access icon free Robust adaptive beamforming algorithms using the constrained constant modulus criterion

The authors present a robust adaptive beamforming algorithm based on the worst-case (WC) criterion and the constrained constant modulus (CCM) approach, which exploits the constant modulus property of the desired signal. Similar to the existing worst-case beamformer with the minimum variance design, the problem can be reformulated as a second-order cone programme and solved with interior point methods. An analysis of the optimisation problem is carried out and conditions are obtained for enforcing its convexity and for adjusting its parameters. Furthermore, low-complexity robust adaptive beamforming algorithms based on the modified conjugate gradient and an alternating optimisation strategy are proposed. The proposed low-complexity algorithms can compute the existing WC constrained minimum variance and the proposed WC-CCM designs with a quadratic cost in the number of parameters. Simulations show that the proposed WC-CCM algorithm performs better than existing robust beamforming algorithms. Moreover, the numerical results also show that the performances of the proposed low-complexity algorithms are equivalent or better than that of existing robust algorithms, whereas the complexity is more than an order of magnitude lower.

Inspec keywords: array signal processing; convex programming

Other keywords: WC-CCM design; minimum variance design; second-order cone programme; constrained constant modulus criterion; interior point method; conjugate gradient; low-complexity robust adaptive beamforming algorithm; worst-case criterion; convexity; optimisation strategy

Subjects: Signal processing theory; Optimisation techniques; Signal processing and detection; Optimisation techniques

