Peak Sidelobe Research Articles

Doppler Sensitive Discrete-Phase Sequence Set Design for MIMO Radar

We consider the design of sets of discrete-phase, including binary/quaternary, sequences for phase-modulated continuous-wave multiple-input multiple-output radar in the presence of nonnegligible Doppler shift. We consider the peak sidelobes of auto- and cross-correlations in a desired interval of the Doppler shift as the performance metric of the design. Then, the design problem is formulated via imposing the discrete-phase constraint for each element of the sequences, with emphasis on binary as well as quaternary cases. This problem is nonconvex and hence hard to solve. We introduce a method based on the block coordinate descent framework to solve the optimization problem. We also modify the proposed method to efficiently update the subproblem associated with each iteration. Also, we extend it to account for only a low-correlation zone in the presence of Doppler shift. Numerical examples are provided to illustrate the effectiveness and performance of the proposed algorithm in comparison with the existing methods.

An ADS-Based Sparse Optimization Method for Sonar Imaging Sensor Arrays

The Mills Cross sonar sensor array, achieved by the virtual element technology, is one way to build a low-complexity and low-cost imaging system while not decreasing the imaging quality. This type of sensor array is widely investigated and applied in sensor imaging. However, the Mills Cross array still holds some redundancy in sensor spatial sampling, and it means that this sensor array may be further thinned. For this reason, the Almost Different Sets (ADS) method is proposed to further thin the Mills Cross array. First, the original Mills Cross array is divided into several transversal linear arrays and one longitudinal linear array. Secondly, the Peak Side Lobe Level (PSLL) of each virtual linear array is estimated in advance. After the ADS parameters are matched according to the thinned ratio of the expectant array, all linear arrays are thinned in order. In the end, the element locations in the thinned linear array are used to determine which elements are kept or discarded from the original Mills array. Simulations demonstrate that the ADS method can be used to thin the Mills array and to further decrease the complexity of the imaging system while retaining beam performance.

Affine transformation for synthesis of low sidelobe patterns in planar array antennas with a triangular element grid using the IFT method

This study deals with the affine transformation that is used to convert the triangular element grid of a planar phased array antenna into a square one. By means of this kind of transformation, it is possible to apply the iterative Fourier transform (IFT) method to synthesise low sidelobe tapers for array antennas featuring a triangular grid. Combination of the IFT method with an affine transformation allows the synthesis of low sidelobe tapers of which the peak sidelobe level does not vary with changing frequency and/or altering main beam position. The considered affine transformation was already briefly addressed in earlier publications of this author. In this study detailed information is given on its use in combination with the IFT method. Examples to demonstrate the effectiveness of the combination affine transformation and the IFT method for triangular grid array antennas are given. It will be shown that the peak sidelobe levels of the obtained tapers are invariant with frequency and scan angle when all far-field directions of the array factor are involved in the low sidelobe taper synthesis.

A hybrid algorithm of orthogonal perturbation method and convex optimization for beamforming of sparse antenna array

ABSTRACT In order to realize the beamforming and suppress the side lobe of the sparse antenna array, a hybrid sparse antenna array optimization algorithm based on orthogonal perturbation method (OPM) and convex (CVX) optimization is proposed. The algorithm aims at the expected beam response of main lobe and the suppression of peak side lobe level (PSLL). The OPM is used to optimize the array layout, and it can improve the time performance of pattern synthesis with its deterministic numerical characteristic. Because it is a local optimization algorithm, its optimal effect depends on the initial array layout and element excitation coefficient. Therefore, considering that the local optimal solution of the CVX algorithm is the global optimal solution, the CVX algorithm is used to obtain the optimal element excitation coefficient to achieve the expected beam response of the main lobe. The simulation results show that the hybrid algorithm can achieve a good trade-off between the optimization time, beam response, and the suppression of the PSLL.

