CN105450275A

CN105450275A - Optimal energy efficiency-based antenna selection method for multi-user and large-scale antenna relay system

Info

Publication number: CN105450275A
Application number: CN201510757563.XA
Authority: CN
Inventors: 李春国; 王毅; 杨绿溪; 王东明; 郑福春
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2015-11-09
Filing date: 2015-11-09
Publication date: 2016-03-30

Abstract

The invention discloses an antenna selection method for a multi-user large-scale antenna relay system based on optimal energy efficiency. The system is composed of multiple source users and multiple sink users with the same number and a relay station. The source users and sink users are paired in pairs to complete information transmission within two time slots through the relay station. All source users and sink users in the system are configured with a single antenna, and the relay station is configured with a large number of antenna arrays, as shown in the attached figure. The method of the invention aims at maximizing the energy efficiency of the system, and establishes a mathematical model with the number of relay station antennas as optimization variables. Since there is no definite analytical expression for the objective function in this optimization problem, with the help of the law of large numbers in the theory of large-dimensional random matrices, an accurate approximate analytical expression for the objective function in the optimization problem is obtained first. Then use the quasi-concave characteristics of the analytical expression about the optimization variable, and at the same time use the Lambert? The W function is finally solved to obtain a closed-form solution for the optimal number of antennas that satisfies the goal of maximizing energy efficiency.

Description

An Antenna Selection Method for Multi-user Large-Scale Antenna Relay System Based on Optimal Energy Efficiency

技术领域technical field

本发明属于无线通信技术领域，具体涉及基于能效最优的多用户大规模天线中继系统天线选择方法。The invention belongs to the technical field of wireless communication, and in particular relates to an antenna selection method for a multi-user large-scale antenna relay system based on optimal energy efficiency.

背景技术Background technique

自2010年美国贝尔实验室科学家Marzetta教授提出大规模多输入多输出(简称大规模MIMO)技术之后，近几年来该项技术以其新颖的特性受到了无线通信领域工业界与学术界的广泛关注，全球各个知名研究机构与课题组针对该项技术进行了深入的研究。所谓大规模MIMO技术，是指在基站端配置大规模数量的天线阵列来同时服务多个用户，并且天线数量级要远大于服务的用户数量级。有学者研究指出，通过在基站端使用大规模天线阵列挖掘空域可用资源，可以获得许多相对于传统MIMO系统的新特性，诸如，可以在基站端采用简单的线性预编码/检测方法来有效消除多用户干扰，显著降低基站端和用户端的发射功率同时不影响系统的可达速率要求，不额外增加时频资源开销的前提下使得系统频谱效率和能量效率的成倍提升，丰富的自由度用于先进的波束赋形等等。大规模MIMO技术的这些特性，也使得其成为第5代移动通信系统的关键技术之一。Since Professor Marzetta, a scientist at Bell Laboratories in the United States, proposed massive multiple-input multiple-output (referred to as massive MIMO) technology in 2010, this technology has attracted widespread attention from the industry and academia in the field of wireless communication in recent years due to its novel characteristics. , various well-known research institutions and research groups around the world have conducted in-depth research on this technology. The so-called massive MIMO technology refers to configuring a large number of antenna arrays at the base station to serve multiple users at the same time, and the order of magnitude of the antennas is much larger than that of the served users. Some scholars have pointed out that by using a large-scale antenna array at the base station to tap the available resources in the air space, many new features compared to the traditional MIMO system can be obtained, such as, a simple linear precoding/detection method can be used at the base station to effectively eliminate multiple User interference significantly reduces the transmit power of the base station and the user end without affecting the system's attainable rate requirements, and doubles the system's spectral efficiency and energy efficiency without additional time-frequency resource overhead. Rich degrees of freedom are used for Advanced beamforming and more. These characteristics of massive MIMO technology also make it one of the key technologies of the 5th generation mobile communication system.

与此同时，成对用户多天线中继系统在近十年来也一直受到业内人士的普遍关注。通过引入多天线中继站，可以大大提升用户覆盖范围，提高边缘用户的传输速率，增强传输链路的可靠性。但是，在多用户中继系统中，用户间干扰一直是限制多天线中继系统的瓶颈所在。针对这一问题，众多学者提出了不同的解决方案用以消除多用户干扰，主要分为两类：一类是通过在不同用户间分配正交时频资源，通过资源划分来抑制用户间干扰；另一类是通过联合设计预编码和接收机算法来达到对抗用户间干扰的目的。然而，第一种方法虽然可以较好地消除用户间干扰，但是带来的是额外时频资源的开销，造成了系统整体频谱效率的下降。第二种方法则会大大增加算法复杂度，对中继站和信宿用户的计算资源开销提出了更高的要求。显然，两类方案都存在严重的缺陷。正基于此，HimalA.Suraweera等人于2013年首次提出将大规模MIMO技术引入多用户多天线中继系统，利用大规模MIMO在多用户传输过程中所提供的良好的抑制干扰能力来解决成对用户多天线中继系统的用户间干扰问题，同时也无需占用额外的时频资源，从而大大提升系统的频谱效率性能。At the same time, the pair-user multi-antenna relay system has also been widely concerned by the industry in the past ten years. By introducing multi-antenna relay stations, the coverage of users can be greatly improved, the transmission rate of edge users can be improved, and the reliability of transmission links can be enhanced. However, in multi-user relay systems, inter-user interference has always been the bottleneck that restricts multi-antenna relay systems. In response to this problem, many scholars have proposed different solutions to eliminate multi-user interference, which are mainly divided into two categories: one is to suppress inter-user interference by allocating orthogonal time-frequency resources among different users and dividing resources; The other is to achieve the purpose of combating inter-user interference by jointly designing precoding and receiver algorithms. However, although the first method can better eliminate inter-user interference, it brings the overhead of additional time-frequency resources, resulting in a decline in the overall spectrum efficiency of the system. The second method will greatly increase the complexity of the algorithm, and put forward higher requirements on the computing resource overhead of the relay station and the sink user. Obviously, both types of schemes have serious flaws. Based on this, HimalA.Suraweera et al first proposed in 2013 to introduce the massive MIMO technology into the multi-user multi-antenna relay system, and use the good interference suppression ability provided by the massive MIMO in the process of multi-user transmission to solve the paired Inter-user interference problem of user multi-antenna relay system does not need to occupy additional time-frequency resources, thereby greatly improving the spectral efficiency performance of the system.

