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... Window types such as [3]- [10] have flexibility for trading off main lobe width against sidelobe magnitude. The Dolph-Chebyshev window [3] has equiripple sidelobes; it is a special case of UW (ultraspherical window) [10] with µ (as in [10]) = 0. ...

... Window types such as [3]- [10] have flexibility for trading off main lobe width against sidelobe magnitude. The Dolph-Chebyshev window [3] has equiripple sidelobes; it is a special case of UW (ultraspherical window) [10] with µ (as in [10]) = 0. The characteristics of Kaiser [4], exponential [5], and cosh [8] windows are very similar and can be approximated by UW with µ = 1. ...

... . The coefficients of the Dolph-Chebyshev window may be computed from values of T M (x 0 cos(ω/2)) evenly spaced on the ω-axis using IDCT (inverse discrete cosine transform). Theories on Dolph-Chebyshev window and IDCT are well established [2], [3]. ...

Many types of window have been designed in the past decades for various applications. Each window type has its own specific characteristics. In this paper, we present a general technique for trading off main lobe width against sidelobe magnitude for any arbitrary window while keeping the number of sidelobe peaks and their relative magnitudes unchanged although their exact locations and magnitudes are changed.

... To lower the SLL while maintaining the total transmission power, we increased the amplitude of the signal applied to the central element of the array antenna and lowered the amplitude of the signal applied to the side element using the tapered amplitude distribution method [10]. Although this method reduces the sidelobe of the beam pattern, it weakens directivity owing to the widening of the beamwidth; therefore, we used the Chebyshev tapered amplitude distribution method, which is efficient and possesses the strongest directivity among distribution methods with the same maximum SLL [11]. Moreover, by limiting all sidelobes to the same level, we minimized the RF radiation power in all directions, except for the main lobe. ...

... To this end, studies frequently use a tapered amplitude distribution to increase the amplitude of the central element antenna and decrease that of the side element antenna. The Chebyshev taper has the narrowest main lobe beamwidth, given a limited SLL [11]; therefore, we applied the Chebyshev taper to the amplitude distribution through an array factor (AF) of far-field approximation. Fig. 2 depicts the structure of the PAA. ...

... where z i are the roots in the AF, β i are the null directions, and i ranges from 1 to M -1; hence, if the null directions are known, the roots of the AF can be found, and the AF expressed as the product of linear terms can be completed. The AF equation, which is the product of a linear term, is developed in polynomial form, and the coefficients of each term are mapped to the amplitude coefficients of the array antenna; hence, it describes the process for finding the null directions by mapping the Chebyshev polynomial [11] using the array factor. To this end, the difference in magnitude between the main lobe and the sidelobe is defined as follows: ...

This paper proposes a sidelobe suppression beamforming scheme using tapered amplitude distribution for microwave power transfer (MPT) with a two-dimensional planar array antenna (PAA). To overcome the undesirable effects of sidelobes, the magnitude of the sidelobes can be lowered by manipulating the amplitude distribution of the PAA. By analyzing the array factor of the PAA, we expressed the amplitude distribution as the product of two one-dimensional vectors. Moreover, we developed a method for obtaining these vectors from an expected sidelobe level (SLL). We used the Chebyshev taper, which has a higher directivity than other distributions given an expected SLL, for the amplitude distribution. To verify the proposed method, we designed and implemented a digital beamforming system with a 4 × 4 transmitter (Tx) array and a receiver (Rx) at 5.8 GHz. Compared with a uniform amplitude distribution, the proposed method reduced the SLL by 7.5 dB but the received RF power by only 0.6 dB. We compared the performance of the proposed MPT system with the results of previous studies.

... Suppressing ambient acoustic noise and other interfering signals emanated from other directions, while enhancing the acoustic signal There are many window optimization algorithms existing for beamforming to address the above conflicting factors but associated with their computational complexities [188][189][190][191][192][193][194]. ...

... Most of the conventional optimisations reported are associated with several computational complexities [188][189][190][191][192][193][194]197]. An interesting solution using null-steered product beamforming is reported in Chapter 3 to efficiently reduce the side lobes that uses the optical interferometry principle [204]. ...

