Response Vector for Calculation of Training Signal based on Progressive Non-Recursive Fusion of Multi-Spectral Image

We have examined the convergence behavior of the image fusion in some simple environments. The results are derived by calculating the improvement in SIR caused by hard-limiting a CM signal plus additive noise and interference. These results help to explain why image fusion converges, and are helpful in explaining the general behavior of image fusion. However, we have made several simplifying assumptions which must be addressed in order to extend the analysis to more realistic situations. We have assumed that the desired signal and the interfering signals are not correlated. The convergence behavior of the Least Squares Constant Modulus Algorithm in an adaptive beam forming application is examined. It is assumed that the desired signal and the interference are uncorrelated. The improvement in output SIR with each iteration of the algorithm is predicted for several different signal environments. Deterministic results are presented for an environment containing two complex sinusoids. Probabilistic results are presented for a constant modulus desired signal with a constant modulus interferer and with a Gaussian interferer. The asymptotic improvement in output SIR as the output SIR becomes high is also derived. The results of Monte Carlo simulations using sinusoidal, FM, and QPSK signals are included to support the derivations.