1. 清华大学 电子工程系, 北京 100084;
2. 中国电子科技集团公司 电子科学研究院, 北京 100041
收稿日期: 2016-04-19
基金项目: 国家“九七三”重点基础研究项目(2012CB316002);国家“八六三”高技术项目(2015AA01A701);国家科技重大专项(2014ZX03003003-002);国家自然科学基金资助项目(61201192,61321061);清华-高通联合研究项目
作者简介: 王璟(1984-),男,博士研究生
通信作者: 周世东,教授,E-mail:zhousd@tsinghua.edu.cn
摘要:该文将各分布式天线簇内的天线单元相关性纳入考虑,且在仅可获得包含发送端大尺度信道状态信息和发送天线单元相关特性的慢变信道统计特性的条件下,研究多小区分布式天线系统(distributed antenna system,DAS)的高能效协同传输问题,通过小区间协同优化输入协方差矩阵,使系统能效最大化。该优化问题为复杂的非凸问题,故难以求解。通过连续Taylor展开方法,使原问题转化成系列拟凸分式规划子问题,然后通过分式规划方法将其进一步转化成易处理的等价凸问题。据此,提供一种原优化问题的迭代法求解方案。仿真结果验证:相比已有方案,该方案改善了系统的能效水平。
关键词: 移动通信 分布式天线系统 高能效 协同传输 天线相关
Energy efficient coordinated transmission scheme for multi-cell distributed antenna systems
WANG Jing1, WANG Yanmin2, FENG Wei1, XIAO Limin1, ZHOU Shidong1
1.Department of Electronic Engineering, Tsinghua University, Beijing 100084, China;
2.Academy of Electronics and Information Technology, China Electronics Technology Group Corporation, Beijing 100041, China
Abstract:The energy efficiency of coordinated transmissions in multi-cell distributed antenna systems (DAS) was analyzed with a focus on the antenna element correlation within each distributed antenna cluster to maximize the system energy efficiency through inter-cell coordinated optimization of the input covariance matrices. The system uses only the slowly varying channel statistics including the large-scale channel state information at the transmitter and the transmit antenna element correlation characteristics. The optimization problem is non-convex and, therefore, is hard to solve. The method of successive Taylor expansions was used to recast the problem into a succession of quasi-convex fractional optimization sub-problems, which were then further converted to tractable equivalent convex forms via the fractional programming approach. An iterative scheme was then used to address the original optimization problem. Simulations show that this scheme provides improved system energy efficiencies compared to existing schemes.
Key words: mobile communicationdistributed antenna system (DAS)energy efficientcoordinated transmissionantenna correlation
现在,追求更高的能量效率已成为未来移动通信系统设计的重要需求[1-2]。分布式天线系统(distributed antenna system,DAS)由于接入距离缩短和相应的传输功耗下降、系统容量提升等优势,从而具备较好的能效性能,成为了高能效通信设计的一种很有前途的技术方案[2-3]。
