Algorithm 1. The information embedding MIMO waveform optimization algorithm

Step 1: Initializing iteration index $i=0$, the covariance matrix ${\mathbf{R}}_{{\mathbf{H}}_0}$ and ${\mathbf{R}}_{{\mathbf{N}}_0}$. Step 2: At time $i=0$, solve for the ensemble of transmitted waveforms ${ℂ}_{{\mathbf{X}}_0}$ based on maximization RE criterion over the spatial domain as presented in step 1. Step 3: At time $i=1$, Form an estimate of the received signal ${\mathbf{Y}}_1$, based on the current estimate for TIR by using (3). The received signals are used to extract the TIR. Step 4: At time $i=1$, solve for ${\mathbf{X}}_1$ transmitted waveforms based on the minimization MI criterion over the temporal domain as presented in step 2. Step 5: At time $i=1$, emission ${\mathbf{X}}_1$ and the updated ${\mathbf{R}}_{{\mathbf{H}}_1}$ and ${\mathbf{R}}_{{\mathbf{N}}_1}$ by using the current received signal ${\mathbf{Y}}_1$. Step 6: If $i=I_{\max }$, the process ends; otherwise, we need to go back to Step 2 and repeat.