值得注意的是，在将大规模天线阵列引入中继站的同时，也不可避免的会带来一些问题。最直接的问题就是大量天线的使用所造成的射频通道固定电路总功耗成倍提升，而固定电路总功耗的提升势必会对中继系统的整体能效性能造成影响。很显然，在未来绿色通信为主流的无线通信系统中，高功耗面临着严峻的挑战。因而，在满足能效性能的前提下，确定中继系统所需要使用的天线数具有十分重要的实际意义和应用背景，而这一问题尚未有研究人员涉足。为了解决中继站最优天线数的问题，我们提出了基于能效最大化的最优天线数优化模型，由于该模型中目标函数过于复杂不便求解，对于最优天线数的闭合形式解更是难以获得，而闭合形式解对于探究最优天线数的影响因素和这些因素的作用机理有着重要的指导意义。It is worth noting that when a large-scale antenna array is introduced into the relay station, some problems will inevitably be brought about. The most direct problem is that the use of a large number of antennas doubles the total power consumption of the fixed circuit of the radio frequency channel, and the increase in the total power consumption of the fixed circuit will inevitably affect the overall energy efficiency of the relay system. Obviously, in the wireless communication system where green communication is the mainstream in the future, high power consumption is facing severe challenges. Therefore, on the premise of satisfying the energy efficiency performance, determining the number of antennas required for the relay system has very important practical significance and application background, and this problem has not been involved by researchers. In order to solve the problem of the optimal number of antennas in the relay station, we propose an optimization model for the optimal number of antennas based on energy efficiency maximization. Because the objective function in this model is too complicated to solve, it is even more difficult to obtain a closed-form solution for the optimal number of antennas. The closed-form solution has important guiding significance for exploring the influencing factors of the optimal number of antennas and the mechanism of these factors.

本发明公开了一种基于能效最优的多用户大规模天线中继系统天线选择方法。该系统由具有相同数目的多个信源用户和多个信宿用户以及一个中继站所组成，信源用户与信宿用户两两配对通过中继站在两个时隙内完成信息传输。系统中所有信源用户与信宿用户均配置单天线，中继站配置大规模数量的天线阵列，如摘要附图中所示。本发明方法以最大化系统能效为目标，以中继站天线数为优化变量建立数学模型。由于该优化问题中目标函数无明确的解析表达式，因此，借助于大维随机矩阵理论中的大数定律，先求得优化问题中目标函数的一种精确近似解析表达式。再利用该解析表达式关于优化变量的拟凹特性，同时借助于LambertW函数，最终求解得出满足能效最大化目标的最优天线数闭合形式解。The invention discloses an antenna selection method for a multi-user large-scale antenna relay system based on optimal energy efficiency. The system is composed of multiple source users and multiple sink users with the same number and a relay station. The source users and sink users are paired in pairs to complete information transmission within two time slots through the relay station. All source users and sink users in the system are configured with a single antenna, and the relay station is configured with a large number of antenna arrays, as shown in the attached figure. The method of the invention aims at maximizing the energy efficiency of the system, and establishes a mathematical model with the number of relay station antennas as optimization variables. Since there is no definite analytical expression for the objective function in this optimization problem, with the help of the law of large numbers in the theory of large-dimensional random matrices, an accurate approximate analytical expression for the objective function in the optimization problem is obtained first. Then, using the quasi-concave characteristics of the analytical expression on the optimization variables, and with the help of the LambertW function, the closed-form solution of the optimal number of antennas that meets the goal of maximizing energy efficiency is finally obtained.

发明内容Contents of the invention

本发明为使成对用户大规模天线中继系统获得较高的能效性能而提出一种基于能效最优的多用户大规模天线中继系统天线选择方法，并求得了最优天线数的闭合形式解。The present invention proposes a multi-user large-scale antenna relay system antenna selection method based on optimal energy efficiency in order to enable the paired-user large-scale antenna relay system to obtain higher energy efficiency performance, and obtains the closed form of the optimal number of antennas untie.

本发明的基于能效最优的多用户大规模天线中继系统天线选择方法，其特征在于，所述方法包括以下步骤：The antenna selection method of the multi-user large-scale antenna relay system based on optimal energy efficiency of the present invention is characterized in that the method includes the following steps:

1).中继站通过信道估计获得它到所有信源用户和信宿用户间的理想信道状态信息，即信道矩阵和其中，h_k表示第k个信源用户到中继站的信道向量且服从复高斯分布表示中继站到第k个信宿用的信道向量且服从复高斯分布假设系统采用时分双工制式，且信道服从平坦块衰落，也即在信道相干时间内信道系数保持不变。1). The relay station obtains the ideal channel state information between it and all source users and sink users through channel estimation, that is, the channel matrix and Among them, h _k represents the channel vector from the kth source user to the relay station and obeys the complex Gaussian distribution Represents the channel vector used by the relay station to the kth sink and obeys the complex Gaussian distribution Assume that the system adopts the time division duplex system, and the channel obeys flat block fading, that is, the channel coefficient remains unchanged during the coherent time of the channel.

