Algorithm 1 Constant-Beamwidth CRA Beamformer Design

Calculate the attenuation weight: for  $m\in \left[1,M\right]$  do    find $f_m$ by solving: ${\beta }_{\mathrm{BW}}=\frac{{\sum }_{i=1}^m{\mathcal{R}}_i\left(f_m,\frac{{\theta }_{\mathrm{BW}}}{2}\right)}{{\sum }_{i=1}^m{N}_i}$ using the Bisection algorithm. end for Define $f_{\mathrm{L}}=f_M$ , $f_{\mathrm{H}}=min\left(f_1,8000\right)$. for $f\in \left[f_{\mathrm{L}},f_{\mathrm{H}}\right]$ do    Calculate ring weight based on (29). end for Modify the beamformer to expand the constant-beamwidth frequency range: for  $m\in \left[1,M\right]$  do    find $f_m$ by solving: ${\beta }_{\mathrm{BW}}=\frac{{\sum }_{i=m}^M{\mathcal{R}}_i\left(f_m,\frac{{\theta }_{\mathrm{BW}}}{2}\right)}{{\sum }_{i=m}^M{N}_i}$ using the Bisection algorithm. end for Define $f_{\mathrm{L}}^{\mathrm{new}}=f_M$. for  $f\in \left[f_{\mathrm{L}}^{\mathrm{new}},f_{\mathrm{L}}\right]$ do    Compute the ring weight based on (33). end for Improve the DI in lower frequencies: for  $f\in \left[0,f_{\mathrm{L}}^{\mathrm{new}}\right]$ do    let $H_M\left(f\right)=1$, find $H_{M-1}\left(f\right)$ s.t $\underset{\_}{\mathit{h}}{\left(f\right)}^T\Gamma \underset{\_}{\mathit{h}}\left(f\right)$ is minimal. end for Implement the desired filters in time domain. Calculate the normalization factor for each frequency.