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

Algorithm 1

Procedure of the SAMP core algorithm.

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

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

Initialize:

   (Initialize the column vector for saving estimations)

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

   (Initialize the residual error as the sampling vector)

   (Initialize the size of the support set as the step size of initial input)

   (Initialize the step size expansion counter)

   (Initialize the subscript)

   (Determine the maximum number of iterations)

Repeat

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

   (Expand the candidate set)

   (Obtain and save the subscripts of L values with the largest least squares solution)

   (Obtain the residual error of this iteration)

  if iteration termination condition tol is satisfies,

   break the loop

  else if

    (The support set is expanded by 1)

    (Expand the support set)

  else

    (Update the support set)

    (Update the residual error)

  end

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

Output: