Pilot Design for Sparse Channel Estimation in Large-Scale MIMO-OFDM System

Algorithm 2

Pilot design algorithm based on alternating projection.

Input:

 (i) An initial matrix set

 (ii) A partial FFT matrix with columns and orthogonal rows

 (iii) The number of iterations

Output:

 (i) The optimized matrix set

Procedure:

 (1) Initialize the iterate counter

 (2) Calculate where

   and ∈

 (3) Use (13) and (14) to find the matrix which is nearest to in and respectively

 (4) Use GA algorithm to solve (15) in which

    (a) Let

    (b) Use GA algorithm to solve the following problem:

          ,

       where = , and is only related to

    (c) Increment , repeat the step (b) to step (c) until and then, obtain the

 (5) Increment

 (6) Repeat the step (2) to step (5) until , then