Transmitted-reference (TR) signaling, in conjunction with an autocorrelation receiver (AcR), offers a low-complexity alternative to Rake reception. Due to its simplicity, there is renewed interest in TR signaling for ultrawide bandwidth (UWB) systems. To assess the performance of these systems, we develop an analytical framework based on the sampling expansion approach. In particular, we derive closed-form expression for the bit-error probability (BEP) of TR signaling with AcR that can be used to exploit multipath diversity inherent in wideband channels. We further extend our analysis to the BEP derivation of modified AcR with noise averaging. Our methodology does not require the Gaussian approximation and is applicable for any fading scenario, provided that the correlator output signal-to-noise ratio (SNR) can be characterized in terms of a characteristic function. We show that the validity of the conventional Gaussian approximation depends on the time-bandwidth product and the number of transmitted pulses per symbol. Our results enable the derivation of a computationally simple lower bound on the BEP of TR signaling with AcR. This lower bound allows us to obtain the SNR penalty associated with an AcR, as compared with All-Rake and Partial-Rake receivers.
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