6. Phase-Coded Pulse

  1. Nadav Levanon and
  2. Eli Mozeson

Published Online: 18 AUG 2004

DOI: 10.1002/0471663085.ch6

Radar Signals

Radar Signals

How to Cite

Levanon, N. and Mozeson, E. (2004) Phase-Coded Pulse, in Radar Signals, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471663085.ch6

Publication History

  1. Published Online: 18 AUG 2004
  2. Published Print: 9 JUL 2004

ISBN Information

Print ISBN: 9780471473787

Online ISBN: 9780471663089



  • radar;
  • pulse compression;
  • phase codes;
  • autocorrelation;
  • perfect codes;
  • Barker;
  • binary;
  • polyphase


Phase coding is one of the early methods for pulse compression. Existing designs of optimal phase codes are given. The mathematical theory behind many of the codes is also provided. The criteria for selecting a specific code are the resolution properties of the resulting waveform and the ease with which the system can be implemented. The different examples are accompanied by various plots showing the shape of the ambiguity function, correlation function, and frequency spectrum.

The codes covered in the chapter include:

  • The well known binary Barker codes, higher length binary minimum peak sidelobe codes (tabulated codes are given up to a length of 69), nested codes and polyphase Barker codes (tabulated up to a length of 45).

  • Wide variety of perfect periodic correlation codes including Frank code and other chirplike codes such as Zadoff-Chu code, P1, P2, P3, P4 and PX codes. The text also proves many interesting properties of the different codes.

  • Golomb code (based on the theory of cyclic difference sets).

  • P(n, k) code (based on the phase history of a non-linear FM pulse).

  • Asymptotically perfect codes such as m-sequences (based on the mathematics of Galois fields).

  • Ipatov code.

  • Huffman code.

The chapter also describes methods for optimizing the reference filter for sidelobe suppression (using simple matrix algebra) and using biphase-to-quadriphase (BTQ) transform or a Gaussian-windowed sinc chip for lowering the transmitted waveform bandwidth.