FDD大规模MIMO系统速率最大化导频信号设计方法

摘要

An optimization model is formulated with respect to the pilot signal in the frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) downlink system by maximizing the downlink ergodic achievable rate with total power constraint,while jointly considering the effects of the channel spatial correlation,channel estimation accuracy and the data beamforming scheme.Because the original objective function is not in closed form,an approximate analytical expression is derived by using the deterministic equivalent approximation technology in large-dimensional random matrix theory,which gives the explicit relations between the ergodic achievable rate and the pilot signal matrix.Based on this,the structural characteristic of the pilot signal matrix is deduced firstly by using the majorization theory,which makes the primal problem be an equivalent power allocation problem for the pilot sequence.Then,the closed-form solution of the optimal pilot signal is obtained by utilizing the Lagrangian dual method.Moreover,the actual length as well as the maximum value of pilot sequence is analyzed.Numerical results validate the accuracy and the effectiveness of the proposed analytical expression of the ergodic rate,and verify the performance gain of our proposed pilot scheme in terms of the ergodic achievable rate and the actual pilot sequence length when compared with the conventional mean square error (MSE) minimization based pilot scheme,and show the difference of the pilot signal power allocation of both schemes.%该文针对FDD大规模MIMO下行系统,联合考虑信道空间相关性、信道估计精度和波束成型方案对导频信号设计的影响,以最大化下行遍历可达速率为目标,以系统总功耗为约束,建立关于导频信号矩阵的优化模型.由于原始优化问题的目标函数没有闭合形式表达式,利用大维矩阵理论中确定性等价原理可获得其近解析表达式,从而得到了遍历速率关于导频矩阵的显示表达式.基于此,利用主导理论,推导出了最优导频信号所具有的矩阵结构特征.进而,将原优化问题转换为等价的导频序列功率分配问题,再利用拉格朗日对偶法求解得到了最优导频信号的闭合形式解.通过分析,给出了最优导频序列长度的实际值与最大范围.数值仿真结果验证了所推导的遍历速率解析表达式的精确性和有效性,并对比了所提出的导频方案与传统基于最小均方误差准则导频方案在遍历速率方面的性能增益,以及所使用的导频序列长度差异,同时给出了两种方案在导频信号功率分配时的差异性.