At present, in the first-generation and second-generation relay satellite systems applied in orbit in China, the tracking signal received by relay satellite antenna is the modulation signal with the code rate of 1Mbps~300Mbps sent by the user satellite. With the development of satellite communication system, part of high dynamic and low bit rate spread spectrum users put forward the demand for relay transmission. Based on the SNR analysis of 1 kbit/s ~ 300kbit/s low speed spread spectrum signal received by relay satellite, a synchronous demodulation scheme is proposed to capture and track the low speed spread spectrum KSA user signal and demodulate the error signal. In order to capture low speed spread spectrum signal in diagonal tracking system, a carrier frequency offset search algorithm based on FFT is proposed, which reduces the two-dimensional search of code phase-carrier frequency offset to one-dimensional search. The algorithm of signal tracking and Angle error signal extraction is introduced in detail. Finally, the proposed algorithm of Angle error signal demodulation is simulated and tested. The test results show that the proposed method is feasible and correct for relay satellite to capture and track Angle error signal of low speed spread spectrum user. In this paper, theoretical analysis and engineering practice are closely combined, and the research conclusions can be used as the basis for the signal acquisition and tracking and error signal demodulation method and parameter design of the third generation relay satellite system to be developed in China.