  This paper analyzes Type I hybrid automatic repeat request (HARQ) over
time-correlated Rayleigh fading channels. Due to the presence of channel time
correlation, the analysis is more challenging than the prior analysis in the
literature. Outage probability is first derived as a weighted sum of joint CDF
of multiple independent Gamma random variables based on an infinite series
representation. A truncation method is proposed for efficient computation of
the outage probability and it is proved that the truncation error decreases
exponentially with the truncation order. Asymptotic outage probability is then
derived in a simple form, with which the impacts of packet transmission rate,
transmit power and channel time correlation could be decoupled and analyzed
clearly. Based on the asymptotic outage probability, diversity order of HARQ is
also analyzed. It is found that full diversity can be achieved even under time
correlated fading channels and the time correlation of the channels has
negative effect on the outage probability under high signal-to-noise ratio
(SNR). Finally, our analytical results are validated by MonteCarlo simulations.
