(4) ← solve the optimization problem of P1 (12) and find the solution .

(5) return S

(6) end function

(7)

(8) function ESTIMATING w BY MAXIMIZING THE OUTPUT SNR

(9) the optimum of P1.

(10) the initial value of .

(11) w ← solve the optimization problem of P2 (15) and find the solution w.

(12)return w

(13) end function

(14)

(15) function ESTIMATING BY MAXIMIZING THE CHANNEL CAPACITY

(16) S ← the optimum S of P1.

(17) w ← the optimum w of P2.

(18) ← solve the optimization problem of P3 (18) and find the solution .

(19) return

(20) end function

(21)

(22) Iteration: Rerun the steps 1 to 20 for some appropriate number of iterations and the

achievable performance will be the average of results at that specific SNR.

(23) return w, S and

(24) Finally, the antennas are chosen corresponding to the -largest diagonal elements of .

Algorithm 1: Processing procedure of the proposed low-complexity and joint transmit antenna selection and beamforming for large-scale MIMO communications.