CN108235425A - Based on the extensive antenna relay system of the optimal pairs of user of efficiency and its resource allocation methods - Google Patents
Based on the extensive antenna relay system of the optimal pairs of user of efficiency and its resource allocation methods Download PDFInfo
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Abstract
本发明公开了一种基于能效最优的成对用户大规模天线中继系统及其资源分配方法,属于无线通信技术领域。该系统由多个信源节点、多个信宿节点和一个中继节点所组成,信源节点与信宿节点一一对应组成通信对,中继节点采用迫零准则对信源节点的信号进行放大转发,在两个时隙内完成信息传递。系统中所有信源和信宿节点均配置单根天线,中继节点配置大规模天线阵列。本发明方法以最大化系统能效为目标,以信源节点发射功率、中继节点发射功率和中继节点天线数三个系统资源参量为优化变量建立数学模型,再采用交替迭代优化算法及目标函数的部分凸性和拉格朗日对偶法,获得了中继节点最优发射功率和中继最优天线数的闭合形式解。
The invention discloses a large-scale antenna relay system for paired users based on optimal energy efficiency and a resource allocation method thereof, belonging to the technical field of wireless communication. The system consists of multiple source nodes, multiple sink nodes and a relay node. The source node and the sink node correspond to each other to form a communication pair. The relay node uses the zero-forcing criterion to amplify and forward the signal of the source node. , the information transmission is completed within two time slots. All source and sink nodes in the system are configured with a single antenna, and the relay nodes are configured with a large-scale antenna array. The method of the present invention aims at maximizing the energy efficiency of the system, uses three system resource parameters of the source node transmission power, the relay node transmission power and the number of relay node antennas as optimization variables to establish a mathematical model, and then uses an alternate iterative optimization algorithm and an objective function The partial convexity and Lagrangian dual method of the method obtained the closed-form solutions of the optimal transmit power of the relay node and the optimal number of antennas of the relay.
Description
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成对用户大规模天线中继系统及其资源分配方法。The invention belongs to the technical field of wireless communication, and in particular relates to a large-scale antenna relay system for paired users based on optimal energy efficiency and a resource allocation method thereof.
背景技术Background technique
近年来,大规模多输入多输出(简称大规模MIMO)技术吸引了无线通信领域学术界与工业界越拉越多的目光,并被广泛认为是第五代移动通信系统的关键技术之一。大规模MIMO技术是指在基站端集中配备大规模数量的天线阵列来同时服务数量相对较小的多个用户,有研究指出,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,信道快衰落和热噪声被平均(又称信道硬化),显著降低基站端和用户端的发射功率而不影响系统的可达速率性能,超高的空间分辨率可用于精准的波束对准,以及简单的线性处理便可以几近完美的消除多用户间干扰影响等等。In recent years, massive multiple-input multiple-output (referred to as massive MIMO) technology has attracted more and more attention from academia and industry in the field of wireless communication, and is widely regarded as one of the key technologies of the fifth-generation mobile communication system. Massive MIMO technology refers to the centralized deployment of a large number of antenna arrays at the base station to serve a relatively small number of multiple users at the same time. Some studies have pointed out that by using large-scale antenna arrays at the base station to tap the available resources in the air space, many Compared with the new features of the traditional MIMO system, such as fast channel fading and thermal noise are averaged (also known as channel hardening), significantly reducing the transmit power of the base station and user end without affecting the system's achievable rate performance, ultra-high spatial resolution The rate can be used for precise beam alignment, and simple linear processing can almost perfectly eliminate the interference effect between multiple users, etc.