The oceans are home to millions of Earth’s plants and animals. It is our life source, supporting humanity’s food and that of every other organism on earth. The ocean produces at least 50% of the planet’s oxygen. It is the home to most of the earth’s biodiversity and is the main source of protein for more than a billion people around the world. The ocean is the key to our economy with an estimated 40 million people being employed by ocean-based industries. Despite regular discoveries about the ocean and its occupants, much remains unknown. More than 80% of the ocean is unmapped and unexplored.
Maritime surveillance and strategies are of great significance to ensure that all events on the oceans are carried out carefully and that national and international security is upheld without any disputes. Today, due to several reasons, the worldwide geopolitical changes have created substantial awareness in the defence research for continuous improvements and the modernisation of surveillance systems to tackle unlawful activities. Recent history recounts that one of the susceptible zones for carrying out these unlawful activities is the maritime domain. Refugee shipping, illegal migrant ships, sea pirates, loss of lives due to accidents, attacks, and robberies, illegal fishing and infiltration, and terror activities are some of the unlawful activities to name a few in this domain. This has led to several national and multinational initiatives in maritime surveillance to know all coastal and high-seas activities relevant to national security. As 71% of the earth surface is enclosed by the ocean, the dependency of maritime surveillance on technologies and research services is inevitable.
The surveillance needs to cover the above-water and underwater environments together for successful maritime surveillance. Most of the technologies that are operative in an above-water environment are not operable underwater. There are not many comparable technologies in the underwater environment as the ocean is a very lossy medium for the propagation of electromagnetic energy because of the high electrical conductivity of seawater. However, it supports acoustic propagation enabling sonar technologies bright for underwater environments. The physics of acoustic propagation say aloud that the sonar technologies cannot offer a long-range or wide-area surveillance coverage as offered by either the radar technologies or space-borne satellite surveillance systems. Therefore, underwater sonar technologies cannot be used in the same way as the ocean environment is unfriendly most of the time.
The above paragraphs define the problem statement of underwater maritime surveillance and the need for continuous research and development to face the threats. But, it dictates that the most dominant technology suitable for underwater maritime surveillance is sonar technology. Therefore, it becomes evident that the sonar systems are the only eyes and ears of any submarines for them to move in the ocean. Sonar systems are also the eyes and ears for ships for ocean surveillance. Sonar systems are the essential fitments on high-value surface and subsurface naval platforms to protect them from potential attacks. Beamformers forms the basis for the actual eyes and ears of any sonar system. Therefore, the key objective of this research work is to develop a reliable and robust sonar beamformer. Several research gaps have been identified in sonar array beamforming and this thesis attempted to resolve some of those issues.
Beamforming design always depends on the spatial weighting functions of window functions. But, the different ways of utilizing the conventional window functions are saturated. The development of new window functions is also rare. Therefore, this thesis took up the challenge of blending the existing conventional window functions through the principle of constructive and destructive interference techniques used in optical physics. It necessitated two window functions and through careful investigation, this research work identified the robust rectangular and null-steered Dolph Chebyshev windows for making an efficient beamformer using product beamforming. The technique developed thereby demonstrated the superior quality of narrow beamwidth with very low sidelobe levels. Effectively, the sidelobes are suppressed by more than 25 dB using this novel technique. The technique is found to be more robust and stable against an array element failure or other array deformations. The sidelobe spread is found to be very minimal against array deformations.
Thereafter, the investigation tried to reduce the complexity of sonar architecture by bridging a nested array concept and the developed product beamformer to enhance the overall performance without sacrificing the similar performance obtainable by a large hydrophone array. The investigation demonstrated that multiple targets can be detected with much more accuracy using the present method than the existing methods. The outcome of this method would reduce the complexity of the signal conditioning hardware to a large extent, thereby it allows us to have a simple sonar architecture and hence making installation and maintenance easy. Beamforming alone is not sufficient to execute maritime surveillance with sonars in the ocean. Once after detecting a target, the tracking of the target is very important to make necessary strategic decisions. The tracking of any underwater target is better done with the help of target motion analysis. The output of the beamformers plays a crucial role in estimating target motion parameters. Therefore, the developed beamforming technique is applied to target motion analysis. The technique has demonstrated that the motions of the potential underwater targets can be resolved, which are otherwise not possible with the conventional beamformers. Interestingly, the developed beamforming technique is implemented in several types of sonars. Different open ocean experiments with actual ocean passing targets are conducted. The experimental results validate the efficacy of the inventions made in this thesis.

... Compared with the Max-SLNR beamforming, conventional ZF beamforming has better orthogonality among desired users' received signals and lower complexity, but poorer anti-eavesdropping capability. In order to decrease the possibility of signals being detected and eavesdropped, low-sidelobe beamforming acts as an effective way in array signal processing, mainly including weighting methods, 18,19 iterative methods 20,21 and optimization methods. 22,23 Genetic algorithm (GA) is used in Reference 24 to constrain sidelobes in DM transmitter radiation patterns, but GA incurs high computation overheads and the distortion of constellation diagrams is static. ...

... gathers all low-sidelobe beamforming column vectors toward K desired directions. Here we choose Dolph-Chebychev weighting algorithm to assist our method, 18 which can design array excitations that control sidelobes and beamwidths explicitly. It results in constant sidelobes and a main beamwidth that is the minimum possible for the given sidelobe level. ...

In this article, an anti‐eavesdropping zero‐forcing plus power‐efficient artificial‐noise optimization method for multibeam directional modulation (DM) synthesis is proposed. It aims to prevent known and unknown eavesdroppers intercepting useful signals as far as possible and achieve a narrower bit error rate (BER) main beamwidth under the premise of limited artificial‐noise (AN) power consumption. Beam pattern nulls are generated in known eavesdroppers directions by utilizing the orthogonality of zero‐forcing beamforming. Low‐sidelobe beamforming is also introduced to DM for the first time to suppress unknown eavesdroppers outside main lobes. The distribution of AN power in all directions is optimized by minimizing the AN transmit power subject to a series of secrecy rate (SR) constraints. Simulation results show that the proposed method outperforms the state‐of‐the‐art DM synthesis methods with regard to power efficiency, SR and BER performance.

... In an event that the application of the system is made to the fragmented spectrum, the selection of B should be done based on the available number of spectral sub-bands. Alternatively, for the streamlining of the whole system, and regulation of spectral characteristics at a granular level, the single sub-band can be divided into minute chunks of same range in each subband, and these particular spectral chunks are called as Physical Resource Blocks (PRB), as in the LTE [34][35][36][37]. There are different options available for the selection of the filter characteristics depending on the window selection and the controllability characteristics of a filter with regards to attenuation of side lobe and main lobe width that determines its selection. ...

... In order to address the limitations of the Dolph-Chebyshev, some researchers have used other alternatives such as the Bohman Filter [5,36]. In the Dolph-Chebyshev window, FIR-coefficients are applied, and they are parameterized based on the side-lobe attenuation [4]. ...

OFDM based waveforms are considered as the main part of the lat-est cellular communications standard (namely 5G). Many inherited problems from the OFDM-Based LTE are still under investigation. Getting rid of the out of band emissions is one of these problems. Ensuring low out of band emission (OOBE) is deemed as one of the most critical challenges to support development of future technologies such as 6G and beyond. Universal Filtered Multi Carrier (UFMC) has been considered as one of the candidate wave-forms for the 5G communications due to its robustness against Inter Carrier Interference (ICI) and the Inter Symbol Interference (ISI). It is also a preferred option because it is the most appropriate for low latency scenarios. In this paper, a novel approach is proposed that makes use of modified Kaiser-Bessel filter-based pulse windowing instead of standard Dolph-Chebyshev filter for UFMC based waveform. The aim of proposing the new approach is to enable the reduction of spectral leakage into nearby sub-bands. A comprehensive study for the modified Kaiser-Bessel filters is performed and the results are presented in terms of several Key Performance Indicators (KPIs). Based on the results of the simulation, the UFMC Kaiser-Hankel window demonstrated lower sidebands and better power spectral density, when compared with the traditional Orthogonal frequency-division multiplexing (OFDM) and UFMC as well as the normal UFMC Kaiser window. In addition, the real test for the kaiser window with 5G waveform is lower OOBE than conventional 5G waveform (CP-OFDM and UFMC). The OOBE reduction of 31% of the Kaiser vs. the Dolph-Chebyshev filter, 68% of Kaiser Hankel over the Dolph-Chebyshev, and 20% of Kaiser Hankel over Kaiser filter have been reported in this paper. The Power Spectral Density has been improved accordingly.

