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In this paper we have presented the results of initial research into new switching and sub-arraying schemes for time-modulated antenna arrays. Conventional time-modulated arrays employ switching schemes in which each element of the array has a common start time and an switch-off time which varies according to a prescribed amplitude taper. In this paper we have examined switching strategies in which the element dasiaswitch-onpsila time can be arbitrary. This approach introduces an extra design variable and can be used to modify the sidelobe pattern of the array pattern at harmonic frequencies. In particular we have shown that relatively simple switching schemes can be used to generate a boresight null at harmonic frequencies.