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

Algorithm 2

Procedure of the CoSaMP algorithm.

Input: Sensing matrix ( dimensions), sampling vector , signal-noise ratio , sparsity ;

Output: Approximation of K-sparsity to the unknown channel impact response ;

Initialize:

   (Initialize the column vector for saving restorations)

   (Initialize the support set to save the column serial numbers of the selected sensing matrix)

   (Initialize the residual error as the sampling vector)

   (Determine the maximum number of iterations)

Repeat

   (Select and save the subscripts of 2K values with the largest inner product)

   (Expand the candidate set)

   (Take the subscripts of values with the largest least squares solution, remove the redundant atoms from the candidate set, and update the support set)

   (Obtain the residual error of this iteration, and update the residual)

  if Iteration termination condition tol is satisfies,

   break the loop

  end

until the iteration termination condition is satisfied or the maximum number of iterations is reached

Output: