Peak to average power ratio reduction of space-time codes that achieve diversity-multiplexing gain tradeoff

A result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, known as the diversity-multiplexing gain (D-MG) tradeoff. The quest for space-time codes that achieve D-MG tradeoff has generated numerous works. However, these space-time codes generally result in a pretty high peak to average power ratio (PAR) value on each antenna. In this paper, we propose two general ways to reduce PAR without affecting code structures and without any side information being transmitted. Therefore, the modified space-time codes still achieve the D-MG tradeoff. The two methods are both based on constellation shaping. The first method is similar to the method proposed by Kwok except we employ the Hermite normal form (HNF) decomposition instead of the Smith normal form (SNF); the second one takes the idea of integer reversible mapping. Both techniques lead to an asymptotical PAR value equal to 3 as the constellation size becomes large. Sphere decoding is performed to verify that the proposed PAR reduction methods do not affect the performance of space-time codes.