suppress the peak side-lobe level (PSLL) and place nulls in the desired directions. Finally, CCPA was used for a pattern synthesis of equally spaced linear arrays to reduce the PSLL under various constraints. Our results show that CCPA performed competitively with other well-known algorithms. Thus, CCPA is a promising option for solving electromagnetic optimization problems.

Optimization method of electronic control parameters of antenna array for null controlling in specific regions and sidelobe suppression

ABSTRACT This paper presents a gradient-based optimisation method of antenna array for null controlling in specific regions and sidelobe suppression. The optimisation problem is formulated as optimising the electronic control parameters (excitation amplitude and phase) of the array to achieve that the maximum value of the peak sidelobe levels (PSLLs) is minimised and the depths of the nulls in specific regions are not greater than a threshold. The Kreisselmeier – Steinhauser (KS) function is used to describe the maximum value of the PSLLs, in this way, the optimisation problem becomes differentiable and can be solved efficiently by gradient-based algorithm. The sensitivities of the objective with respect to the design variables are analytically derived. Typical numerical examples and detailed evaluations are provided to validate the effectiveness of the proposed method. The results show that the null controlling in the predefined specific single, single-wide, dual, multiple, and annular regions is realised, and the PSLL suppression is performed comparing to the uniform planar arrays. In the 28 GHz base station transmitting antenna-array example, the proposed method effectively suppresses the PSLL and greatly saves the calculation time while maintaining the various specific null regions controlling.

Synthesis of Large Ultrawideband Sparse Planar Arrays by Utilizing a Cooperative Coevolutionary Iterative Fourier Transform

This letter introduces a cooperative coevolutionary iterative Fourier transform (CCIFT) technique to extend the conventional IFT to large ultra-wideband (UWB) sparse planar array synthesis. In the proposed CCIFT, a dense initial element position grid such as a spacing of half a wavelength at the highest frequency is adopted to avoid the presence of grating lobes at high frequency band, and a probability-assisted element selection mechanism is presented to guarantee the obtained array layout to meet a preset minimum spacing constraint, enabling the placement of physical UWB antenna elements. In addition, a cooperative coevolutionary strategy is presented to avoid prematurity by establishing the information interaction between different excitation distributions from multiple parallel IFT procedures. Two examples are conducted and results show that the CCIFT can achieve a considerably lower peak sidelobe level (PSL) than some state-of-art algorithms within an acceptable CPU time, which demonstrates its effectiveness and superiority.

Supervised Reciprocal Filter for OFDM Radar Signal Processing

In this paper, we address the problem of the range-Doppler map evaluation in continuous wave radar exploiting OFDM signals. This stage is usually implemented by resorting to a suboptimal batches algorithm and a typical choice is to fragment the signal in batches with length equal to the OFDM symbol length and to apply at each batch an appropriate range compression strategy: typically, either Matched Filter (MF) or Reciprocal Filter (RF). The former provides the best performance against noise-limited scenarios, whereas the latter against clutter-limited scenarios, thanks to its high Peak SideLobe Level (PSL). Using “OFDM fragmentation” requires symbol synchronization and sets constraints on the coherent processing chain; moreover, we show that it provides a Signal-to-Noise Ratio (SNR) loss both when using MF and RF. Therefore, we investigate the case of “non-OFDM fragmentation”, which does not require synchronization and avoids setting constraints on the processing chain. Specifically, we address the case of batch lengths longer than a single OFDM symbol that can potentially reduce the SNR loss at long ranges. We find that this is effective for the MF, but causes an even higher SNR loss for the direct application of the RF filter, which still provides a low level of sidelobes. Aiming at preserving the potential benefits of the RF over the MF against the clutter-limited scenarios, we propose some modified versions of the RF for the non-OFDM fragmentation case, which are shown to offer a trade-off between SNR losses and sidelobes level control. The effectiveness of the proposed approaches is demonstrated both by providing theoretical performance prediction expressions and by using simulated analyses. To this purpose, a case study is considered for a passive radar exploiting DVB-T transmissions

Chaotic Coding for Interference Suppression of Digital Ionosonde

External interference in ionospheric sounding seriously degrades the quality of echo signals and data; thus, it should be eliminated. This paper presents a method for suppressing interference using chaotic coding with a set of Bernoulli map sequences; compared with other commonly used coding methods such as Barker code, complementary code, and Barker-like codes, through simulation, the ambiguity function (AF) of Bernoulli map codes has better performance in terms of peak sidelobe level (PSL), integral sidelobe ratio (ISL), noise suppression (NS), and signal-to-noise ratio (SNR). Experimental tests were performed using a vertical ionosonde in Yinchuan, Ningxia Hui Autonomous Region, China, and the ionosonde was operated by alternating 40-bit Barker-like coding and 40-bit Bernoulli map coding each day to compare the effectiveness of interference suppression. The results showed that using Bernoulli map coding could remove interference and improve SNR significantly, thereby improving the data quality of the resulting ionograms.

Synthesis of linear thinned array based on improved binary brain storm optimization

In this paper, an improved binary brain storm optimization (ImBBSO) method is presented for pattern synthesis of linear thinned array. To avoid local convergence and obtain the global optimum, on the basic of original binary brain storm optimization (BBSO) algorithm, the designed method mainly modifies three aspects, containing the clustering centers selection, the forced bit transposition mechanism and the survival of population. The interactions of these three operations drive optimization variables to move toward a better direction. During optimization process, the formulated cost function balances the relationship among the number of active elements, the peak sidelobe level and the half power beam width, which are eventually in the best balance state after completing iterations. Besides, the subarray partition strategy is also integrated into the proposed optimization framework with slight amendments, which can be applied to many engineering fields with space restrictions. Finally, several numerical examples demonstrate the effectiveness and applicability of the proposed method compared with other existing results of state-of-the-art methods, whether in benchmarking functions or linear array application.

A new window function for the spectral analysis of effect of celestial body on Taiji mission below 0.1 mHz

The Taiji project is a space gravitational wave detection mission consisting of three satellites that form a large equilateral triangle with a side length of approximately 3×109 m in heliocentric orbit. It may have the potential to detect gravitational waves below 0.1 mHz. Gravitational wave signals in the μHz range have a strain sensitivity as large as 2.9×10-14, or approximately 8.7×10-5 m variation in inter-satellite distance. However, inter-satellite distances are affected by the celestial bodies in the solar system, introducing changes that may reach magnitudes of 3×107 m; thus, the effect of celestial bodies on these distances may exceed the gravitational signals below 0.1 mHz. Therefore, it is necessary to accurately estimate the effect of the gravity of celestial bodies below 0.1 mHz. In this study, based on the inter-satellite distances in the Taiji mission, a window function design method is proposed and a six-term cosine window function is designed. It has a high decay rate of h-12 and a good peak sidelobe level of −88 dB. It improves the attenuation of spectral leakage while maintaining an acceptable minimum number of signal periods, which is beneficial for signals where it is difficult to obtain more periods, such as for the Taiji mission. Based on the analytical results of the states of satellites in cases when the satellites move only in the gravitational field of the Sun, the ability of the new window function is validated.

Efficient waveform design with jamming characteristics for precision electronic warfare

The goal of precision electronic warfare (PREW) is to implement blanket jamming on the targets precisely and ensure that friendly devices are not affected; thus, it requires controlling energy precisely in the spatial domain and covering the working bandwidth of the target equipment in the frequency domain. In this paper, we propose the algorithms to design waveforms with jamming characteristics for PREW, where the frequency requirement is converted to mitigation on the autocorrelation peak sidelobe level (APSL) of the combined waveform in the time domain. Then, we establish two multiobjective problems (MOPs) based on one-step and two-step methods, which have their own advantages in practice; that is, the former performs better on the computational efficiency by obtaining the waveform directly, and the latter controls the energy better in the worst-case scenario by recovering the covariance matrix of the waveform. To solve the two MOPs, the ℓp-norm and a reasonable conversion are employed to approximate the highly nonconvex APSL terms, and the objective functions are transformed into quadratic terms within the majorization-minimization (MM) framework. An accelerating scheme is applied to expedite the proposed algorithms. Numerical examples demonstrate that the two proposed algorithms outperform the existing algorithms on the jamming performance and computational burden.

Worst-case analysis of array beampatterns using interval arithmetic.