... The coefficients are arbitrary and express the amplitude distribution [9]. In a non-uniform amplitude array antenna, the length of the line of each point source is proportional to the amplitude [5]. Therefore, to determine the Array amplitude ( ) of this new configuration; the amplitude (coefficients) of the first element (pentagram) of the Star array was deduced as [9]; 2 0 = 2 1 = 2 2 = 2 3 = 2 4 = 1 ...

... The half-power beamwidth and the directivity of the newly configured (Penta-Hexa)gram Star Array antenna was deduced from figure (4 ) as 4.5° and 11.72dB respectively using (15), (16), (17) and (18) given by [5] and [10] as; ...

This paper presents a newly configured dual-band non-uniform amplitude pentagram-hexagram six (6) elements Star array antenna at VHF and UHF frequency bands for multipurpose applications. The pentagram-hexagram (Penta-Hexa)gram Star array has been designed to control it radiation characteristics by properly selecting the amplitude distribution of the elements. The design was set out to achieve a very few side lobes and a higher directivity Star array antenna. This antenna was constructed based on the design specifications using an Aluminum sheet. Both Pentagram and Hexagram star shapes were assembled together to form the Star array. The field pattern of each element and that of the array were determined and plotted using MatlabR2014a. The Performance analysis of the array shows a Dolph-Tschebyscheff field pattern with main lobes maximum at 0° and 180° and very few smaller side lobes. Further evaluations give the half-power beamwidth (HPBW) of the array to be 4.5° and directivity to be 11.72dB.The Star array shows good performance in the horizontal plane when compared with the standard antenna at UHF band. The test performance of the Star array antenna over the dual-band shows that the (Penta-Hexa)gram Star array antenna is very versatile for multipurpose applications.

... The literature describes a number of methods for ULAs synthesis. The most popular are Uniform, Dolph-Chebyshev's [1], Taylor-Kaiser's [2], Binomial [3], Villeneuve's [4], Matrix Computation of Element Currents [5] etc. The basis of most methods is a polynomial approximation of Kronecker-delta function, which represents an ideal array factor of array antenna. ...

... defined by the angle ΔθHPBW. Equating(1) ...

In the paper an approximation of ideal array factor of uniform linear array antenna – Kronecker-delta function, with two approximation polynomials in Hausdorff metric is performed. Equations for half-power bandwidth angle are proposed. Analytical and comparative analysis of the uniform linear array antenna selectivity is done.

... On the other hand, zero-padding in the frequency domain is equivalent to multiplication by a rectangular window and thus corresponds to convolution with a sinc kernel in the time domain; forĤ not vanishing at the boundaries, this may introduce extra sinc-shaped tails around each impulse within the estimated channel impulse response. 2 Therefore, in the present approach,Ĥ is first multiplied by a Dolph-Chebyshev window [7] (centred around the carrier frequency), w, with attenuation set to 60 dB 3 , and then extended to 16-times the original length through zero-padding (pad 15 0 ). Overall, the channel impulse response is estimated through ...

In this paper, the task of channel sounding using software defined radios (SDRs) is considered. In contrast to classical channel sounding equipment, SDRs are general purpose devices and require additional steps to be implemented when employed for this task. On top of this, SDRs may exhibit quirks causing signal artefacts that obstruct the effective collection of channel estimation data. Based on these considerations, in this work, a practical algorithm is devised to compensate for the drawbacks of using SDRs for channel sounding encountered in a concrete setup. The proposed approach utilises concepts from time series and Fourier analysis and comprises a signal restoration routine for mitigating artefacts within the recorded signals and an encompassing channel sounding process. The efficacy of the algorithm is evaluated on real measurements generated within the given setup. The empirical results show that the proposed method is able to counteract the shortcomings of the equipment and deliver reasonable channel estimates.

... By spacing out the zeros in the unit circle differently, many patterns could be synthesized. Dolph [13] proposed to use the properties of Chebyshev polynomials [14] of the first kind to achieve equal Sidelobe Level and the narrowest main beam. Subsequently, Riblet [15] discovers that Dolph's method only applies to scenarios where the antenna elements spaced at least half wavelength. ...

Flat top beam pattern synthesis is increasingly important for beamformer in high mobility scenarios due to the rapid change of Direction of Arrival (DOA). A Zero Placement for Flat Top (ZPFT) beam pattern synthesis algorithm is presented in this paper. It works in Z domain directly and breaks down the total response into two portions. The first portion satisfies the beamwidth requirement with low Sidelobe Level (SLL) which is realized through algorithms like Dolph-Chebyshev algorithm. The second portion is then used to create a broadening effect. The location of the broadening zeros are derived using principles result from the broadening effect analysis of two quadratic functions. Compared to conventional Finite Impulse Response (FIR) method or iterative methods, the proposed method identifies the zeros of the array factor directly and computes the weight without iteration. Since it works in the spatial angle domain directly, the steering of the mainlobe beam could be implemented through a simple angle shift. Numerical simulation confirms the effectiveness of the algorithm. ZPFT can achieve 22dB lower SLL while maintaining the same main beam performance as compared with FIR method for an Uniform Linear Array (ULA) with 7 elements. It can achieve the same optimal performance as the iteration based global optimisation techniques like Semi-Definite Relaxation (SDR) with about 380 times less computing time in an Intel Core i7 Windows platform. ZPFT can steer the main beam easily in real time. All these make it an ideal candidate for high mobility applications where the DOA changes rapidly.

... 2) Dolph-Chebyshev Window: In what follows, we propose to apply Dolph-Chebyshev (DC) window at the transmitter or the receiver to improve the channel sparsity when CSI is not available. In fact, it has been proved that the DC window is effective [28] in the sense that: 1) given the specified sidelobe level, the width of the mainlobe in the window response is the narrowest; or 2) given the fixed mainlobe width, the sidelobe level is minimized. Note that the effective channel only has a considerably large entry when it is located in the mainlobe of the window response function in (52). ...

