Physics-Informed Deep Neural Network for Low Sidelobe Cosecant-Squared Pattern Time-Modulated Antenna Array with Harmonic Suppression

Time modulated arrays (TMA) suffer from relatively low efficiencies due to radiations at different harmonics (sidebands) of modulation frequency in addition to main frequency. In order to increase this efficiency, optimization algorithms are usually used, but the performance and solution time of the optimizations must be studied. In this study, the two-stage optimization method is proposed for suppressing sidelobe level (SLL) and switching-induced sideband levels (SBL) in the time-modulated linear antenna array. It is shown through a sample scenario that the proposed method gives more effective results than the classical optimization approach.

Time modulated antenna arrays attracted the attention of researchers for the synthesis of low/ultra-low side lobes in recent past. In this article we propose an improved variant of a recently developed ecologically inspired metaheuristic, well-known as Invasive Weed Optimization (IWO), to solve the real parameter optimization problem related to the design of time-modulated linear antenna arrays with ultra low Side Lobe Level (SLL), Side Band Level (SBL) and Main Lobe Beam Width (BWFN). We improvise the classical IWO by introducing two parallel populations and a more explorative routine of changing the mutation step-size with iterations. Experimental results indicate that the proposed algorithm achieves better performance over the design problem as compared to the conventional Taylor Series based method and the only known metaheuristic approach based on the Differential Evolution (DE) algorithm.

An improved procedure to lessen side lobe levels (SLLs) and side band levels (SBLs) in time modulated linear antenna arrays (TMLAAs) by using the optimization process. In that optimization process we give the discrete values of static excitation amplitudes and phase of continuous values of on-time duration of the elements of antenna array. We used the particle swarm optimization (PSO) technique to reduce the maximum of SLLs and SBLs to a pre defined desired value of antenna element. This has been optimized in a way that the discrete values of input excitation amplitude are obtained by PSO algorithm. The simulation result of time-modulated linear antenna array (TMLAA) is presented by reducing SLL and SBLmax to below −40 dB and to −35 dB respectively by taking 30 elements.

This paper introduces an application of the dandelion optimization (DO) algorithm in antenna arrays. This is the first time that the DO algorithm has been used for optimizing antenna arrays. For antenna array optimization, sidelobe level (SLL) and deep nulls are key technical indicators. A lower SLL can improve the signal-to-noise ratio and reduce the impact of clutter signals outside the main beam. Deep nulls need to be aligned with the direction of interference to eliminate the influence of interference sources. The combination of the two can effectively improve the anti-interference ability of the entire system. Therefore, antenna arrays with ultra-low sidelobes and ultra-deep nulls are currently hot in the field of antenna array design and are also some of the key technologies needed to achieve modern high-performance radar systems. As a new type of evolutionary algorithm inspired by nature, the DO algorithm is inspired by the wind propagation behavior of dandelions in nature. This algorithm iteratively updates the population from three stages of ascent, descent, and landing, ultimately finding the optimal position. It has good optimization ability in solving complex problems such as those involving nonlinearity, discreteness, and non-convexity, and the antenna array pattern synthesis optimization problem belongs to multivariate nonlinear problems. Therefore, the DO algorithm can be effectively applied in the field of antenna array optimization. In this work, we use the following method to obtain an optimized pattern of a linear array with the lowest sidelobe level (SLL), null placement in particular directions, and a lower notch in particular directions: by controlling the antenna array’s element spacing and leaving the phase unchanged to optimize the current amplitudes and by controlling the excitation current and phase fixation of the antenna array and changing the element spacing. In the first and second examples, different algorithms are used to reduce the SLL of the antenna. In the first example, the DO algorithm reduces the SLL to −33.37 dB, which is 2.67 dB, 2.67 dB, 3.77 dB, 2.74 dB, and 2.52 dB lower than five other algorithms. In the second example, the SLL optimized by the DO algorithm is −42.56 dB, which is 5.04 dB and 1.48 dB lower than two other algorithms. In both examples, the DO algorithm reduces the SLL lower than other algorithms when the main lobe of the antenna is not significantly widened. Examples 3, 4, and 5 use the DO algorithm to optimize the amplitude of the current, generating deep nulls and deep notches in specific directions. In Example 3, the DO algorithm obtains a depth of nulls equal to −187.6 dB, which is 66.7 dB and 44.3 dB lower than that of the flower pollination algorithm (FPA) and the chaotic colony predation algorithm (CCPA), respectively. In Example 4, the deep null obtained by the DO algorithm is as low as −98.69 dB, which is 6.67 dB lower than the deep null obtained by the grey wolf optimization (GWO) algorithm. In Example 5, the deep notch obtained by the DO algorithm is as low as −63.1 dB, which is 6.4 dB and 1.9 dB lower than the spider monkey optimization (SMO) algorithm and the grasshopper optimization algorithm (GOA), respectively. The data prove that the DO algorithm produces deeper nulls and notches than other algorithms. The last two examples involve reducing sidelobe levels and generating deep nulls by optimizing the spacing between elements. In Example 5, the SLL obtained using the DO algorithm is −22.8766 dB, which is 0.1998 dB lower than the lowest SLL of −22.6768 dB among other algorithms. In Example 6, the SLL obtained using the DO algorithm is −20.1012 dB, and the null depth is −125.1 dB, which is 1.592 dB lower than the SLL obtained by the cat swarm optimization (CSO) algorithm and 19.1 dB lower than the deep null obtained by the GWO algorithm, respectively. In summary, the results of six simulation experiments indicate that the DO algorithm has better optimization ability in linear array optimization than other evolutionary algorithms.

