he calibration method of phased array seeker with the hantom-bit technology

Introduction Phased array seeker, a kind of advanced seeker, searches and tracks the target by controlling phases of units in the array ntenna. This avoids complicated servo control system and realizes bigger seeker probe diameter, thus increasing operating istance of the seeker, rapidity of scanning and tracking, as well as quick target tracking capacity. It has become an important esearch field of precision guidance [1–4]. To guarantee stability and reliability of the guiding system, phased array seeker ses digital phase shifter for beam control. Bits of the digital phase shifter determine the scanning beam step. More bits will ause smaller step, better scanning continuity and higher extraction accuracy of guidance signal. Phantom-bit technology ould improve scanning beam step accuracy of phased array seeker, but also will bring beam pointing errors [5,6]. In Ref. [7], obtaining of LOS of strap-down phased array seeker is calculated from inertial measurements of missile ttitude angle and beam angle. Obtaining error of LOS caused by beam pointing error will cause disturbance rejection rate, hus resulting in disturbance rejection rate parasitical loop in the guidance loop. This disturbance rejection rate parasitical oop will affect stability and accuracy of strap-down guidance system significantly. In strap-down phased array seeker, it mploys open-loop control between beam angle instruction to actual rotating beam angle. Such control accuracy is difficult o be guaranteed during flight and ground calibration is necessary to maintain accurate matching between beam-control ode and beam pointing. Therefore, studying distribution law of beam point error caused by phantom-bit technology is of mportant significance to calibration of phased array seeker as well as stability and accuracy of flight system. Some scholars have studied problems caused by pointing error of strap-down phased array seeker [6–8]. However, they id not make a deep analysis on causes of scale-factor errors. Researches on digital phase shift of phased array seeker mainly ocus on problems caused by quantization error of the digital phase shifter and corresponding solutions [9]. Researches on ∗ Corresponding author. E-mail address: duxiao.63@163.com (X. Du). http://dx.doi. org/10.1016/j.ijleo. 2016.05. 066 030-4026/© 2016 The Author(s). Published by Elsevier GmbH. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ icenses/by-nc-nd/4.0/). 7226 X. Du, Q. Xia / Optik 127 (2016) 7225–7234 Fig. 1. Phase shifter setting. phantom-bit technology emphasize on an effect of sidelobe quantization. However, only few researches on beam pointing error distribution brought by phased phantom-bit technology as well as existing problems have been reported yet [10]. This paper analyzed one of causes of beam pointing error. Considering the phantom-bit technology of digital phase shifter in phased array seeker, two phase calculation models (end-off approach and round-off approach) were established and beam pointing formula after the use of phantom-bit technology was derived. Phase error distribution law caused by different phantom bits under two models as well as corresponding beam pointing error distribution law and variation was analyzed. Moreover, it discussed effect of beam pointing error distribution changes caused by phantom-bit technology on ground calibration of phased array seeker, and proposed a calibration point selection method that takes beam-control code as an independent variable. Research results provide important theoretical supports to R&D of phased array seeker and phantom way selection as well as error calibration of phase shifter. 2. Phantom-bit technology With the phantom-bit technology, phased array seeker could achieve approximate performances of high-bit phase shifter by using low-bit phase shifter. Suppose that the actual bit of phase shifter is m and the phantom bit is b. Due to the use of phantom-bit technology (Fig. 1), the phase control computer will calculate (m + b) bits, while the digital phase shifter uses m-bit. Phase setting code is expressed by binary figure in control signal register and arithmetric unit. Logically, the control signal register and arithmetric unit are corresponding to the phase shifter from high bit. During phase shifter setting, low m-bit binary codes of the arithmetric unit will be eliminated, while high-bit binary codes will be sent to the phase shifter to finish unit phase setting. Low-bit binary codes are eliminated by end-off approach and round-off approach [1]. When the phantom-bit technology is not used, all phase-shift units in the phase shifter are real bit. Beam pointing of phased array could be calculated from Eq. (1): B theory = sin−1( 2 d B theory) (1) where —wavelength of radar signal; d—interval between antenna elements; B theory—phase difference between adjacent antenna elements. The in-array phase difference between adjacent antenna elements is a constant. When the phantom-bit technology is used, the phase difference between adjacent antenna elements is changeable due to the existence of the virtual phase shifter. Therefore, beam pointing under current phase shift command could not be calculated from Eq. (1). To acquire accurate beam pointing, this paper got the maximum value of phased array pattern function (2) through derivation: F( ) = N−1 ∑ n=0 ane j(n 2 d sin − n) (2) where —target angle ai—weight coefficient of each antenna element, ai = 1 in this paper; N—number of linear array antenna elements; = (2 d sin )/ —‘spatial phase difference’ between adjacent elements; n —phase shifting of antenna radiating elements of antenna beam pointing. X. Du, Q. Xia / Optik 127 (2016) 7225–7234 7227