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For ultra-wideband (UWB) impulse radios, noncoherent energy detectors are motivated for their simple circuitry and effective capture of multipath energy. A major performance-degrading factor in energy detection is the noise floor, which is aggravated for low-duty-cycle UWB signals with a large time-bandwidth product. In this paper, weighted energy detection (WED) techniques are developed for effective noise suppression. The received signal is processed by a set of parallel integrators, each corresponding to a different integration time-window within a symbol period. The outputs of these integrators are weighted and linearly combined to generate decision statistics, while the weights are determined by the signal power collected from the corresponding integrators to improve the effective signal to noise ratio. The WED principle is applied to all phases of receiver processing, including signal detection, timing synchronization and data demodulation. For each phase, the optimal linear detector parameters, including decision thresholds and weighting coefficients, are derived analytically. Simulations show that the proposed noncoherent WED receiver enhances the bit-error-rate performance compared to conventional energy detectors.