2).在第一时隙内，K个信源用户同时向中继站节点发送信息符号，则在中继站处的接收信号向量为r，如附图1中第一时隙末所示，r表示为如下形式，2). In the first time slot, K source users send information symbols to the relay station node at the same time, then the received signal vector at the relay station is r, as shown at the end of the first time slot in Figure 1, r is expressed as in the following form,

$r r = = \sqrt{{ρ ρ}_{s the s}} H h x x + + {n no}_{r r}$

其中，x＝[x₁,x₂,…,x_K]^T，x_k(k＝1,2,…,K)表示第k个信源用户的发射符号且n_r表示第一时隙在中继站处的单位功率加性白噪声且满足复高斯分布 Wherein, x=[x ₁ ,x ₂ ,…,x _K ] ^T , x _k (k=1,2,…,K) represents the transmitted symbol of the kth source user and n _r represents the unit power additive white noise at the relay station in the first time slot and satisfies the complex Gaussian distribution

3).在第二时隙内，中继站采用最大比合并和最大比发送预编码矩阵对接收到的信号r进行放大，形成转发信号向量t，如附图1中第二时隙起始时所示，t可以表示为如下形式，3). In the second time slot, the relay station adopts maximum ratio combination and maximum ratio transmission precoding matrix Amplify the received signal r to form a forwarding signal vector t, as shown at the beginning of the second time slot in Figure 1, t can be expressed as the following form,

$t t = = V V r r = = \sqrt{ξ ξ} {GH GH}^{H h} r r$

其中，ξ为功率归一化因子用以满足中继站处的平均总发射功率约束ρ_r，即，where ξ is the power normalization factor to satisfy the average total transmit power constraint ρ _r at the relay station, namely,

则， $ξ = \frac{ρ_{r}}{θ} = \frac{ρ_{r}}{T r (ρ_{s} {(H^{H} H)}^{2} G^{H} G + H^{H} {HG}^{H} G)} .$ 然后，中继站将信号t转发至所有信宿用户，则第k个信宿用户接收到的信号为y_k，如附图1中第二时隙末所示，y_k可以表示为如下形式，but, $ξ = \frac{ρ_{r}}{θ} = \frac{ρ_{r}}{T r (ρ_{the s} {(h^{h} h)}^{2} G^{h} G + h^{h} {HG}^{h} G)} .$ Then, the relay station forwards the signal t to all sink users, then the signal received by the kth sink user is y _k , as shown at the end of the second time slot in Figure 1, y _k can be expressed as follows,

${y the y}_{k k} = = \sqrt{{ρ ρ}_{s the s}} {g g}_{k k}^{H h} {Vh Vh}_{k k} {x x}_{k k} + + \sqrt{{ρ ρ}_{s the s}} {Σ Σ}_{i i = = 11,, i i &NotEqual; &NotEqual; k k}^{K K} {g g}_{k k}^{H h} {Vh Vh}_{i i} {x x}_{i i} + + {g g}_{k k}^{H h} {Vn vn}_{r r} + + {n no}_{k k}$

其中，n_k表示第k个信宿用户处的单位功率加性白噪声且满足复高斯分布 Among them, n _k represents the unit power additive white noise at the kth sink user and satisfies the complex Gaussian distribution

4).基于步骤3)中信宿用户的接收信号表达式，可以得第k个信宿用户的接收信干燥比SINR表达式如下所示，4). Based on the expression of the received signal of the sink user in step 3), the expression of the received signal-to-dry ratio SINR of the kth sink user can be obtained as follows,

${γ γ}_{k k} = = \frac{{A A}_{k k}}{{B B}_{k k} + + {C C}_{k k} + + θ θ / / {ρ ρ}_{r r} {ρ ρ}_{s the s}}$

其中， $A_{k} \overset{Δ}{=} | g_{k}^{H} {GH}^{H} h_{k} |^{2}, B_{k} \overset{Δ}{=} Σ_{i = 1, i &NotEqual; k}^{K} | g_{k}^{H} {GH}^{H} h_{i} |^{2}, C_{k} \overset{Δ}{=} \frac{σ_{r}^{2}}{ρ_{s}} | | g_{k}^{H} {GH}^{H} | |^{2} .$ 从而可以得到第k个信宿用户的平均频谱效率如下式所示，in, $A_{k} \overset{Δ}{=} | g_{k}^{h} {GH}^{h} h_{k} |^{2}, B_{k} \overset{Δ}{=} Σ_{i = 1, i &NotEqual; k}^{K} | g_{k}^{h} {GH}^{h} h_{i} |^{2}, C_{k} \overset{Δ}{=} \frac{σ_{r}^{2}}{ρ_{the s}} | | g_{k}^{h} {GH}^{h} | |^{2} .$ Thus, the average spectral efficiency of the kth sink user can be obtained as shown in the following formula,

其中，表示将占用的两个时隙资源考虑在内所产生的频谱效率损失。in, Indicates the spectral efficiency loss caused by taking the two occupied time slot resources into consideration.

5).基于步骤4)中平均频谱效率表达式，在中继站处建立以最大化系统总能效函数η(N)为目标，以中继站天线数为变量的数学优化模型，如下所示，5). Based on the average spectrum efficiency expression in step 4), set up at the relay station to maximize the total system energy efficiency function η (N) as the goal, and take the number of relay station antennas as a variable mathematical optimization model, as shown below,

其中，η(N)表示能效函数，S_Σ表示所有用户的总频谱效率，P_Σ表示系统的总功率消耗，μ_s≥1表示每个信源用户发射机功放器件的效率损耗常量因子，μ_r≥1表示中继站发射机功放器件的效率损耗常量因子，P_s表示每个信源用户发射机的常量固定功率消耗，P_r表示中继站收发机每根天线上的常量固定功率消耗。Among them, η(N) represents the energy efficiency function, S _Σ represents the total spectral efficiency of all users, P _Σ represents the total power consumption of the system, μ _s ≥ 1 represents the efficiency loss constant factor of each source user transmitter power amplifier device, μ _r ≥ 1 means the efficiency loss constant factor of the relay station transmitter power amplifier device, P _s means the constant fixed power consumption of each source user transmitter, and P _r means the constant fixed power consumption on each antenna of the relay station transceiver.

