Abstract: Complex beams play important roles in wireless communications, radar, and satellites, and have attracted great interest in recent years. In light of this background, we present a fast and efficient approach to realize complex beams by using semidefinite relaxation (SDR) optimization and amplitude-phase digital coding metasurfaces. As the application examples of this approach, complex beam patterns with cosecant, flat-top, and double shapes are designed and verified using full-wave simulations and experimental measurements. The results show excellent main lobes and low-level side lobes and demonstrate the effectiveness of the approach. Compared with previous works, this approach can solve the complex beam-forming problem more rapidly and effectively. Therefore, the approach will be of great significance in the design of beam-forming systems in wireless applications.

利用幅相数字编码超表面和半定松弛实现复杂波束

[1]Balanis CA, 2011. Modern Antenna Handbook. John Wiley & Sons, Hoboken, USA.

[2]Bao L, Wu RY, Fu XJ, et al., 2019. Multi-beam forming and controls by metasurface with phase and amplitude modulations. IEEE Trans Antenn Propag, 67(10):6680-6685.

[3]Boyd S, Vandenberghe L, 2004. Convex Optimization. Cambridge University Press, Cambridge, USA.

[4]Bucci OM, D’Elia G, Mazzarella G, et al., 1994. Antenna pattern synthesis: a new general approach. Proc IEEE, 82(3):358-371.

[5]Bucci OM, Caccavale L, Isernia T, 2002. Optimal far-field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions. IEEE Trans Antenn Propag, 50(11):1539-1554.

[6]Caorsi S, Massa A, Pastorino M, et al., 2005. Optimization of the difference patterns for monopulse antennas by a hybrid real/integer-coded differential evolution method. IEEE Trans Antenn Propag, 53(1):372-376.

[7]Cui TJ, Liu S, Zhang L, 2017. Information metamaterials and metasurfaces. J Mater Chem C, 5(15):3644-3668.

[8]Dolph CL, 1946. A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level. Proc IRE, 34(6):335-348.

[9]Fazel M, Hindi H, Boyd S, 2004. Rank minimization and applications in system theory. Proc American Control Conf, p.3273-3278.

[10]Grant M, Boyd S, 2020. CVX: Matlab Software for Disciplined Convex Programming, Version 2.2. http://cvxr.com/cvx [Accessed on Jan. 30, 2020].

[11]Kajenski PJ, 2012. Phase only antenna pattern notching via a semidefinite programming relaxation. IEEE Trans Antenn Propag, 60(5):2562-2565.

[12]Khodier MM, Christodoulou CG, 2005. Linear array geometry synthesis with minimum sidelobe level and null control using particle swarm optimization. IEEE Trans Antenn propag, 53(8):2674-2679.

[13]Lebret H, Boyd S, 1997. Antenna array pattern synthesis via convex optimization. IEEE Trans Signal Process, 45(3):526-532.

[14]Li JY, Qi YX, Zhou SG, 2017. Shaped beam synthesis based on superposition principle and Taylor method. IEEE Trans Antenn Propag, 65(11):6157-6160.

[15]Liang JC, Cheng Q, Gao Y, et al., 2022. An angle-insensitive 3-bit reconfigurable intelligent surface. IEEE Trans Antenn Propag, 70(10):8798-8808.

[16]Lou Y, Jin L, Wang HM, et al., 2023. Multi-stream signals separation based on space-time-isomeric (spatio) array using metasurface antenna. Sci China Inform Sci, early access.

[17]Luo ZQ, Ma WK, So AMC, et al., 2010. Semidefinite relaxation of quadratic optimization problems. IEEE Signal Process Mag, 27(3):20-34.

[18]Nai SE, Ser W, Yu ZL, et al., 2010. Beampattern synthesis for linear and planar arrays with antenna selection by convex optimization. IEEE Trans Antenn Propag, 58(12):3923-3930.

[19]Palacios J, De Donno D, Widmer J, 2016. Lightweight and effective sector beam pattern synthesis with uniform linear antenna arrays. IEEE Antenn Wirel Propag Lett, 16:605-608.

[20]Shi L, Deng YK, Sun HF, et al., 2012. An improved real-coded genetic algorithm for the beam forming of spaceborne SAR. IEEE Trans Antenn Propag, 60(6):3034-3040.

[21]Strang G, 2023. Introduction to Linear Algebra. Wellesley-Cambridge Press, Wellesley MA, USA.

[22]Sun S, Ma HF, Gou Y, et al., 2023. Spin- and space-multiplexing metasurface for independent phase controls of quadruplex polarization channels. Adv Opt Mater, 11(3):2202275.

[23]Tsui KM, Chan SC, 2010. Pattern synthesis of narrowband conformal arrays using iterative second-order cone programming. IEEE Trans Antenn Propag, 58(6):1959-1970.

[24]Wang F, Balakrishnan V, Zhou PY, et al., 2003. Optimal array pattern synthesis using semidefinite programming. IEEE Trans Signal Process, 51(5):1172-1183.

[25]Wu JW, Wang ZX, Fang ZQ, et al., 2020. Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces. Adv Funct Mater, 30(39):2004144.

[26]Wu JW, Wang ZX, Zhang L, et al., 2021. Anisotropic metasurface holography in 3-D space with high resolution and efficiency. IEEE Trans Antenn Propag, 69(1):302-316.

[27]Wu JW, Wang ZX, Wu RY, et al., 2023. Simple and comprehensive strategy to synthesize Huygens metasurface antenna and verification. IIEEE Trans Antenn Propag, 71(8):6652-6666.

[28]Yang F, Yang SW, Chen YK, et al., 2018. Convex optimization of pencil beams through large-scale 4-D antenna arrays. IEEE Trans Antenn Propag, 66(7):3453-3462.