Statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter (or constraint vector) and generates a sequence of filters that converges to the minimum-variance-distortionless-response (MVDR) solution for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple, noninvasive, recursive procedure that avoids any form of explicit autocorrelation matrix inversion, decomposition, or diagonalization. Theoretical analysis reveals basic properties of the algorithm and establishes formal convergence.When the input autocorrelation matrix is replaced by a conventional sample-average (positive definite) estimate, the algorithm effectively generates a sequence of MVDR filter estimators; the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample-matrix-inversion (SMI) estimator. In fact, formal convergence of the estimator sequence to the SMI estimate is established. However, for short data records, it is the early, nonasymptotic elements of the generated sequence of estimators that offer favorable bias/covariance balance and are seen to outperform in mean-square estimation error, constraint-LMS, RLS-type, orthogonal multistage decomposition, as well as plain and diagonally loaded SMI estimates. An illustrative interference suppression example is followed throughout this presentation.Index Terms-Adaptive filters, algorithms, code division multiaccess, estimation, interference suppression, iterative methods, least mean square methods.
The Welch lower bound on the total squared correlation (TSC) of signature sets is known to be tight for real-valued signatures and loose for binary signatures whose number is not a multiple of four. In this letter, we derive new bounds on the TSC of binary signature sets for any number of signatures and any signature length. Then, for almost all , in 1 2. .. 256 , we design optimum binary signature sets that achieve the new bounds. The design procedure is based on simple transformations of Hadamard matrices.
The maximization of a full-rank quadratic form over a finite alphabet is NP-hard in both a worst-case sense and an average sense. Interestingly, if the rank of the form is not a function of the problem size, then it can be maximized in polynomial time. An algorithm for the efficient computation of the binary vector that maximizes a rank-deficient quadratic form is developed based on an analytic procedure. Auxiliary spherical coordinates are introduced and the multi-dimensional space is partitioned into a polynomial-size set of regions; each region corresponds to a distinct binary vector. The binary vector that maximizes the rank-deficient quadratic form is shown to belong to the polynomial-size set of candidate vectors. Thus, the size of the feasible set is efficiently reduced from exponential to polynomial.
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