6).由于步骤5)中目标函数中包含S_k，其精确解析表达式难以获得，不利于后续优化问题的解决。此处，根据大数定律(参见文献1中公式(44)：S.Jin,X.Liang,K.-KWong,X.Gao,andQ.Zhu,“ErgodicrateanalysisformultipairmassiveMIMOtwo-wayrelaynetworks,”IEEETransactionsonWirelessCommunication,vol.14,no.3,pp.1488,Mar.2015.)，如下所示，6). Since S _k is included in the objective function in step 5), its precise analytical expression is difficult to obtain, which is not conducive to the solution of subsequent optimization problems. Here, according to the law of large numbers (see formula (44) in Document 1): S.Jin, X.Liang, K.-KWong, X.Gao, and Q.Zhu, "Ergodicrate analysis for multipair massive MIMO two-wayrelaynetworks," IEEE Transactions on Wireless Communication, vol.14, no.3, pp.1488, Mar.2015.), as shown below,

大数定律：Law of Large Numbers:

设N维向量p和q为独立同分布的复高斯随机向量，即和则满足如下特性，Let the N-dimensional vectors p and q be independent and identically distributed complex Gaussian random vectors, namely and but satisfy the following properties,

对步骤4)中γ_k表示式所包含的各项进行近似，可得到如下表达式，Approximating the items contained in the γ _k expression in step 4), the following expression can be obtained,

${A A}_{k k} \approx \approx \overset{~ ~}{A A} k k = = {Σ Σ}_{j j = = 11}^{K K} | | {g g}_{k k}^{H h} {g g}_{j j} {| |}^{22} | | {h h}_{j j}^{H h} {h h}_{k k} {| |}^{22}$

${B B}_{k k} \approx \approx {\overset{~ ~}{B B}}_{k k} = = {Σ Σ}_{i i = = 11,, i i &NotEqual; &NotEqual; k k}^{K K} {Σ Σ}_{j j = = 11}^{K K} | | {g g}_{k k}^{H h} {g g}_{j j} {| |}^{22} | | {h h}_{j j}^{H h} {h h}_{i i} {| |}^{22}$

${C C}_{k k} \approx \approx {\overset{~ ~}{C C}}_{k k} = = \frac{{σ σ}_{r r}^{22}}{{ρ ρ}_{s the s}} {Σ Σ}_{j j = = 11}^{K K} | | {g g}_{k k}^{H h} {g g}_{j j} {| |}^{22} | | | | {h h}_{j j} | | {| |}^{22}$

$θ θ \approx \approx \overset{~ ~}{θ θ} = = {Σ Σ}_{i i = = 11}^{K K} (({ρ ρ}_{s the s} {Σ Σ}_{j j = = 11}^{K K} | | {h h}_{i i}^{H h} {h h}_{j j} {| |}^{22} + + {σ σ}_{r r}^{22} | | | | {h h}_{i i} | | {| |}^{22})) | | | | {g g}_{i i} | | {| |}^{22}$

则，S_k可以近似表示为如下所示，Then, S _k can be approximated as follows,

从和的表达式中可以看到，这四项都是由若干非负随机变量求和组成，利用如下定理1(参见文献2中的Lemma1：Q.Zhang,S.Jin,K.K.Wong,andH.B.Zhu,“PowerscalingofuplinkmassiveMIMOsystemswitharbitrary-rankchannelmeans,”IEEEJournalOfSelectedTopicsInSignalProcess.,vol.8,no.5,pp.969,Oct.2014.)，From and It can be seen from the expression that these four terms are composed of the sum of several non-negative random variables, using the following theorem 1 (see Lemma1 in literature 2: Q.Zhang, S.Jin, KKWong, and H.B.Zhu , "Powerscaling of uplink massive MIMO system with bitrary-rank channel means," IEEE Journal Of Selected Topics In Signal Process., vol.8, no.5, pp.969, Oct.2014.),

定理1：Theorem 1:

设两个随机变量P和Q满足和其中，P_n和Q_m均为非负随机变量，则，可以得到如下近似表达式Suppose two random variables P and Q satisfy and Among them, P _n and Q _m are both non-negative random variables, then the following approximate expression can be obtained

同时，可以保证当N和M逐渐增大时，上式近似精确度将越来越高。At the same time, it can be guaranteed that when N and M gradually increase, the approximation accuracy of the above formula will become higher and higher.

进一步将近似为如下所示，further will approximately As follows,

利用复高斯随机向量乘积的统计特性可以直接计算得到的解析表达式如下所示，Using the statistical properties of the complex Gaussian random vector product can be directly calculated to get The analytical expression for is as follows,

${S S}_{k k} \approx \approx {\overset{&OverBar; &OverBar;}{S S}}_{k k} = = \frac{11}{22} {log log}_{22} ((11 + + \frac{{\overset{&OverBar; &OverBar;}{A A}}_{k k}}{{\overset{&OverBar; &OverBar;}{B B}}_{k k} + + {\overset{&OverBar; &OverBar;}{C C}}_{k k} + + {\overset{&OverBar; &OverBar;}{F f}}_{k k}}))$

其中，in,

8).考虑到中继站部署的大规模天线数通常远大于用户数，即N＞＞K，并利用高信噪比条件，即ρ_r＞＞1和ρ_s＞＞1，将步骤7)中得到的解析表达式S_k近似化简为如下形式，8). Considering that the number of large-scale antennas deployed by the relay station is usually much larger than the number of users, that is, N>>K, and using the condition of high signal-to-noise ratio, that is, ρ _r ＞>1 and ρ _s ＞>1, the step 7) The obtained analytical expression S _k is approximately simplified to the following form,

