Abstract
Constant modulus algorithm (CMA) is an adaptive technique for correcting multipath and interference-induced degradations in constant envelope waveforms. The algorithm exploits the fact that both multipath and additive interference can disrupt the constant envelope of the received signal. By detecting the received envelope variations, the adaptive algorithm has the ability to reset the coefficients vector so as to remove the variations, and in the process, reject the various interference components from the desired signal. If both the interferer and the signal of interest have constant envelope and are spectrally non-overlapped, it is possible to find two different solutions for the coefficient vector, in which one suppresses the interferer and the other “captures” the interferer. The problem of how “capture” can occur and how it may be prevented in Gaussian noise environment has been perfectly developed in the previous work (Treichler, Larimore, IEEE Trans Acoust Speech Signal Process, 33:946–958, 1985). However, recent investigation on the physical channels in wireless communication shows that there is aggregate noise component exhibiting high amplitudes for small duration time interval. This paper proposes a GCMA (Generalized CMA) which generalizes the CMA by introducing the α-stable distribution as the noise model. Here the original CMA is only a special case of the GCMA. In order to describe the average behavior of the GCMA, a simple model consisting of only two sinusoids is presented. As assuming slow adaptation, the adaptive weight recursion is shown to compress into a two-by-two recursion in the tone output amplitudes. The simplified recursion is analyzed to determine what combination of signals power and initialization on coefficient vectors leads to “lock” and what leads to the capture of the interferer. The method to determine lock and capture zone boundaries is analyzed. These convergence properties of the GCMA are studied by computer simulations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Treichler J.R., Agee B.G. (1983) A new approach to multipath correction of constant modulus signals. IEEE Transactions on Acoustics, Speech, and Signal Processing 31(2): 459–472
Johnson C.R., Schniter P., Endres T.J., Behm J.D. et al (1998) Blind equalization using the constant modulus criterion: A review. Proceedings of the IEEE 86(10): 1927–1950
Sanchez M.G., Haro L.D., Ramon M.C., Mansilla A. et al (1999) Impulsive noise measurements and characterization in a UHF digital TV channel. IEEE Transactions on Electromagnetic Compatibility 41(2): 124–136
Button M.D., Gardiner J.G., Glover I.A. (2002) Measurement of the impulsive noise environment for satellite-mobile radio systems at 1.5 GHz. IEEE Transaction on Vehicular Technology 51(3): 551–560
Bertocco M., Paglierani P. (1998) Nonintrusive measurement of impulsive noise in telephone-type networks. IEEE Transactions on Instrumentation and Measurement 47(4): 864–868
Blankenship T.K., Krizman D.M., Rappaport T.S. (1997) Measurements and simulation of radio frequency impulsive noise in hospitals and clinics. IEEE 47(h Vehicular Technology Conference 3, 1942–1946): 47th Vehicular Technology Conference 3, 1942–1946
Blackard K.L., Rappaport T.S. (1993) Measurements and models of the radio frequency impulsive noise for indoor wireless communications. IEEE Journal on selected areas in communications 11(7): 991–1001
Ahandra A. (2002) Measurements of radio impulsive noise from various sources in an indoor environment at 900MHz and 1800MHz. The 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications 2: 639–643
Nikias C.L., Shao M. (1995) Signal processing with alpha-stable distribution and application. Wiley, New York
Shao M., Nikias C.L. (1993) Signal processing with fractional lower order moments: Stable processes and their applications. Proceedings of the IEEE 81(7): 986–1010
Ma X., Nikias C.L. (1995) Parameter estimation and blind channel identification in impulsive signal environments. IEEE Transactions on Signal Processings 43(12): 2884–1897
Tsakalides P., Nikias C.L. (1996) The robust covariation-based MUSIC (ROC-MUSIC) algorithm for bearing estimation in impulsive noise environment. IEEE Transactions signal processing 44: 1623–1633
Bodenschatz J.S., Nikias C.L. (1999) Maximum-likelihood symmetric α-stable parameter estimation. IEEE Transactions on Signal Processing 47(5): 1382–1384
Rupi M., Tsakalides P., Del Re E., Nikias C.L. (2004) Constant modulus blind equalization based on fractional lower-order statistics. Signal Processing 84: 881–894
Treichler J.R., Larimore M.G. (1985) The tone capture properties of CMA-based interference suppressiors. IEEE Transactions on acoustic, speech and signal processing 33(4): 946–958
Qiu, T., Tang, H., & Zha, D. (2005). Capture properties of the generalized CMA in alpha-stable noise environment. In The 7th international conference on signal processing (pp. 439–442). Beijing, China.
Shynk J.J., Chan C.K. (1990) Error surfaces of the constant modulus algorithm. IEEE International Symposium on Circuits and Systems 2: 1335–1338
Shynk J.J., Chan C.K. (1993) Performance surfaces of the constant modulus algorithm based on a conditional Gaussian model. IEEE Transactions on Signal Processing 41(5): 1965–1969
http://www.answers.com/topic/binomial-theorem?cat=technology.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tang, H., Qiu, T. & Li, T. Capture Properties of the Generalized CMA in Alpha-Stable Noise Environment. Wireless Pers Commun 49, 107–122 (2009). https://doi.org/10.1007/s11277-008-9560-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11277-008-9560-8