Table 1 Review of the implementation procedures of the proposed beamformer algorithm

I.

Signals in Eq. (1) are arranged to form the 2-D matrix data representation in Eq. (3). Different firing events correspond to different steering angles thus, the calculated time delay is different. For each emission, the RF data are collected and combined with the calculated time delays to get the CPWC signals

II.

Estimate CM for the receive aperture. The spatial smoothing, the temporal averaging and the DL approach are performed in order to obtain a robust estimate of CM as in Eq. (19)

III.

Combine the data CM estimate with the steering vector a to compute the MV beamformer weight as in Eq. (6)

IV.

Compute the GSC beamformer weight in Eq. (13) by combining the adaptive Eq. (11) and the nonadaptive braces Eq. (12), respectively

V.

Perform the eigen decomposition of CM in order to construct the signal subspace in Eq. (9) and, compute the EGSC weight using Eq. (15)

VI.

Compute the weights for the CF based methods \(\text {EGSC}_1\), \(\text {EGSC}_2\) and \(\text {EGSC}_3\) in Eqs. (16)–(19) using Eqs. (15), (16), (15)–(17) and (15)–(19), respectively

VI.

Using Eq. (8) apply Eqs. (20)–(22) to compute the beamformer output for the proposed methods