Described embodiments provide sidelobe cancellation for Simultaneous Transmit and Receive systems. The sidelobe cancellation system includes an array having a primary aperture and an auxiliary array. The auxiliary array includes a plurality of antenna elements disposed adjacent to at least one side of the primary aperture. Each element of the auxiliary array is coupled to a variable attenuator, a variable phase shifter or a variable true time delay unit. A controller tunes the auxiliary array to cancel sidelobes of the primary aperture by adaptively selecting an attenuation value of the variable attenuator, a phase shift value of the variable phase shifter and a time delay value of the variable true time delay unit for each element of the auxiliary array. The auxiliary array operates as an adaptive finite-impulse response (FIR) filter with each antenna element of the auxiliary array operating as an adaptive tap of the adaptive FIR filter.