Algorithm 1: The proposed waveform optimization design algorithm.

S1: Transmit initial LFM signal ${\mathit{s}}_0$, where ${\overline{\mathit{S}}}_0=\mathit{F}{\mathit{s}}_0$, ${\mathit{S}}_0=diag\left({\overline{\mathit{S}}}_0\right)$.

S2: Capture the signal reflected from the target and interference. The received waveform vector is ${\mathit{Y}}_{i,0}=\left({\mathit{S}}_0{\hat{\mathit{G}}}_{i,0|0}+{\mathit{S}}_0{\mathit{C}}_0+{\mathit{N}}_0\right){\mathit{H}}_0$.

S3: Estimate the initialize the estimated TSC and MSE matrix of the target as ${\hat{\mathit{G}}}_{i,0|0}$ and ${\mathit{P}}_{i,0|0}$ by the received waveform vector ${\mathit{Y}}_0$ and transmit waveform matrix ${\mathit{S}}_{i,0}$.

S4: Set the iteration index $k=1$, and the maximal number of iteration as $K_{\max }$.

S5: while $k\le K_{\max }$ do

S6: Predict the estimated TSC ${\hat{\mathit{G}}}_{i,k|k-1}$ according to ${\hat{\mathit{G}}}_{i,k-1|k-1}$ by (10).

S7: Update the MSE matrix ${\mathit{P}}_{i,k|k-1}$ according to ${\mathit{P}}_{i,k-1|k-1}$ by (11).

S8: Define ${\hat{\mathit{G}}}_{i,k}=dia\mathit{g}\left({\hat{\mathit{G}}}_{i,k|k-1}\right)$, solve for ${\left|{\overline{S}}_k\left(m\right)\right|}^2$.

S9: Obtain ${\hat{\mathit{G}}}_{i,k|k}$ and ${\mathit{P}}_{i,k|k}$ with ${\mathit{S}}_k$, ${\mathit{Y}}_{i,k}$, ${\hat{\mathit{G}}}_{i,k|k-1}$ and ${\mathit{P}}_{i,k|k-1}$ by Kalman filter.

S10: Let $k=k+1$.

S11: end while