Enumeration and Generation of $\rm PSL$ Equivalence Classes for Quad-Phase Codes of Odd Length

Quad-phase codes of a given length can be grouped into equivalence classes based on operations preserving autocorrelation peak sidelobe level, or “ ${\rm PSL}$ -preserving operators.” The task of enumerating these equivalence classes is facilitated by establishing a relationship with the problem of enumerating equivalence classes of $2\times N$ binary grids with respect to a pair of binary grid symmetries. We show this connection by a one-to-one mapping between even-length quad-phase codes and $2\times N$ binary grids. When $N$ is even, this mapping allows the known enumeration of $2\times N$ binary grids to be applied to the enumeration of even-length quad-phase code PSL equivalence classes. Furthermore, this equivalence instructs the development of a simpler algorithm for visiting single representatives of quad-phase-code equivalence classes relative to the operations that preserve PSL. Lastly, we conduct exhaustive searches to determine the optimal ${\rm PSL}$ for quad-phase codes of lengths 25 and 26 (for the smaller of these lengths, the search space contains $4^{25}=2^{50}$ , or roughly 1 quadrillion codes). One of the devices used to narrow the search space while achieving an exhaustive search is to seed the search with the equivalence class representatives of length $N=6$ . The optimal ${\rm PSL}$ for length-25 quad-phase codes is determined to be 2, achieved by the codes in a single size-32 equivalence class. For length 26, the optimal ${\rm PSL}$ is found to be $\sqrt{5}$ , achieved by $604\,480$ codes belonging to 9445 equivalence classes of size 64.

Encoded Hybrid PSK/FSK Waveform for LPI Radar

Since the advantage of pulse compression radar, the pseudo random codes and poly time codes and non linear frequency modulation has been mostly widely used low probability intercept (LPI) radar waveforms. By changing frequencies time to time in frequency modulation known as non-linear frequency modulation (frequency hopping (FH)), peak to side lobe ratio (PSLR) can be achieved to make less severe the covering effect of nearby targets and to improve the useful dynamic range. Adding an appropriate binary encoded ternary phase shift signal (PSK) as form as Binary encoded Hybrid-PSK/FSK (BEH PSK/FSK), the peak side lobe ratios are obtained very low values (e.g., PSLR<-70dB), similar to the antenna side lobes. In advanced microwave power amplifier technology, now a day’s using low peak to average power modules requires them to be amalgamated at the radio frequency (RF) stage in that way to obtain the required emitted radiated power. The deterministic waveforms are represents Noise waveform radar technology is a valid alternative. The pseudo-random waveform-realization of a noise process, the higher its bandwidth-time (or BT) product, the lower the (numerical) peak side lobe ratio. With practical Bandwidth-time values, the achievable peak side lobe using pure random is not sufficient the generated pseudorandom waveforms undergoes optimized genetic algorithm Hamming Scan (HS) to achieve optimized pseudo random (OBC), in order to achieve the desired side lobe level. This manuscript proposes a general analysis of the two modes of radar waveforms, i.e., Ternary and Binary alphabetic waveforms of coincidence detection.

Optimization of Sparse Concentric Ring Arrays Based on Multiple Constraints

This letter is concentrated on the peak sidelobe level (PSLL) suppression problem of equal amplitude concentric ring array (CRA), which is constrained by the array aperture, the minimum element spacing, and the number of elements. Taking the minimum PSLL as the optimization objective, the joint optimization strategy of CRA aperture and ring array spacing is adopted to reduce the computational complexity. A quantum genetic algorithm based on hybrid coding is used to optimize the CRA. The proposed method has the advantages of fast searching speed and powerful searching ability. The simulation results demonstrate the superiority of the algorithm.

OFDM Chirp Waveform Design Based on Imitating the Time–Frequency Structure of NLFM for Low Correlation Interference in MIMO Radar

The orthogonal frequency division multiplexing (OFDM) chirp signal has its special merits of high-range resolution by exploiting a full bandwidth as multiple input multiple output (MIMO) radar signal. After simulation, there are some high peaks in the autocorrelation function and cross correlation function of conventional OFDM chirp signals, which may increase the correlation interference and reduce the detection performance of MIMO radar signal. This letter proposes to reduce the autocorrelation sidelobe peak (ASP) of OFDM chirp signal by subsection imitating the nonlinear frequency modulation (NLFM) signal's time-frequency structure. Since a suitable difference should be made between the subchirp rates and subchirp carrier frequencies of each of the two designed OFDM chirp signals for reducing the cross correlation peaks (CP), the imitated NLFM waveforms' design problem is solved by the proposed optimized method. At last, subchirps of the designed signals are coded by a group of optimized codes. The simulation shows the designed OFDM chirp signals have lower ASP and CP than the conventional ones and referenced previous OFDM signals, and their ASP decreases as the number of subchirps increases.