This paper proposes a trapezoidal pulse-based ON-OFF switching approach for the optimum beamforming performance in a time-modulated linear antenna array (TMLAA). The Fourier series property is used to adjust the transient behaviour trapezoidal switching function (τn1) and constant slope (τn2) of the trapezoidal pulse to obtain the highest steering main beam of the fundamental and harmonic components of the radiation pattern. Also, the sidelobe level (SLL) and sideband level (SBL) are simultaneously lowered. Despite the fact that harmonic beams are typically thought of as an interfering radiated pattern in time-modulated antenna arrays, the shifted harmonic frequency can also be useful in a variety of contexts. The beam steering of the harmonic is made possible by the optimal adjustment of the switch time instant τn1 and τn2 of the trapezoidal pulse signal without any optimization of the excitation amplitude weights. The optimal switching ON and OFF duration is evaluated by utilizing an evolutionary algorithm called Cultural Algorithm (CA). The antenna radiation characteristics are changed by using a series of Radio Frequency (RF) switches to modulate the static excitations using a trapezoidal pulse sequence to alter the time-modulation. Toward this approach, unique cost functions are designed and simulated for the simultaneous reduction of SLL, SBL and harmonic beam steering in TMLAA. The proposed cost function-based CA algorithm is able to get beam steering as arbitrary beam steering, multi-beam steering and beam steering in a user-defined direction.

In time-modulated antenna arrays (TMAAs), as a result of periodical switch-on and switch- ofi of the antenna elements, including operating frequency (termed as center frequency) signal, sideband signals are appeared at either sides of the center frequency in integer multiples of the modulation frequency. In this paper, it is shown that without using phase shifters, just by suitably controlling the on-time instants (OTIs) and on-time durations (OTDs) of a time-modulated linear antenna array (TMLAA) elements, simultaneously, along with a pencil beam pattern at the operating frequency, a shaped beam pattern can be obtained at both the flrst positive and negative harmonics of the time- modulation frequency. The important advantage of such a technique is that realization of multi-beam pattern in conventional antenna array (CAA) system generally requires complex feed network, whereas by using simple radio frequency (RF) switching circuit in the feed network of TMLAA, by virtue of the properties of harmonic radiations, synthesis of a shaped pattern at either (positive or negative) harmonic results in generating the same pattern in its opposite harmonic, and the synthesized patterns at difierent harmonics can be simultaneously used as independent communication channels. By employing a difierential evolution (DE) based optimization method, numerical results for a 16-element TMLAA with uniform excitation show that in conjunction with a pencil beam pattern at the center frequency, a ∞at-top or a cosec square pattern at flrst positive and negative sidebands of side-lobe levels (SLL) i20dB can be synthesized by suppressing the higher sideband level (SBL) to below i10dB.

