Phase-Only Control for Antenna Pattern Synthesis of Linear Arrays Using the Levenberg-Marquardt Algorithm

General Near Field Synthesis of Reflectarray Antennas for Their Use as Probes in Catr

“…This model is then employed in a near field Phase-Only Synthesis (POS) to improve the quiet zone generated by the reflectarray antenna. The chosen algorithm is the Levenberg-Marquardt (LMA), which has been effectively used in array synthesis with success [20][21][22][23][24][25][26][27], and it takes into account both amplitude and phase of the near field, since CATR requirements impose a maximum allowable ripple in both, making it a more challenging task than an amplitude-only synthesis. The optimization is performed in several near field planes, flattening the amplitude and phase, greatly improving the size of the quiet zone.…”

Systematic Framework for Reflectarray Synthesis Based on Phase Optimization

“…It defines the steps size to achieve the minimum, closer to the gradient descent direction. One of the most extended techniques to choose this parameter consists in starting with μ 0 proportional to the maximum value of diag (J T i • J i ) [18], and defining a real parameter β > 1, so that μ i+1 = μ i β or μ i+1 = μ i /β if the cost function increases or decreases, respectively, each iteration i [19]. The high number of variables in the current reflectarray problem requires an exhaustive control of μ i , so its increase is only allowed when the cost function decreases in more than five iterations consecutively, forcing a decrease every time F LM,i goes higher.…”

“…The high number of variables in the current reflectarray problem requires an exhaustive control of μ i , so its increase is only allowed when the cost function decreases in more than five iterations consecutively, forcing a decrease every time F LM,i goes higher. Note that μ i = 0 converts LM into the Gauss-Newton's method [19], easy to diverge in a nonlinear problem with a high number of unknowns, so this value must be disregarded.…”

“…Some well-known optimization and random search algorithms exist in the scientific literature able to solve this problem, such as Newton-Raphson (NR) [15], Genetic Algorithms [16], or Differential Evolution Algorithm [17], but LM has been chosen as a reasonable tradeoff between complexity and performance on synthesis tasks, due to its robustness in the resolution of nonlinear least squared problems [18]. Moreover, this method has been found useful in some synthesis problems, dealing with phase-only optimization [19], or magnitude and phase synthesis of the feeding weights [20] when it is applied to linear arrays. In this paper, using and adequate cost function, the method can be applied to a planar reflectarrays, subject to demanding full 2D requirements, such as the specifications of an antenna for an LMDS central station.…”

Smart Antenna Array Patterns Synthesis: Null Steering and Multi-User Beamforming by Phase Control

“…However, several challenges remain in the development of these adaptive systems. The techniques of placing nulls in the antenna patterns to suppress interference and the maximizing their gain in the direction of desired signal has received considerable attention in the past and still of great interest [4][5][6][7][8][9][10][11][12][13][14]. These techniques are very important in communication system, sonar, and radar applications for maximizing signal-to-interference ratio (or signal to interference and noise ratio) [11].…”