Over the past decade, interval arithmetic (IA) has been used to determine tolerance bounds of phased-array beampatterns. IA only requires that the errors of the array elements are bounded and can provide reliable beampattern bounds even when a statistical model is missing. However, previous research has not explored the use of IA to find the error realizations responsible for achieving specific bounds. In this study, the capabilities of IA are extended by introducing the concept of "backtracking," which provides a direct way of addressing how specific bounds can be attained. Backtracking allows for the recovery of the specific error realization and corresponding beampattern, enabling the study and verification of which errors result in the worst-case array performance in terms of the peak sidelobe level (PSLL). Moreover, IA is made applicable to a wider range of arrays by adding support for arbitrary array geometries with directive elements and mutual coupling in addition to element amplitude, phase, and positioning errors. Last, a simple formula for approximate bounds of uniformly bounded errors is derived and numerically verified. This formula gives insights into how array size and apodization cannot reduce the worst-case PSLL beyond a certain limit.

COSECANT-SQUARED BEAM PATTERN SYNTHESIS OF CONCENTRIC CIRCULAR ANTENNA ARRAY IN A RANGE OF AZIMUTH PLANE USING EVOLUTIONARY ALGORITHM

This paper presents, a pattern synthesis method based on Differential Evolutionary Algorithm. A cosec2 beam pattern has been generated from different concentric circular ring arrays of isotropic elements by finding the optimum set of elements amplitude and phase using the Differential Evolution algorithm. The shaped beam pattern (cosec2) is generated in three predefined azimuth planes (φ=0°, 5° and 10°) from a Concentric Circular Antenna Array (CCAA) having two rings, three rings, and four rings. The total number or isotropic elements are equal for array geometries. The optimum excitation for array geometries is also verified for a range of arbitrarily chosen azimuth planes. The obtained main beam is similar to the desired pattern with some minor variations in peak Side Lobe Level (peak SLL) and ripple. Dynamic range ratio (DRR) is improved by using 4-bit discrete Amplitudes and 5-bit discrete Phases. These discrete excitations also simplify the design complexity of the feed networks.

Sparse hydrophone array synthesis for frequency‐invariant and multi‐angle beampatterns using block‐structured Bayesian compressive sensing

AbstractTo solve the synthesised accuracy degradation of traditional Bayesian compressive sensing (BCS) in wideband multi‐beam hydrophone array synthesis, a novel sparse array synthesis method based on block‐structure Bayesian compressive sensing (BS‐BCS) is proposed for frequency‐invariant and multi‐angle beampatterns. The multi‐angle beampatterns at different frequencies are synthesised in block structure using the shared position strategy which effectively reduces the number of array elements. In order to meet the minimum spacing requirement of adjacent array elements in practical engineering, the constraint converted off‐grid method is proposed to improve the array synthesis accuracy. The grid scaling is introduced to obtain the possible array element positions. The array positions and weights can be solved by the BCS solver and corrected by Taylor perturbation. To validate the effectiveness and feasibility of the proposed method, simulations and actual experiments are carried out. The synthesised errors and peak sidelobe levels (PSLLs) of multi‐angle beampatterns obtained by the constraint converted off‐grid method outperforms those of other methods. The beamforming results of actual experiments in marine environment show that the PSLLs of the beampatterns obtained by BS‐BCS is lower at least 6.3 dB than that of uniform array, which demonstrates the effectiveness of the proposed method.

Costas Sparse 2-D Arrays for High-Resolution Ultrasound Imaging.

Two-dimensional arrays enable volumetric ultrasound imaging but have been limited to small aperture size and hence low resolution due to the high cost and complexity of fabrication, addressing, and processing associated with large fully addressed arrays. Here, we propose Costas arrays as a gridded sparse 2-D array architecture for volumetric ultrasound imaging. Costas arrays have exactly one element for every row and column, such that the vector displacement between any pair of elements is unique. These properties ensure aperiodicity, which helps eliminate grating lobes. Compared with previously reported works, we studied the distribution of active elements based on an order-256 Costas layout on a wider aperture ( 96 λ×96 λ at 7.5 MHz center frequency) for high-resolution imaging. Our investigations with focused scanline imaging of point targets and cyst phantoms showed that Costas arrays exhibit lower peak sidelobe levels compared with random sparse arrays of the same size and offer comparable performance in terms of contrast compared with Fermat spiral arrays. In addition, Costas arrays are gridded, which could ease the manufacturing and has one element for each row/column, which enables simple interconnection strategies. Compared with state-of-the-art matrix probes, which are commonly 32×32 , the proposed sparse arrays achieve higher lateral resolution and a wider field of view.

