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“A Linearly Constrained Adaptive Algorithm for Constant Modulus Signal Processing”
by Michael J. Rude
August 1990
This dissertation introduces an adaptive technique that is suitable for signal processing tasks in severe co-channel interference and multipath environments. The new approach is based on the minimization of complex envelope variations at the processor output subject to a set of linear constraints on the processor coefficients. As a result, it does not require a training, reference or desired signal for adaptation. This Linearly Constrained Constant Modulus (LCCM) method combines two existing untrained adaptive techniques: linearly constrained minimization of output power and unconstrained minimization of complex envelope or modulus variations.
LCCM addresses the signal cancellation problem that occurs when untrained adaptive processors are used in hostile signal environments; minimization of output power can lead to signal cancellation in multipath scenarios and unconstrained minimization of envelope variations can lead to signal cancellation in applications that include constant envelope co-channel interference. Analysis of a narrowband array application shows that the LCCM approach will eliminate the signal cancellation problem when appropriate a priori information is incorporated into the constraint set. An additional result is that the signal of interest does not necessarily need to have the constant envelope property.
Adaptive implementation of the LCCM method is accomplished using the common technique of Stochastic Gradient Descent (SGD.) Stable adaptive recursions are derived via comparison with other SGD recursions that are used for existing adaptive approaches. In addition, the roles of convergence parameters are described and practical values are specified. For special cases, convergence in the mean is shown.
In a typical signal processing scenario, LCCM is used for initial acquisition of a signal and then adaptive processing is switched to a decision directed mode. Simulation results for LCCM in the start-up or acquisition mode are presented for both single and multi-channel reception of a digitally modulated signal. The single channel experiment consists of a fractionally spaced LCCM equalizer with a signal subspace based linear constraint. The multi-channel experiment consists of a narrowband array with a look direction constraint. In both cases, the LCCM processor rejects the co-channel interference and compensates for the multipath distortion.