${\overset{&OverBar; &OverBar;}{S S}}_{k k} \approx \approx \frac{11}{22} {log log}_{22} ((11 + + \frac{{ρ ρ}_{r r} {ρ ρ}_{s the s} ((N N + + 22))}{22 ((K K - - 11)) {ρ ρ}_{r r} {ρ ρ}_{s the s} + + {ρ ρ}_{r r} + + {Kρ Kρ}_{s the s}}))$

9).基于步骤8)中的解析表达式将步骤5)中的优化问题的目标函数η(N)近似表达为并用来代替步骤5)中优化问题的目标函数，从而近似转化为如下形式的优化问题，9). Based on the analytical expression in step 8) The objective function η(N) of the optimization problem in step 5) is approximately expressed as and use to replace the objective function of the optimization problem in step 5), thus approximately transforming into an optimization problem of the following form,

10).由于步骤9)中优化变量N属于正整数集合，该优化问题属于非凸整数规划。为了便于问题求解，将变量N先释放为连续实数变量，则可以直接证明步骤9)中的近似表达式关于N是拟凹的。同时，利用一阶导数和二阶导数可以证明关于变量N是先增后减的变化趋势。进而，利用如下定理2(参见文献3中的Lemma2：E.Bjornson,L.Sanguinetti,J.HoydisandM.Debbah,“DesigningmultiuserMIMOforenergyefficiency:WhenismassiveMIMOtheanswer？,”ProceedingsofIEEEWirelessCommunicationsandNetworkingConference,Istanbul,Apr.2014,pp.244.)10). Since the optimization variable N in step 9) belongs to a set of positive integers, the optimization problem belongs to non-convex integer programming. In order to facilitate the solution of the problem, the variable N is first released as a continuous real variable, then the approximate expression in step 9) can be directly proved is quasi-concave with respect to N. At the same time, using the first and second derivatives, it can be shown that Regarding the variable N, it shows a trend of first increasing and then decreasing. Furthermore, the following theorem 2 is used (see Lemma2 in Document 3: E.Bjornson, L.Sanguinetti, J.HoydisandM.Debbah, "DesigningmultiuserMIMOforenergyefficiency:WhenismassiveMIMOtheanswer?,"ProceedingsofIEEEWirelessCommunicationsandNetworkingConference, Istanbul, Apr.2014, pp.244.)

定理2：Theorem 2:

关于变量z的优化问题如下所示，The optimization problem with respect to the variable z is shown below,

$\underset{z z}{m m a a x x} \frac{f f {log log}_{22} ((a a + + b b z z))}{c c + + d d z z}$

其中，a,c≥0，b,d,f＞0。则，目标函数关于z是严格拟凹的，且具有唯一的最优解如下所示，Wherein, a, c≥0, b, d, f>0. Then, the objective function is strictly quasi-concave with respect to z, and has a unique optimal solution as shown below,

其中，e为自然常数，且当z＞z^opt时，目标函数是单调减小的，当z＜z^opt时，目标函数是单调增加的。Wherein, e is a natural constant, and when z>z ^opt , the objective function decreases monotonically, and when z<z ^opt , the objective function increases monotonically.

并借助于LambertW函数可以直接得到最优天线数的闭合形式解，如下式所示，And with the help of the LambertW function, the closed-form solution of the optimal number of antennas can be directly obtained, as shown in the following formula,

其中， $α \overset{Δ}{=} \frac{ρ_{r} ρ_{s}}{2 (K - 1) ρ_{r} ρ_{s} + ρ_{r} + {Kρ}_{s}}, β \overset{Δ}{=} K (μ_{s} ρ_{s} + P_{s}) + μ_{r} ρ_{r},$ e表示自然常数，表示LambertW函数，其定义为：关于变量x的方程θ＝υe^υ，则关于υ的解可以用LambertW函数表示，即 in, $α \overset{Δ}{=} \frac{ρ_{r} ρ_{the s}}{2 (K - 1) ρ_{r} ρ_{the s} + ρ_{r} + {Kρ}_{the s}}, β \overset{Δ}{=} K (μ_{the s} ρ_{the s} + P_{the s}) + μ_{r} ρ_{r},$ e represents a constant of nature, Represents the LambertW function, which is defined as: the equation θ=υe ^υ about the variable x, then the solution about υ can be expressed by the LambertW function, namely

11).由于步骤10)中求出的最优天线数N^opt通常不是整数，根据步骤10)中能效函数关于N的变化关系，最终可以得到最优天线数为round{N^opt}。11). Since the optimal number of antennas N ^opt obtained in step 10) is usually not an integer, according to the energy efficiency function in step 10) Regarding the variation relationship of N, the optimal number of antennas can finally be obtained as round{N ^opt }.

其中，(·)^H—表示矩阵的共轭转置运算，—表示正整数集合，—针对随机量(向量)的数学期望运算，Tr{·}—矩阵的迹，round{x}—表示取与实数x最近的整数，—表示几乎确定收敛，—表示均值为μ方差为σ²的复高斯随机分布，||·||—表示向量2范数运算，N—中继站天线数，K—用户对总数，ρ_s—每个信源用户的平均发射功率，ρ_r—中继站的平均发射总功率。Among them, (·) ^H — represents the conjugate transpose operation of the matrix, —Represents a set of positive integers, —mathematical expectation operation for random quantities (vectors), Tr{ }—the trace of the matrix, round{x}—represents taking the nearest integer to the real number x, — indicates almost certain convergence, —represents a complex Gaussian random distribution with mean value μ and variance σ ² , ||·||—represents the vector 2 norm operation, N—the number of relay station antennas, K—the total number of user pairs, ρ _s —the average value of each source user Transmitting power, ρ _r —average total transmitting power of the relay station.

