Note that we used ZF receiver for the open loop scheme while for the closed loop scheme, the MMSE receiver was employed.
Due to its simplicity and robust performance, the use of linear precoding has been widely studied as a closed loop scheme [2, 3].
The stability of the overall closed loop system in each scheme is established using Lyapunov Krasovskii functionals.
Now, Figure 5 illustrates the comparison of AGSSK and AGSSK-TOSD with closed-loop schemes and the open-loop GSSK for a rate of 4 bpcu.
As we see in this case, AGSSK-TOSD outperforms EGT with selection of the best subset of antennas and significantly the other closed-loop schemes for the examined SNR range and up to an ABEP value of 10-5.
Figure 2 Performance comparison of AGSSK and AGSSK-TOSD with closed-loop schemes and the open-loop GSSK for N t = 3, N a = 2, and a rate of 1 bpcu.
Figure 4 shows the performance comparison of AGSSK and AGSSK-TOSD with closed-loop schemes and the open-loop GSSK for a rate of 3 bpcu, where the N t = 6, N a = 4 configuration was chosen.
Figure 3 illustrates the performance comparison of AGSSK and AGSSK-TOSD with closed-loop schemes and the open-loop GSSK for N t = 4, N a = 2, and a rate of 2 bpcu.
Figure 2 illustrates the performance comparison of AGSSK and AGSSK-TOSD with closed-loop schemes and the open-loop GSSK and GSSK for N t = 3, N a = 2, and a rate of 1 bpcu.
As far as closed-loop schemes are concerned, to the best of the authors' knowledge there is only the work of [23] in which the authors introduced a feedback-based method suitable for 2 ×1 SSK systems where a phase variable is fed to the transmitter.
The asymptotic stability of the closed loop system under the robust adaptive boundary control scheme is proved through the use of semigroup theory.
