Signal space diversity (SSD) is a well-known technique providing excellent performance gain over fading channels. This paper investigates the system design of bit-interleaved coded modulation with iterative demodulation and SSD (BICM-ID-SSD). It demonstrates that within SSD the average mutual information (AMI) between the signal after rotated constellation mapping and that before the soft demapper varies with the rotation angle. Therefore, a new criterion for searching the optimal rotation angle by maximizing such AMI is proposed. Based on this criterion it is shown that the optimal rotation angle is not relevant to the labeling, and 45-degree is found to be the optimal or near optimal rotation angle for square quadrature amplitude modulation (QAM) at low to moderate code rates. Furthermore, the procedure of BICM-ID-SSD system design could be divided into two independent steps: 1) determining the optimal rotation angle based on the above criterion, and 2) choosing well-fitted labeling and outer channel code with the aid of extrinsic information transfer (EXIT) charts. Analysis and simulation results show that the proposed system exhibits a near-capacity performance, meanwhile being robust over both additive white Gaussian noise (AWGN) and Rayleigh fading channels.