与此同时,多天线中继通信系统作为未来异构网络中的重要组成部分也一直受到众多研究机构和设备厂商的广泛关注。通过引入多天线中继节点,可以在小区覆盖范围、边缘用户吞吐量、链路可靠性和传输功耗等方面获得诸多性能提升。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性能的主要因素。针对该问题,业界提出两类主流的解决方案:一类是利用时频资源的正交性,将不同用户调度在不同的时频资源块上,通过增加视频资源消耗来抑制用户间干扰;另一类则是通过联合设计预编码和接收机模块来达到降低用户间干扰的目的。然而,第一类方法虽然可以获得较好的用户间干扰消除效果,但是消耗了过多的系统时频资源,对系统整体的频谱效率性能的负面影响较大。第二种方法在实现复杂度方面带来了较大的困难,联合设计的算法通常复杂度过高,对中继节点和信宿节点的硬件计算资源提出了更高的要求。考虑到大规模MIMO技术采用低复杂度线性处理即可较好消除用户间干扰这一特性,Himal A.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在多用户通信中所提供的抑制多用户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,这使得大规模天线中继的系统性能有了较大的增长潜力,同时,也可以利用大规模MIMO技术的简单线性处理方式大大降低中继节点与信宿节点的计算资源开销。At the same time, as an important part of the future heterogeneous network, the multi-antenna relay communication system has been widely concerned by many research institutions and equipment manufacturers. By introducing multi-antenna relay nodes, many performance improvements can be obtained in terms of cell coverage, edge user throughput, link reliability, and transmission power consumption. However, in multi-user relay systems, inter-user interference has always been the main factor limiting the performance of multi-antenna relay systems. To solve this problem, the industry has proposed two mainstream solutions: one is to use the orthogonality of time-frequency resources to schedule different users on different time-frequency resource blocks, and to suppress inter-user interference by increasing video resource consumption; One is to achieve the purpose of reducing interference between users by jointly designing precoding and receiver modules. However, although the first type of method can obtain a better inter-user interference cancellation effect, it consumes too many system time-frequency resources and has a relatively large negative impact on the overall spectrum efficiency performance of the system. The second method brings greater difficulties in terms of implementation complexity. The jointly designed algorithm is usually too complex, which puts forward higher requirements for the hardware computing resources of the relay node and the sink node. Considering that massive MIMO technology can better eliminate inter-user interference by using low-complexity linear processing, Himal A. Massive MIMO provides the ability to suppress multi-user interference in multi-user communication to solve the problem of inter-user interference in a pair-user multi-antenna relay system, which makes the system performance of large-scale antenna relay have greater growth potential. At the same time, the simple linear processing method of the massive MIMO technology can also be used to greatly reduce the computing resource overhead of the relay node and the sink node.
值得注意的是,在将大规模天线阵列引入中继节点的同时,也不可避免的会带来若干问题。大规模天线阵列的使用可以使信源用户发射功率和中继节点发射功率成倍降低而不影响系统频谱效率,这对于提升系统的发射功率效率是十分有益的。然而,与大规模天线阵列密切相关的射频链路固定功耗将随天线数成倍提升,而固定电路总功耗的提升势必会对中继通信系统的整体能效性能造成影响。特别是当固定电路总功耗远大于发射功耗时,持续增加天线数会使得系统的总能效性能不升反降。由此可见,中继天线数的增加可以减少发射功耗,却会增加射频链路的电路功耗,在中继天线数与发射功率之间,存在着一个折中,联合考虑信源节点发射功率、中继节点发射功率以及中继天线数的资源分配问题具有十分重要的实际意义和应用背景,特别是在绿色通信概念下,发射功率和天线数的分配会直接影响到系统的能效水平,而这一问题尚未有研究人员涉足。为了解决大规模天线中继系统中的资源分配问题,我们提出了基于能效最大化的信源节点发射功率、中继节点发射功率和中继节点天线数联合资源分配优化模型,由于该模型中目标函数过于复杂且没有精确的解析表达式,因而优化问题求解过程十分困难。It is worth noting that when introducing a large-scale antenna array into a relay node, it will inevitably bring about several problems. The use of a large-scale antenna array can reduce the transmit power of the source user and the transmit power of the relay node by multiples without affecting the system spectral efficiency, which is very beneficial for improving the transmit power efficiency of the system. However, the fixed power consumption of the radio frequency link, which is closely related to the large-scale antenna array, will increase exponentially with the number of antennas, and the increase in the total power consumption of the fixed circuit will inevitably affect the overall energy efficiency of the relay communication system. Especially when the total power consumption of the fixed circuit is much greater than the transmission power consumption, continuously increasing the number of