Differential space-time modulation over frequency-selective channels

We present herein a new differential space-time-frequency (DSTF) modulation scheme for systems that are equipped with an arbitrary number of transmit antennas and operate in frequency-selective channels. The proposed DSTF modulator consists of a concatenating spectral encoder and differential encoder that offer full spatio-spectral diversity and significant coding gain. A unitary structure is imposed on the differential encoder to admit linear, decoupled maximum likelihood (ML) detection in space and time. Optimum criteria based on pairwise error probability analysis are developed for spectral encoder design. We introduce a class of spectral codes, namely, linear constellation decimation (LCD) codes, which are nonbinary block codes obtained by decimating a phase-shift-keying (PSK) constellation with a group of decimation factors that are co-prime with the constellation size. Since LCD codes encode across a minimally necessary set of subchannels for full diversity, they incur modest decoding complexity among all full-diversity codes. Numerical results are presented to illustrate the performance of the proposed DSTF modulation and coding scheme, which compares favorably with several existing differential space-time schemes in frequency-selective channels.