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Orthogonal pulse-shape modulation using Hermite pulses for ultra-wideband communications is reviewed. Closed-form expressions of cross-correlations among Hermite pulses and their corresponding transmit and receive waveforms are provided. These show that the pulses lose orthogonality at the receiver in the presence of differentiating antennas. Using these expressions, an algebraic model is established based on the projections of distorted receive waveforms onto the orthonormal basis given by the set of normalized orthogonal Hermite pulses. Using this new matrix model, a number of pulse-shape modulation schemes are analyzed and a novel orthogonal design is proposed. In the proposed orthogonal design, transmit waveforms are constructed as combinations of elementary Hermites with weighting coefficients derived by employing the Gram-Schmidt (QR.) factorization of the differentiating distortion model's matrix. The design ensures orthogonality of the vectors at the output of the receiver bank of correlators, without requiring compensation for the distortion introduced by the antennas. In addition, a new set of elementary Hermite Pulses is proposed which further enhances the performance of the new design while enabling a simplified hardware implementation.