| In each time slot with instantaneous channel realization , do the followings: |
| (I)Initialization: Consider , e.g., , sets of precoding matrices and combining matrices , |
| , randomly selected from the pre-defined codebook and . |
| (II) Selection: For each and , evaluate the instantaneous value of the objective metric , |
| , for example end-to-end throughput (5). Find the best beamforming matrix which |
| results in the best value of the considered metric, named as the Queen, e.g., and satisfies |
| , if the end-to-end throughput is the objective function. |
| (III) Save the Queen: , |
| (IV) Genetic operation I-Crossover: Create , e.g., , beamforming matrices and , |
| , around the Queen and . These sets are generated |
| by making small changes in the Queen and . |
| (V) , , . |
| (VI) Genetic operation II-Mutation: Regenerate the remaining sets and , , |
| randomly with the same procedure as in Step (I). |
| (VII) Go back to Step (II) and run for iterations, is a fixed number decided by designer. |
| Return the final Queen as the beam selection rule for the current time slot. |
