Algorithm 1. The adaptive waveform design and selection algorithm

Initialize the transmit matrix $X_0$ and the covariance matrix of the noise $R_N^{}$. 1. At the initial time $t=0$, measure the target scattering signal $Y_0$ and calculate the covariance of the target-scattering signal $R_{Y_0}$. The covariance matrix of the channel response $R_{H_0}^{}$ can be obtained through successive measurements with uniform power allocation over the transmit antennas by solving (36). 2. The optimized waveform ensemble ${ℂ}_{{\widehat{X}}_0}$ can be obtained through the waveform design process by solving (30). 3. At time $t=1$, measure $Y_1$ and calculate $R_{Y_1}$ and the cross-covariance matrix $R_{Y_0,Y_1}$. The actual channel response $H_1$ is obtained by de-convolving the target-scattering signal with the transmit signal by using (23). 4. Calculate the corresponding singular values $d_{0,1}^m,m=1,\dots ,M$ of $R_{Y_0,Y_1}$ and ${\widehat{X}}_1\in {ℂ}_{{\widehat{X}}_0}$ can be acquired through the waveform selection process by solving (38). 5. At time $t=1$, emission ${\widehat{X}}_1$ and observe the corresponding received signal ${\widehat{Y}}_1$ to achieve $R_{H_1}^{}$ by using (36). 6. If $i=I_{\max }$, the iterative procedure ends; or else, repeat steps 2–5 iteratively.