Sparse Multi-carrier Frequency Diverse Array Transmit Beampattern Optimization

Frequency diverse array (FDA) has been extensively studied due to its unique range-dependent characteristics. To obtain an enhanced transmit beampattern, the multi-carrier technique, which applies multiple carrier frequencies on each antenna element, has been employed in many FDA schemes. However, as the number of antenna elements increases, the computational complexity and cost of the FDA system using the multi-carrier technique also become higher. In order to alleviate this issue, a sparse multi-carrier FDA (MCFDA) beampattern synthesis algorithm is proposed in this paper. We first establish a cost function that minimizes the difference between the designed and desired radiation parameters. Then the modified genetic algorithm (MGA) is used to solve this global optimization problem since the cost function is nonlinear and has multiple local minima. Numerical simulation results demonstrate that the proposed algorithm can save about 50% of the antenna elements compared to the existing same aperture-sized full uniform FDA beampattern synthesis methods, while generating a dot-shaped beampattern with a slightly deteriorating sidelobe level.