We present an inter-satellite coherent laser communication prototype system, highlighting a low complexity receiver with a simplified two independent real-valued (TIR) equalizer suitable for space laser communication scenarios. An extensive comparison of classical single complex-valued equalizer, 2×2 real-valued equalizer, TIR, and two dependent real-valued (TDR) equalizer is presented on the basis of equalization principles, algorithm performance, and computational complexity. The analysis results show that TIR equalizer has the advantages of low logic resource consumption in implemented on field programmable gate array (FPGA) and zero sensitivity penalty to combat I/Q gain imbalance and I/Q skew caused by device aging. The constant modulus algorithm-based TIR equalizer fits binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), or higher-order QAM modulation format, while the traditional complex-valued equalizer needs to customize the tap coefficient updating algorithm for different modulation formats. In addition, to show the feasibility of the proposed TIR equalizer-based coherent laser receiver as a promising candidate for forthcoming inter-satellite networks, we demonstrate single polarization (SP) on-line 2.5 GBaud data rate, QPSK and BPSK coherent transmissions using an FPGA-based transmitter and receiver prototype. Thanks to our proposed equalizer, the number of hardened multipliers is reduced by 47%, while no receiver sensitivity penalty is observed both in numerical simulation and in real-time FPGA experiment.