We optimized the clock recovery algorithm and forward error correction code to address the challenges associated with an autonomous clock source and intricate transmission channel in a real-time, low-power-consumption scenario for low-orbit satellite laser communication. The successful implementation of this optimization includes an all-digital clock recovery algorithm and a low-density parity check (LDPC) compilation code, demonstrating minimal resource consumption, low latency, and power consumption of only 0.129 W and 1.199 W, respectively. Subsequently, we constructed a desktop demonstration system that effectively showcases real-time spatial optical transmission using binary phase shift keying (BPSK) modulation and coherent detection at a communication rate of 1.024 Gbit/s. Notably, the clock error in this system is approximately 1.50 × 10^-4. This achievement reflects a fine balance between performance and efficiency in the context of low-orbit satellite laser communication.