Efficient Mathematical Method to Suppress Sidelobes and Sidebands in Time-Modulated Linear Arrays

An efficient mathematical method is developed to design a time-modulated linear array (TMLA) with desired sidelobe and sideband levels with maximum achievable directivity. The array factor of the TMLA is represented in terms of a finite series of Chebyshev polynomials of the first and the third kind for the case of odd and even number of elements in the TMLA, respectively. Furthermore, it is shown that the positions of sidelobes can be obtained by only finding the roots of a polynomial generated by Chebyshev polynomials of the second or the fourth kind, respectively. In addition, by obtaining the accurate positions of all the sidelobes in terms of the switch- on durations of the TMLA array, it is possible to determine, accurately, the optimum regions of the switch- on durations that satisfy the desired specifications in the design. Finally, numeric simulations and comparison with the differential evolution method are performed to show the effectiveness of the proposed mathematical method.