In this paper, we propose a method for designing a set of pulses whose spectrum is efficiently contained in amplitude and bandwidth. Because these pulses are derived from and have shapes that are either equal or similar to the Hermite pulses, we name our proposed transmit pulses as spectrally efficient Hermite pulses. Given that the proposed set of pulses does not constitute an orthonormal one, we also propose a set of receive templates which permit orthonormal detection of the incoming signals at the receiver. The importance of our proposal is in the potential implementation of M-ary pulse shape modulation systems, for ultra wideband communications, with sets of pulses that are efficiently contained within a specific bandwidth and limited to a certain amplitude.

In this paper we present a novel method for improving RAKE receiver reception in UWB systems. Due to the fact that practical pulses that can be produced for UWB-IR (Ultra Wideband-Impulse Radio) may occupy a longer time than the typical multipath resolution of the actual UWB channel, multiple channel components may arrive within this typical pulse width. Performance degradation may occur due to the resulting intrapulse (overlapping received pulses) interference. We here propose an adaptive, pilot aided RAKE receiver for UWB communications in the multipath environment. The proposed system estimates the actual received signal with intrapulse interference in each RAKE finger using projections onto a Hadamard-Hermite subspace. By exploiting the orthogonality of this subspace it is possible to decompose the received signal so as to better match the template waveform and reduce the effects of intrapulse interference. By using the projections onto this subspace, the dimension of the received signal is effectively increased allowing for adaptive correlator template outputs. RAKE receivers based on this proposal are designed which show significant performance improvement and require less fingers to achieve required performance than their conventional counterparts.