where [[epsilon].sub.0] = ([[epsilon].sub.A]/(1/[square root of (3)] - (1 + 1/[square root of (3)])[[epsilon].sub.A]) + [epsilon])([[parallel][??][parallel].sub.F]/(1 - [epsilon])), then GBCD can exactly recover the support set [GAMMA].
In order to guarantee that GBCD selects a correct index [i.sub.0] [member of] [GAMMA], combining step (4) of Algorithm 1 and (20), we should verify the following inequality:
Assume that GBCD always picks up indices from the support [GAMMA] for n [less than or equal to] k (k [greater than or equal to] 1 is an integer).
In the work of , the authors provided that the condition for GBCD is [[delta].sub.K+1] < 1/([square of (K)] + 1).
In this section, giving a matrix [??], whose RIC is a slight relaxation of 1/[square root of (K + 1)], we will verify that GBCD can fail to recover the support of sparse matrix from (62).
Recall that condition (27) is the criterion of recovery for GBCD. Note that [[parallel][p.sup.i](0)[parallel].sub.2] = [[parallel][beta][a'.sub.i][??][parallel].sub.2].
They showed that the GBCD algorithm fails when using [bar.A] as measurement matrix.
In this section, under the total perturbations, we test the performance of the GBCD algorithm for solving the DOA estimation problem.
Figure 1, fixing matrix E, describes the performance of GBCD. The results show that RMSE decreases as SNR1 increases.