A high-rate generalized coded delay diversity scheme and its diversity-multiplexing tradeoff

Multiple antennas can be used for increasing the amount of diversity (diversity gain) or increasing the data rate (the number of degrees of freedom or spatial multiplexing gain) in wireless communication. As quantified by Zheng and Tse, given a multiple input multiple output (MIMO) channel, both gains can, in fact, be simultaneously obtained, but there is a fundamental tradeoff (called the diversity-multiplexing tradeoff) between how much of each type of gain any coding scheme can extract. It is well known that space-time trellis codes (STTC) can be used to achieve full-diversity and better coding gain than space-time block codes (STBC). There have many STBC constructions, which achieve the diversity-multiplexing tradeoff, but to the best of our knowledge no such construction is proposed for the case of STTC. A delay diversity scheme used to construct STTC introduced in Tarokh et al. (2002) is known to achieve full-diversity, for any number of transmit antennas. In this paper, we show that the delay diversity scheme can achieve the optimal diversity-multiplexing tradeoff, only for one receive antenna. Then we propose a generalized construction of a high-rate generalized coded delay diversity scheme (HRGCDD). We show that the HRGCDD scheme meets both the extreme points (corresponding to zero diversity gain and zero multiplexing gain) of the optimal diversity-multiplexing tradeoff curve for any number of transmit and receive antennas. Also by using the HRGCDD scheme we construct STTC for 2 transmit antennas. Furthermore we also show that the new proposed STTC achieves the optimal diversity-multiplexing tradeoff for 2 transmit and 2 receive antennas by simulation.