该文针对成对用户大规模MIMO中继系统，研究了最优能效准则下的系统参数设计。在中继采用最大比合并/最大比发射(MRC/MRT)预编码方案下，借助于大数定律，推导出能效函数关于用户发射功率、中继发射功率和中继天线数的解析表达式。根据能效函数性质，分别证明了全局最优发射向量和最优天线数的存在性和唯一性。为了求解最优发射功率，利用分数规划，将原优化问题转换为等价的减法形式，进而提出一种新的低复杂度迭代优化算法，并求得最优发射功率的闭合解。对于最优天线数，则利用Lambert W函数，得到了能效最大时的最优天线数闭合解。通过数值仿真，验证了所提功率优化算法以极少迭代次数取得了接近最优算法的性能，并验证了所给出的最优天线数闭合解的精确性。%The optimal system design based on maximizing the Energy Efficiency (EE) is investigated for the multi- pair massive Multiple-Input Multiple-Output (MIMO) relaying system. By virtue of the law of large numbers, an analytical expression of the involved EE function is derived with respect to the transmit power at the users and the relay, and the antenna number of the relay, when the Maximum Ratio Combining Maximum Ratio Transmission (MRC/MRT) precoding is adopted at the relay. The existences of a unique globally optimal transmit power vector and a unique globally optimal antenna number at relay are demonstrated separately by exploring the properties of the EE function. In order to obtain the optimal transmit power vector, the original fractional optimization problem is first transformed into an equivalent subtractive form by using the properties of fractional programming. Then, a low-complexity iterative algorithm is developed and the closed-form solution is deduced. Regarding the optimal number of relay antennas, a closed-form solution is also achieved by use of the Lambert W function. Numerical simulations show that the proposed power optimization algorithm converges to a near optimal solution only with a few numbers of iterations and the provided closed-form solution to the optimal number of relay antennas is also accurate.
展开▼
