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This paper presents a new predistortion linearization scheme for single-sideband mixers to be used for removing unwanted harmonics and intermodulation products of the digital IF in an heterodyne transmitter. The proposed algorithm, called poly-harmonic predistortion linearization, relies on an orthogonal expansion in the frequency domain of the nonlinearities for the mixer modeling. It takes into account memory effects that are piece-wise quasi-memoryless and enables the independent cancellation of unwanted spurious sidebands of the digital IF harmonics. The poly-harmonic predistortion linearization scheme for the weak-nonlinear regime was implemented in a field-programmable gate array and experimentally investigated for the linearization of a four-path polyphase single-sideband upconverter. The ability of the poly-harmonic predistortion algorithm to linearize the four-path polyphase mixer for input signals with high envelope fluctuation is demonstrated. -70-dBc/-62-dBc/-60-dBc spurious rejection and 18-dB/10-dB/8-dB linearization improvement of the third-order distortions are achieved for a two-tone RF signal, a 64-tone 10-MHz bandwidth multisine signal and orthogonal frequency-division multiplexing signal, respectively. The combination of the polyphase multipath technique and the poly-harmonic predistortion linearization technique offers an attractive filterless approach for the development of multimode broadband software-defined radio.