Multichannel fast QRD-LS adaptive filtering: New technique and algorithms

In this paper, a direct, unified approach for deriving fast multichannel QR decompostion (QRD) least squares (LS) adaptive algorithms is introduced. The starting point of the new methodology is the efficient update of the Cholesky factor of the input data correlation matrix. Using the new technique, two novel fast multichannel algorithms are developed. Both algorithms comprise scalar operations only and are based exclusively on numerically robust orthogonal Givens rotations. The first algorithm assumes channels of equal orders and processes them all simultaneously, It is highly modular and provides enhanced pipelinability, with no increase in computational complexity, when compared with other algorithms of the same category. The second multichannel algorithm deals with the general case of channels with different number of delay elements and processes each channel separately. A modification of the algorithm leads to a scheme that can be implemented on a very regular systolic architecture. Moreover, both schemers offer substantially reduced computational complexity compared not only with the first algorithm but also with previously derived multichannel fast QRD schemes. Experimental results in two specific application setups as well as simulations in a finite, precision environment are also included.