References

    1. 1)
      • 28. Grant, M., Boyd, S.: ‘CVX: matlab software for disciplined convex programming, version 1.21’. http://www.cvxr.com/cvx, January 2011.
    2. 2)
    3. 3)
    4. 4)
    5. 5)
    6. 6)
    7. 7)
    8. 8)
    9. 9)
    10. 10)
    11. 11)
    12. 12)
    13. 13)
    14. 14)
    15. 15)
    16. 16)
    17. 17)
    18. 18)
    19. 19)
    20. 20)
    21. 21)
      • 27. Chang, P.S., Willson, A.N.: ‘Analysis of conjugate gradient algorithms for adaptive filtering’, IEEE Trans. Signal Process., 2000, 48, pp. 409418 (doi: 10.1109/78.823968).
    22. 22)
      • 2. Li, J., Stoica, P.: ‘Robust adaptive beamforming’ (Wiley: Hoboken, NJ, 2006).
    23. 23)
      • 5. Vorobyov, S.A., Gershman, A.B., Luo, Z.-Q.: ‘Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem’, IEEE Trans. Signal Process., 2003, 51, pp. 313324 (doi: 10.1109/TSP.2002.806865).
    24. 24)
      • 12. Gershman, A.B., Sidiropoulos, N.D., Shahbazpanahi, S., Bengtsson, M., Ottersten, B.: ‘Convex optimization-based beamforming’, IEEE Signal Process. Mag., 2010, 27, (3), pp. 6275 (doi: 10.1109/MSP.2010.936015).
    25. 25)
      • 22. Wang, L., de Lamare, R.C.: ‘Low-complexity adaptive step size constrained constant modulus sg algorithms for blind adaptive beamforming’, Signal Process., 2009, 89, (12), pp. 25032513 (doi: 10.1016/j.sigpro.2009.04.018).
    26. 26)
      • 6. Stoica, P., Wang, Z., Li, J.: ‘Robust capon beamforming’, IEEE Signal Process. Lett., 2003, 10, (6), pp. 172175 (doi: 10.1109/LSP.2003.811637).
    27. 27)
      • 26. Niesen, U., Shah, D., Wornell, G.W.: ‘Adaptive Alternating Minimization Algorithms‘, 2009, 55, no. 3.
    28. 28)
      • 7. Li, J., Stoica, P.: ‘On robust capon beamforming and diagonal loading’, IEEE Trans. Signal Process., 2003, 51, (7), pp. 17021715 (doi: 10.1109/TSP.2003.812831).
    29. 29)
      • 16. Chen, Y., Le-Ngoc, T., Champagne, B., Xu, C.: ‘Recursive least squares constant modulus algorithm for blind adaptive array’, IEEE Trans. Signal Process., 2004, 52, (5), pp. 14521456 (doi: 10.1109/TSP.2004.826167).
    30. 30)
      • 28. Grant, M., Boyd, S.: ‘CVX: matlab software for disciplined convex programming, version 1.21’. http://www.cvxr.com/cvx, January 2011.
    31. 31)
      • 15. de Lamare, R.C., Haardt, M., Sampaio-Neto, R.: ‘Blind adaptive constrained reduced-rank parameter estimation based on constant modulus design for CDMA interference suppression’, IEEE Trans. Signal Process., 2008, 56, (2), pp. 24702482 (doi: 10.1109/TSP.2007.913161).
    32. 32)
      • 13. Khabbazibasmenj, A., Vorobyov, S., Hassanien, A.: ‘Robust adaptive beamforming based on steering vector estimation with as little as possible prior information’, IEEE Trans. Signal Process., 2012, 60, (6), pp. 29742987 (doi: 10.1109/TSP.2012.2189389).
    33. 33)
      • 19. Feldman, D.D., Griffiths, L.J.: ‘A projection approach to robust adaptive beamforming’, IEEE Trans. Signal Process., 1994, 42, pp. 867876 (doi: 10.1109/78.285650).
    34. 34)
      • 10. Chen, C.-Y., Vaidyanathan, P.P.: ‘Quadratically constrained beamforming robust against direction-of-arrival mismatch’, IEEE Trans. Signal Process., 2007, 55, (8), pp. 41394150 (doi: 10.1109/TSP.2007.894402).
    35. 35)
      • 25. Sturm, J.F.: ‘Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones’, Optim. Meth. Softw., 1999, 11, (12), pp. 625653 (doi: 10.1080/10556789908805766).
    36. 36)
      • 23. de Lamare, R.C., Sampaio-Neto, R., Haardt, M.: ‘Blind adaptive constrained constant-modulus reduced-rank interference suppression algorithms based on interpolation and switched decimation’, IEEE Trans. Signal Process., 2011, 59, (2), pp. 681695 (doi: 10.1109/TSP.2010.2091274).
    37. 37)
      • 3. Cox, H., Zeskind, R.M., Owen, M.H.: ‘Robust adaptive beamforming’, IEEE Trans. Acoust. Speech Signal Process., 1987, ASSP-35, pp. 13651376 (doi: 10.1109/TASSP.1987.1165054).
    38. 38)
      • 18. Luenberger, D.G.: ‘Linear and nonlinear programming’ (Addison-Wesley, Reading, MA, 1984, 2nd edn.).
    39. 39)
      • 1. Trees, H.V.: ‘Optimum array processing’ (John Wiley, 2002).
    40. 40)
      • 20. de Lamare, R.C., Wang, L., Fa, R.: ‘Adaptive reduced-rank LCMV beamforming algorithms based on joint iterative optimization of filters: design and analysis’, Signal Process., 2010, 90, (2), pp. 640652 (doi: 10.1016/j.sigpro.2009.08.002).
    41. 41)
      • 11. Hassanien, A., Vorobyov, S.A.: ‘Robust adaptive beamforming using sequential quadratic programming: an iterative solution to the mismatch problem’, IEEE Signal Process. Lett., 2008, 15, pp. 733736 (doi: 10.1109/LSP.2008.2001115).
    42. 42)
      • 4. Gershman, A.B.: ‘Robust adaptive beamforming in sensor arrays’, Int. J. Electron. Commun., 1999, 53, pp. 305314.
    43. 43)
      • 8. Li, J., Stoica, P., Wang, Z.: ‘Doubly constrained robust capon beamformer’, IEEE Trans. Signal Process., 2004, 52, (9), pp. 24072423 (doi: 10.1109/TSP.2004.831998).
    44. 44)
      • 21. Vorobyov, S.A., Gershman, A.B., Rong, Y.: ‘On the relationship between the worst-case optimization-based and probability-constrained approaches to robust adaptive beamforming’. Proc. IEEE ICASSP, 2, Honolulu, HI, Apr. 2007, pp. 977980.
    45. 45)
      • 9. Lorenz, R., Boyd, S.: ‘Robust minimum variance beamforming’, IEEE Trans. Signal Process., 2005, 53, pp. 16841696 (doi: 10.1109/TSP.2005.845436).
    46. 46)
      • 24. Meng, Y., You, M., Liu, J.: ‘Robust noise suppression least square constant modulus interference cancellation’. Proc. 2009 IEEE 20th Int. Symp. Personal, Indoor and Mobile Radio Communications, September 2009, pp. 526530.
    47. 47)
      • 14. de Lamare, R.C., Sampaio-Neto, R.: ‘Blind adaptive code-constrained constant modulus algorithms for CDMA interference suppression in multipath channels’, IEEE Signal Process. Lett., 2005, 9, (4), pp. 334336.
    48. 48)
      • 17. Wang, L., de Lamare, R.C.: ‘Constrained adaptive filtering algorithms based on conjugate gradient techniques for beamforming’, IET Signal Process., 2010, 4, pp. 686697 (doi: 10.1049/iet-spr.2009.0243).
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