Cone constrained adaptive algorithms and multiple access interference cancellation

A parameterization of the cone around a given vector in N-dimensional vector space is derived. Vectors obtained by changing the parameter values can not escape the cone. The constraint is useful when it is known that an optimal vector of filter coefficients is close in direction with the given vector. Adaptive filtering algorithms that use the steepest descent method and stochastic gradient approximation are developed for the case of filter coefficients constrained in the cone. There is no need for monitoring the constraint since it is always satisfied by the construction. Two optimization criteria are explicitly considered: the least mean square and constant modulus. The cone constrained constant modulus algorithm (CMA) is applied to the problem of user detection in a synchronous direct sequence code division multiple access system. Its convergence is compared with the plain CMA and back projection CMA. Under severe conditions the cone constrained CMA is the only one which locks to the desired user.