On the robustness of algebraic STBCs to coefficient quantization

In this paper, we study the robustness of high-rate algebraic space-time block codes (STBCs) to coefficient quantization (CQ) at the transmitter in 2 × 2 MIMO fading channels. In particular, we investigate the impact of CQ on the bit error rates of the Golden code and the Silver code with M-QAM constellations. We assume infinite-precision operations at the receiver. Towards generating the matrix codewords, we find the minimum number of bits needed to represent and perform the arithmetic operations such that the finite-precision versions of these codes provide BER close to their infinite-precision counterparts. We show that the Golden code and the Silver code suffer very slight degradation in the BER performance so long as at least 7-bits and 6-bits are used for 4-QAM constellations, respectively. Also, both codes are shown to need a minimum of 8-bits for 16-QAM constellation. Finally, we propose an example of a full-rate, full-diversity STBC which can be encoded with as low as 3-bits for 4-QAM constellation. The advantages of the proposed code are also discussed.