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We propose and demonstrate a photonic approach for frequency multiplication of microwave signals based on the self-induced nonlinear polarization rotation arising in semiconductor optical amplifiers (SOAs). The proposed frequency doubling module consists of a Mach-Zehnder interferometer and an SOA. A double or quadruple time of the microwave frequency can be achieved in the optical domain using one or two cascaded frequency doubling modules. The experimental results show that, with an original microwave signal of 10 GHz, a 20- or 40-GHz microwave signal with high spectral purity and stability can be generated over the entire C-band (1520-1560 nm). The suppression of undesired lower order harmonic frequencies exceeds 25 dB, and the generated microwave signal has a carrier-to-noise ratio of 50 dB.