A differential ultra-wideband (UWB) receiver can mitigate the 50% loss in rate and power inherent to conventional transmitted reference (TR) systems, under the assumption that channel induced inter-pulse interference (IPI) is absent or negligible. Consequently, restrictions on minimum frame length and maximum achievable bit rate are imposed. Using orthogonal Walsh-Hadamard sequences to remove IPI at the receiver, we show that the no-IPI condition can be relaxed without penalty in error performance and a small increase in complexity, leading to higher data rates. Assuming that timing has been acquired, error performance of the novel UWB radio is evaluated analytically and via simulations. A multi-user version of the detector is also developed and its performance is compared with multi-user TR.