In this paper, the throughput performance of an ARQ scheme is analyzed with noisy feedback channel, in order to exactly analysis for performance of an ARQ scheme. An ARQ mechanism is presented by state diagram, and the throughput of an ARQ scheme is mathematically derived using generation function for a signal flow graph. The channel is modeled by the Nakagami-m fading channel which is distributed over far and wide, and the throughput performance of an ARQ scheme, which is applied in BPSK and BFSK systems, according to feedback gain and fading index m is analyzed through computer simulation. In the results, It is shown conformed that the throughput of an ARQ scheme decreased according to the increase of the noise for feedback channel, but it increased according to the increase of the feedback gain and fading index m. Also, it is shown that the throughput of an ARQ scheme using BPSK system is superior to BFSK system because of the difference of bit error probability between BPSK and BFSK systems.