Constrained adaptation algorithms employing Householder transformation

Adaptive projected subgradient method and set theoretic adaptive filtering with multiple convex constraints

“…If, for example, one defines Θ n (u) := d(u, V n ), ∀u ∈ V , for a sequence of hyperplanes (V n ) n∈N , then the Constrained NLMS [6] is obtained. We provide, now, with three examples that generalize the corresponding ones in [23] by Lemma 2.…”

“…The classical Normalized Least Mean Squares (NLMS) algorithm [1,2] originated the development of various projection based adaptive filtering algorithms [3][4][5][6][7] that have been demonstrating extensive applicability to a wide range of signal processing problems such as adaptive arrays [8], adaptive receivers for communication systems [9], and acoustic echo cancellation [9,10]. This broad use stems partially from their low computational load and their algorithmic simplicity.…”

“…The method is a natural extension of Polyak's algorithm [24] where the convex objective remains fixed in the whole process. It was discovered that many existing projection based adaptive filtering algorithms such as NLMS, APA, Projected NLMS [5], Constrained NLMS [6], Adaptive Parallel Subgradient Algorithm [7], Adaptive Parallel Outer Projection Algorithm [7,25], Adaptive Parallel Min-Max Projection Algorithm [23] and their embedded constraint versions [23] can be obtained as simple examples of the APSM by an appropriate design of the convex objectives. More than that, the algorithm has recently exhibited remarkably fast and stable convergence properties for highly demanding signal processing applications like stereophonic acoustic echo cancellation [26] and blind multiple access interference reduction for DS/CDMA systems [27].…”

Adaptive Beamforming by Constrained Parallel Projection in the Presence of Spatially-Correlated Interferences

“…The linearly constrained adaptive filtering problem has received considerable attention due to its important applications such as adaptive beamforming, multiuser detection in CDMA, and spectral estimation [1][2][3][4][5][6][7][8][9]. We focus on the adaptive beamforming application, although similar discussion could be possible for other applications.…”

Efficient Adaptive Blind MAI Suppression in DS/CDMA by Embedded Constraint Parallel Projection Techniques

“…Hence, the algorithm shows faster convergence than the projected NLMS algorithm (see [9] and references therein). Unfortunately, the CNLMS still does not show sufficient speed of convergence because it takes just one datum into account at each iteration.…”