Symbol Level Precoding And Receive Beamforming For MU-MIMO

Multiple-input multiple-output（MIMO）system can provide rich spatial freedom for eliminating interference and scheduling more users by configuring a large number of transceiver antennas at the base station.Symbol level precoding（SLP）can achieve better performance than precoding,and has received extensive attention.Large-scale MIMO can further increase the spatial degree of freedom,but the introduction of large-scale antennas will bring great challenges to the complexity of equipment and the cost of radio frequency（RF）devices.Constant envelope（CE）precoding and1-bit precoding can effectively solve this problem.In this paper,the following studies are carried out respectively for the above systems and problems.Firstly,the joint design of SLP and receive beamforming（RBF）is studied for multi-user MIMO（mu-mimo）systems.Existing SLP articles are all targeted at multiple-user multiple-input single-output（MISO）systems,but this paper studies the scenario of receiving multiple-antenna users.In this paper,we first establish an optimization problem aiming at minimizing the Symbol error probability（SEP）of the receiver under the constraint of transmitting power.Due to the existence of RBF matrix in the objective function,the optimization problem has non-convex constraints.Therefore,this paper first transforms the l₂ norm factors in the objective function into l₂ norm constraints through problem equivalence transformation.Then,the log-sum-exp function is used to approximate the infinite norm in the objective,and the problem is transformed into a form suitable for gradient projection algorithm.Finally,an Accelerated Projected Gradient APG algorithm is designed to solve the optimization problem efficiently.The simulation results verify the effectiveness of the decomposition design and the APG algorithm in this paper.Secondly,for large-scale MU-MIMO systems,the joint design of SLP and RBF under constant envelop constraint of preencoder is studied.In this paper,the problem of l₂ norm factor of objective function is solved by equivalent transformation at first.Then,the problem of non-smooth objective function is solved by log-sum-exp function.Finally,an APG algorithm based on non-convex is designed in this paper.During projection,the normalized projection is used to make the modulo value of the variable after each iteration constant,which solves the CE constraint problem in the APG algorithm.The simulation results verify the effectiveness of the proposed scheme and algorithm.