How Is Gain of Hybrid Sparse Adaptive Filtering Algorithm Affected by Input Correlation?

摘要

We propose a simple adaptive controlling technique for the weighting parameters that govern the metric employed in the hybrid sparse adaptive filtering algorithm. The proposed technique shifts the weights (linearly in time) from IPNLMS to TD-NLMS once an estimate of the mean squared output-error falls below some threshold. For a fair comparison between two adaptive algorithms, a gain measure based on the geometric mean of the MSE ratios is introduced. Numerical examples support the following: (ⅰ) the gain of IPNLMS against TD-NLMS drops from positive to negative as the correlation of inputs becomes strong, (ⅱ) the gain of the proposed algorithm against TD-NLMS is approximately constant regardless of the strength of the correlation, (ⅲ) the gain of the proposed algorithm against IPNLMS grows as an increase of the correlation.%本稿では，ハイブリッド型スパース適応アルゴリズムの計量を定める重みの自動制御法を提案している．提案法は，平均二乗出力誤差の推定値が閥値以下になった時，IPNLMS法からTD－NLMS法へ計量の重みを（時間に対して線形に）シフトさせる．二種類の適応アルゴリズムを公平に評価すべく，MSE比の幾何平均に基づく利得を新たに定義している．数値例により，以下のことを明らかにしている：（ⅰ）入力信号の相関が強くなるにつれてTD－NLMSに対するIPNLMSの利得が正から負へ転ずる，（ⅱ）提案法は，相関の強さに関わらずTD－NLMSに対してほぼ一定の利得を得る，（ⅲ）IPNLMSに対しては，相関の増加とともに提案法の利得が増加する．