Table 1 Algorithm of ZMNL sample extraction
From: Locally optimal detector design in impulsive noise with unknown distribution
Step 1: Find the maximum of \(\widetilde {f}[x_{l}]\) as \(\widetilde {f}\left [x_{L_{max}} \right ]\), where L max denotes its position in {x1,x2,…,x L }. |
Step 2: Find the two values of \(\widetilde {f}[\!x_{l}]\) which are nearest to \(\widetilde {f}[x_{L_{max}}]/2\) for l<L max and l′>L max , respectively. Denote the corresponding number as L lowh and L uph . Initialize L low =L lowh and L up =L uph . |
Step 3: Use (12) to calculate two linearity values, i.e., ρ low for \(\widetilde {g}[x_{l}]\) in \(\Omega _{low}=\left [x_{(L_{low}-1)}, x_{L_{up}}\right ]\) and ρ up for \(\widetilde {g}[x_{l}]\) in \(\Omega _{up}=\left [x_{L_{low}}, x_{(L_{up}+1)}\right ]\). |
Step 4: If max(ρ low ,ρ up )≤ρth, go to Step 5. Otherwise, continue. If ρ low >ρ up , let L low =L low −1; if ρ low ≤ρ up , let L up =L up +1. Then, go to Step 3. |
Step 5: The near-linear region is defined as \(\Omega =\left [x_{L_{low}}, x_{L_{up}}\right ]\). The samples \(\widetilde {g}[x_{l}]\) in Ω are extracted and denoted as \(\breve {{g}}[x_{i}]\). |