In this paper, we investigate the impacts of transmitter and receiver windows on the performance of orthogonal time-frequency space (OTFS) modulation and propose window designs to improve the OTFS channel estimation and data detection performance. In particular, assuming ideal pulse shaping filters at the transceiver, we derive the impacts of windowing on the effective channel and its estimation performance in the delay-Doppler (DD) domain, the total average transmit power, and the effective noise covariance matrix. When the channel state information (CSI) is available at the transceiver, we analyze the minimum squared error (MSE) of data detection and propose an optimal transmitter window to minimize the detection MSE. The proposed optimal transmitter window can be interpreted as a mercury/water-filling power allocation scheme, where the mercury is firstly filled before pouring water to pre-equalize the time-frequency (TF) domain channels. When the CSI is not available at the transmitter but can be estimated at the receiver, we propose to apply a Dolph-Chebyshev (DC) window at either the transmitter or the receiver, which can effectively enhance the sparsity of the effective channel in the DD domain. Thanks to the enhanced DD domain channel sparsity, the channel spread due to the fractional Doppler is significantly reduced, which leads to a lower error floor in both channel estimation and data detection compared with that of rectangular window. Simulation results verify the accuracy of the obtained analytical results and confirm the superiority of the proposed window designs in improving the channel estimation and data detection performance over the conventional rectangular window design.

... In a present mobile base station antenna, an equally spaced linear array configuration is employed as shown in Figure 1(a). Low sidelobe characteristics are achieved by giving adequate excitation coefficients (amplitude and phase) to array elements [5][6][7], and/or changing the radiation characteristics of elements in the array [8,9]. In case of providing excitation coefficients to all elements, feeding network includes multiple power dividers and feeder lines that have different values [10][11][12]. ...

In this paper, wideband characteristics of density tapered arrays are clarified by comparing directly the array factors and radiation patterns of 3 tapered arrays structures with array factors and radiation patterns of equally spaced arrays. Calculated results for a density tapered distribution array consisting of 30 elements claims that the array can perform within a bandwidth of 2.5:1 with grating lobe levels lower than -7.8 dB. Additionally, this paper shows a method of determining the effectiveness of unequal spacing arrays in the design of actual antennas. The method is based on calculation and analysis of input impedance of array elements caused by mutual coupling effects among array elements.

... The results confirm that a non-uniform distribution ratio in the emissive beam provides better performance than the uniform distribution and the Gaussian distribution allows one to achieve a better suppression effect than the other two distributions. Similar to microwaves, light waves also belong to the electromagnetic wave, and the physical characteristics of the two are usually consistent [16]. Therefore, we can directly analyze the radiation characteristics of the beamlet array in the far-field by analyzing the radiation characteristics of the Gaussian beam with the same diameter as the circumscribed circle of the beamlet array in the far-field, and then use stochastic parallel gradient descent (SPGD) algorithm to directly optimize the amplitudes of the outgoing beamlets in CBC system so that the effect of beamlet amplitude modulation can be verified [17], [18]. ...

Coherent beam combination of fiber laser phased array is a promising technique to achieve high-brightness laser output. In this paper, we focus on central-lobe energy enhancement of the combined beam in the far-field by theoretically and experimentally investigating the relationship between the power-in-the-bucket (PIB) of the combined beam in the far-field and the beamlets amplitude modulation in the near-field. We employ a 19-elements fiber laser phased array integrating adaptive fiber-optic collimators with a beamlet filling factor of 0.903 and achieve phase-locking and beamlet pointing correction among fiber lasers using the SPGD algorithm. The amplitude modulation applied to the tiled sub-apertures is used to control the shape of the emissive array's amplitude envelope to further change the PIB of the combined beam under the same total output power. According to theoretical analysis, the fiber laser phased array achieves PIB = 0.51 for a zero truncation ratio (Tr), which is increased to PIB = 0.57 for Tr = 1.3. Experimentally, we observe PIB = 0.49 for Tr = 0 and PIB= 0.56 for Tr = 1.3. The experimental results are in good agreement with the theoretical analysis, suggesting that the amplitude modulation is helpful for further improving the energy density of central-lobe.

... In what follows, we propose to apply the Dolph-Chebyshev (DC) window at the transmitter or the receiver to improve the channel sparsity when channel state information (CSI) is not available. In fact, it has been proved that the DC window is effective [23] in the sense that: 1) given the specified sidelobe level, the width of the mainlobe in the window response is the narrowest; or 2) given the fixed mainlobe width, the sidelobe level is minimized. Note that the effective channel only has a considerably large entry when it is located in the mainlobe of the window response function in (31). ...

In this paper, we investigate the impacts of transmitter and receiver windows on orthogonal time-frequency space (OTFS) modulation and propose a window design to improve the OTFS channel estimation performance. Assuming ideal pulse shaping filters at the transceiver, we first identify the role of window in effective channel and the reduced channel sparsity with conventional rectangular window. Then, we characterize the impacts of windowing on the effective channel estimation performance for OTFS modulation. Based on the revealed insights, we propose to apply a Dolph-Chebyshev (DC) window at either the transmitter or the receiver to effectively enhance the sparsity of the effective channel. As such, the channel spread due to the fractional Doppler is significantly reduced, which leads to a lower error floor in channel estimation compared with that of the rectangular window. Simulation results verify the accuracy of the obtained analytical results and confirm the superiority of the proposed window designs in improving the channel estimation performance over the conventional rectangular or Sine windows.

... A cylindrical array beamformer can be easily developed by stacked circular array using a rotator, but circular array has high side-lobe level in the azimuth angle domain. In [3] approach using phase mode excitation [4] has been proposed. ...

This paper discusses intrinsic problems to realize low side-lobe beam forming by synthetic cylindrical array, and presents some indeterminate results. It is shown that the phase mode excitation based beamformer on the circular array is useful only if all impinging waves have the same elevation angle, but is applicable to the multi-path signals having arbitrary elevation angles which are usually unknown.

