In this paper, we develop an efficient training beam sequence design approach for millimeter wave MISO tracking systems. We impose a discrete state Markov process assumption on the evolution of the angle of departure and introduce the maximum a posteriori criterion to track it in each beam training period. Since it is infeasible to derive an explicit expression for the resultant tracking error probability, we turn to its upper bound, which possesses a closed-form expression and is therefore leveraged as the objective function to optimize the training beam sequence. Considering the complicated objective function and the unit modulus constraints imposed by analog phase shifters, we resort to the particle swarm algorithm to solve the formulated optimization problem. Numerical results validate the superiority of the proposed training beam sequence design approach.

翻译：在本文中,我们为毫米波 MISO 跟踪系统开发了高效的培训波束序列设计方法。 我们对启程角度的演进设置了离散状态的Markov 程序假设,并引入了在每一波束训练期间跟踪它的最大后继标准。由于无法对由此产生的跟踪误差概率作出明确表达,我们转向其上界,它具有封闭式表达方式,因此被作为优化培训波束序列的客观功能加以利用。考虑到目标功能的复杂性和模拟相向转换器对单元模量的限制,我们采用粒子群算法来解决所拟订的优化问题。数字结果验证了拟议培训波束序列设计方法的优越性。