Performance analysis on conditional error ratio in HARQ transmission

In hybrid automatic repeat request (HARQ) process, a retransmission occurs on the condition that the first transmission failed. Multiple received packets are combined for detection at the receiver. Equivalent noise after combining is not additive Gaussian white noise and not independent on the transmitted signal. Unfortunately, the assumption of zero-mean-Gaussian and independent noise after combining is widely used in the analysis of HARQ, as well as other similar techniques. In this paper, conditional error ratio of the retransmission is accurately analyzed by taking the failure of the first transmission into account. Furthermore, approximate expressions of conditional error ratio are also presented for flexibility of analysis and application. Numerical results demonstrate that estimation error of the traditional estimation is much visible when channel quality of retransmission is worse than that of the first transmission.