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Time-hopping ultra wideband (TH-UWB) and direct-sequence ultra wideband (DS-UWB) systems are among the standards proposed for UWB communications scenarios. A general unified mathematical approach has been proposed for calculating the bit error rate (BER) for both TH-UWB and DS-UWB systems in the presence of multiple-user interference and a strong narrow-band interference in a multi-path scenario. Unlike many other mathematical models that provide upper or lower bounds for BER, this model calculates the exact values for BER in given scenarios. A partial rake receiver has been chosen as the receiving terminal. The modified Saleh-Valenzuela channel model has been used in this analysis. The model can asses the effect of any given narrow-band interfering systems. For the purpose of simulation, the narrow-band interfering system used is a Wi-Max transceiver based on IEEE 802.16-2004 standard. The validity of the model has been checked by comparing the mathematical results with numerical values achieved trough simulation. It is important to notice that this method can simultaneously be applied to both TH-UWB and DS-UWB.