本发明提出了一种基于能效最优的多用户大规模天线中继系统天线选择方法，可直接通过闭合解析表达式求得满足系统能效最大化的最优中继站天线个数。通过选择最优天线数，使得大规模天线中继系统在获得大规模天线阵列带来的好处的同时，尽可能降低由于庞大的天线数所产生的过高的电路功耗开销，从而使得系统总能效达到最佳水平。相对于传统拉格朗日对偶问题求解方法，本专利所提方法不需要交替迭代求解过程，大大地降低了算法复杂度。The present invention proposes a multi-user large-scale antenna relay system antenna selection method based on optimal energy efficiency, which can directly obtain the optimal number of relay station antennas satisfying the maximum energy efficiency of the system through closed analytical expressions. By selecting the optimal number of antennas, the large-scale antenna relay system can obtain the benefits of large-scale antenna arrays while reducing the excessive circuit power consumption caused by the large number of antennas as much as possible, so that the total system Energy efficiency at an optimum level. Compared with the traditional Lagrangian dual problem solving method, the method proposed in this patent does not require an alternate iterative solution process, which greatly reduces the complexity of the algorithm.

附图说明Description of drawings

图1为本发明方法的系统模型；Fig. 1 is the system model of the inventive method;

图2为本发明算法基本流程图；Fig. 2 is the basic flowchart of algorithm of the present invention;

图3为在不同的用户对数目K场景下，本专利所提出的频谱效率解析表达式与蒙特卡洛仿真结果对比图；Fig. 3 is a comparison diagram of the spectral efficiency analytical expression proposed by this patent and the Monte Carlo simulation results under different scenarios of the number of user pairs K;

图4为在不同的中继站天线固定功耗P_r场景下，本专利所提出的最优天线数方法所达到的能效性能与蒙特卡洛数值仿真性能对比图。Fig. 4 is a comparison diagram of the energy efficiency performance achieved by the optimal number of antennas method proposed in this patent and the Monte Carlo numerical simulation performance under different fixed power consumption P _r scenarios of relay station antennas.

具体实施方式：detailed description:

结合图2所示的算法流程图对本发明的一种基于能效最优的多用户大规模天线中继系统功率分配方法作具体说明，包括如下步骤：In conjunction with the algorithm flow chart shown in Fig. 2, a kind of energy efficiency optimal multi-user large-scale antenna relay system power allocation method based on the present invention is specifically described, including the following steps:

2).在中继站处建立以最大化系统总能效函数η(N)为目标，以中继站天线数为变量的数学优化模型，如下所示，2). Establish a mathematical optimization model at the relay station with the goal of maximizing the total energy efficiency function η(N) of the system and taking the number of relay station antennas as a variable, as shown below,

其中，η(N)表示能效函数，S_k表示第k个信宿用户的平均频谱效率，S_Σ表示所有信宿用户的总频谱效率，P_Σ表示整个系统的总功率消耗，μ_s≥1表示每个信源用户发射机功放器件的效率损耗常量因子，μ_r≥1表示中继站发射机功放器件的效率损耗常量因子，P_s表示每个信源用户发射机的常量固定功率消耗，P_r表示中继站收发机每根天线上的常量固定功率消耗，γ_k表示第k个信宿用户的接收信干燥比SINR，如下所示，Among them, η(N) represents the energy efficiency function, S _k represents the average spectral efficiency of the kth sink user, S _Σ represents the total spectral efficiency of all sink users, P _Σ represents the total power consumption of the entire system, and μ _s ≥ 1 represents the The efficiency loss constant factor of each source user transmitter power amplifier device, μ _r ≥ 1 represents the efficiency loss constant factor of the relay station transmitter power amplifier device, P _s represents the constant fixed power consumption of each source user transmitter, and P _r represents the relay station The constant fixed power consumption on each antenna of the transceiver, γ _k represents the receiving signal-to-dry ratio SINR of the kth sink user, as follows,

其中， $A_{k} \overset{Δ}{=} | g_{k}^{H} {GH}^{H} h_{k} |^{2}, B_{k} \overset{Δ}{=} Σ_{i = 1, i &NotEqual; k}^{K} | g_{k}^{H} {GH}^{H} h_{i} |^{2}, C_{k} \overset{Δ}{=} \frac{σ_{r}^{2}}{ρ_{s}} | | g_{k}^{H} {GH}^{H} | |^{2} .$ in, $A_{k} \overset{Δ}{=} | g_{k}^{h} {GH}^{h} h_{k} |^{2}, B_{k} \overset{Δ}{=} Σ_{i = 1, i &NotEqual; k}^{K} | g_{k}^{h} {GH}^{h} h_{i} |^{2}, C_{k} \overset{Δ}{=} \frac{σ_{r}^{2}}{ρ_{the s}} | | g_{k}^{h} {GH}^{h} | |^{2} .$

3).结合大数定律和说明书中定理1，并考虑大规模天线数与高信噪比区间，即N＞＞K、ρ_r＞＞1和ρ_s＞＞1，可将步骤2)中频谱效率S_k近似化简为如下形式，3). Combining the law of large numbers and Theorem 1 in the specification, and considering the large-scale antenna number and the high signal-to-noise ratio interval, that is, N>>K, ρ _r ＞>1 and ρ _s ＞>1, step 2) can be The spectral efficiency S _k is approximately simplified to the following form,

${S S}_{k k} \approx \approx {\overset{&OverBar; &OverBar;}{S S}}_{k k} = = \frac{11}{22} {log log}_{22} ((11 + + \frac{{ρ ρ}_{r r} {ρ ρ}_{s the s} ((N N + + 22))}{22 ((K K - - 11)) {ρ ρ}_{r r} {ρ ρ}_{s the s} + + {ρ ρ}_{r r} + + {Kρ Kρ}_{s the s}}))$

4).基于步骤3)中的频谱效率近似表达式将步骤2)中优化问题的目标函数进行替换，近似转换为如下形式的优化问题，4). Based on the approximate expression of spectral efficiency in step 3) Replace the objective function of the optimization problem in step 2), and approximately convert it into an optimization problem of the following form,

