In this paper, we propose a theoretical framework to analyze the performance of ultra wideband acquisition (UWB) system based on energy detection (ED) over IEEE 802.15.3a channel. The proposed framework enables to calculate probability density function (PDF) of square-sum of multipath components (MPCs) gain collected by receiver, and the averaged criteria. In particular, the expectation and variance of the sum variant characterized approximately by log-normal distribution are expressed in a closed form based on cluster point process. Moreover, the calculating methods of averaged criteria, through Markov chain model and signal flow graph, are clearly demonstrated for different applicable scenarios. The proposed framework is well consistent with simulation results with respect to each calculation method.