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From the observed signals, the DOAs are estimated, which are used to construct the blocking matrix and the spatial filter.

The SNR-weighted beamformer presented in the previous section referred to as the first beamformer (see Fig. 8) is used as a precursor to the adaptive blocking matrix and the interference canceler presented in the following section.

As detailed in the justifications section, linear programming is used to select a small number of metabolites that optimally cover the lighter grey cells in the blocking matrix and propose these to the user as candidate externals.

The matrix L k is a block matrix and the trace is the sum of the traces of the blocks.

In addition, the influence of the blocking matrix used to create the reference signals is investigated.

Alternative solutions such as the blocking matrix preprocessing (BMP) method [3] and the eigen-projection matrix preprocessing (EMP) method [4] for suppressing the mainlobe interference are proposed.

The blocking matrix produces (19).

5. Consolidate blocks by reordering rows and columns according to hierarchical clustering now applied to the combined blocking matrix.

3. Combine row and column blocking matrices by elementwise averaging: (1.5) s i j = 1 2 (r i j + c i j ) The combined blocking matrix obtained in this way is shown in Figure 3(c).

Fig. 3 Blocking matrix output gain.

where R y y denotes the 2D×2D correlation matrix of the output signal vector y of length 2D, bdiag refers to considering block matrix and describes the operation of setting all off-diagonal block matrices of the block matrix to zero.