Abstract: To address the high computational complexity and the challenge of meeting real-time processing requirements in existing phase-coded waveform design algorithms against noise frequency-modulated jamming， this paper proposes an efficient optimization algorithm based on frequency-domain coordinate descent. First， the joint optimization objective function in the time domain is transformed into the frequency domain， establishing a frequency-domain optimization model for phase-coded waveforms. This transformation not only effectively circumvents the high computational cost associated with large-scale matrix operations in time-domain optimization but also simplifies the structure of the optimization problem， thereby facilitating subsequent algorithm design. Next， the Frequency-Domain Coordinate Descent Method （FCDM） is integrated with the Alternating Direction Method of Multipliers （ADMM） framework， resulting in the proposed ADMM-FCDM algorithm. This algorithm simplifies the complex high-dimensional optimization task by decomposing it into multiple independent single-variable optimization steps. By deriving closed-form solutions for the frequency-domain sequence elements of the waveform， the algorithm substantially reduces the computational load per iteration and significantly enhances global optimization efficiency. Furthermore， the Fast Fourier Transform （FFT） technique is incorporated to accelerate the ADMM-FCDM algorithm， resulting in the frequency-domain coordinate descent method with fast fourier transform under the ADMM framework （ADMM-FFT-FCDM）. The use of FFT significantly reduces the computational time required for transformations between the time and frequency domains， thereby further enhancing the algorithm’s overall efficiency. Simulation results demonstrate that， compared to existing methods， the proposed ADMM-FFT-FCDM algorithm exhibits significant improvements in computational speed while maintaining comparable radar detection performance and anti-jamming capabilities.