BER analysis of QAM with transmit diversity in Rayleigh fading channels

In this paper, we present a log-likelihood ratio (LLR) based approach to analyze the bit error rate (BER) performance of quadrature amplitude modulation (QAM) on Rayleigh fading channels without and with transmit diversity. We derive LLRs for the individual bits forming a QAM symbol both on flat fading channels without diversity as well as on channels with transmit diversity using two transmit antennas (Alamouti's scheme) and multiple receive antennas. Using the LLRs of the individual bits forming the QAM symbol, we derive expressions for the probability of error for various bits in the QAM symbol, and hence the average BER. In addition to being used in the BER analysis, the LLRs derived can be used as soft inputs to decoders for various coded QAM schemes including turbo coded QAM with transmit diversity, as in high speed downlink packet access (HSDPA) in 3G.