Acceleration of adaptive parallel projection algorithms by Pairwise Optimal WEight Realization

The adaptive Parallel Subgradient Projection (PSP) technique improves the convergence speed, in noisy environment, of linear-projection-based algorithms (e.g., NLMS and APA), with low computational complexity. The technique utilizes weighted average of the metric projections onto a series of closed half-spaces which contain, with high probability, unknown system to be identified. So far, mainly for simplicity, uniform weighting has been used. However, it is of great interest to develop more strategic weighting for further improvements of convergence, where the weight design should also be with low computational complexity. This paper presents a novel weighting technique named Pairwise Optimal WEight Realization PSP (POWER-PSP). For each pair of half-spaces, the proposed technique realizes the exact metric projection onto their intersection. Even for q(≥ 3) half-spaces, the technique can approximate, in computationally efficient way, the exact projection onto their intersection by applying the same idea to certain hierarchical structure of half-spaces. Simulation results exemplify that the proposed technique yields drastic improvements of convergence speed and robustness against noise, while keeping linear computational complexity.