Joint Reduction of PMEPR and Sidelobe in Multicarrier Radar Signals using ZC and SC Method

Employing the multitone waveforms for radar applications has attracted many authors in recent days. Several researchers have investigated the use of multitone waveform and challenges associated while implementation. The serious drawback of using multicarrier waveforms is the high Peak to Mean Envelope Power Ratio (PMEPR) values recorded and large sidelobes. To overcome PMEPR and sidelobe drawbacks a novel method is suggested for reducing sidelobe levels. The projected method applies zad-off chu phase sequence for multicarrier complementary phase coded (MCPC) signals. The comparison of integrated sidelobe ratio and peak sidelobe is obtained. Autocorrelations and complex envelope of the MCPC signal is obtained from the above methods are analyzed with extensive simulations. It is also possible to reduce the PMEPR and sidelobe simultaneously by using secondary user method. The suggested technique results with reduction in sidelobe and PMEPR levels.

Improved high‐precision approach based on deconvolution in MIMO sonar imagery

Multiple-input multiple-output (MIMO) sonar enables high-resolution imaging, which is extremely useful in underwater acoustic high-precision imagery. However, the first peak sidelobe levels and beamwidth performance degrade significantly when conventional tapering is applied due to the non-uniformity of the spanned virtual linear array, which prevents MIMO sonar from obtaining high-precision images with high resolution and high definition. Therefore, an improved high-precision approach in MIMO sonar imagery is proposed based on deconvolution to realise sidelobe suppression and to narrow the mainlobe width. The relationship between the target's beam power function and the pattern of the actual transmitting–receiving arrays is derived first, and design criteria are presented for MIMO sonar arrays to enhance the resolution. Subsequently, according to the orthogonality of the transmitting signals, the echo is separated by matched filtering, and then joint beamforming is employed to attain the beam data. Finally, the focused images are processed by deconvolution to enhance the clarity of the image and simultaneously obtain higher resolution. Numerical simulations and lake experiments are presented to demonstrate that high-precision images in MIMO sonar are achieved utilising the proposed approach, which also involves a lower computation load.

Sidelobe Level Optimization of Rectangular Microstrip Patch Antenna Array using Binary Coded Genetic Algorithm

In modern world, communication systems requires development of low cost, minimal weight, and low profile antennas which are capable of maintaining high performance over wide range of frequencies. Patch antenna is one such antenna which fulfills the demands of current communication systems. The widely used microstrip patch antennas are rectangular patch antennas. This paper presenting the application of binary coded Genetic Algorithm (BGA) which is applied to the rectangular patch microstrip antenna with uniform linear arrays. The fitness function of GA is maximum reduction in peak side lobe level of the radiation pattern of the antenna with maximum reduction in the side lobe level and also achieved the minimum possible null to null beam width, the resultant radiation patterns for both before GA and after GA of microstrip array are compared. The radiation patterns are presented for 20,50,100 number of elements. All the simulated results are obtained by using MATLAB software.

High-Resolution Radar Waveform Design Based on Target Information Maximization

Although the transmit radar waveform design problem for maximizing target information has been studied widely in the past, the resolution requirement is normally ignored in such designs. Using maximizing target information as a criterion, a new radar waveform design method meeting the high-resolution requirement is proposed in this article, which makes no assumptions on the statistical distribution of target scattering. The objective function is proposed by maximizing the Pearson correlation coefficient and the design is then transformed into an optimization problem, which is solved in two steps. First, a closed-form expression for the discretized waveform with constant power constraint is derived in the time domain. Second, based on the bandwidth analysis of the optimal solution, a resolution improvement method considering information distortion is introduced and a suboptimal waveform is proposed while satisfying the constant power and resolution requirements. Finally, performance of the proposed radar waveform in terms of information acquisition, classification, and resolution is analyzed and compared with the classic high-resolution linear frequency modulated waveform (LFMW). Simulation results show that the resolution of the suboptimal waveform is slightly lower than the LFMW, but more desirable in terms of peak sidelobe ratio, information acquisition, and classification.

