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Application of power transformation and moments in time based UWB ranging

For ultra-wideband (UWB) ranging, TOA estimation with the energy detection (ED) receiver is to detect the energy sample that contains the first path (FP) signal in dense multipath. Threshold crossing (TC) is used frequently. However, it is difficult to determine the threshold. Some threshold setting methods are based on constant false alarm rate (CFAR) and the chi-squared distribution. However, the distribution is complicated. Moreover, it depends on the degree of freedom (DOF). If the DOF used is wrong, it will degrade the detection performance. The study bypasses the distribution. We first examine the distribution of the output of the ED receiver after power transformation. Based on the new characteristics of the transformed data and approximate distributions, we propose some practical TOA estimation methods. Similarly, the moments of the output of the ED receiver, such as the second or one-third order moments, are also analysed and used. The proposed methods are easy to implement and can achieve about the same ranging performance with methods based on the chi-squared distribution. We provide both theoretical and simulation results to prove their effectiveness.