... In what follows, we propose to apply the Dolph-Chebyshev (DC) window at the transmitter or the receiver to improve the channel sparsity when channel state information (CSI) is not available. In fact, it has been proved that the DC window is effective [23] in the sense that: 1) given the specified sidelobe level, the width of the mainlobe in the window response is the narrowest; or 2) given the fixed mainlobe width, the sidelobe level is minimized. Note that the effective channel only has a considerably large entry when it is located in the mainlobe of the window response function in (31). ...

... An adjustable window has two or more independent parameters which include the window length. A variety of adjustable window functions also exist in literature like the Kaiser window [9], ultraspherical window [10] and Dolph Chebychev window [11]. The independent parameters are used to control the window characteristics. ...

... With the enormous development of the communication systems, the millimeter-wave frequency band is becoming more appealing owing to its features of miniaturized antennas, high data rate, less interference from nearby applications due to the limited number of functioning devices at this band [1]. Microstrip patch antenna (MPAs) are of special interest due to their peculiar characteristics of low profile, light weight, ease of fabrication, simple structure, conformability, and low fabrication cost [2]. On the other hand, some drawbacks are inherently associated with MPAs such as low gain, narrow bandwidth, spurious radiations, and less efficiency due to ohmic losses at higher frequencies [1]. ...

In this paper a novel, miniaturized, single layer, high gain comb-line linear antenna array is designed for millimeter-wave band. The proposed design is based on five elements array with an end feeding technique, consequently achieving a simple antenna structure. The antenna composition is novel owing to the combination of the radiating element with the matching stub. A shorting pin (via) is placed at the corner of the feedline to suppress un-radiated power. The antenna is perfectly matched to 28 GHz by employing a matching stub. The proposed antenna is designed on a flexible Rogers RT/Duroid 5880 laminate (ϵr=2.2, tangent loss=0.001, and thickness=0.127 mm). The performance of the designed antenna is evaluated based on various parameters such as return loss, gain, and radiation patterns.

... On the emission plane, the subapertures are usually arranged in the shape of regular hexagon. This is because the regular hexagon is the most compact arrangement scheme, which is beneficial to reduce sidelobe energy and obtain high quality combined beams [28][29][30][31][32][33]. However, regular hexagonal arrangement belongs to centrosymmetric arrangement, which will cause potential phase ambiguity. ...

There exists the phase ambiguity problem in the coherent beam combining (CBC) system with centrosymmetric arrays, which means that multiple different piston aberrations may generate the same far-field image. This will cause that the far-field image can not correctly reflect the phase information, resulting in the performance degradation of image-based intelligent algorithms. In this paper, we make a theoretical analysis on phase ambiguity. To the best of our knowledge, we give the number and descriptions of all solutions of the phase ambiguity problem in above system for the first time. A method to solve phase ambiguity is proposed, which requires no additional optical devices. We designed simulations to verify our conclusions and methods. We believe that our work solves the phase ambiguity problem in theory and is conducive to improving the performance of image-based algorithms. In addition, we designed a two-stage algorithm to generate Bi-beam, which have valuables application in laser propagation.

... In the past decades, a number of advanced techniques have been proposed to synthesize sum and difference patterns [2]- [17]. When the complexity and cost of a beam forming network (BFN) are affordable in a certain application, classical methods like the Dolph-Chebyshev [4] and the Bayliss approach [5] as well as some other independent excitation optimization methods [6] will be adequate. However, to result in a simplified BFN, in most cases people prefer to obtain sum and difference patterns by using some compromised schemes to avoid two completely independent sets of excitations. ...

This communication presents a novel method of synthesizing both sum and difference patterns by optimizing the element rotations and positions for linear dipole array. The common element rotations and positions are optimized by using the particle swarm optimization (PSO) method to produce sum and difference patterns with reduced sidelobe levels (SLLs) and cross-polarization levels (XPLs), and as steep slope as possible for the difference pattern at the target direction. Such method leads to a sum-and-difference array with sparsely distributed uniform amplitude elements, thus saving many antenna elements and unequal power dividers. Three examples for synthesizing sparse rotated dipole arrays with sum and difference patterns are provided. Synthesis results show that the obtained arrays with uniform amplitudes can produce satisfactory sum and difference patterns while saving about 34.69% ~ 42.27% of the antenna elements when compared with λ/2-spaced arrays occupying the same aperture.

... La Paz and Miller [184] purported to show that the maximum directivity from an aperture of a given size was fixed, but then Bouwkamp and De Bruijn [185] correctly demonstrated that there was no theoretical limit on the directivity from an aperture of any size. Dolph realized that one could control the sidelobe levels of the pattern by properly weighting (Chebyshev polynomial tapering) the amplitudes of the element excitations [186]. Riblet [187], [188] illustrated that such amplitude tapering has an associated cost of widening the mainlobe of the pattern. ...

Multipole expansions are an essential analysis tool in the foundations of the descriptions of the electromagnetic fields radiated by electric and magnetic sources. Nevertheless, practical antenna systems generally rely on them as an academic explanation, not as a fundamental building block. An overview of the recent surge in interest in multipole sources and their fields to achieve useful radiated and scattered fields with, for example, high directivities in preferred directions is given. Topics include Huygens sources, dielectric-based Mie-tronics, edge-singularity multipoles, and exotic metamaterial-inspired superdirective lenses and radiators. While there has been a never-ending stream of physics publications, little has happened in the engineering electromagnetics community. I will try to answer the title with examples that may stimulate interest in the field.

... Consequently, the synthesis of digital beamforming can be regarded as the design of a finite impulse response (FIR) filter. Herein, we adopt the Dolph-Chebyshev window function ω d � [ω n ] N×1 , which can achieve the lowest sidelobe level (SLL) for a given beamwidth among all weightbased beam designing methods [35]. It can be expressed as equation (8) ...