antennas will cause the total energy efficiency of the system to decrease rather than increase. It can be seen that the increase in the number of relay antennas can reduce the transmission power consumption, but it will increase the circuit power consumption of the radio frequency link. There is a trade-off between the number of relay antennas and the transmission power. The resource allocation of power, relay node transmit power and relay antenna number has very important practical significance and application background, especially under the concept of green communication, the allocation of transmit power and antenna number will directly affect the energy efficiency level of the system. And this question has yet to be tackled by researchers. In order to solve the problem of resource allocation in large-scale antenna relay systems, we propose a joint resource allocation optimization model based on energy efficiency maximization of source node transmit power, relay node transmit power, and relay node antenna numbers. The function is too complex and there is no precise analytical expression, so the optimization problem solving process is very difficult.
本发明公开了一种基于能效最优的成对用户大规模天线中继系统资源分配方法。该系统包括多个信源节点、多个信宿节点和一个中继节点,所述信源节点与信宿节点一一对应,组成通信对,中继节点采用迫零准则对信源节点的信号进行放大转发,在两个时隙内完成信息传递。系统中所有信源和信宿节点均配置单根天线,中继节点配置大规模天线阵列。本发明方法以最大化系统能效为目标,以信源节点发射功率、中继节点发射功率和中继节点天线数三个系统资源参量为优化变量建立数学模型。由于该优化问题中目标函数无精确解析表达式,因此,借助于Jensen不等式和逆Wishart矩阵统计特性,求目标函数的一种精确下界解析表达式。利用该解析表达式关于优化变量的各自拟凹特性,获得信源节点与中继节点最优发射功率的数学关系式,将三变量优化问题转化为两变量优化问题。进而,利用分式规划性质将原优化问题等价转化为减法形式,提出一种交替迭代优化算法。再根据减式形式目标函数的部分凸性和拉格朗日对偶法,获得了中继节点最优发射功率和中继最优天线数的闭合形式解。The invention discloses a method for resource allocation of a large-scale antenna relay system for paired users based on optimal energy efficiency. The system includes multiple source nodes, multiple sink nodes and a relay node. The source nodes correspond to the sink nodes one by one to form a communication pair. The relay node uses the zero-forcing criterion to amplify the signal of the source node. Forwarding, information transmission is completed within two time slots. All source and sink nodes in the system are configured with a single antenna, and the relay nodes are configured with a large-scale antenna array. The method of the invention aims at maximizing the energy efficiency of the system, and establishes a mathematical model with three system resource parameters, the transmission power of the source node, the transmission power of the relay node and the number of antennas of the relay node, as optimization variables. Since there is no exact analytical expression for the objective function in this optimization problem, an exact lower bound analytical expression for the objective function is obtained by means of Jensen's inequality and the statistical properties of the inverse Wishart matrix. Using the quasi-concave characteristics of the analytical expressions about the optimization variables, the mathematical relational expression of the optimal transmit power of the source node and the relay node is obtained, and the three-variable optimization problem is transformed into a two-variable optimization problem. Furthermore, using the property of fractional programming, the original optimization problem is equivalently transformed into a subtractive form, and an alternate iterative optimization algorithm is proposed. Then, according to the partial convexity of the objective function in subtractive form and the Lagrangian dual method, the closed-form solutions of the optimal transmit power of the relay node and the optimal number of antennas of the relay are 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资源分配方法,给出一种交替迭代优化算法求得了中继节点发射功率与中继节点天线数的闭合形式解。The present invention proposes a resource allocation method for a multi-user large-scale antenna relay system based on optimal energy efficiency in order to enable the paired-user large-scale antenna relay system to obtain higher energy efficiency performance, and provides an alternate iterative optimization algorithm to obtain The closed-form solution of relay node transmit power and relay node antenna number.
