LLR based BER analysis of orthogonal STBCs using QAM on Rayleigh fading channels

We derive analytical expressions for the bit error rate (BER) of space-time block codes (STBC) from complex orthogonal designs (COD) with quadrature amplitude modulation (QAM) on Rayleigh fading channels. We take a bit log-likelihood ratio (LLR) based approach to derive the BER expressions. We first derive the LLRs for the various bits forming the QAM symbol and use these LLRs to derive analytical expressions for the error rate of the individual bits forming the QAM symbol and hence the average BER of the system. The approach presented in this paper can be used in the BER analysis of any STBC from COD with linear processing, for any value of M in a M-QAM system. Here, we present the BER analysis and results for a 16-QAM system with i) (2-Tx, L-Rx) antennas using Alamouti code (rate-1 STBC), ii) (3-Tx, L-Rx) antennas using a rate-1/2 STBC and iii) (5-Tx, L-Rx) antennas using a rate-7/11 STBC. The LLRs derived can also be used as soft inputs to decoders for various coded QAM schemes, including turbo coded QAM with space-time coding.