Pulse autocorrelation binary Barker has a maximum sidelobe level equal, .

Definition 1.

Binary sequences that allow for side-lobe level, although not satisfying the Barker code, but, nevertheless, which is globally optimal (i.e., having the minimum possible value of maximum modulus sidelobe for a given N), called optimal sequences with minimum sidelobe (or MPS sequences ) (from minimum peak sidelobe).

In this sense, the Barker codes should be viewed as a form of MPS sequences with sidelobe . Other sequences have MPS sidelobe pulse autocorrelation with values

Definition 2.

The synthesis problem of optimal binary sequences by minimax criterion formulated as follows. For a given length N binary sequence to find the minimum possible value of side lobe level provided that each sample pulse ACF discrete sequence satisfies


Select subcategory:

  • Barker Codes (PSL-1)
  • Minimum peak sidelobe sequences (PSL-2)
  • Minimum peak sidelobe sequences (PSL-3)
  • Minimum peak sidelobe sequences (PSL-4)
  • Minimum peak sidelobe sequences (PSL-5)

  • 1. Свердлик М.Б. Оптимальные дискретные сигналы. — М.: Сов. радио, 1975, 200 с.

    2. Гантмахер В.Е., Быстров Н.Е., Чеботарев Д.В. }Шумоподобные сигналы. Анализ, синтез, обработка. — Спб.: Наука и техника, 2005, 400 с.

    3. Turyn R. Sequences with small correlation. Error correcting codes. — New York, John Wiley and Sones, 1968.

    4. Lindner J. Binary sequences up to length 40 with best possible autocorrelation function//Electronics Letters, 16 October 1975, V. 11, № 21, p. 507.

    5. Cohen M.N., Baden J.M., Cohen P.E. Biphase codes with minimum peak sidelobes// Proceedings of the IEEE National Radar Conference, 1989, pp. 62–66.

    6. Cohen M.N., Fox M.R., Baden J.M. Minimum peak sidelobes pulse compression codes// Proceedings of the IEEE International Radar Conference. — Arlington, VA, May 1990, pp. 633–638.

    7. Elders-Boll H., Schotten H., Busboom A. A comparative study of optimization methods for the synthesis of binary sequences with good correlation properties// In 5th IEEE Symposium on Communication and Vehicular Technology in the Benelux/ IEEE, 1997, pp. 24–31.

    8. Coxson G.E., Hirschel A., Cohen M.N. New results on minimum-PSL binary codes, Proceedings of the 2001 IEEE Radar Conference. — Atlanta, GA, May 2001, pp. 153–156.

    9. Coxson G.E., Russo J. Efficient exhaustive search for optimal-peak-sidelobe binary codes// IEEE Trans. Aerospace and Electron. Systems, 2005, V. 41, pp. 302–308.

    10. Levanon N., Mozeson E. Radar Signals. — John Wiley\& Sons, Chichester, 2005.

    11. C.J.Nunn, G.E.Coxson. Best-Known Autocorrelation Peak Side Levels for Binary Codes of Length 71 to 105// IEEE Trans. On Aerospace and Electronic Systems, Vol.44, No.1, 2008, pp.392-395.