Gaussian integers and interleaved rank codes for space–time block codes

This paper presents the design of space–time block codes (STBCs) over maximum rank distance (MRD) codes, energy-efficient STBCs, STBCs using interleaved-MRD codes, the use of Gaussian integers for STBCs modulation, and Gabidulin's decoding algorithm for decoding STBCs. The design fundamentals of STBCs using MRD codes are firstly put forward for different number of transmit antennas. Extension finite fields (Galois fields) are used to design these linear block codes. Afterward, a comparative study of MRD-based STBCs with corresponding orthogonal and quasi-orthogonal codes is also included in the paper. The simulation results show that rank codes, for any number of transmit antennas, exhibit diversity gain at full rate contrary to orthogonal codes, which give diversity gain at full rate only for two transmit antennas case. Secondly, an energy-efficient MRD-STBC is proposed, which outperforms orthogonal STBC at least for 2 × 1 antenna system. Thirdly, interleaved-MRD codes are used to construct higher-order transmit antenna systems. Using interleaved-MRD codes further reduces the complexity (compared with normal MRD codes) of the decoding algorithm. Fourthly, the use of Gaussian integers is utilized in mapping MRD-based STBCs to complex constellations. Furthermore, it is described how an efficient and computationally less complex Gabidulin's decoding algorithm can be exploited for decoding complex MRD-STBCs. The decoding results have been compared against hard-decision maximum likelihood decoding. Under this decoding scheme, MRD-STBCs have been shown to be potential candidate for higher transmit antenna systems as the decoding complexity of Gabidulin's algorithm is far less, and its performance for decoding MRD-STBCs is somewhat reasonable.