Differential space-time modulation with LCD codes and APSK constellation

We present herein a new differential space-time modulation scheme using amplitude phase shift keying (APSK) symbols. The proposed scheme exploits space-time code matrices, each as a product of a phase matrix, which is diagonal and unitary, and an amplitude coefficient, which controls the total transmitted power. The phase matrix is cyclic with diagonal entries formed from the so-called linear constellation decimation (LCD) codes, which offer full spatial diversity and coding gain under the Rayleigh fading assumption, as well as flexibility in terms of trade-offs between spectral efficiency and diversity. The amplitude ratio of APSK is optimized by maximizing a minimum product distance of the transmitted code matrices. The proposed scheme results in truly APSK transmission (i.e., no constellation expansion), and can easily accommodate the case with more than two transmit antennas. For differential demodulation, we show that the maximum likelihood (ML) decoding of the amplitude coefficient and phase matrix is decoupled. As a result, the decoding complexity is only slightly more involved compared to that of a PSK based counterpart, viz., the conventional differential space-time modulation scheme using diagonal code matrices formed from PSK constellation. Numerical results show that the proposed APSK based scheme outperforms the PSK based scheme as the transmission rate increases.