Optimization And Simulation Of Cosecant-Squared Beam For Linear Array Antennas

In the field of wireless communications,in order to make the antenna system have high gain or obtain specific radiation characteristics,it is often necessary to use array antennas.Since the cosecant-squared beam can obtain the same radiation power at different distances from the antenna,it is widely used in base stations in personal mobile communications.In this thesis,particle swarm optimization(PSO),an intelligent optimization algorithm,is mainly adopted to synthesize the shaped pattern of linear array antennas,and the cosecant-squared patterns with low ripple and low sidelobes are obtained.Firstly,the basic analysis theory of linear array antennas is introduced.For the linear array with half wavelength spacing,according to the definition of directivity(D),the formula for calculating the directivity of shaped pattern is deduced,and then the aperture efficiency(ηa)formula of the shaped pattern is given.For the traditional synthesis methods,Taylor’s method and Woodward-Lawson’s method are given to synthesize pencil beam and cosecant-squared beam,respectively.The pattern calculated by Woodward’s method is real,unique,and with definite zeros.The PSO algorithm is introduced in detail,including the principle,steps and the relevant parameters,and the accuracy of the algorithm is verified by four benchmark functions.The Taylor pattern is synthesized by the PSO algorithm,and the results are compared with those obtained by Taylor’s method,the correctness and effectiveness of PSO for array antennas pattern synthesis are further demonstrated.Then,the PSO algorithm is used to synthesis the cosecant-squared pattern of the array factor of the linear array.The fitness is determined by the two masks method,and the comprehensive results are compared with those of Woodward’s method.It can be seen that the PSO algorithm can constrain both the ripple(δA)and sidelobe level(SLL),a shaped pattern with lower δA and SLL is obtained.There are,however,zero fillings in the sidelobe area.In order to decrease the null depth of the pattern,a moving roots technique by combining PSO and Schelkunoff’s unit circle is proposed.By moving the position of the roots,the cosecant squared pattern with null depth is obtained.In the process of pattern synthesis,by computation,it is found that a variety of excitation sets can meet the same requirements of the target pattern.In order to discuss the multiple solutions of the pattern,the maximum beam direction,the number of minimums of the power pattern,SLL,δA constrains are added to the two masks method,and patterns with nearly the same shape are obtained.The equal sidelobe patterns of SLL=-20dB,SLL=-25dB,SLL=-30dB and dual equal sidelobes are synthesized respectively.It is found that 16 sets of excitation can achieve the nearly same target cosecant squared pattern,and the ηa and dynamic range ratio(DRR)corresponding to the excitation are also calculated respectively.It can be seen that for the same SLL,ηa is approximately equal,and DRR changes from 3-7 times,when SLL is decreased,ηa decreased and DRR increased.For the pattern with dual equal sidelobes pattern(SLL=-25dB,-30dB),ηa and DRR are between the results of equal sidelobe patterns SLL=-25dB and SLL=-30dB.Finally,the influences of mutual coupling on the cosecant squared pattern are studied.A magneto-electric dipole(MED)is selected as an array element,and a 16 element linear array is simulated.An array with equal amplitude and in-phase excitation is simulated,the SLL is close to the theoretical value.The array patterns with SLL=-25dB equal sidelobes and dual equal sidelobes are compared with the array factor,the shape in the shaped area declines and SLL increases.The isolated element pattern is substituted as the element factor,and it is found that the simulation pattern and the target pattern is improved,but SLL still increases.Then the element factors of full array elements are extracted for calculation,it can be seen that the simulation pattern is basically consistent with the target pattern.In order to simplify the calculation,a mutual coupling compensation method based on the isolated element pattern is proposed.By compensating the excitation,the simulated pattern is close to the target pattern.Through the first compensation,the shape of the shaped area is basically consistent,the SLL increases,and the shape of the pattern is better consistent through the second compensation.