A Sparse CoSaMP Channel Estimation Algorithm With Adaptive Variable Step Size for an OFDM System

Table 1

Differences between the CoSaMP algorithm and the Vss-CoSaMP algorithm.

Step	CoSaMP algorithm	Vss-CoSaMP algorithm
1	Input: Sensing matrix ( dimensions), sampling vector , signal-noise ratio (SNR) , step size	Input: Sensing matrix ( dimensions), sampling vector , SNR , step size ;
2	Initialize , , ,	Initialize , , , , ,
3	Calculate the inner products of sensing matrix and residual error, select the subscripts with the maximum values of term to expand the candidate set ( term)	No difference ( term)
4	Calculate the least squares solution for signal approximation, and select the subscripts with the maximum values of term to remove the redundant atoms from the candidate set	No difference
5	Update the support set for signal approximation	No difference
6	Update the residual error	No difference
7	Judge the iteration termination condition. If satisfied, break the iteration loop. If not, the number of iterations increases by 1, and enter Step 3	Judge the iteration termination condition. If satisfied, break the iteration loop. If not, enter Step 8
8	None	Judge the step size reduction condition. If satisfied,
9	None	Judge whether it satisfies . If satisfied, , or start the next iteration
10	Output	No difference