Synthesis of a sparse linear array with multiple simultaneous frequency-invariant focused beams

Abstract

As we all know, in broadband arrays situation, the beam width would narrow down with the increasing of frequency, which means the signal spectrum would be distorted in the interested frequency domain. Frequency-invariant beam pattern (FIBP) is the one whose amplitude keep almost constant in the specified range. For the superiority of the FIBP, quantities of work have been done recent years, however, almost all of these works require a large number of elements to get frequency invariant (FI) characteristics in the required mainlobe region. We now propose a new method to synthesize a frequency-invariant multi-beam pattern with space-frequency nulls, in which we can save the element number as many as possible. Besides, the pattern with multiple simultaneous FI focused beam which means radiating multiple beams at the same time, would be helpful in element reduction and system cost reduction. In order to get the desired performance, we provide multiple constraints to control the FI property and sidelobe level respectively, such as the spatial response variation (SRV) constraint, the sidelobe constraint and the look-direction constraint. We apply the iterative second-order cone programming (SOCP) along with the reweighted l 1 -norm optimization here to simplify the problem as to minimize the effective filters in filter-and-sum structure. We carry out two examples to validate the effectiveness and advantages of the proposed method. In the first example, we construct multiple FI focused beam patterns (7-beam, 11-beam and 15 beam) and compare the results with those obtained by the methods in literature [1] and [2]. Besides good FI property and exact sidelobe control, results show that the new method performs better in element reduction. In the second example, we construct an 11-beam FI focused pattern with a space-frequency null to make the referred pattern more adaptive to real situation. The results show that not only can the element saving keep good but also can the null reach the desired level (−50 dB) at least.