  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.
