Energy Efficiency Analysis And Optimization For Reconfigurable Intelligent Surface Aided DF Relay Cooperation System

Reconfigurable intelligent surface（RIS）has become one of the potential key technologies for the future 6th generation mobile communication systems（6G）due to its low cost,low power consumption,easy deployment,reconfigurability,ability to improve channels,etc.However,the passive nature of RIS also leads to significant multiplicative path loss,especially in the high frequency band,which requires considerable transmit power or RIS scale to outperform traditional decode-and-forward（DF）relay in terms of performance.At the same time,the rapidly increasing energy consumption in communication network have attracted more and more attention to green communication.Energy efficiency（EE）has become a key performance indicator to measure the quality of a system.To fully utilize the advantages of RIS and DF relay,a RIS assisted DF relay cooperation communication system is studied in this article,and theoretical analysis and optimization of the system EE are conducted.Specifically,we introduce RIS on the basis of existing relay cooperation systems to construct an adaptive wireless environment and provide passive beam gain with low power consumption.At the same time,DF relay is used to compensate for the multiplicative path loss,so that the number of required RIS reflecting elements as well as the configuration and design complexity in practical applications can be reduced.The main contributions of this article are summarized as follows:（1）For a simple scenario with single antenna and perfectly known channel state information（CSI）,first,the ergodic energy efficiency upper bound is derived using the Jensen inequality and statistical properties of Rayleigh channel.Next,for fixed total transmit power and flexible total transmit power upper bounded by P_max,the EE optimization problem is respectively formulated and solved under the minimum rate constraint.In the fixed power scenario,the optimal RIS phase shifts at two slots are optimized based on CSI.Then the problem is transformed into an equivalent optimal power allocation（OPA）problem with minimum-rate guarantee and the optimal close-form solution is derived.In the upper-bounded power scenario,the non-convex fractional optimization problem is solved by fractional programming and generalized Dinkelbach’s algorithm,of which the convergence and global optimality are proved.Finally,illustrative simulation results demonstrate the superiorities of the considered RIS-aided DF relay cooperation scheme as compared with the benchmark ones.Besides,the results reveal the effects of various factors on the performance,such as discrete quantization of RIS phase shift,target rate,imperfect CSI,and number of relays,etc.（2）Considering that the passive nature of RIS makes it difficult to obtain the perfect CSI in practical applications,the multiple input multiple output（MIMO）scenario with bounded/statistical channel estimation error（CEE）is further considered.For bounded CEE,a worst-case robust EE optimization problem is firstly formulated,where the precoding matrices of the source and destination nodes as well as the RIS passive beamforming are jointly designed under maximum total transmit power and minimum rate constraints.With the help of fractional programming and S-procedure,the original fractional optimization problem with indeterminacy is reformulated into a deterministic subtractive problem which is easy to process.Next,the problem is decoupled into two subproblems of precoding matrix and RIS phase shift.For the latter,the non-convex phase shift constraints are processed by two methods,i.e.,semi-definite relaxation（SDR）and penalty concave convex procedure（PCCP）.Finally,the alternative optimization（AO）&SDR/PCCP-based Dinkelbach robust EE optimization algorithms are proposed to solve the problem in an iterative manner.For statistical CEE,an outage probability constrained EE optimization problem is firstly fomulated,where the precoding matrices and passive beamforming are jointly optimized to maximize robust EE under the constraints of maximum total transmit power and outage probability.Next,the problem is transformed into a tractable one by the method similar to that in the case of bounded CEE.Due to the difficulty in deriving a simple close-form expression for the outage probability constraint,Bernstein type inequality are employed to approximate the probability constraint to several addressable inequality constraints.Finally,the proposed AO&SDR/PCCP-based Dinkelbach algorithms are used to solve the problem.The simulation results show that the multi-antenna DF relay cooperative MIMO scheme assisted by RIS is superior to the scheme assisted only by RIS or DF relay;Compared to non-robust method where CEE is neglected,the proposed robust design can achieve significant gains in terms of performance;In addition,simulations are conducted to compare the performance of the two proposed algorithms,and the effects of different parameters are studied.