Low-rank adaptive filters

A channel subspace post-filtering approach to adaptive equalization

“…A reduction in error was obtained once the true dimension of the signal subspace was estimated. Concurrently, extensive research resulted in generalized algorithms for: subspace based blind channel identification (23,1,20,9), equalization (35), data adaptive rank shaping (30), and linear prediction (1) that exploited the reduced rank nature of the signal subspace. These generalized methods are conceptually quite comparable to the types of algorithms that need to be developed to demonstrate the relevance and need for using a channel subspace based approach to solve equivalent problems in UWA communications.…”

Soft Iterative Channel Estimation With Subspace and Rank Tracking

“…In the LORAF approach, the order is reduced to [i.e., the complexity required by the updating of the matrix , according to (7)] providing a complexity gain of . Moreover, a more efficient implementation for the QR decomposition, the matrix and updating processes, provides a further computational cost reduction to [5].…”

“…The forgetting factor defines in fact the effective length of the temporal window used for multiblock averaging. This can be expressed in number of blocks as [5]. Usually, delays are characterized by slow variations over the blocks, calling thereby for large values of (i.e., long memory length) so as to reduce the MSE of the channel estimate.…”

“…This can be accomplished by updating burst by burst the matrix (5), using an exponential weighting (6) where denotes the forgetting factor. The LORAF method, proposed in [5] for tracking the subspace spanned by the eigenvectors of the covariance matrix of a parameter vector, has been adapted here to our problem. First, let be the EVD of the matrix (6) truncated to the leading eigenvalues.…”

“…We assume that the path delays are slowly varying and also that the number of paths can change (due to the birth-and-death process of the paths). The low-rank adaptive filter (LORAF) [5] is employed to track the subspace spanned by the channel impulse responses associated to the varying paths; both the MSE of the estimate and the bit error rate (BER) performances are evaluated through computer simulations. A rank-tracking technique [6] is used in conjunction with subspace tracking.…”