Efficient Rank-Adaptive Least-Square Estimation and Multiple-Parameter Linear Regression Using Novel Dyadically Recursive Hermitian Matrix Inversion

Least-square estimation (LSE) and multiple-parameter linear regression (MLR) are the importantestimation techniques for engineering and science, especially in the mobile communications and signalprocessing applications. The majority of computational complexity incurred in LSE and MLR arisesfrom a Hermitian matrix inversion. In practice, the Yule-Walker equations are not valid, and hence theLevinson-Durbin algorithm cannot be employed for general LSE and MLR problems. Therefore, themost efficient Hermitian matrix inversion method is based on the Cholesky factorization. In this paper,we derive a new dyadic recursion algorithm for sequential rank-adaptive Hermitian matrix inversions. In addition, we provide the theoretical computational complexity analyses to compare our new dyadicrecursion scheme and the conventional Cholesky factorization. We can design a variable model-orderLSE (MLR) using this proposed dyadic recursion approach thereupon. Through our complexity analysesand the Monte Carlo simulations, we show that our new dyadic recursion algorithm is more efficient thanthe conventional Cholesky factorization for the sequential rank-adaptive LSE (MLR) and the associatedvariable model-order LSE (MLR) can seek the trade-off between the targeted estimation performanceand the required computational complexity. Our proposed new scheme can benefit future portable andmobile signal processing or communications devices