Capture Properties of the Generalized CMA in Alpha-Stable Noise Environment

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 alpha-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.