Multiple-input and multiple-output (MIMO) technology can not only provide huge data rates but also overcome the severe propagation attenuation effect, especially in millimeter-wave (mmWave) bands by utilizing beamforming. The nonreciprocal beam is a novel transmission pattern, which indicates that transceivers adopt asymmetrical beamwidths. Such a special pattern can achieve fast beam alignment and alleviate equipment costs. Thorough knowledge of the corresponding wireless channel is pivotal to the system design and optimization, which remains to be investigated. In this paper, we first propose a 3-dimensional (3D) channel model based on ray-tracing, which is capable of reflection simulation. Based on this model, the ray-based beamforming mechanism is illustrated. The angular distribution is pivotal to beam channel modeling and characterization since transceiver beams filter rays in the angular domain. Then, we conduct an omnidirectional antenna-based channel simulation in an urban macro cell scenario via the ray-tracing platform. On this basis, we focus on the distribution of the quasi-angles, i.e., angles between departure/arrival reflected rays and the line-of-sight (LoS) path. We find that Gamma distribution is a better option to fit the quasi-arrival angular distribution than the Von Mises distribution. Furthermore, to characterize the relationship between quasi-angles of departure (AoD) and quasi-angles of arrival (AoA), the gaussian mixture model (GMM) is adopted and the expectation-maximization (EM) algorithm is used to estimate the unknown parameters of GMM. Our findings provide useful insights to beam channel modeling, which should take the joint angular distribution into consideration.

... On the other hand, zero-padding in the frequency domain is equivalent to multiplication by a rectangular window and thus corresponds to convolution with a sinc kernel in the time domain; forĤ not vanishing at the boundaries, this may introduce extra sinc-shaped tails around each impulse within the estimated channel impulse response. 2 Therefore, in the present approach,Ĥ is first multiplied by a Dolph-Chebyshev window [7] (centred around the carrier frequency), w, with attenuation set to 60 dB 3 , and then extended to 16-times the original length through zero-padding (pad 15 0 ). Overall, the channel impulse response is estimated through ...

In this paper, the task of channel sounding using software defined radios (SDRs) is considered. In contrast to classical channel sounding equipment, SDRs are general purpose devices and require additional steps to be implemented when employed for this task. On top of this, SDRs may exhibit quirks causing signal artefacts that obstruct the effective collection of channel estimation data. Based on these considerations, in this work, a practical algorithm is devised to compensate for the drawbacks of using SDRs for channel sounding encountered in a concrete setup. The proposed approach utilises concepts from time series and Fourier analysis and comprises a signal restoration routine for mitigating artefacts within the recorded signals and an encompassing channel sounding process. The efficacy of the algorithm is evaluated on real measurements generated within the given setup. The empirical results show that the proposed method is able to counteract the shortcomings of the equipment and deliver reasonable channel estimates.

... where z n are zeros on the complex unit circle. The zeros of the Chebyshev pattern are calculated in [17]. However, the problem of achieving Taylor super-directive patterns is that infinite zeros have to reside on the complex unit circle to produce such a pattern with tapered sidelobes. ...

Recently, the super-oscillation phenomenon has attracted attention because of its ability to super-resolve unlabelled objects in the far-field. Previous synthesis of super-oscillatory point-spread functions used the Chebyshev patterns where all sidelobes are equal. In this work, an approach is introduced to generate super-oscillatory Taylor-like point-spread functions that have tapered sidelobes. The proposed method is based on the Schelkunoff’s super-directive antenna theory. This approach enables the super-resolution, the first sidelobe level and the tapering rate of the sidelobes to be controlled. Finally, we present the design of several imaging experiments using a spatial light modulator as an advanced programmable grating to form the Taylor-like super-oscillatory point-spread functions and demonstrate their superiority over the Chebyshev ones in resolving the objects of two apertures and of a mask with the letter E.

This paper studies hybrid beamforming for active sensing applications, such as millimeter-wave or ultrasound imaging. Hybrid beamforming can substantially lower the cost and power consumption of fully digital sensor arrays by reducing the number of active front ends. Sparse arrays can be used to further reduce hardware costs. We consider phased arrays and employ linear beamforming with possibly sparse array configurations at both the transmitter and receiver. The quality of the acquired images is improved by adding together several component images corresponding to different transmissions and receptions. In order to limit the acquisition time of an image, we formulate an optimization problem for minimizing the number of component images subject to achieving a desired point spread function. Since this problem is not convex, we propose algorithms for finding approximate solutions in the fully digital beamforming case, as well as in the more challenging hybrid and analog beamforming cases that employ quantized phase shifters. We also determine upper bounds on the number of component images needed for achieving the fully digital solution using fully analog and hybrid architectures, and derive closed-form expressions for the beamforming weights in these cases. Simulations demonstrate that a hybrid sparse array with very few elements, and even fewer front ends, can achieve the resolution of a fully digital uniform array at the expense of a longer image acquisition time.

Microwave wireless power transmission (MWPT) via radio waves has been an important research topic of the WPT systems, where the overall power transfer and conversion efficiency is a key factor to evaluate the system performance. The state-of-the-art work on MWPT has only taken the end-to-end power transfer efficiency in free space or the power conversion efficiency of the receiver (rectenna) into consideration separately when optimizing the power transfer efficiency of the overall system. To comprehensively consider the system-level matching of the entire MWPT system, a novel space matching concept, including aperture field matching, power matching, and impedance matching, is proposed for optimizing the overall power transfer efficiency. By using the space matching method in this work, the optimal designs of the subsystem components such as the transmitting antenna, receiving antenna, and rectifying circuit can be separately obtained to avoid the complex systematic optimization of the large-scale and complicated MWPT system, therefore, significantly improving the overall power transfer efficiency by 19.4% compared with the traditional methods, and reducing the complexity in large-scale system-level design. This work will have valuable implications in the system design of MWPT applications.

Over a decade, the evolutionary and social inspired computing techniques have revolutionarised the nonlinear problem-solving methods with their efficiency in searching for the global optimum solutions. Several engineering problems are dealt with such nature-inspired techniques. In the recent past, the evolutionary computing and socio-inspired algorithms have been applied to antenna array synthesis problems. In this chapter, the novel social group optimization algorithm (SGOA) is used for the antenna array synthesis. Three different and potential pattern synthesis problems like sidelobe level (SLL) optimization, null positioning, and failure compensation are dealt for demonstrating the effectiveness of the SGOA over the conventional uniform patterns. In all the cases, the simulation-based experimentation is repeated for 20-element and 28-element linear array. The robustness of the algorithm to deal with the constrained objectives of antenna array synthesis is discussed with relevant outcomes from the simulations in terms of the convergence plots.

