A Stochastic Model for a Pseudo Affine Projection Algorithm

This paper presents a statistical analysis of a Pseudo Affine Projection (PAP) algorithm, obtained from the Affine Projection algorithm (AP) for a step size alpha < 1 and a scalar error signal in the weight update. Deterministic recursive equations are derived for the mean weight and for the mean square error (MSE) for a large number of adaptive taps N compared to the order P of the algorithm. Simulations are presented which show good to excellent agreement with the theory in the transient and steady states. The PAP learning behavior is of special interest in applications where tradeoffs are necessary between convergence speed and steady-state misadjustment.

...The challenge to analyze the properties of the algorithm was then set in [2] and finally solved 11 years later (at least in parts) in a classical MSE context [10]...
...We use two sets of prediction coefficients in the following: Example 1: The first set is an example, taken from [10]...
...Example 2: The second example takes only two AR coefficients . Different to the previous example and all examples from [10] is that here the unusual situation occursthatalsoalowerstabilityboundforthestep-sizeexists.The stabilitybounds accordingto Theorem3.1are 0.45forthelower bound and 1.16 for the upper bound of the PAP algorithm...
...Fig. 2 depicts the mismatch for PAP as well as GAP algorithm over various step-sizes employing the set of coefficients from Example 1. For the PAP algorithm an even better agreement compared to [10] is found [compare to Fig. 4(a) in [10] repeated as dashed line in Fig. 2] with a much simpler formula according to Theorem 4.1...
...Fig. 2 depicts the mismatch for PAP as well as GAP algorithm over various step-sizes employing the set of coefficients from Example 1. For the PAP algorithm an even better agreement compared to [10] is found [compare to Fig. 4(a) in [10] repeated as dashed line in Fig. 2] with a much simpler formula according to Theorem 4.1...
...simulation at . The theory in [10] is not predicting it at all (see dashed line in the figure)...
...As the figure reveals, our assumption that is sufficiently large seems to hold for even small values , sacrificing precision but definitely for practical values of . A comparison to the misadjustment from [10] reveals large discrepancies for small as well as large values of the filter order . The Matlab code for these experiments is available under https://www.nt.tuwien.ac.at/downloads/featured-downloads...

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Related Publications (1)

A Stochastic Model for a Pseudo Affine Projection Algorithm,10.1109/TSP.2008.2007109,IEEE Transactions on Signal Processing,SÉrgio J. M. de Almeida,Jo

Citation Context (2)

Markus Rupp. Pseudo Affine Projection Algorithms Revisited: Robustness and Stabilit...

Sérgio J. M. de Almeida, et al. A STOCHASTIC MODEL FOR THE DEFICIENT LENGTH PSEUDO AFFINE PROJECTION A...

References (9)

Convergence behavior of affine projection algorithms (Citations: 64)

Tracking capability of the least mean square algorithm: Application to an asynchronous echo canceller (Citations: 19)

Fixed point error analysis of the normalized ladder algorithm (Citations: 64)

A stochastic model for the affine projection algorithm operating in a nonstationary environment (Citations: 1)

A statistical analysis of the affine projection algorithm for unity step size and autoregressive inputs (Citations: 25)

Citations (3)

Stochastic analysis of the LMS algorithm for non-stationary white Gaussian inputs

Pseudo Affine Projection Algorithms Revisited: Robustness and Stability Analysis

A STOCHASTIC MODEL FOR THE DEFICIENT LENGTH PSEUDO AFFINE PROJECTION ADAPTIVE ALGORITHM (Citations: 1)


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