ENERGY EFfiCIENT TRANSMISSION IN MULTI-USER MIMO RELAY CHANNELS WITH PERFECT AND IMPERFECT CHANNEL STATE INFORMATION
ABSTRACT
We design novel transmission strategies to maximizethe energy efficiency (EE) of the uplink multi-user MIMO relaychannel. In this channel, K multi-antenna users communicatewith a multi-antenna base station (BS) through a multi-antennarelay. To achieve the goal of EE maximization, we propose newiterative algorithms to jointly optimize the multi-user precoderand the relay precoder under transmit power constraints fortwo cases. In the first case, the perfect global channel stateinformation (CSI) is available, while in the second case, the CSIbetween the relay and the BS is imperfect. To surmount the nonconvexityof our formulated EE optimization problems in bothcases, we introduce the parameter subtractive function into theproposed algorithms. Then the EE parameter in the parametersubtractive function is updated by the Dinkelbach’s algorithm inthe perfect CSI case, and by the bisection method in the imperfectCSI case. Moreover, in the perfect CSI case the relay precoderis optimized by the diagonalization operation and the multi-userprecoder is optimized based on the weighted minimum meansquare error method. Differently, in the imperfect CSI case weapply the sign-definiteness lemma to promote the semidefiniteprogramming formulation of the EE optimization problem.Furthermore, we present numerical results to demonstrate thatour proposed iterative algorithms have a good convergence ratein both cases. In addition, we show that our proposed iterativealgorithms achieve a higher EE performance than the existingalgorithms in both CSI cases.
EXISTING SYSTEM:
In the aforementioned studies, a key assumptionadopted is that the perfect channel state information (CSI)is available at each communication node. We note that thisassumption does not always hold in practical scenarios wherefeedback and quantization errors may occur. This has inspireda great extent of studies contributing to the EE improvementof wireless communication systems without perfect CSI,e.g. When the statistical CSI is available, determined the optimal EE precoding of the two-hop relaychannel, and demonstrated that the diagonalizationoperation can be used for robust EE optimization in a singlecellrelay-aided network. Differing from focused on the robust EE optimization from the worst-case CSIperspective. For example, the maximum worst-case EE of themulti-cell multi-user network was achieved by an alternatingoptimization algorithm.In this paper, we maximize the EE performance of theuplink in the multi-user MIMO relay channel for both perfectand imperfect CSI cases, which are of theoretical and practicalsignificance. To the best knowledge of the authors, suchmaximization has not been conducted in the literature.
PROPOSED SYSTEM:
The novel contributionsof our work are summarized as follows:1) In the perfect CSI case, we first show that the diagonalizationoperation is optimal to design the relayprecoder when the multi-user precoder is given. Thenwe apply the fractional programming method, i.e., theparameter subtractive function, to determine the optimalrelay precoder by solving a standard convex optimizationproblem. Once the optimal relay precoder is determined,we jointly use the weighted minimum mean squareerror (WMMSE) method and the parameter subtractivefunction to iteratively determine the optimal multi-userpreoder. We clarify that that the WMMSE methodis based on the equivalent relationship between thesignal-to-interference-plus-noise ratio (SINR) and theMSE. Finally, we use the Dinkelbach’s algorithm to update the key parameters in the parametersubtractive function.2) In the imperfect CSI case, we adopt the norm boundederror model to characterize the CSI between the relayand the BS. To maximize the robust EE based on theWMMSE method and the parameter subtractive functionin this case, we first introduce the sign-definitenesslemma to transform the robust EE optimizationproblem into a series of semidefinite programming (SDP)subproblems, which can be efficiently solved by theinterior point method. Then we propose a two-layer iterativeoptimization algorithm. In the inner optimization,the transformed SDP subproblems are solved iteratively.In the outer optimization, the bisection method overthe parameter in the parameter subtractive function isapplied to find the optimal EE.
CONCLUSION
In this paper, we proposed novel algorithms to maximize theEE of the uplink multi-user MIMO relay channel by jointlyoptimizing the multi-user precoder and the relay precoder.Notably, our algorithms were proposed for both the perfectglobal CSI case and the imperfect relay-to-BS CSI case. Toaddress the non-convexity of the formulated EE optimizationproblems in both cases, we proposed iterative algorithms andthe corresponding parametric subtractive function to optimizethe multi-user precoder and the relay precoder. With the aidof numerical results, we demonstrated the good convergencerate of our proposed algorithms. We also demonstrated thatour proposed algorithms achieve a higher EE gain than theexisting algorithms in both cases. We further evaluated theimpact of the transmit power, the circuit power consumption,and the CSI error threshold on this EE gain.
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