Mostly the design engineering problems are consisting of integer, discrete, and mixed design variables. Associated to these types of variables, the accessible search space is very limited which may increase the complexity of problems. To solve such problems, traditional optimization methods such as Newton’s method, Newton–Raphson method, Gradient methods, etc. are unable to work efficiently. In order to overcome this limitation, various bio-based (Genetic Algorithm (GA)) and social-based (Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Firefly Algorithm (FA), etc.) optimization approaches were introduced. In the present work, a socio-based Cohort Intelligence (CI) algorithm proposed by Kulkarni et al. [1] is implemented to solve discrete variable truss structure problem, mixed variable design engineering problem, and integer variable. The CI algorithm is incorporated with a group of learning candidates which interact and compete with one another within a cohort to achieve their individual goal and further make to improve the overall cohort behavior. The variables involved with these problems are handled using simple round-off technique. Also, the well-known static penalty approach is adopted to handle the inequality constraints. Further, CI is successfully compared with several algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Mine Blast Algorithm (MBA), Harmony Search Algorithm (HS), etc. The reported solutions using CI were significantly better than that of other algorithms reviewed in literature with a lesser amount of computational cost (function evaluations and computational time).

New methods for maximizing directivities of the array antennas are proposed. First, the array pencil beam (PB) directivity maximization problems without or with sidelobe constraints are formulated as convex optimization problems, which are solved optimally to achieve better optimized directivity results, compared with traditional method with radiation intensity maximization only. Then, to deal with the non-convexity in the wide beam (WB) directivity maximization problem, a novel iterative directivity optimization method based on Taylor expansion of the quadratic function is proposed, and the original non-convex problem can be efficiently solved by the convex optimization methods in an iterative way. Finally, a two-stage iterative directivity maximization method is further proposed to deal with the sidelobe constraints in the WB directivity maximization problem. Two initial point schemes for the iterative algorithms are studied in detail with the performance comparisons. The two-stage algorithm can be used to yield very good results, even under very wide beamwidth and strict sidelobe constraint conditions. With the proposed methods, the array directivity maximization problems can be solved by the convex optimization methods in a very efficient way. Several representative examples are presented to demonstrate the excellent performance of the proposed methods.

All antenna arrays are roughly subdivided into two groups: scanning arrays and non‐scanning arrays. The non‐scanning arrays are used for various directional‐power applications; they compete with the reflector antennas. The scanning arrays have an ability to steer the main beam electronically, in contrast to mechanical scanning with the reflector antennas. The Hansen‐Woodyard array is a first example of an array with a modest superdirectivity. The numerical simulations have been carried out for the array of center‐fed ribcage with Ansys HFSS commercial CEM software. The numerical solution was obtained with a perfectly matched layer box and used about 100 000 tetrahedra. The chapter presents some design results for small arrays. It aims to establish theoretical/numerical results for impedance bandwidth improvement and for the array directivity with full‐wave numerical simulations.

Sonar arrays are extensively utilized in maritime surveillance and for the safe navigation of passing vessels in the ocean. The characteristic of the beam pattern is one of the most vital properties of a soanr array. A directional main lobe with low sidelobe levels (SLLs) efficiently improve the sonar performance and reduce the interferences. Beamformers have been employed for forming the beam pattern and controlling the lobes of the beam. They are intended to filter out noises and other incoherent signals from all directions while boosting the signal-to-noise ratio from the desired direction essentially to detect targets and estimate their location. Both pre-formed beams in all directions or beam steering are usually followed during a sonar operation. Such pre-formed beams are required to be identical and undistorted. Diverse beams produce errors in the bearing, resolution and judgement of target detection, etc. Beamwidth, SLLs, beam sensitivity and tolerance to the array distortion are the key factors of beam identicality. They can be regulated by optimizing the individual elements of the array with a proper weighting factor called windowing. These optimizations are often complex and sensitive to mismatches in individual sensors, namely variations in receiving sensitivity, error in sensor location, failure of sensors, and acoustic centre, etc. and hence distort the beam pattern and introduce spread in lobes. This paper presents an investigation on the SLL spread due to array distortions. The four most commonly used standard beamformers and a novel product beamformer are chosen for the comparative analysis. The presented results suggest that the product beamformer is more robust with less SLL spread than the traditional beamformers.

Nowadays, email is an important medium of communication used by almost everyone whether for official or personal purposes, and this has encouraged some users to exploit this medium to send spam emails either for marketing purposes or for potentially harmful purposes. The massive increase in the number of spam messages led to the need to find ways to identify and filter these emails, which encouraged many researchers to produce work in this field. In this paper, we present a method for identifying and detecting spam email messages based on their contents. The approach uses the mutual information contents method to define the relationship between the text the email contains and its class to select the most frequently used text in spam emails. The random forest classifier was used to classify emails into legitimate and spam due to its performance and the advantage of overcoming the overfitting issue associated with regular decision tree classifiers. The proposed algorithm was applied to a dataset containing 3000 features and 5150 instances, and the results obtained were carefully studied and discussed. The algorithm showed an outstanding performance, which is evident in the accuracy obtained in some cases, which reached 97%, and the optimum accuracy which reached 96.4%.

Ocean surveillance using sonar uses a panoramic display for a 360° undersea investigation. Beamformers have been widely used for this purpose. They are designed to filter out noises and other incoherent signals from all directions while enhancing the signal-to-noise ratio from the desired direction essentially to detect targets and estimate their location. Sonar arrays formed by several sensing elements arranged in different shapes are used for forming pre-formed or steered beams in all directions. Such pre-formed beams are expected to be identical and unperturbed. Non-identical beams result in errors in bearing, resolution and discrimination, etc. Beamwidth, sidelobe levels (SLL), beam sensitivity and tolerance to the array integrity are the deciding factors of beam identicality. They can be controlled by providing optimized individual weighting called windowing. These optimizations are often complex and sensitive to mismatches in individual sensors, namely variations in receiving sensitivity, error in sensor location, failure of sensors, and acoustic centre, etc. Reliability analysis of a novel product beamformer is made in this paper against the seven most commonly used standard beamformers to choose a reliable beamformer. Failure in the array element is the criteria set for the analysis. The presented results suggest that the product beamformer is more stable than traditional beamformers.