Application of optimal FrFT order for improving the azimuth resolution of range Doppler imaging algorithm

The traditional range Doppler (RD) imaging algorithm has become the most intuitive and classical method in synthetic aperture radar (SAR) imaging processing because of its easy implementation and high processing efficiency. However, owing to the poor quality of the image produced by RD algorithm, this traditional imaging method is growing increasingly unable to meet practical needs. In an effort to solve the problem of poor azimuth imaging quality, this study proposes a high-resolution RD azimuth imaging algorithm. The expression of the optimal order of the SAR azimuth signals using fractional Fourier transform (FrFT) is derived in detail herein. A theoretical analysis shows that this optimal order is unique and depends on the azimuth imaging parameters. The experimental results based on airborne SAR simulation data and spaceborne SAR measurement data indicate that the azimuth resolution of the proposed algorithm is improved by 31.6 or 46.8% as against that of the traditional RD algorithm, whereas the peak side lobe ratio (PSLR) and integrated side lobe ratio (ISLR) values obtained via the proposed algorithm are approximately equivalent to those obtained via the traditional RD algorithm.

Broadband Generalized Sidelobe Canceler Beamforming Applied to Ultrasonic Imaging

A broadband generalized sidelobe canceler (Broadband-GSC) application for near-field beamforming is proposed. This approach is implemented in the wavelet domain. Broadband-GSC provides a set of complex, adapted apodization weights for each wavelet subband. The proposed method constrains interference and noise signal to improve the lateral resolution with only one single emission. Performance of the proposed beamforming is tested on simulated data obtained with Field II. Experiments have proved that the new beamforming can significantly increase the image quality compared with delay-and-sum (DAS) and synthetic aperture (SA). Imaging of scattering points show that Broadband-GSC improves the lateral resolution by 43.2% and 58.0% compared with SA and DAS, respectively. Meanwhile，Broadband-GSC reduces the peak sidelobe level by 11.6 dB and 26.4 dB compared with SA and DAS, respectively. Plane wave emission experiment indicates that Broadband-GSC can improve the lateral resolution by 44.2% compared with DAS. Furthermore, the new beamforming introduces the possibility for higher frame-rate and higher investigation depth with increased lateral resolution.

Synthesis of Sparse Linear Arrays With Reduced Excitation Control Numbers Using a Hybrid Cuckoo Search Algorithm With Convex Programming

Sparse linear arrays based on a novel subarrayed scheme are proposed and synthesized in this letter. The array with a fixed aperture size is partitioned into several uniformly spaced subarrays while number, spacing, and excitation in each subarray are optimized with multiple constraints. Compared with conventional sparse linear array with all the elements excited independently, the sparse linear array with the novel subarrayed scheme provides excitations at the subarray port and reduces the excitation control numbers remarkably. By integrating the cuckoo search (CS) algorithm with convex programming (CP), a hybrid CS–CP method is proposed and applied to the synthesis problem while the constraints are satisfied during the optimization process. Three examples with series of cases are presented, and the obtained results are compared to those presented in some state-of-the-art references. The optimized array achieves an improved peak sidelobe level and reduced excitation control number.

Optimization of Weighting Window Functions for SAR Imaging via QCQP Approach.