本发明的基于能效最优的成对用户大规模天线中继系统资源分配方法,所述中继系统包括K个信源节点、K个信宿节点和一个中继节点,所述信源节点与信宿节点一一对应,组成通信对,所述中继节点采用迫零准则对信源节点的信号进行放大转发,在两个时隙内完成信息传递;所述中继系统采用时分双工制式,采用了一定的用户调度策略,将具有相同大尺度衰落的信源节点或信宿节点放在一个时频资源块中,且信道服从平坦块衰落,其特征在于,所述方法包括以下步骤:According to the resource allocation method of the large-scale antenna relay system for paired users based on optimal energy efficiency of the present invention, the relay system includes K source nodes, K sink nodes and a relay node, and the source node and the sink node The nodes correspond one by one to form a communication pair. The relay node adopts the zero-forcing criterion to amplify and forward the signal of the source node, and completes the information transmission within two time slots; the relay system adopts the time-division duplex system. A certain user scheduling strategy is established, and the source node or the sink node with the same large-scale fading is placed in a time-frequency resource block, and the channel is subject to flat block fading. It is characterized in that the method includes the following steps:
S1.建立以最大化系统总能效为目标,以信源节点发射功率、中继节点发射功率和中继节点天线数三个系统资源参量为优化变量的数学模型;S1. Establish a mathematical model with the goal of maximizing the total energy efficiency of the system, and taking the three system resource parameters of source node transmit power, relay node transmit power and relay node antenna number as optimization variables;
S2.利用Jensen不等式和逆Wishart矩阵的各阶距特性,求用户频谱效率的下界解析表达式;并基于所述中继节点部署的大规模天线数远大于用户数对所述的下界解析表达式近似化简,将所述近似化简的下界解析表达式,以及将信源节点与中继节点最优发射功率数学关系式代入原始优化问题的目标函数;S2. Using Jensen's inequality and the characteristics of each step distance of the inverse Wishart matrix, find the lower bound analytical expression of the user's spectral efficiency; and based on the number of large-scale antennas deployed by the relay node is much greater than the number of users for the lower bound analytical expression Approximate simplification, substituting the lower bound analytical expression of the approximate simplification, and substituting the mathematical relationship between the optimal transmission power of the source node and the relay node into the objective function of the original optimization problem;
S3.用交替迭代算法,求中继节点最优发射功率和中继节点最优天线数;以及S3. Using an alternate iterative algorithm to find the optimal transmit power of the relay node and the optimal number of antennas of the relay node; and
S4.中继节点将信源节点最优发射功率值反馈通知所有信源节点,并将中继节点发射功率和中继节点天线数调至S3所得的最佳值。S4. The relay node notifies all source nodes of the optimal transmission power value of the source node, and adjusts the transmission power of the relay node and the number of antennas of the relay node to the optimal values obtained in S3.
