In this study, the application of information theory to describe radar measurement problems is investigated. In Shannon's information theory, mutual information is used to quantify the reduction in the a priori uncertainty of the transmitted message. Similarly, the authors define the spatial information in the phased-array radar as the mutual information between range, direction of arrival (DOA), scattering properties, and the received signal. Such information content is composed of two parts. The first part is range-DOA information. The theoretical expression and its asymptotic upper bound are presented in a single target scenario. It is concluded that the range information is independent of DOA information at high signal-to-noise ratio. The relationship between the upper bound and the Cramér-Rao bound is discussed. The second part is scattering information. The corresponding expression is formulated theoretically. Based on spatial information, the authors put forth a definition of entropy error (EE) to evaluate the estimation performance in the phased-array radar. Numerical simulation of the information content confirms their theoretical observations. The regularity of information change reflects the information acquisition efficiency of a radar system, providing guidance for system designers. Numerical results of EE are also presented to demonstrate its effectiveness as an evaluation index.

References

1. 1)
  - 23. Trees, Van, H.L.: ‘Optimum array processing: part IV of detection, estimation, and modulation theory’, in Detection, estimation, and modulation theory (John Wiley & Sons, NY, USA, 2002), pp. 491–501, Available at https://books.google.com/books?id=K5XJC\_fMMAwC.
2. 2)
  - 17. Zhao, L.C., Krishnaiah, P.R., Bai, Z.D.: ‘On detection of the number of signals when the noise covariance matrix is arbitrary’, J. Multivariate Anal., 1986, 20, (1), pp. 26–49. Available at http://www.sciencedirect.com/science/article/pii/0047259X86900187.
3. 3)
  - 2. Woodward, P.M.: ‘Information theory and the design of radar receivers’, Proc. IRE, 1951, 39, (12), pp. 1521–1524.
4. 4)
  - 12. Wax, M., Kailath, T.: ‘Detection of signals by information theoretic criteria’, IEEE Trans. Acoust. Speech Signal Process., 1985, 33, (2), pp. 387–392.
5. 5)
  - 5. Kanaya, F., Nakagawa, K.: ‘On the practical implication of mutual information for statistical decisionmaking’, IEEE Trans. Inf. Theory, 1991, 37, (4), pp. 1151–1156.
6. 6)
  - 9. Kay, S.: ‘Waveform design for multistatic radar detection’, IEEE Trans. Aerosp. Electron. Syst., 2009, 45, (3), pp. 1153–1166.
7. 7)
  - 24. Shannon, C.E.: ‘A mathematical theory of communication’, Bell Syst. Tech. J., 1948, 27, (3), pp. 379–423. Available at https://onlinelibrary.wiley.com/doi/abs/10.1002/j.1538-7305.1948.tb0133 8.x.
8. 8)
  - 3. Woodward, P.M., Davies, I.L.: ‘Information theory and inverse probability in telecommunication’, Proc. IEE - Part III: Radio Commun. Eng., 1952, 99, (58), pp. 37–44.
9. 9)
  - 6. Bell, M.R.: ‘Information theory and radar waveform design’, IEEE Trans. Inf. Theory, 1993, 39, (5), pp. 1578–1597.
10. 10)
  - 19. Xu, S., Xu, D., Luo, H.: ‘Information theory of detection in radar systems’. 2017 IEEE Int. Symp. on Signal Processing and Information Technology (ISSPIT), Bilbao, Spain, 2017, pp. 249–254.
11. 11)
  - 20. Xu, D., Yan, X., Xu, S., et al: ‘Spatial information theory of sensor array and its application in performance evaluation’, IET Commun., 2019, 13, pp. 2304–12.
12. 12)
  - 25. Jaynes, E.T.: ‘Information theory and statistical mechanicsc, Phys. Rev., 1957, 106, pp. 620–630. Available at https://link.aps.org/doi/10.1103/PhysRev.106.620.
13. 13)
  - 10. Sen, S., Nehorai, A.: ‘Adaptive ofdm radar for target detection in multipath scenarios’, IEEE Trans. Signal Process., 2011, 59, (1), pp. 78–90.
14. 14)
  - 18. Zhao, L.C., Krishnaiah, P.R., Bai, Z.D.: ‘Remarks on certain criteria for detection of number of signals’, IEEE Trans. Acoust. Speech Signal Process., 1987, 35, (2), pp. 129–132.
15. 15)
  - 15. Rissanen, J.: ‘Modeling by shortest data description’, Automatica, 1978, 14, (5), pp. 465–471. Available at http://www.sciencedirect.com/science/article/pii/0005109878900055.
16. 16)
  - 8. Setlur, P., Devroye, N.: ‘Adaptive waveform scheduling in radar: an information theoretic approach’, 2012, 8361.
17. 17)
  - 14. Akaike, H.: ‘A new look at the statistical model identification’, IEEE Trans. Autom. Control, 1974, 19, (6), pp. 716–723.
18. 18)
  - 22. Pasupathy, S., Venetsanopoulos, A.N.: ‘Optimum active array processing structure and space-time factorability’. IEEE Trans. Aerosp. Electron. Syst., 1974, AES-10, (6), pp. 770–778,.
19. 19)
  - 27. Cover, T.M., Thomas, J.A.: ‘Elements of information theory’, ch. 9 (John Wiley & Sons, NJ, USA, 2006), pp. 224–238. Available at https://onlinelibrary.wiley.com/doi/abs/10.1002/0471200611.ch9.
20. 20)
  - 4. Frost, V.S., Shanmugan, K.S.: ‘The information content of synthetic aperture radar images of terrain’, IEEE Trans. Aerosp. Electron. Syst., 1983, AES-19, (5), pp. 768–774.
21. 21)
  - 21. Dogandzic, A., Nehorai, A.: ‘Cramer-rao bounds for estimating range, velocity, and direction with an active array’, IEEE Trans. Signal Process., 2001, 49, (6), pp. 1122–1137.
22. 22)
  - 13. Wax, M., Ziskind, I.: ‘Detection of the number of coherent signals by the mdl principle’, IEEE Trans. Acoust. Speech Signal Process., 1989, 37, (8), pp. 1190–1196.
23. 23)
  - 1. Woodward, P.M., Davies, I.L.: ‘Xcii. a theory of radar information’, London, Edinburgh, and Dublin Philos. Mag. J. Sci., 1950, 41, (321), pp. 1001–1017. Available at https://doi.org/10.1080/14786445008561035.
24. 24)
  - 26. Johnson, O.: ‘Information theory and the central limit theorem’ (Imperial College Press, London, 2004). Available at https://doi.org/10.1142/9781860945373.
25. 25)
  - 16. Zhao, L.C., Krishnaiah, P.R., Bai, Z.D.: ‘On detection of the number of signals in presence of white noise’, J. Multivariate Anal., 1986, 20, (1), pp. 1–25. Available at http://www.sciencedirect.com/science/article/pii/0047259X86900175.
26. 26)
  - 7. Leshem, A., Naparstek, O., Nehorai, A.: ‘Information theoretic adaptive radar waveform design for multiple extended targets’, IEEE J. Sel. Top. Signal Process., 2007, 1, (1), pp. 42–55.
27. 27)
  - 11. Sen, S., Nehorai, A.: ‘Ofdm mimo radar with mutual-information waveform design for low-grazing angle tracking’, IEEE Trans. Signal Process., 2010, 58, (6), pp. 3152–3162.

Spatial information in phased-array radar

References

Related content