Weighting window functions are commonly used in Synthetic Aperture Radar (SAR) imaging to suppress the high Peak SideLobe Ratio (PSLR) at the price of probable Signal-to-Noise Ratio (SNR) loss and mainlobe widening. In this paper, based on the method of designing a mismatched filter, we have proposed a Quadratically Constrained Quadratic Program (QCQP) approach, which is a convex that can be solved efficiently, to optimize the weighting window function with both amplitude and phase, expecting to offer better imaging performance, especially on PSLR, SNR loss, and mainlobe width. According to this approach and its modified form, we are able to design window functions to optimize the PSLR or the SNR loss under different kinds of flexible and practical constraints. Compared to the ordinary real-valued and symmetric window functions, like the Taylor window, the designed window functions are complex-valued and can be asymmetric. By using Synthetic Aperture Radar (SAR) point target imaging simulation, we show that the optimized weighting window function can clearly show the weak target hidden in the sidelobes of the strong target.

Minimum local peak sidelobe level waveform design with correlation and/or spectral constraints

The problem of designing waveforms with specified aperiodic/periodic correlation and spectral properties has received much attention because of its wide applicability in sonar, radar, and communications. In particular, a waveform with low peak sidelobe level (PSL) of autocorrelation can improve the detection performance of a weak target masked by a nearby strong target in range compression radar systems, and that with adaptive spectrum nulls/notches can make the sensing systems not be interfered by other electromagnetic equipment. On the other hand, a constant modulus (CM) waveform can maximize the transmit power efficiency of the system. Whereas, it is difficult to design a CM waveform with minimum local PSL and specified autocorrelation and/or spectral properties due to numerous nonconvex inequality and equality constraints. To develop efficient algorithms for this problem, we first express the waveform autocorrelation in the frequency domain, then use the proximal method of multipliers to tackle the resultant nonconvex and nonsmooth constrained optimization. Numerical examples have shown that the proposed methods can produce the waveforms satisfying these challenging requirements.

Efficient Generation of Low Autocorrelation Binary Sequences

Simple and efficient algorithm based on heuristic search by shotgun hill climbing to construct binary sequences with small peak sidelobe levels (PSL) is suggested. The algorithm is applied for generation of binary sequences of lengths between 106 and 300. Improvements are obtained in almost half of the considered lengths while for the rest of the lengths, binary sequences with the same PSL values as reported in the state-of-the-art publications are found.

Min-Max Metric for Spectrally Compatible Waveform Design Via Log-Exponential Smoothing

To ensure the proper functioning of active sensing systems in the presence of interferences from other electromagnetic equipment in a spectrally crowded environment, we devise four new solutions for spectrally compatible waveform design based on the min-max metric, namely, minimum modulus dynamic range, min-max spectral shape, minimum weighted peak sidelobe level, and minimum similarity. To address the resultant nonconvex and nonsmooth optimization problems, a unified algorithm framework is proposed. That is, we first approximate the min-max metric by using the “log-exponential smoothing” technique, then apply majorization-minimization to smooth and simplify the approximate optimization formulations, and finally use the Karush-Kuhn-Tucker theory to tackle the majorized problems. Besides, we develop an adaptive approximation parameter selection scheme, which monotonically decreases the approximation error at each iteration. The proposed algorithms are computationally efficient as they can be realized via fast Fourier transform. Finally, numerical examples are presented to demonstrate their excellent performance.

On method of composing low frequency signals based on array structures

Generating low-frequency electromagnetic waves based on high-frequency antenna and illuminating targets with multi-band signals can be an effect way that can not only reduce the physical dimension of a low frequency antenna, but also improve the performance of radar detection. Combining the electromagnetic wave doppler effect principle and the array antenna architecture, a method of generating a low-frequency signal around the illuminated target is proposed based on the controlling of array antenna parameters, including array radiation element signal timing, phase and element spacing. The principles of array parameter design are described. Composite signals are simulated respectively under two typical geometric relationships between targets and array antenna, target located along the array direction and in the direction of 45° scanning angle. The peak sidelobe ratio (PSLR) and integral sidelobe ratio (ISLR) are used to evaluate the quality of the composite signals. Aiming at practical applications, the effects of array element spacing error, phase error and target location error on the composite signal are simulated and analyzed. Under the condition of sparse uniform array, the influence of the radiation element spacing on the composite signal is analyzed. The simulation results show that the harmonic components of the composite signal increase with the radiating element spacing error and phase error growing.