Distributed radar can provide an efficient detection performance by accumulating signals from multiple widely separated radars. However, distributed radar systems usually face communication constraints, including bandwidth limitation, communication delay, packet loss, and bit error, which impede practical application. To the best of the authors' knowledge, investigating the distributed detection problem with joint consideration of the above constraints is still an unexplored topic. Consequently, this paper studies the target detection problem in distributed radar systems, and these constraints are simultaneously addressed. First, to mitigate the communication burden, the least squares quantization is considered, and a computationally efficient algorithm is proposed to calculate the quantization parameters, enabling low-bit transmission to a fusion center (FC). Second, by incorporating the communication constraints into the communication channels, we formulate the model of the received test statistics at the FC, which are shown as a function of the constraints. Finally, two detectors are developed based on the Neyman-Pearson and nonparametric fusion criteria, and theoretical performance analyses of both detectors are included. Simulation results indicate that the proposed algorithm can significantly improve the computational efficiency in solving quantization parameters, and compared to clairvoyant fusion, the proposed detectors with 3-bit quantization merely cause 0.12 dB signal-to-noise ratio loss.