Abstract: With the rapid development of internet and mobile communication, the higher and higher transmission rate is required. The transmission rate is one of important indicators for wireless communication network and the maximum transmission rate is decided by signal-to-noise ratio (SNR). In order to achieve the maximum expected rate, it is necessary to know the channel state information (CSI). Besides, bursty transmission can improve the reliability of the wireless transmission under low SNR. Since many systems have limited power, we should consider how to maximize transmission rate under the condition of power constraint. To this end, this paper investigates the expected rate with quantized feedback over a fading channel subject to power constraints. For systems with a short-term power constraint, we can derive an equality about channel gain by using a period power. And then, we obtain the optimum quantization schemes with bursty transmission. For systems with a long-term power constraint, we use alternating minimization ideas to find the optimization solutions, which includes two parts:In the first part, system power is fixed, then we analyze the change of channel gain and find the optimization scheme. This case is similar to short-term power constraint. In the second part, channel gain is fixed, then we analysis the power allocation of parallel channel. For this case, we propose a two-step power allocation method based on the traditional water-filling followed by a water adjustment step, which can achieve the maximum expected rate. From the analysis and simulation results, it can be known that the proposed algorithm based on traditional water-filling can achieve a higher transmission rate than traditional water-filling algorithm under the same power constraint. Hence, the proposed algorithm has better performance for improving the transmission rate.