Algorithm 3 CPNN-based sensor nodes’ authentication.

Input: The $i^{\mathrm{th}}$ CSI to authenticate ${\mathit{x}}^{\left(i\right)}$

Output: The label of unknown CSI ${\widehat{\mathit{y}}}^{\left(i\right)}$, the new weight matrix ${\mathit{W}}^{\perp }$, and threshold vector ${\mathit{\xi }}^{\perp }$ of CPNN

1: Initialize: training the CNN by the pre-acquired CSIs to obtain the convolution kernels ${\mathit{V}}^{\perp }$; the dataset ${\mathit{D}}^{\perp }={\left\{\left({\overline{\mathit{x}}}_k,{\mathit{y}}_k\right)\right\}}_{k=1}^m$ obtained by convolution; the weights ${\mathit{W}}_0^{\perp }$ and thresholds ${\mathit{\xi }}_0^{\perp }$ in the neural network will be obtained through the training of CPNN, using dataset ${\mathit{D}}^{\perp }={\left\{\left({\overline{\mathit{x}}}_k,{\mathit{y}}_k\right)\right\}}_{k=1}^m$;

2: Convolution pre-processing of the CSI ${\mathit{x}}^{\left(i\right)}$ into ${\overline{\mathit{x}}}^{\left(i\right)}$;

3: Compute ${\widehat{\mathit{y}}}^{\left(i\right)}$ by the well-trained CPNN;

4: Update the training set ${\mathit{D}}^{\perp }={\left\{\left({\overline{\mathit{x}}}_k,{\mathit{y}}_k\right)\right\}}_{k=1}^m$ by $\left({\mathit{x}}^{\left(i\right)},{\widehat{\mathit{y}}}^{\left(i\right)}\right)$;

5: Retrain the CPNN by the new dataset, and get new weight matrix ${\mathit{W}}^{\perp }$ and threshold vector ${\mathit{\xi }}^{\perp }$;

6: Return ${\widehat{\mathit{y}}}^{\left(i\right)}$, ${\mathit{W}}^{\perp }$, ${\mathit{\xi }}^{\perp }$.