A new technique for power-pattern synthesis in time-modulated linear arrays

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.

In this paper, a physics-informed deep neural network (PIDNN)-based approach with phase-only weighting is proposed for the synthesis of a cosecant-squared radiation pattern time-modulated linear array (TMLA). A deep neural network is trained using a physics-informed loss function to minimize deviation between the desired shaped beampattern and the actual one, thus eliminating the need for timeconsuming optimization techniques, such as evolutionary optimization algorithms. The sidelobe level (SLL) of the fundamental signal and the maximum sideband levels (SBLs) of the harmonic signals are simultaneously reduced by controlling both the phase and periodic switching time sequence of each element of the TMLA. The simulation results reveal that the proposed method achieved the desired patterns along with very low SLL and SBLs for 30- and 40-element TMLAs. For the 30-element TMLA, an SLL of −39.54 dB and a maximum SBL of −42.27 dB was achieved. For the 40-element TMLA, the obtained SLL and maximum SBL were −29.28 dB and −32.02 dB, respectively. Moreover, PIDNN demands considerably less computation time than evolutionary optimization algorithms—for a 30-element TMLA, the genetic algorithm took 47.13 minutes to complete the optimization process while PIDNN took only 2.87 minutes.

This study developed a gradient-based algorithm to synthesize arbitrary power patterns with only element phases. This algorithm does not rely on any general-purpose nonlinear solver and requires only a matrix computation toolbox; thus, the algorithm is compatible with different platforms. The algorithm locally finds the analytical gradient, and therefore reduces the time for computing the gradient. The pattern synthesis performance of the proposed algorithm was evaluated for linear arrays with continuous phase control, linear arrays with quantized phase control, and planar arrays with continuous phase control. The performance of the proposed algorithm was also compared with that of general-purpose optimization algorithms. For both linear and planar arrays, the proposed algorithm obtained solutions with comparable lower SLLs in small arrays, with improvement in SLL in large arrays and time-increasing rate with the array size. Therefore, the results of this study suggest that the proposed algorithm is highly suitable for generating radiation power patterns for large arrays.

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.

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.

In this letter, a novel direction-finding method with spatial spectrum estimation is proposed and verified, based on the time-modulated linear array (TMLA) and a single radio-frequency channel. Its principle is as follows. The TMLA receives and periodically modulates the incident signal. After the power combiner, the modulated signal is down-converted to the intermediate frequency and sampled in the single-channel receiver. In the digital domain, the array manifold vector can be calculated from the Fourier coefficients and the harmonic characteristic matrix related to modulation sequences, and thus, the autocorrelation matrix can be estimated. Afterward, the multiple signal classification algorithm is applied to estimate the incident angle, and the spatial smoothing method is exploited to deal with the direction finding of coherent sources. The proposed method has a simple structure and low computational complexity. Numeric simulations and corresponding experiments have been conducted to verify its effectiveness.

A novel strategy for harmonic beamforming in time-modulated linear arrays is proposed. The pulse splitting technique is exploited to simultaneously generate two harmonic patterns, one at the central frequency and another at a preselected harmonic of arbitrary order, while controlling the maximum level of the remaining sideband radiations. An optimization strategy based on the particle swarm optimizer is developed in order to determine the optimal parameters describing the pulse sequence used to modulate the excitation weights of the array elements. Representative numerical results are reported and discussed to point out potentialities and limitations of the proposed approach.

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.

The pattern synthesis technique of antenna arrays has a wide range of applications in radar and communication systems, which is an important research direction in the field of smart antennas. In order to improve the optimization performance of pattern synthesis of linear antenna arrays, an optimization method based on the Modified RIME Optimization Algorithm (MRIME) is proposed. RIME is a new heuristic algorithm inspired by the condensation process of frost ice in nature, which has a unique update mechanism with strong convergence as well as randomization. In the present work, MRIME is used for optimal pattern synthesis of a linear antenna array (LAA). One part of the present study is to optimize the side lobe level by optimizing the antenna current amplitude while maintaining a uniform spacing; the other part is to optimize the antenna position while assuming a uniform excitation in the synthesis of a sparse LAA, where constraints are imposed on the spacing of the array elements and aperture length, and suppression of the side lobe level with the position of the zeros in the specified direction is also achieved. In this article, simulation experiments for uniform linear arrays as well as sparse linear arrays are presented in detail, and the results show that the MRIME optimization algorithm outperforms most of the existing evolutionary classes of optimization algorithms in optimizing the side lobe level. This illustrates the potential of utilizing the MRIME optimization algorithm for antenna arrays and various other electromagnetism-related challenges.

A novel strategy for synthesizing shaped power pattern by using element rotation and phase optimization for a linear dipole array is presented. Element rotation can be considered as an array amplitude weighting technique, and it provides additional degrees of freedom in the pattern synthesis, but potentially increases the cross-polarization level (XPL). In order to obtain a desired copolarized shaped pattern with both the sidelobe level and XPL constrained, we simultaneously optimize all the rotation angles and excitation phases of all the dipole elements by applying the dynamic differential evolution algorithm. Two experiments for synthesizing flat-top and cosecant-squared patterns are conducted to validate the effectiveness and advantages of the proposed strategy.

A novel method of designing the aperture illumination of an N-element linear array of equispaced radiators to produce an approximation to a specified beam shape is described. The method essentially consists of selecting a ‘scanning function’, which itself is a physically realisable power pattern for the array. Convolution of the scanning function with the desired power pattern gives the physically realisable approximation to the desired pattern, here termed the ‘realised power pattern’. A suitable choice of scanning function can provide desirable properties such as freedom from ripple in the angular passband and extremely low sidelobes. In theory, there are 2(N−1) different illuminations which can produce the same power pattern, but in practice only a fraction of these correspond to illumination functions having significantly different shapes. The different illuminations produce different far-field phase patterns and guidance is given on how to select this phase pattern so as to exercise some control over the general shape of the aperture illumination.

This paper presents an efficient method for the pattern synthesis of linear antenna array based on the differential evolution algorithm. A number of examples are presented to demonstrate the various capabilities of the this method for different number of elements. The main objective of this paper is to achieve a set of current weights in order to steer the nulls in undesired directions (nulling the undesired signals) and steering the main beam towards the desired direction(direction of desired signal) by changing the phase excitation currents. The fitness function is obtained from maximization of error between actual pattern and desired pattern.

Methods are available for the independent synthesis of array excitations which provide either optimum sum or optimum difference pattern performance. In the paper a technique is described to effect the simultaneous synthesis of both sum and difference patterns of a linear antenna array which utilises sub-arraying to increase the number of degrees of freedom above that available with the usual two-section feed network. The particular approach (referred to here as excitation matching) attempts to obtain an optimum sum (difference) and a ‘best compromise’ difference (sum) pattern, by dealing directly with the independently optimum excitations and appropriately adjusting the sub-array weights.

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem