Research On Hybrid Analog-Digital Precoding Problem Based On Multi-Scale Optimization

The rapid development of mobile communication technology has brought great influence on human society and changed people’s lives.With the wide deployment of large-scale antenna arrays,digital beamforming alone will cause great hardware overhead,while analog beamforming alone is often difficult to accurately adjust the beam direction.In order to save hardware overhead and ensure certain communication performance,hybrid analog and digital beam forming(HBF)structure came into being.In the traditional single-time scale hybrid precoding scheme,the design of analog precoding and digital precoding depends on the instantaneous Channel State Information(CSI),but the acquisition of CSI will cause great signaling overhead.In multi-scale mixed analog-digital precoding,this paper considers optimizing digital precoding and analog precoding at different time scales,designing analog precoding according to channel statistical characteristics,and designing digital precoding by using equivalent channel state information(that is,the cascade equivalent channel of analog precoding and wireless channel).The research shows that this multiscale hybrid precoding scheme can further reduce the complexity and signaling overhead of hybrid precoding with almost no performance loss.This paper studies the design of multi-scale hybrid precoding based on multi-scale optimization method.Firstly,two multi-scale optimization methods are introduced,including PDDSSCA method based on two-level Primal-Dual Decomposition(PDD)and stochastic successive convex approximation(SSCA),and multi-scale optimization method based on random matrix theory.Then,the problems of Sub 6G low-frequency hybrid precoding and millimeter-wave high-frequency hybrid precoding are studied respectively,and the corresponding hybrid precoding schemes and optimization algorithms are designed.In this paper,the general Sub 6G low-frequency multi-scale precoding system model is studied,and a unified multi-scale hybrid precoding scheme is proposed.Based on PDD-SSCA method,the analog precoding of slow time scale and the digital precoding of fast time scale are jointly optimized.In the design of multi-scale hybrid precoding,the analog precoder is updated on a long time scale based on the statistical information of channel samples.The digital precoder is optimized on a faster time scale according to the low-dimensional equivalent channel state information.PDDSSCA divides the original optimization problem into optimization variables according to different time scales.For the digital precoding optimization subproblem with fast time scales,we use the traditional optimization algorithm WMMSE algorithm to solve it.For the analog precoding optimization subproblem with slow time scale,we use the constrained stochastic successive convex approximation(CSSCA)algorithm framework to solve it.Simulation results show that PDD-SSCA can significantly reduce the complexity of the algorithm and achieve better performance than the existing solutions.Aiming at the problem of millimeter-wave high-frequency hybrid precoding,this paper proposes a two-time scale hybrid precoding scheme based on user grouping and codebook selection(GCTHP).In this scheme,the analog precoder is selected from the codebook with N beams,and the users are divided into J groups according to the statistical characteristics of the channel.Because a single analog precoder can’t serve all users,L analog precoders are used to serve different user packets in time division multiplexing,so as to achieve the best compromise between throughput and user fairness in the system.According to the statistical characteristics of channel in N dimensional beam domain,the scheduling vectors of analog precoder and related user groups and time division factors are optimized on the slow time scale to maximize the proportional fair utility.User scheduling and digital precoding matrix are jointly optimized on a fast time scale to maximize the spatial multiplexing gain.By selecting the number of beams N and the number of user packets J in the codebook,a flexible trade-off between performance and implementation complexity is achieved.Simulation results show that the proposed GC-THP achieves better performancecomplexity tradeoff than the existing hybrid precoding schemes.Finally,we explain the innovation of this paper from the perspectives of multi-scale hybrid precoding scheme design,optimization problem modeling and optimization algorithm design,and look forward to the follow-up work and future research direction from the perspectives of enhancing algorithm universality and reducing algorithm complexity.