DAS系统在工程部署实现时,因站址获取受限等客观约束,系统的各分布式天线单元在部署范围内往往会被成簇配置成多个分布式天线簇(distributed antenna cluster,DAC)[4-6]。由于在基站一侧的各DAC一般放置得比较高,这样在其附近就难以满足富散射条件,因此在同一DAC中的各个天线单元之间通常会具有相关性[4-7]。研究表明在发送天线单元间所存在的相关性会明显降低通信系统的性能[8],为此需匹配天线相关特性而对传输方案进行专门设计(如在文[7]中优化设计输入协方差矩阵),从而改善通信系统的性能[6-7]。
在多小区DAS系统设计中,小区间干扰成为一种重要的系统性能瓶颈问题,为此可通过小区间协同传输来应对该问题[9-10]。在协同传输方案的设计中,发送端所获信道状态信息(channel state information at the transmitter,CSIT)的情况很关键[11-12]。相比完全的CSIT条件,大尺度CSIT变化缓慢、更易于估测、获取开销少,因此仅基于大尺度CSIT条件进行多小区DAS协同传输方案设计往往更适合于工程实际应用[13-15]。文[14]利用大尺度CSIT条件,研究了多小区下行DAS中高能效协同功率分配问题,使得系统能效最大化。此外,文[15]也仅利用大尺度CSIT条件,在多小区下行DAS中对各用户的输入协方差矩阵,进行了小区间协同优化设计。然而,文[14-15]均基于理想的发送天线不相关的假设,而没有将实际的天线相关性考虑在内。在实际信道条件下考虑天线相关性,以实现多小区DAS中高能效协同传输,目前尚无较为有效的设计方案。
本文以下行多小区DAS作为研究对象,将各DAC内的天线单元相关性纳入考虑,且在仅可获得慢变信道统计特性(包括含路径损耗、阴影衰落等的大尺度CSIT和发送天线单元相关特性)的条件下,研究通过小区间协同优化输入协方差矩阵以使得系统能效最大化的高能效协同传输问题。该优化问题为复杂的非凸问题,故难以求解。为此首先,通过连续Taylor展开方法,使该问题转化成系列拟凸分式规划子问题; 然后,通过分式规划方法将其进一步转化成等价凸子问题以有效处理。最终,据此提供一种该高能效协同传输问题的迭代法求解方案。仿真结果验证,该方案显著改善了DAS能效水平。
1 系统描述本文研究下行的多小区DAS系统见图 1,该系统的小区数为K,小区k(k=1,2,…,K)内有1个配备Mk个天线的用户k以及Nk个散布放置的DAC。 各DAC中均配备V个天线单元,每个DAC中这V个天线单元之间存在相关性。每小区内部,各DAC经过光纤或同轴电缆等高速传输媒介与中心处理单元联接,对小区内信号实现联合处理。小区之间,各小区的中心处理单元间通过有限的协同链路获取大尺度CSIT与有关控制信令等,进行跨小区间的协同传输。
图 1 多小区DAS图 |
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用户k处下行接收信号为
${{y}_{k}}={{H}_{k,k}}{{x}_{k}}+\sum\limits_{j=1,j\ne k}^{K}{{}}{{H}_{k,j}}{{x}_{j}}+{{n}_{k}}.$ |
${{H}_{k,j}}={{W}_{k,j}}R_{j}^{1/2}{{F}_{k,j}}.$ |
$~{{R}_{j}}=diag(R_{j}^{(1)},R_{j}^{(2)},\ldots ,R_{j}^{({{N}_{j}})}).$ |
${{F}_{k,j}}=diag(f_{k,j}^{(1)}{{I}_{V}},f_{k,j}^{(2)}{{I}_{V}},\ldots ,f_{k,j}^{({{N}_{j}})}{{I}_{V}}).$ |
2 问题建模因为发送端仅能获得慢变信道统计特性(含大尺度CSIT{Fk,j|k,j=1,2,…,K}与发送天线单元相关特性{Rk|k=1,2,…,K}),故可通过把系统瞬时和容量关于小尺度W={Wk,j|k,j=1,2,…,K}求期望,得到系统遍历和容量[13]为
$C\left( Q \right) = \sum\limits_{k = 1}^K {} {E_{W}}\left[ {lbdet\left( {{I_{{M_k}}} + \frac{{{H_{k,k}}{Q_k}H_{k,k}^H}}{{z_k^2\left( Q \right)}}} \right).} \right]$ |
$~z_{k}^{2}\left( Q \right)=\sum\limits_{j=1,j\ne k}^{K}{{}}tr({{F}_{k,j}}{{R}_{j}}{{F}_{k,j}}{{Q}_{j}})+\sigma _{k}^{2}.$ |
$~{{\eta }_{EE}}\left( Q \right)=\frac{C\left( Q \right)}{\xi \sum\limits_{k=1}^{K}{{}}tr({{Q}_{k}})+{{P}_{C}}}.$ |
然后,经过小区间协同优化输入协方差矩阵以使得系统能效最大化的高能效协同传输问题,可构建为