$\underset{N N &GreaterEqual; &Greater Equal; 11}{m m a a x x} η η ((N N)) \approx \approx \overset{&OverBar; &OverBar;}{η η} ((N N)) = = \frac{\frac{K K}{22} {log log}_{22} ((11 + + \frac{{ρ ρ}_{r r} {ρ ρ}_{s the s} ((N N + + 22))}{22 ((K K - - 11)) {ρ ρ}_{r r} {ρ ρ}_{s the s} + + {ρ ρ}_{r r} + + {Kρ Kρ}_{s the s}}))}{K K (({μ μ}_{s the s} {ρ ρ}_{s the s} + + {P P}_{s the s})) + + {μ μ}_{r r} {ρ ρ}_{r r} + + {NP NP}_{r r}}$

5).基于步骤4)中优化问题，直接得出最优天线数的闭合表达式如下所示，5). Based on the optimization problem in step 4), the closed expression for directly obtaining the optimal number of antennas is as follows,

6).将系统参数代入步骤6)中的最优天线数闭合表达式获得数值解，再进行取整运算round{N^opt}，即可得到最终的最优天线数整数解。算法结束。6). Substituting the system parameters into the closed expression of the optimal number of antennas in step 6) to obtain a numerical solution, and then performing the rounding operation round{N ^opt } to obtain the final integer solution of the optimal number of antennas. Algorithm ends.

其中，(·)^H—表示矩阵的共轭转置运算，—表示正整数集合，—针对随机量(向量)的数学期望运算，Tr{·}—矩阵的迹，round{x}—表示取与实数x最近的整数，表示均值为μ方差为σ²的复高斯随机分布，||·||表示向量2范数运算，N—中继站天线数，K—用户对总数，ρ_s—每个信源用户的平均发射功率，ρ_r—中继站的平均发射总功率。Among them, (·) ^H — represents the conjugate transpose operation of the matrix, —Represents a set of positive integers, —mathematical expectation operation for random quantities (vectors), Tr{ }—the trace of the matrix, round{x}—represents taking the nearest integer to the real number x, Indicates a complex Gaussian random distribution with mean value μ and variance σ ² , ||·|| represents the vector 2 norm operation, N—the number of relay station antennas, K—the total number of user pairs, ρ _s —the average transmit power of each source user , ρ _r —average total transmit power of the relay station.

图3给出了不同的用户对个数场景下，发射功率ρ_r＝ρ_s＝10dB时，随着中继站天线数的增长，本专利所给出的频谱效率近似解析表达式与蒙特卡洛数值仿真结果的对比曲线。从图中可以看到，本专利所提出的解析近似表达式具有非常好的近似效果，与蒙特卡洛数值仿真曲线之间的差异几乎可以忽略不计，表明了本专利所提出的近似解析表达式具有很好地效果。图4给出了不同的中继站天线固定功耗P_r，用户对个数K＝16，信源用户天线固定功耗发射功率P_s＝0dB和发射功率ρ_r＝ρ_s＝10dB时，本专利所提出的最优天线数求解方法性能对比图。从图中可以看出，系统总能效随着天线数呈现先增后减的趋势，并且本方案所给出的最优天线数闭合解精确的匹配了能效变化曲线上的最优能效值。Figure 3 shows the approximate analytical expression and Monte Carlo value of the spectral efficiency given in this patent when the transmit power ρ _r = ρ _s = 10dB under different scenarios of the number of user pairs, as the number of relay station antennas increases Comparison curve of simulation results. It can be seen from the figure that the analytical approximate expression proposed by this patent has a very good approximation effect, and the difference between it and the Monte Carlo numerical simulation curve is almost negligible, which shows that the approximate analytical expression proposed by this patent Has very good effect. Figure 4 shows different relay station antenna fixed power consumption P _r , the number of user pairs K=16, when the source user antenna fixed power consumption transmit power P _s =0dB and transmit power ρ _r =ρ _s =10dB, this patent Performance comparison chart of the proposed optimal antenna number solution method. It can be seen from the figure that the total energy efficiency of the system increases first and then decreases with the number of antennas, and the closed solution for the optimal number of antennas given by this scheme accurately matches the optimal energy efficiency value on the energy efficiency change curve.

Claims

1. A multi-user large-scale antenna relay system antenna selection method based on optimal energy efficiency is characterized by comprising the following steps:

1) the relay station obtains ideal channel state information from the relay station to all source users and all sink users through channel estimation, namely a channel matrixAndwherein h is_kRepresenting the channel vector from the kth source user to the relay station and obeying a complex Gaussian distribution Representing the channel vector of the repeater to the kth sink user and obeying a complex Gaussian distributionAssuming that a system adopts a time division duplex system, and a channel obeys flat block fading, namely a channel coefficient is kept unchanged in channel coherence time;

2) in the first slot, K source users transmit information symbols to the relay node at the same time, then the received signal vector r at the relay can be represented in the form,

r = \sqrt{ρ_{s}} H x + n_{r}

wherein x is [ x ]₁,x₂,...,x_K]^T，x_k(K ═ 1, 2.. times, K) denotes the transmission symbol of the kth source user andn_rwhite noise per unit power at the relay station representing the first slot and satisfying a complex Gaussian distribution

3) In the second time slot, the relay station transmits the precoding matrix by adopting the maximum ratio combination and the maximum ratioThe received signal r is amplified to form a forwarded signal vector t as follows,

t = V r = \sqrt{ξ} {GH}^{H} r

wherein ξ is a power normalization factor to satisfy an average total transmit power constraint ρ at the relay_rThat is to say that,

then the process of the first step is carried out,

ξ = \frac{ρ_{r}}{θ} = \frac{ρ_{r}}{T r (ρ_{s} {(H^{H} H)}^{2} G^{H} G + H^{H} {HG}^{H} G)};

the relay station then forwards the signal t to all sink users, the signal received by the kth sink user can be represented in the form,

y_{k} = \sqrt{ρ_{s}} g_{k}^{H} {Vh}_{k} x_{k} + \sqrt{ρ_{s}} Σ_{i = 1, i &NotEqual; k}^{K} g_{k}^{H} {Vh}_{i} x_{i} + g_{k}^{H} {Vn}_{r} + n_{k}

wherein n is_kRepresents white noise of unit power at k-th sink user and satisfies complex Gaussian distribution

