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In this paper, we consider the demodulation and equalization problem of differential impulse radio (IR) ultra-wideband (UWB) Systems with inter-symbol-interference (ISI). The differential IR UWB systems have been extensively discussed recently. The advantage of differential IR UWB systems include simple receiver frontend structure. One challenge in the demodulation and equalization of such systems with ISI is that the systems have a rather complex model. The input and output signals of the systems follow a second-order Volterra model. Furthermore, the noise at the output is data dependent. In this paper, we propose a reduced-complexity joint demodulation and equalization algorithm. The algorithm is based on reformulating the nearest neighborhood decoding problem into a mixed quadratic programming and utilizing a semi-definite relaxation. The numerical results show that the proposed demodulation and equalization algorithm has low computational complexity, and at the same time, has almost the same error probability performance compared with the maximal likelihood decoding algorithm.