A proposal for toeplitz matrix calculations
Studies in Applied Mathematics
Digital Transmission Engineering (IEEE Series on Digital & Mobile Communication)
Digital Transmission Engineering (IEEE Series on Digital & Mobile Communication)
Spectral Properties of Banded Toeplitz Matrices
Spectral Properties of Banded Toeplitz Matrices
Toeplitz and circulant matrices: a review
Communications and Information Theory
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
Design of Spectrally Efficient Hermite Pulses for PSM UWB Communications
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Achievable information rates of M-ary PPM impulse radio for UWB channels and rake reception
IEEE Transactions on Communications
IEEE Transactions on Signal Processing
Design of orthogonal pulse shapes for communications viasemidefinite programming
IEEE Transactions on Signal Processing
Optimal waveform design for UWB radios
IEEE Transactions on Signal Processing - Part I
The wavelet transform, time-frequency localization and signal analysis
IEEE Transactions on Information Theory
Information rates of photon-limited overlapping pulse position modulation channels
IEEE Transactions on Information Theory
On the convergence of the inverses of Toeplitz matrices and its applications
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Spectral shaping of UWB signals for time-hopping impulse radio
IEEE Journal on Selected Areas in Communications - Part 1
| Hi-index | 0.08 |
In this paper we consider the design of spectrally efficient time-limited pulses for ultra-wideband (UWB) systems using an overlapping pulse position modulation scheme. For this we investigate an orthogonalization method, which was developed in 1950 by Lowdin [1,2]. Our objective is to obtain a set of N orthogonal (Lowdin) pulses, which remain time-limited and spectrally efficient for UWB systems, from a set of N equidistant translates of a time-limited optimal spectral designed UWB pulse. We derive an approximate Lowdin orthogonalization (ALO) by using circulant approximations for the Gram matrix to obtain a practical filter implementation as a tapped-delay-line [7]. We show that the centered ALO and Lowdin pulses converge pointwise to the same square-root Nyquist pulse as N tends to infinity. The set of translates of the square-root Nyquist pulse forms an orthonormal basis for the shift-invariant-space generated by the initial spectral optimal pulse. The ALO transformation provides a closed-form approximation of the Lowdin transformation, which can be implemented in an analog fashion without the need of analog to digital conversions. Furthermore, we investigate the interplay between the optimization and the orthogonalization procedure by using methods from the theory of shift-invariant-spaces. Finally we relate our results to wavelet and frame theory.