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Transmitted reference (TR) modulation schemes, initially proposed for spread-spectrum systems in the 1920s, have regained popularity in the context of ultra-wideband (UWB) communications, where accurate channel estimation is a challenging task. By exploiting the statistics of the received signals, optimal and suboptimal correlation receivers for a single-user ultra-wideband communication system have been previously proposed. Performance analysis of these schemes is investigated and verified via simulations. UWB systems are likely to be employed in wireless indoor environments with different channel characteristics for different locations. Thus, the length of the integration interval is an important design parameter with respect to the achievable performance. An optimization of the length of the integration interval with respect to the effective SNR of the decision variable is proposed and simulation results reveal that optimizing the effective SNR provides significant performance improvements.