Multi-beam antenna is an important way to increase the channel capacity of cellular communications. It is available in two ways, one is based on optical methods, such as Luneberg lens and Rotman lens. However, the common problem with this method is that the lens size is too large or difficult to process. Another method is based on beam-forming network composed of coupler and phase shifter, such as Butler matrix. The Butler matrix has been studied for a long time, in the form of microstrip, stripline, or substrate-integrated waveguide. The substrate-integrated waveguide with low insertion loss is mainly used in the higher frequency such as millimeter wave band. The microstrip is mainly used in 4G/5G base stations, suitable for broadband design and process. Low side-lobe level, narrow beams are especially important for multi-beam base station antennas. The traditional Butler matrix is 4 × 4 Butler matrix for 4-beam base stations. However, the traditional Butler matrix can only output equal-amplitude power, with a side-lobe level higher than −13.4 dB. The beam width is too wide due to the few number of antenna. The 4 × 4 Butler Matrix with attenuator can reduce the side-lobe level, but it will increase the insertion loss of the beam-forming network. The 4 × 4 Butler matrix with phase shifter and power divider can form a 4 × 6 Butler matrix, which reduce the beam width beam and side-lobe level. However, for large-angle scanning, not only the side-lobe level, but also the grating-lobe problem caused by the wide-angle scanning and wide antenna spacing needs to be solved. The array with triangle arrangement can reduce the side-lobe and grating-lobe level. A wide-band 4-beam antenna array and beam-forming network for 4G base stations are presented in this paper. Adopting triangular arrangement, the number of antenna in sub-array is increased, and the antenna spacing is reduced, resulting in good side-lobe and grating-lobe level suppression. The output amplitude and phase errors are small over a wide band, with low insertion loss.

The time modulation technique is utilized for the synthesis of power patterns in linear arrays. The differential evolution algorithm is employed both to shape the beam requirements and to suppress the sideband patterns. Numerical results show that the time-modulated linear array can be successfully used to synthesize power patterns and the excitation dynamic-range ratio can be reduced significantly as compared to those of conventional arrays.

This work is concerned with the methodology for improvement of the radiation pattern performance and eliminating the effect of unwanted interference of symmetric time modulated linear antenna array (STMLAA) in the predefined direction. This is achieved using evolutionary technique called Novel Particle Swarm Optimization with Wavelet Mutation (NPSOWM) for various application specific optimization like SLL only reduction, dual broad null and multiple broad null optimization. The optimized results obtained by using NPSOWM are validated by CST-MWS by captivating practical elements of dipole antenna and its array configuration. The numerical results show the effect of the particular (practical) antenna on the array. Various examples have taken for this purpose. A set of 16-element antenna array have designed for SLL only reduction. 16-, 32-, and 64-element STMLAA for incorporating the dual broad nulls in the angular range from 400 to 700 over the elevation plane. A set of 24-, 30-, and 32-element antenna array have occupied for multiple broad nulls. The strength of the adopted algorithm is tested for different number of array antenna configuration, which establish the efficacy of the optimization technique NPSOWM adopted for achieving the interference cancellation in the predefined direction and performance improvement of the antenna array such as simultaneous improvements of broad nulls (BNs), sidelobe level (SLL), sideband level (SBL), and the directivity. From the simulated results it is clear that NPSOWM can perform better than that of un-optimized linear antenna array with respect to BNs, SLL, and SBLs and Directivity.

A novel approach to realize uniform amplitude time modulated linear arrays with both suppressed sidelobes and sidebands is proposed. The approach utilizes the direct optimization of the switch-on time sequence of each array element via the simple genetic algorithm (SGA). As compared to previous time modulated linear arrays, the new array has the advantages of having low sidelobe level (SLL), low sideband level (SBL) and uniform excitations simultaneously. Experimental results on an experimental prototype of a 16-element printed dipole linear array with the SGA optimized time sequences verified the approach.