$\begin{array}{*{35}{l}} \underset{Q}{\mathop{\max }}\,{{\eta }_{EE}}\left( Q \right); \\ s.t.tr({{Q}_{k}})\le P_{k}^{max}; \\ {{Q}_{k}}\succcurlyeq 0,\forall k. \\\end{array}$ | (1) |
3 高能效协同传输方案为了简化式(1)求解过程,考虑对其目标函数ηEE(Q)引进一个闭式表达的上界函数[5]为
$\begin{align} & \eta _{EE}^{ub}\left( Q \right)= \\ & \frac{\sum\limits_{k=1}^{K}{{}}lb~det\left( {{I}_{{{N}_{k}}V}}+\frac{{{M}_{k}}{{Q}_{k}}{{F}_{k,k}}{{R}_{k}}{{F}_{k,k}}}{z_{k}^{2}\left( Q \right)} \right)}{\xi \sum\limits_{k=1}^{K}{{}}tr({{Q}_{k}})+{{P}_{C}}}. \\ \end{align$ |
$\begin{align} & \underset{Q}{\mathop{\max }}\,\text{ }\eta _{EE}^{ub}\left( Q \right); \\ & s.t.~tr({{Q}_{k}})\le P_{k}^{max}; \\ & {{Q}_{k}}\succcurlyeq 0,\forall k. \\ \end{align}$ | (2) |
$\eta _{EE}^{ub}\left( Q \right)=\frac{{{\varphi }_{1}}\left( Q \right)-{{\varphi }_{2}}\left( Q \right)}{\xi \sum\limits_{k=1}^{K}{{}}tr({{Q}_{k}})+{{P}_{C}}}.~$ |
$\begin{align} & {{\varphi }_{1}}\left( Q \right)=\sum\limits_{k=1}^{K}{{}}lb~det(z_{k}^{2}\left( Q \right){{I}_{{{N}_{k}}V}}+{{M}_{k}}{{Q}_{k}}{{F}_{k,k}}{{R}_{k}}{{F}_{k,k}}), \\ & {{\varphi }_{2}}\left( Q \right)=\sum\limits_{k=1}^{K}{{}}{{N}_{k}}Vlb(z_{k}^{2}\left( Q \right)).~ \\ \end{align}$ |
将函数φ2(Q)于Q点处作一阶Taylor展开如下:
${{\varphi }_{2}}(Q|\bar{Q})={{\varphi }_{2}}(\bar{Q})+\sum\limits_{k=1}^{K}{{}}tr(Gk(\bar{Q})[Q\text{-}\bar{Q}]).$ |
$\begin{align} & {{G}_{k}}\left( Q \right)=diag\{{{G}_{k,1}}\left( Q \right),{{G}_{k,2}}\left( Q \right),\ldots ,{{G}_{k,K}}\left( Q \right)\}; \\ & {{G}_{k,j}}\left( Q \right)=lb(e)\frac{{{N}_{k}}V}{z_{k}^{2}\left( Q \right)}\left( {{F}_{k,j}}{{R}_{j}}{{F}_{k,j}} \right){{}^{T}}, \\ & k\ne j,\text{ }k,\text{ }j=1,2,\ldots ,K; \\ & {{G}_{k,k}}\left( Q \right)=0,\text{ }k=1,2,\ldots ,K. \\ \end{align}$ |
$\begin{align} & \underset{Q}{\mathop{\max }}\,\hat{\eta }_{EE}^{ub}(Q|\bar{Q})=\frac{{{\varphi }_{1}}(Q)-{{{\hat{\varphi }}}_{2}}(Q|\bar{Q})}{\xi \sum\limits_{k=1}^{K}{{}}tr(Qk)+{{P}_{C}}}; \\ & s.t.tr({{Q}_{k}})\le P_{k}^{max}; \\ & {{Q}_{k}}\succcurlyeq 0,\forall k. \\ \end{align}$ | (3) |
$\begin{align} & \underset{Q}{\mathop{\max }}\,\lambda \left( Q|\bar{Q},\mu \right); \\ & s.t.\text{ }tr({{Q}_{k}})\le P_{k}^{max}; \\ & {{Q}_{k}}\succcurlyeq 0,\forall k. \\ \end{align}$ | (4) |
