Set-Membership Affine-Projection with Estimated Parameters for non-White Inputs

This article proposes versions of the set-membership affine-projection algorithm that estimate an adequate threshold and a proper constraint-vector for a system identification scenario. A novel constraint-vector is proposed for a non-white input, since the Simple-Choice Constraint Vector is asymptotically optimum for white inputs. Non-white inputs are commonplace in communication systems when there is channel encoding or precoding in the transmitter. A fixed and a time-varying threshold set-membership version are used. Simulations show that the proposed algorithm presents lower mean-square error and updates in fewer iterations than the traditional Simple-Choice and Exponential-Decay Constraint Vectors. For the time-varying threshold, the computational complexity of the algorithm is similar to the Simple-Choice Constraint Vector.