The signal detection algorithm is proposed for the energy detection based ultra wideband (UWB) receiver which utilizes the square law (SL) narrowband interference (NBI) mitigation technology to mitigate the narrowband interference. Because of the energy detection scheme, the decision statistic can be expressed as the sum of the squares of statistically independent Gauss variates in white Gaussian noise. When the signal is absent, the decision statistic obeys the central chisquare (χ2) distribution with the number of degrees of freedom equal to the twice of the timebandwidth product of the input before the integrator. When the useful signal exists, the decision statistic obeys the noncentral χ2 distribution with the same number of degrees of freedom and depends on the factor λ. λ is associated with system parameters, including the energy and bandwidth of the useful signal, the power spectral density and bandwith of the interference, and the power spectral density of the noise. The noncentral χ2 distribution can be converted to the central χ2 distribution by changing the threshold and the number of degrees of freedom. Numerical computations by MATLAB demonstrate the receiver operating characteristic (ROC) curves which represent the relationship between the probability of detection Qdand the probability of false alarm Q0. From the curves in the figures, we can see that the system parameters have close relationships with the detection performance, for example, when the bandwith of the system is changed, the probability of false alarm can remain unchanged, while the probability of detection can be changed to two times than the origal one. The results show that the desired detection performance can be achieved by changing system parameters.