tailieunhanh - Báo cáo hóa học: "The Finite Heisenberg-Weyl Groups in Radar and Communications"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: The Finite Heisenberg-Weyl Groups in Radar and Communications | Hindawi Publishing Corporation EURASIP Journal on Applied Signal Processing Volume 2006 Article ID 85685 Pages 1-12 DOI ASP 2006 85685 The Finite Heisenberg-Weyl Groups in Radar and Communications S. D. Howard 1 A. R. Calderbank 2 and W. Moran3 1 Defence Science and Technology Organisation . Box 1500 Edinburgh 5111 Australia 2 Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA 3 Department of Electrical and Electronic Engineering The University of Melbourne Victoria 3010 Australia Received 6 April 2005 Accepted 18 April 2005 We investigate the theory of the finite Heisenberg-Weyl group in relation to the development of adaptive radar and to the construction of spreading sequences and error-correcting codes in communications. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate following recent developments in the theory of error-correcting codes that the finite Heisenberg-Weyl groups provide a unified basis for the construction of useful waveforms sequences for radar communications and the theory of error-correcting codes. Copyright 2006 S. D. Howard et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. INTRODUCTION The continuous Heisenberg-Weyl groups have a long history in physics 1 in the theory of radar detection 2 3 and in signal processing. However their discrete variants 4-6 have been scarcely noticed notable exceptions being 7 8 . Our interest in the finite Heisenberg-Weyl groups stems from an attempt to develop an information theory of radar that is flexible enough to be applied to modern radars. Such modern radars have the capacity to adaptively switch waveforms on a pulse-to-pulse basis and to retain coherence over many pulses .