Comprehensive study on a 2 × 2 full-rate and linear decoding complexity space–time block code

This paper presents a comprehensive study on the Full-Rate and Linear-Receiver (FRLR) STBC proposed as a newly coding scheme with the low decoding complexity for a 2×2 MIMO system. It is shown that the FRLR code suffers from the lack of the non-vanishing determinant (NVD) property that is a key parameter in designing a full-rate STBC with a good performance in higher data rates, across QAM constellation. To overcome this drawback, we show that the existence of the NVD feature for the FRLR code depends on the type of the modulation. In particular, it is analytically proved that the FRLR code fulfills the NVD property across the PAM constellation but not for the QAM scheme. Simulation results show that, at a BER equal to 10-4, utilising the PAM modulation for the FRLR-STBC, provides about 2 dB gain over a use of the QAM when the bandwidth efficiency is 6b/s/Hz. In addition, for the PAM constellation, the FRLR code significantly outperforms some existing full-rate STBCs. Finally, we utilise the moment generating function approach to derive an exact closed-form expression for the average error probability of the FRLR code with the BPSK modulation.