Radar Precision And Resolution

RADAR PRECISION AND RESOLUTION G. J. A. Bird, C.Eng .. M.I.E.R.E. EMI Electronics Limited, Wells. Somerset PENTECH PRESS LONDON © G. 1. A. Rird. 1974 First Published 1974 Pentech Press Limited: London 8 John Street, wei N 2HY ISBN 07273 1801 2 Printed in England by The Whitefriars Press Ltd., London and Tonbridge PREFACE This book was w r i t t e n t o h e l p practISIng enginee r s, and s t u d e n t s o f r a d a r t h e o ry, t o u n d e r s t a n d h ow unce r t a i n t y fun c t i o n t ec hn i q u e s c an be used t o analy se the p e r fo rmanc e o f rada r system s . It is comm o n fo r mode r n systems t o employ sophist ic a t ed m o dul a t i o n, a n d t h e i r chara c t e ristics are n o t always apparen t from a n i n t u i t i ve t r e a t me n t . Engi ne e r s must h ave c o n fidence i n m a t h em a t ic al t e c h n iques (and kn owledge o f any lim i t a t ions) if they are to apply t h em t o new p rob l e m s . It is the a u t ho r ' s opinion that t h i s c o n fidence is best i n s p i re d b y s t ressing b a s i c principles and by giving t h e proofs o f all mathem a t i c al resu l t s, the reby establ ishing t h e c o n d i t i o n s nece ssa ry for t h e i r vali d i t y . This philosophy has b e e n adopt e d i n w r i t i ng t h e book. To facilit a t e a fi rst reading, t h e c o n c l u sions a n d discussion usually precede the de t ailed m a t h emat i c s; t h i s a l so m akes it easy to u se the book for reference purpose s . The book h as b e e n d i v i d e d i n t o t wo part s . Chapt e rs 1 t o 5 cover t h e r a d a r t h e o r y and i nclude nume rous r e fe r e nces t o Ch aptErs 6 and 7 which p rovide a firm fo u n d a t i o n of t h e unde rlying t ra nsfo r m theory . It is sugge s t e d t hat the reade r may l i k e to c o n c e n t r a t e i n i t i ally on Cha p t e r 1, fol lowe d by S e c t ions 4.1, 4.2, 4.6 and Chap t e r 5. This -procedure will acq u a in t h i m w i t h t he significance of the u n c e rt a i n t y fun c t io n a n d h o w i t c an be u s e d t o divi d e r a d a r receivers i n t o t w o cl asses-m a t c h ed fil t e r receive rs and Four i e r t r a nsform receivers . The th e ory is c onsolidat e d in Chapt e r 5 b y ap ply ing the re sult s t o two practical m o d u l ati o n wave forms; the reader should then be in a po s i tion to understand the more advanced resu l t s given i n the established literature . The second part of the b oo k provides the m athem a ti cal b a c k gro u n d to Chapt ers 1 to 5 . Chapter 6 de als with t h e rel a t i o n s hip be tween Lapl ace and Fourier transforms . The discrete Fourier transform (OFT) is also discussed and it is shown how two OFT theorems lead to the fast Fourier transform ( F FT) process. Chapter 7 covers the Hilbert transform and complex analytic signals. The author has always found 'engineering' treatments of this lat ter sub ject t o be particularly unconvincing-it is hoped that the reader will find the present treatment t o b e much more satisfactory. The author has fou nd Part 2 to be a useful reference source when working in other fields of signal processing. The summary of the main notation in Appendix 5 is also useful in this respect. Preface The fi rst d raft of this book was written as an inte rnal report for the Wells laboratories of EMI Elect ronics L t d . The mate rial has also been used as the b asi s of a series of aft e r-hours lectures t o the au thor's coll eagues. The au thor would like to th ank EMI Electronics L t d. for permission t o publ ish and a l so his coll eagues for m a ny helpful di scussion s. G. J. A. Bi rd CONTENTS Preface PART l. RA D A R THEORY I. THE RADAR UNCERTAINTY FUNCTION 1.1 1.2 1.3 1.4 1.5 2.