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Transmitted reference (TR) systems have recently been proposed for ultra wideband (UWB) communications. They considerably simplify synchronization and channel estimation, which are known to be difficult problems in UWB communications. We extend existing receivers for TR-UWB systems by replacing the correlation operation by a linear combination of specific parts of the correlation and weighting the parts that have a small noise contribution more than parts that have a large noise contribution. This turns out to improve the performance considerably.