Research On Antenna Selection In Massive MIMO Systems Based On Submodular Functions

In recent years,the traffic of wireless data service is increasing exponentially,and the demand for higher quality communication service is also growing stronger.As one of the key technologies of the fifth generation(5G)mobile communication systems,massive Multi-Input Multi-Output(MIMO)can significantly increase spectrum efficiency and system capacity,which will play an important role in the future communication systems.Compared with the conventional scale MIMO systems,massive MIMO systems are equipped with large scale antennas at the base station and can serve more user terminals with the same time-frequency resources.However,large-scale antenna arrays need more radio frequency(RF)chains.Compared to the cheap antenna units,the RF chains are relatively expensive components in communication systems.Therefore,while the massive MIMO systems have a huge capacity gain,the corresponding price paid is the high cost of the RF chains,but also the high complexity of full transceiver design for a large antenna array.Antenna selection is an effective method to solve the problems above,which can reduce overhead and complexity of the systems and guarantee that the system performance meets the demand of communication service.This paper focuses on the antenna selection problem in massive MIMO systems.First,we propose an improved 2-norm based antenna selection scheme.After that,we analyze the antenna selection problem from the view of the submodular functions.According to the "Law of Diminishing Returns" under the framework of submodularity,we design a customized capacity increment maximized greedy algorithm with guaranteed theoretical performance,and give out the corresponding theoretical analysis afterwards.The main contents and work of this article are as follows:1.This paper introduces massive MIMO system model,along with the discussion and analysis of system channel capacity.The theoretical basis of submodular functions is shown,mainly including the formal definition of submodualr functions,the source of research of submodualr functions,and the application of submodualr functions.2.In this paper,the model of antenna selection in the uplink of massive MIMO systems isestablished.We design an improved 2-norm based antenna selection scheme to reduce the number of antennas while guarantee the sufficient channel capacity performance with a low complexity.Aided by a selection coefficient,this scheme dynamically adjusts the number of antennas in use,which is determined by the different channel condition.3.According to the in-depth analysis of antenna selection,this paper explore that antenna selection problem actually possesses the nature of discrete set selection problems.Then submodular functions in discrete set functions is introduced to antenna selection issues.Firstly this paper combines the submodular functions with antenna selection and explores the submodularity inner the antenna selection model.Secondly the model of antenna selection in the uplink of massive MIMO systems is formulated to constrained submodular functions optimization(SFO)under the framework of submodularity,along with a customized capacity increment maximized greedy algorithm inspired by the "Law of Diminishing Returns".Then the dual problem of proposed optimization model as well as its dual capacity increment maximized greedy algorithm is further investigated.4.The theoretical analysis of the greedy algorithm for antenna selection model based on submodular functions in this paper shows that: the approximate ratio between the suboptimal solution obtained by the greedy selection algorithm and the optimal solution of the original problem provides the theoretical guarantee in the worst case.In other words,the suboptimal solution of this algorithm can be treated as the lower bound of the optimal solution of the antenna selection problem in the uplink of massive MIMO systems.