In an underdetermined system, compressive sensing can be used to recover the support vector. Greedy algorithms will recover the support vector indices in an iterative manner. Generalized Orthogonal Matching Pursuit (GOMP) is the generalized form of the Orthogonal Matching Pursuit (OMP) algorithm where a number of indices selected per iteration will be greater than or equal to 1. To recover the support vector of unknown signal ‘

Compressed sensing will aid to recover a

The smallest constant

Sufficient condition to guarantee the support recovery for GOMP algorithm has been derived using the coherence of the sensing matrix

GOMP can select

Step 1: Input:

Step 2: Initialize:

Step 3: For Each

Step 4: Compute the correlation and find the first Q indices where correlation is

Step 5: Select the first ‘Q’ largest value indices

Step 6: Update sub band support indices

Step 7: Estimate the signal vector

Step 8: Update residual

Step 9:

Step 10: Go to step 2

Step 11: End For Return index set of sub band support indices

Step 12: Output: Support vector indices

Step 13: end

Algorithm for generalized orthogonal matching pursuit shown in GOMP algorithm has three parts identification, augmentation and residual update. In the step 4, magnitude of the correlation between each column of matrix

Line 7 finding the least square estimate of the signal vector, to find the residual

Coherence of sensing matrix

In this lemma 3 lower bound can be defined with the help of coherence

The above expression plays a key role in proving the theorem 1. It holds good for generalized case of OMP.

The proof for the special case

First we need to prove that the selection of

Instead of proving

By expression

residual in the algorithm at ^{th} iteration can be expressed as

Thus, by

It is a two-step process to fond the lower bound. To find the lower bound on maximum of

Lower bound on

Hence the proof.

Remark: from the expression

In the simulation, the unknown sparse signal is defined as^{th} sub-band in the wide bandwidth,

Number of support indices selected in each iteration should satisfy the constraint

In this paper, successful recovery of support vector indices with respect to SNR for given sparsity of P using generalized orthogonal matching pursuit is shown in the

We note that the precise reconstruction probability and the computation time of the sparse signal vary with the level of sparsity. Reconstruction results for the different algorithms are presented in

In this paper, it has been proved that