On designing good doppler tolerance waveform with low PSL of ambiguity function

Although the thumbtack-type ambiguity functions (AF) of the existing phase-coded signals are of good range-Doppler resolutions, they are not suitable for detection of high-speed targets due to their poor Doppler tolerance. In this paper, we address the design of waveform with good Doppler tolerance, which is expected to be of both diagonal-ridge-type AF and also local low peak sidelobe level (PSL). First we formulate the design model of Doppler tolerant waveform via minimizing the ratio of PSL to the minimum mainlobe level. Then, we solve the resulting fractional programming problem via quartic polynomial transfer and high-order polynomial optimization. Numerical results demonstrate the excellent Doppler tolerance and low PSL performance of our design.

Adaptive p‐norm weighted cyclic algorithm‐new algorithm for designing unimodular multiple input multiple output radar waveforms with good correlations

AbstractThis letter formulates a high‐dimensional multi‐objective optimization model to minimize all correlation function values for multiple input multiple output (MIMO) radar waveforms. Then, to solve this problem, this letter proposes an adaptive weighted cyclic algorithm‐new (CAN), named p‐norm weighted cyclic algorithm‐new (p‐WeCAN). Specifically, the adaptive weight updating function is constructed using p‐norm to minimize peak side‐lobe level (PSL) and integrated side‐lobe level (ISL) simultaneously. Numerical results show that the p‐norm weighted cyclic algorithm‐new obtains similar PSL values as the best PSL minimization algorithm and low integrated side‐lobe level values close to its lower bound at the same time.

Approximating the pareto fronts for synthesis of planar antenna array using binary cat swarm optimization algorithm

Various performance indices like peak sidelobe level (PSLL), first null beamwidth (FNBW) and count of elements contrast to each other while designing an antenna array. A swarm-based intelligence mechanism has been discussed here for optimizing these performance indices. In particular, a pareto front is approximated for bringing out the best compromised array performance having low PSLL with narrow FNBW while maintaining a smaller number of antenna elements. A thinned planar antenna array of 20×10 was synthesized using multi-objective modified binary cat swarm optimization (MO-BCSO) algorithm to obtain the optimal positions of the array elements. The indicated technique is most appropriate for the synthesis of large antenna arrays.

An Irregular Tiled Array Technique for Microwave Wireless Power Transmission

An irregular tiled array technique with the maximization of beam collection efficiency (BCE) for microwave wireless power transmission (WPT) is addressed in this paper, where the radiating elements are irregularly partitioned into multiple subarrays for reducing the number of radio frequency (RF) chain. The system architectures of WPT based on irregular tiled arrays are analyzed for the exhibition of its low-cost advantages. To achieve a good trade-off between the manufacturing cost and beampattern, a mixed-integer optimization problem (MIOP) accounting for the maximization of BCE satisfying the subarray tiling configuration, scanning direction and peak sidelobe level (SLL) constraints is established. By equivalently reformulating the beampattern, the MIOP in terms of subarray tiling configuration and subarray excitations is decoupled, and a two-stage solution method can be implemented. Firstly, resort to ‘generalized BCE’, the binary quadratic optimization problem (BQOP) for maximizing the BCE at considered scanning angles while guaranteeing the full aperture coverage is reduced to a binary second-order cone optimization problem. After the subarray tiling configuration is determined, the non-convex Rayleigh entropy maximization problem at a given scanning angle with respect to subarray complex excitations while satisfying peak SLL constraint is globally solved by using iterative convex approximation algorithm. Owing to the high efficiency of convex optimization, the BCE is able to monotonically increase to a stable value. Several numerical results with different array size and subarray shapes are provided to assess the effectiveness of the proposed method by comparing to the competitive counterparts in the open literatures.