A Comprehensive Study On the Full-Rate and Linear-Receiver Space-Time Block Code

This paper presents a comprehensive study on the Full-Rate and Linear-Receiver (FRLR) Space-Time Block Code (STBC) proposed as a newly coding scheme with the low decoding complexity of order O(M), for a 2× 2 Multiple-Input Multiple-Output (MIMO) system that uses a modulation scheme with cardinality M . It is shown numerically 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 Quadrature Amplitude Modulation (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 scheme. In particular, it is analytically proved that the FRLR code fulfills the NVD property across the Pulse Amplitude Modulation (PAM) constellation but not for the QAM scheme. We use the coding gain and the union bound with the exact pairwise error probability criteria as a pseudo global-local search to find the optimum parameters of the FRLR code for the PAM constellation. Simulation results show that, at a bit error rate equal to 10−4, utilizing the PAM modulation for the FRLR-STBC, provides about 0.5 dB gain over a use of the QAM modulation when the bandwidth efficiency is 4 b/s/Hz. Due to the existence of the NVD property across the PAM constellation, this gain grows up to 2 dB when the bandwidth efficiency increases to 6 b/s/Hz. In addition, for the PAM constellation, the FRLR code significantly outperforms some existing full-rate STBCs with a high computational decoding complexity. Finally, we utilize 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 as a function of the signal-to-noise ratio and the design parameters. S. S. Hosseini and S. Talebi are with the Department of Electrical Engineering, Shahid Bahonar University of Kerman, Iran (e-mails: [email protected], [email protected]). J. Abouei is with the Department of Electrical and Computer Engineering, Yazd University, Yazd, Iran, email: [email protected].