4) Based on the received signal expression of the sink user in step 3), the receiving drying ratio SINR expression of the kth sink user can be obtained as follows,

γ_{k} = \frac{A_{k}}{B_{k} + C_{k} + θ / ρ_{r} ρ_{s}}

wherein,

A_{k} \overset{Δ}{=} | g_{k}^{H} {GH}^{H} h_{k} |^{2},

B_{k} \overset{Δ}{=} Σ_{i = 1, i &NotEqual; k}^{K} | g_{k}^{H} {GH}^{H} h_{i} |^{2},

C_{k} \overset{Δ}{=} \frac{σ_{r}^{2}}{ρ_{s}} | | g_{k}^{H} {GH}^{H} | |^{2},

so that the average spectral efficiency of the kth sink user can be obtained as shown in the following formula,

wherein,represents the spectral efficiency loss generated by taking the occupied two time slot resources into account;

5) establishing a mathematical optimization model with the number of relay station antennas as a variable and with the goal of maximizing the total energy efficiency function eta (N) of the system at the relay station based on the average spectral efficiency expression in the step 4), as shown below,

wherein η (N) represents the energy efficiency function, S_ΣRepresenting the total spectral efficiency, P, of all users_ΣRepresents the total power consumption, μ, of the system_sMore than or equal to 1 represents the constant factor of the efficiency loss of each power amplifier device of the source user transmitter, mu_rThe constant factor P of the efficiency loss of the power amplifier device of the repeater station transmitter is more than or equal to 1_sRepresenting a constant fixed power consumption, P, of each source user transmitter_rRepresents a constant fixed power consumption on each antenna of the repeater transceiver;

6) applying law of large numbers to γ in step 4)_kThe terms contained in the expression are approximated, resulting in the following expression,

A_{k} \approx {\tilde{A}}_{k} = Σ_{j = 1}^{K} | g_{k}^{H} g_{j} |^{2} | h_{j}^{H} h_{k} |^{2}

B_{k} \approx {\tilde{B}}_{k} = Σ_{i = 1, i &NotEqual; k}^{K} Σ_{j = 1}^{K} | g_{k}^{H} g_{j} |^{2} | h_{j}^{H} h_{i} |^{2}

C_{k} \approx {\tilde{C}}_{k} = \frac{σ_{r}^{2}}{ρ_{s}} Σ_{j = 1}^{K} | g_{k}^{H} g_{j} |^{2} | | h_{j} | |^{2}

θ \approx \tilde{θ} = Σ_{i = 1}^{K} (ρ_{s} Σ_{j = 1}^{K} | h_{i}^{H} h_{j} |^{2} + σ_{r}^{2} | | h_{i} | |^{2}) | | g_{i} | |^{2}

then, S_kCan be approximately expressed asAs will be shown below, in the following,

then, toBy approximation, can obtainAs will be shown below, in the following,

the statistical property of complex Gaussian random vector product can be directly calculatedThe analytical expression of (a) is as follows,

S_{k} \approx {\overset{&OverBar;}{S}}_{k} = \frac{1}{2} \log_{2} (1 + \frac{{\overset{&OverBar;}{A}}_{k}}{{\overset{&OverBar;}{B}}_{k} + {\overset{&OverBar;}{C}}_{k} + {\overset{&OverBar;}{F}}_{k}})

wherein,

8) consider that the number of large-scale antennas deployed at a relay station is usually much larger than the number of users, i.e., N > K, and utilize the high signal-to-noise ratio condition, i.e., ρ_r> 1 and ρ_s> 1, using the analytical expression obtained in step 7)The approximation is simplified to the form that,

{\overset{&OverBar;}{S}}_{k} \approx \frac{1}{2} \log_{2} (1 + \frac{ρ_{r} ρ_{s} (N + 2)}{2 (K - 1) ρ_{r} ρ_{s} + ρ_{r} + {Kρ}_{s}})

9) based on the analytical expression in step 8)Approximately expressing the objective function η (N) of the optimization problem in step 5) asIn combination withInstead of the objective function of the optimization problem in step 5), to approximately translate into an optimization problem of the form,

10) step 9) the optimization variable N belongs to a set of positive integers, the optimization problem belongs to a non-convex integer program; firstly, the variable N is released into a continuous real variable, and a closed form solution of the optimal antenna number can be directly obtained by means of a LambertW function, as shown in the following formula,

wherein,

α \overset{Δ}{=} \frac{ρ_{r} ρ_{s}}{2 (K - 1) ρ_{r} ρ_{s} + ρ_{r} + {Kρ}_{s}},

β \overset{Δ}{=} K (μ_{s} ρ_{s} + P_{s}) + μ_{r} ρ_{r},

e represents a natural constant, and e represents a natural constant,represents the LambertW function, which is defined as: equation θ e for variable x^υThe solution for v can then be represented by a lambert w function, i.e.

11) Due to the number N of the optimal antennas found in step 10)^optUsually not an integer, according to step 10) energy efficiency functionRegarding the variation relation of N, the optimal number of antennas can be finally obtained to be round { N^opt}；

Wherein, (.)^H-representing a conjugate transpose operation of the matrix,-representing a set of positive integers,-for the mathematical expectation operation of a random quantity (vector), Tr {. -the trace of the matrix, round { x } -represents taking the integer closest to the real number x,-mean value μ variance σ²The complex Gaussian random distribution, | | · | -,ρ_s-average transmission power per source user, p_r-average total transmit power of the relay station.