In this paper, low-sidelobe cavity-backed slot antenna array with simplified feeding structure for vehicular communication is proposed. Conventional low-sidelobe antennas are realized using power dividing network to obtain the in-phase and nonuniform-amplitude excitation, which causes complicated antenna structure and antenna design. To tackle this challenge, a simplified feeding method without using power dividing network is introduced to design the low-sidelobe slot antenna array. The slots at the top walls serve as the radiation elements, and the slots are directly fed by the electric field of the cavity mode. Nonuniform amplitude is obtained by simply modifying the slots sizes and positions, while the in-phase excitation of the elements is remained. The nonuse of power dividers brings out a simpler antenna structure than conventional full-metal waveguide-based antennas. Besides, the full-metal structure introduces a high power-handling capacity. Then, two linear arrays with 14, 17 elements and a planar array with 54 elements are presented to show the design feasibility. Finally, the 54 antenna array is fabricated and measured, which can achieve 18.2 dBi gain, -20 dB sidelobe level, 94% radiation efficiency, and -42 dB cross-polarization. Good agreement between measurement and simulation verifies the feasibility of the proposed design concept.

Optimization for the reduction of power losses in sidebands and side lobes of time-modulated antenna array (TMLAA) is dealt in this work. Optimization for the reduction of power in TMLAA is analyzed by considering two ways of the power loss analysis: one with the minimization of power loss with optimization of Toff instant with Ton instant as zero for each element along with optimal inter-element spacing with uniform amplitude and second, by taking optimization of Ton and Toff instant of each element of TMLAA along with optimal inter-element spacing with uniform amplitude. Distance between any two consecutive antennas and switch ON and OFF instants are considered as optimizing variables for reduction of power due to sidebands at harmonic frequencies and side lobes at the fundamental harmonic. Towards this approach, an evolutionary algorithm-based approach called harmony search algorithm (HSA) is applied. Optimal values of the variable parameters of the TMLAA are obtained after optimization by using particle swarm optimization (PSO) and HSA. MATLAB simulation results are presented in this work for different array sets of 16-, 20-, 24-, 28-, and 32-element antenna arrays. To validate in electromagnetic (EM)-simulated environment, a 16-element TMLAA is designed in CST-MWS with parameters obtained after optimization, and these results are validated with those of MATLAB results.

A challenge in array antenna theory is to obtain
an array with a maximally selective array factor implemented
with minimum number of radiators. The simplest array antenna
consists of two radiators only. This paper presents an approach
for designing such an array antenna with an array factor with
the following properties: two-dimensional selectivity of the main
lobe with an arbitrary half-power beamwidth (HPBW), absence
of side lobes, arbitrary distance between the elements, azimuthal
steering of the main lobe without appearance of side lobes. The
proposed theory is verified using numerical simulations. In
addition, a new closed-form expression for the HPBW for
binomial array antennas is proposed.

An effective optimization method is proposed for the synthesis of sparse antenna arrays subject to constraint on directivity in this letter. Based on the framework of thinned arrays synthesis, a real-value mixed integer programming problem for the minimization of the number of elements under given maximum sidelobe level, scan range, and minimum directivity in a limited array aperture is established. In order to solve this problem efficiently, an iterative convex optimization method is proposed, where the strategies of weighted
l
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-norm minimization and the polygonal expansion and contraction of the element position are integrated together organically. Owing to the adoption of such two strategies, both the search space regarding the element positions and the convergence speed can be controlled flexibly. Several representative numerical examples are presented in comparison with reported advanced methods to demonstrate the effectiveness of the proposed method.

The aim of the present research is to define families of adaptive functions that could be used in various branches of scientific knowledge, in particular in the approximation of a number of classical impulse signals, point sets in the plane and supplemented graphs of discontinuous functions. In this book, we consider only some aspects related to the disclosure of intrinsic properties of some of the proposed families of adaptive functions in a purely methodological aspect. Many of the proposed new models could not be used as ''feasible models-diagrams'' in practice. In this connection, the specialists working in the indicated field have the floor.
We study some properties of an exponentially optimal filter proposed by Tadmor and Tanner. More precisely, we consider the problem for approximating the function of rectangular type by the class of exponential functions about Hausdorff metric. A new activation and ''semi-activation'' functions are defined. We consider also modified families of functions with ''polynomial variable transfer''. Analysis of typical diagram functions with restrictions is also given. Numerical examples, illustrating our results using CAS MATHEMATICA are given.
Chapter 2 is devoted to generating the adaptive functions for approximating some ''specific functions'' from the field of Antenna and Filters Synthesis. Particular attention is paid to the: flexible Weibull-Bur XII cumulative distribution function; new cumulative distribution function of Gompertz-type and ''adaptive function'' of Lindley-type. In Chapter 3 we study some general approximation problem for smooth approximation to |x(1-x)…(n-1-x)| using Gaussian error function. Some related problems and applications are also given.

A novel method based on alternating linear programming optimization (ALPO) is presented to synthesize sparse linear arrays with sum and difference patterns. This method can find the optimized element positions and excitations shared for both sum and difference patterns with accurate control of multi-region sidelobe distribution and difference pattern null slope. In addition, the constraints on the minimum element spacing and dynamic range ratio (DRR) of the obtained excitations can be also appropriately incorporated into this alternating optimization process. Two synthesis examples with different pattern shape requirements are conducted to validate the effectiveness and advantages of the proposed method.

In this study, an adaptive pattern nulling approach of half-wave dipole uniform linear arrays (DULA), inspired by binary bat algorithm (BBA)-based beamformers and the phase-only control of array excitation weights, has been proposed. This helps suppress interference with unknown directions in the sidelobe region. Several scenarios have been conducted to investigate the performance of the proposal including operation speed and adaptive pattern nulling with or without the effect of mutual coupling. The simulation results show that the proposed approach is a potential solution to precisely place nulls at any direction of unknown interferences while maintaining the main lobe and suppressing the sidelobes. In addition, regarding the pattern nulling, the approach proposed in this study demonstrates greater efficiency and higher speed than those using binary particle swarm optimization (BPSO).

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