# Residual Echo Suppression Considering Harmonic Distortion and Temporal Correlation
## 5 Experiments
### Computational Complexity of the Proposed RES Algorithm  
We investigated the computational complexity of the proposed RES algorithm. The proposed RES algorithm in our experiment requires \(\{2(2K+1)H+5T+S+46\}M\) real-valued multiplications per frame, while HDRES algorithm [28] requires \(\{(2K+1)H+S+22\}M\) real-valued multiplications and the PFRES algorithm [27] requires \((6p^{2}+13p+3)M\) real-valued multiplications, where \(p\) denotes the order of the polynomial model of the nonlinear echo path. For the parameter values we used in the experiments (e.g., \(M=257\), \(T=1\), \(S=3\), \(H=5\), \(K=1\), and \(p=3\)), the computational complexity of the proposed method is approximately twice of that of the HDRES [28] and 10% less than that of the PFRES [27]. We can see that the proposed method has reasonable computational complexity considering the performance improvement shown in Tables 1-4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Noise Type** & **SNR** & **SER** & **AEC [8,30] & **AEC [8,30] + PFRES [27]** & **AEC [8,30] + HDRES [28]** & **AEC [8,30] + Proposed Method** \\ \hline \multirow{4}{*}{clean} & \multirow{2}{*}{\(5\) dB} & \(3.178\) & \(3.206\) & \(3.243\) & \(\mathbf{3.275}\) \\ \cline{3-6}  & & \(0\) dB & \(3.013\) & \(3.057\) & \(3.087\) & \(\mathbf{3.135}\) \\ \cline{3-6}  & & \(-5\) dB & \(2.815\) & \(2.874\) & \(2.879\) & \(\mathbf{2.962}\) \\ \hline \multirow{4}{*}{Pub} & \multirow{2}{*}{\(20\) dB} & \(5\) dB & \(3.005\) & \(3.024\) & \(3.033\) & \(\mathbf{3.065}\) \\ \cline{3-6}  & & \(0\) dB & \(2.910\) & \(2.944\) & \(2.953\) & \(\mathbf{3.000}\) \\ \cline{3-6}  & & \(-5\) dB & \(2.747\) & \(2.799\) & \(2.792\) & \(\mathbf{2.871}\) \\ \cline{3-6}  & & \(5\) dB & \(2.767\) & \(2.788\) & \(2.779\) & \(\mathbf{2.807}\) \\ \cline{3-6}  & & \(0\) dB & \(2.719\) & \(2.753\) & \(2.740\) & \(\mathbf{2.780}\) \\ \cline{3-6}  & & \(-5\) dB & \(2.603\) & \(2.653\) & \(2.623\) & \(\mathbf{2.694}\) \\ \cline{3-6}  & & \(5\) dB & \(2.684\) & \(2.707\) & \(2.694\) & \(\mathbf{2.720}\) \\ \cline{3-6}  & & \(0\) dB & \(2.642\) & \(2.675\) & \(2.657\) & \(\mathbf{2.696}\) \\ \cline{3-6}  & & \(-5\) dB & \(2.543\) & \(2.593\) & \(2.554\) & \(\mathbf{2.624}\) \\ \hline \multirow{4}{*}{Road} & \multirow{2}{*}{\(20\) dB} & \(5\) dB & \(3.097\) & \(3.123\) & \(3.144\) & \(\mathbf{3.174}\) \\ \cline{3-6}  & & \(0\) dB & \(2.969\) & \(3.010\) & \(3.029\) & \(\mathbf{3.074}\) \\ \cline{3-6}  & & \(-5\) dB & \(2.781\) & \(2.838\) & \(2.838\) & \(\mathbf{2.913}\) \\ \cline{3-6}  & & \(5\) dB & \(2.904\) & \(2.935\) & \(2.940\) & \(\mathbf{2.969}\) \\ \cline{3-6}  & & \(0\) dB & \(2.824\) & \(2.867\) & \(2.871\) & \(\mathbf{2.913}\) \\ \cline{3-6}  & & \(-5\) dB & \(2.681\) & \(2.736\) & \(2.724\) & \(\mathbf{2.797}\) \\ \cline{3-6}  & & \(5\) dB & \(2.828\) & \(2.861\) & \(2.864\) & \(\mathbf{2.892}\) \\ \cline{3-6}  & & \(0\) dB & \(2.758\) & \(2.802\) & \(2.804\) & \(\mathbf{2.846}\) \\ \cline{3-6}  & & \(-5\) dB & \(2.637\) & \(2.693\) & \(2.675\) & \(\mathbf{2.748}\) \\ \hline \multirow{4}{*}{Callcenter} & \multirow{2}{*}{\(20\) dB} & \(5\) dB & \(3.056\) & \(3.078\) & \(3.092\) & \(\mathbf{3.127}\) \\ \cline{3-6}  & & \(0\) dB & \(2.944\) & \(2.983\) & \(2.994\) & \(\mathbf{3.043}\) \\ \cline{3-6}  & & \(-5\) dB & \(2.769\) & \(2.824\) & \(2.817\) & \(\mathbf{2.897}\) \\ \cline{3-6}  & & \(5\) dB & \(2.836\) & \(2.858\) & \(2.858\) & \(\mathbf{2.889}\) \\ \cline{3-6}  & & \(0\) dB & \(2.776\) & \(2.810\) & \(2.806\) & \(\mathbf{2.851}\) \\ \cline{3-6}  & & \(-5\) dB & \(2.641\) & \(2.693\) & \(2.674\) & \(\mathbf{2.747}\) \\ \cline{3-6}  & & \(5\) dB & \(2.750\) & \(2.774\) & \(2.769\) & \(\mathbf{2.800}\) \\ \cline{3-6}  & & \(0\) dB & \(2.702\) & \(2.736\) & \(2.728\) & \(\mathbf{2.772}\) \\ \cline{3-6}  & & \(-5\) dB & \(2.589\) & \(2.638\) & \(2.618\) & \(\mathbf{2.687}\) \\ \hline \multicolumn{2}{c}{Average} & \multicolumn{1}{c}{\(2.806\)} & \(2.844\) & \(2.843\) & \(\mathbf{2.892}\) \\ \hline \hline \end{tabular}
\end{table}