Multi-carrier HF radar is making full use of cleared band to achieve range high resolution. Due to randomness of high frequency silence band, the paper adopts a multicarrier phase-coded (MCPC) signal structure to restrain the waveform spectra. We deduced the echo expression of the random discontinuous spectra MCPC signal, and analyzed the signal performance in different SNR and Doppler. Based on the fast Fourier transform we proposed the frame of this waveform processing. For the discontinuous spectra signal generating a great number of higher peak sidelobe level (PSL) problem, we design objective function, using convex optimization method to solve least square (LS) filter coefficients iteratively and filter the range dimension suppression the side lobes. It is better solving the poor resolution of HF radar, and the method is easy to engineering implementation.