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This paper derives optimal receiver structures for an ultra-wideband transmitted reference (UWB TR) system in multipath environments, based on the average likelihood ratio test (ALRT) with Rayleigh or lognormal path strength models. Several suboptimal receivers are obtained by either applying an approximation to the log-likelihood function without any specific channel statistical models or by approximating two ALRT optimal receiver structures. It is shown that the generalized likelihood ratio test optimal receiver is one of the suboptimal receiver structures in the ALRT sense. Average bit error probabilities of ALRT receivers are evaluated. Results show that ALRT optimal and suboptimal receivers derived from Rayleigh and lognormal models can perform equally well in each other's environments. This paper also investigates ad hoc cross-correlation receivers in detail, and discusses the equivalence between cross-correlation receivers and one theoretically derived ALRT suboptimal receiver. Results show that the noise × noise term in a cross-correlation receiver can be modeled quite accurately by a Gaussian random variable when the noise time×bandwidth product is large, and cross-correlation receivers are suboptimal structures which have worse performance than ALRT receivers.