The application of a fractionally sampled autocorrelation receiver (AcR) is proposed for the demodulation of transmitted-reference (TR) signals, to simplify synchronization and suppress nonlinear intra-symbol-interference and inter-symbol-interference (ISI) by means of linear weighting. A system model is presented for the TR system and its statistical properties are derived, taking into account both noise and ISI. The weighting coefficients are computed in closed form and a method is presented to compute the bit error probability. Multiple ultra-wideband TR systems are compared, which differ with respect to correlation lag, bandwidth, sampling rate, and bit rate. In the absence of ISI, a 250-MHz bandwidth system outperforms the larger bandwidth systems. On the other hand, the larger bandwidth systems are found to be inherently less sensitive to ISI. Furthermore, increasing the fractional sampling ratio is shown to enable the AcR to equalize more (nonlinear) ISI.