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In this work, we present a framework analysis of full-duplex (FD) systems for Millimeter Wave (mmWave) analog architecture. Given that FD systems can double the ergodic capacity, such systems experience large losses caused by the loopback self-interference (SI). In addition, systems with analog architecture also suffer from other forms of losses mainly incurred by the constant amplitude (CA) constraint. For this purpose, we propose the projected Gradient Ascent algorithm to maximize the sum rate under the unit-norm and CA constraints. Unlike previous works, our approach achieves the best spectral efficiency while minimizing the losses incurred by the CA constraint. We also consider an adaptive step size to compensate for the perturbations that may affect the cost function during the optimization. The results will show that the proposed algorithm converges to the same optimal value for different initializations while the number of iterations required for the convergence changes for each case. In this context, we primarily consider the gradient search method for a two-nodes FD systems and then we extend the analysis for a dual-hop FD relaying systems. Finally, we evaluate the robustness of our method in terms of rate and outage probability and compare with previous approaches.