$\begin{align} & \lambda (Q|\bar{Q},\mu )= \\ & {{\varphi }_{1}}(Q){{{\hat{\varphi }}}_{2}}(Q|\bar{Q})\text{-}\mu \sum\limits_{k=1}^{K}{{}}tr(Qk)-\mu {{P}_{C}}. \\ \end{align}$ |
$\begin{array}{l}{\mu ^*} = \mathop {\max }\limits_Q \hat \eta _{EE}^{ub}(Q|\bar Q),\\\Lambda = \mathop {\max }\limits_Q \lambda (Q|\bar Q,\mu ).\end{array}$ |
综合以上研究,本文提供一种两层迭代算法对高能效协同传输问题进行求解。基于文[15, 17],该算法的收敛性能够确保。该算法各次迭代(n、m为外层迭代与内层迭代的次数)当中,需求解以下凸子问题:
$\begin{align} & \underset{Q}{\mathop{\max }}\,\lambda (Q|{{Q}^{(n-1,m-1)}},\mu ); \\ & s.t.\text{ }tr({{Q}_{k}})\le P_{k}^{max}; \\ & {{Q}_{k}}\succcurlyeq 0,\forall k. \\ \end{align}$ | (5) |
步骤1?外层迭代初始化。设Q(0)=diag(Q1(0),Q2(0),…,QK(0)),Qk(0)=
步骤2?执行外层的第n次迭代,n=1,2,…。 在本次外层迭代中,进行内层迭代的初始化: 令Qk(n-1,0)=Qk(n-1),k=1,2,…,K,令μ=0,并配置内层迭代的误差限值参数δI。
步骤3?执行内层的第m次迭代,m=1,2,…。解式(5)中凸子问题,得出优化后输入协方差矩阵Qk(n-1,m),k=1,2,…,K,以及对应Λ(μ)。 然后,对μ进行更新: μ=
步骤4?若Λ(μ)<δI,令Qk(n)=Qk(n-1,m),k=1,2,…,K; 否则,转步骤3。
步骤5?令Q(n)=diag(Q1(n),Q2(n),…,QK(n))。 若[ηEEub(Q(n))-ηEEub(Q(n-1))]/ηEEub(Q(n-1))<δO,则结束本算法; 否则,转步骤2。
4 仿真结果与分析在仿真分析时,K设为3,各小区半径设为 1 000 m,在各小区k中都满足Mk=3、Nk=3、V=3,用户与DAC于各小区范围中服从均匀随机部署。路径损耗指数设成4,阴影衰落标准差设成 8 dB,σk2均设成-107 dBm,ρ设成35%,τ设成 12 dB,PC设成30 dBm[16, 19]。根据典型的指数相关模型[4]来建模DAC中天线单元的相关特性,具体地即把 Rj(n)∈$\gg $V×V中序数为(p,q)的矩阵元素设成Rk(n,p,q)=(rk(n))|p-q|,rk(n)为系统各DAC中天线单元相关系数,0≤rk(n)≤1。 仿真时还考察了文[14]中面向能效优化设计的未考虑天线单元相关性的协同传输方案和文[7]中面向频谱效率优化设计的已考虑天线单元相关性的传输方案。 rk(n)为0.6与 0.9 这2种情形下3种方案的能效性能仿真情况分别如图 2和3所示。
图 2 不同方案的能效性能(r(n)k=0.6) |
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图 3 不同方案的能效性能(r(n)k=0.9) |
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由图 2和3中可以发现,3种方案中本文方案所获系统能效水平最高。相比文[7]方案,本文方案实现了能效水平的大幅改善,且在传输功率较高区域的能效改善幅度尤为可观; 这是由于文[7]方案是面向频谱效率优化而非面向能效优化而设计,故而其在传输功率较高区域旨在达成更高的频谱效率目标时,就会不可避免地有更多的能效性能损失; 这也表明依托天线相关性实施高能效的传输优化,对实现更优的系统能效收益具有重要意义。相比文[14]方案,本文方案同样实现了能效水平的切实改善,这是由于文[14]方案未能匹配应对DAC中的天线相关特性而对传输方案进行专门设计; 将图 2和3进行对照观察还能发现,当DAC中天线单元相关性加强(具体表现为r(n)k由0.6增加到0.9)时,本文方案的能效水平比文[14]方案的有较大改善。
5 结 论本文将各DAC内的天线单元相关性因素纳入考虑,且在系统仅可获得慢变信道统计特性的条件下,研究了多小区下行DAS系统的高能效协同传输问题。该问题通过小区间协同优化设计输入协方差矩阵,使得系统能效最大化。由于该优化问题具有复杂非凸性,本文先后通过连续Taylor展开方法与分式规划方法,最终使问题转化成一系列凸子问题以有效处理,并据此提供了一种该高能效协同传输问题的迭代法求解方案。仿真结果验证: 相比当前已有方案,该方案显著改善了系统的能效水平,这将对高能效DAS系统工程实践有所裨益。
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