Time-modulated linear antenna array (TMLAA) with periodic time modulation of antenna elements radiates infinite inevitable harmonic beams. The infinite harmonic sideband radiation is a wastage of power unless the power is exploited. This paper aims to minimize inevitable power wastage in the harmonic beams radiated from TMLAA by employing an optimized periodic timing sequence. The optimization of the timing sequence is conducted employing harmony search (HS) to suppress the power wastage, However, conventional HS achieves an acceptable sidelobe level (SLL) below – 30 dB. Nevertheless, a modified harmony search algorithm (MHSA) is proposed to attain more power in the desired fundamental beam. The algorithm is validated using an array of 4-, 10-, and 16-element uniform half-wavelength spacing TMLAA. The optimization is conducted on the ON and OFF time instants and the real current of the elements. The simulation results exhibit that HS and MHSA perform potentially alike to suppress the SLL of fundamental below –30 dB. However, the further suppression of the sideband levels employing MHSA justifies the modification proposed in this work. The MHSA performance in terms of radiation parameters is compared with the HS and also with previous works to show the potentiality of the modification.

In this paper, we present a novel scheme to train a deep neural network (DNN) for a cosecant-squared (csc2) radiation pattern synthesis speedily and accurately without relying on numerical optimization methods. Our approach is to train a DNN using a physics-informed loss function that minimizes the deviation between the desired shaped beam pattern and the actual one. The physics-informed deep neural network (PIDNN) makes array synthesis effective because it can efficiently achieve two desired features, namely, low sidelobe level (SLL) and small deviation (ripples) in the shaped beam region. To obtain a desired csc2 pattern with the SLL constrained, PIDNN optimizes the excitation amplitude and phase weights of the array elements. To illustrate the effectiveness of the proposed method, the beam pattern with specified characteristics is obtained for the same array by using genetic algorithm (GA) and particle swarm optimization (PSO).

In this letter, an efficient synthesis method for near-field multifocus (NFMF) sparse planar arrays (SPAs) is proposed, utilizing a structured sparsity learning (SSL)-based deep neural network (DNN) model. The model is established by connecting physical equations in tandem with the DNN to map the relation between the desired near-field radiation characteristics and SPA geometry. To enhance the sparsity of the SPA, the SSL method, incorporating a group <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sub> (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GL</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sub>) regularizer seamlessly embedded into the model, is employed to prune redundant nodes that represent unnecessary array elements. By incorporating both the physical equations and SSL method, prior knowledge is provided to improve the training efficiency of the model. Through appropriate training, the synthesis of the SPA is achieved, generating an optimal SPA layout along with element excitations. The proposed method allows for precise control of the focal position and sidelobe level (SLL) of the near-field pattern with a minimal number of array elements. The effectiveness of this method is demonstrated by two examples focusing on single- and eight-point near-field targets with low SLL. Results show that the proposed method achieves over 65% savings in the number of array elements and at least a 45% reduction in synthesis time compared with the existing synthesis methods.

Array Antennas used in some applications such as RFID systems, WiMAX, and collision avoidance radar, must have very low side lobes. Antenna with higher beam efficiency (BE) and lower side lobe level (SLL) can increase the coverage area of RFID systems, transmission bit rate and at the same time decrease the energy consumption and interference levels. The application of RFID system at 860–960 MHz frequency band will likely be witnessed in different emerging wireless applications as well as associated increase in energy consumption will also be witnessed in the near future. It is possible to achieve higher BE and lower SLL by implementing different amplitude or phase distribution technique in the array antenna. This paper describes a new method of SLL reduction and increase of BE by adopting staircase concept of power distribution of array antenna. The new beam forming technique optimizes between SLLs and BE.

In this paper, two universal reinforcement learning methods are considered to solve the problem of maximum power point tracking for photovoltaics. Both methods exhibit fast achievement of the MPP under varying environmental conditions and are applicable in different PV systems. The only required knowledge of the PV system are the open-circuit voltage, the short-circuit current and the maximum power, all under STC, which are always provided by the manufacturer. Both methods are compared to a Fuzzy Logic Controller and the universality of the proposed methods is highlighted. After the implementation and the validation of proper performance of both methods, two evolutionary optimization algorithms (Big Bang—Big Crunch and Genetic Algorithm) are applied. The results demonstrate that both methods achieve higher energy production and in both methods the time for tracking the MPP is reduced, after the application of both evolutionary algorithms.