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During the demodulation process of spread-spectrum telemetry signals, the computational load of acquisition operations is extremely large. Without the assistance of hardware peripherals, traditional CPU-based software demodulation devices struggle to achieve real-time acquisition and processing of spread-spectrum signals. This paper proposes a parallel architecture based on CPU + GPU to accelerate the PMF - FFT acquisition algorithm. By means of block compensation, the influence of pseudo-code Doppler on the despreading operation is eliminated. The overall process of the parallel PMF - FFT algorithm and the corresponding computational kernels for each step are designed and the algorithm verified through experiments. The experiments show that for spread-spectrum telemetry data with a sampling rate of 56 MHz, this algorithm can achieve real-time acquisition of spread-spectrum signals. It has an acceleration ratio of approximately 24 times compared with the serial computing method. It can effectively acquire spread-spectrum signals with different signal parameters and meet the corresponding signal-to-noise ratio requirements. The relevant parameters of the algorithm can be flexibly adjusted according to the parameters of the processed signals. Compared with hardware peripherals such as DSP and FPGA, it shows good scalability, which conforms to the development trend of software-based measurement and control.