进一步地,所述步骤S1包括如下步骤:Further, the step S1 includes the following steps:
1).中继节点通过信道估计获得它到所有信源节点和信宿节点间的理想信道状态信息,即信道矩阵和其中,hk表示第k个信源节点到中继节点的信道向量且服从复高斯分布 表示信源节点到中继节点的大尺度衰落因子,表示中继节点到第k个信宿节点的信道向量且服从复高斯分布 表示中继节点到信宿节点的大尺度衰落因子;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;假设系统采用了一定的用户调度策略,将具有相同大尺度衰落的信源节点(信宿节点)放在一个时频资源块中;1). The relay node obtains the ideal channel state information between it and all source nodes and sink nodes through channel estimation, that is, the channel matrix and Among them, h k represents the channel vector from the kth source node to the relay node and obeys the complex Gaussian distribution Indicates the large-scale fading factor from the source node to the relay node, Represents the channel vector from the relay node to the kth sink node and obeys the complex Gaussian distribution Indicates the large-scale fading factor from the relay node to the sink node; assuming that the system adopts a time-division duplex system, and the channel obeys flat block fading, that is, the channel coefficient remains unchanged during the channel coherence time; assuming that the system adopts a certain user scheduling strategy , put the source nodes (sink nodes) with the same large-scale fading in one time-frequency resource block;
2).在第一时隙内,K个信源节点同时向中继节点发送信息符号,则在中继节点处的接收信号向量r可以表示为如下形式,2). In the first time slot, K source nodes send information symbols to the relay node at the same time, then the received signal vector r at the relay node can be expressed as the following form,
其中,s=[s1,s2,...,sK]T,sk(k=1,2,...,K)表示第k个信源节点的发射符号且nr表示第一时隙在中继节点处的加性白噪声且满足复高斯分布ρs表示每个信源节点的平均发射功率变量;Among them, s=[s 1 ,s 2 ,...,s K ] T , s k (k=1,2,...,K) represents the transmitted symbol of the kth source node and n r represents the additive white noise at the relay node in the first time slot and satisfies the complex Gaussian distribution ρ s represents the average transmit power variable of each source node;
3).在第二时隙内,中继节点采用迫零接收和迫零预编码对接收到的信号r进行放大转发,其处理矩阵为所形成的转发信号向量yt如下所示,3). In the second time slot, the relay node uses zero-forcing reception and zero-forcing precoding to amplify and forward the received signal r, and its processing matrix is The resulting forwarded signal vector y t is shown below,
yt=Dyr y t =Dy r
其中,ψ为功率归一化因子用以满足中继节点处的平均总发射功率约束ρr,即,where ψ is the power normalization factor to satisfy the average total transmit power constraint ρ r at the relay node, namely,
则,然后,中继节点将信号yt转发至所有信宿节点,则第k个信宿节点接收到的信号可以表示为如下形式,but, Then, the relay node forwards the signal y t to all sink nodes, and the signal received by the kth sink node can be expressed as follows,
其中,nk表示第k个信宿节点处的加性白噪声且满足复高斯分布 Among them, n k represents the additive white noise at the kth sink node and satisfies the complex Gaussian distribution
4).基于步骤3)中信宿节点的接收信号表达式,可以得第k个信宿节点的接收信干噪比表达式如下所示,4). Based on the received signal expression of the sink node in step 3), the received SINR expression of the kth sink node can be obtained as follows,
从而可以得到第k个信宿节点的平均频谱效率如下式所示,Thus, the average spectral efficiency of the kth sink node 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 occupied two time slot resources into account;
5).基于步骤4)中平均频谱效率表达式,在中继节点处建立以最大化系统总能效函数η(ρs,ρr)为目标,以信源节点发射功率ρs和中继节点发射功率ρr为变量的数学优化模型,如下所示,5). Based on the average spectral efficiency expression in step 4), establish at the relay node to maximize the total system energy efficiency function η(ρ s , ρ r ) as the goal, take the source node transmit power ρ s and the relay node The mathematical optimization model where the transmit power ρ r is a variable is as follows,
其中,EE(p,N)表示能效函数,S(p,N)表示系统的总频谱效率,Ptot(p,N)表示系统的总功率消耗,μs≥1表示每个信源节点发射机功放器件的效率损耗常量因子,μr≥1表示中继节点发射机功放器件的效率损耗常量因子,Ps表示每个信源节点发射机的常量固定功率消耗,Pr表示中继节点收发机每根天线上的常量固定功率消耗;Among them, EE(p, N) represents the energy efficiency function, S(p, N) represents the total spectral efficiency of the system, P tot (p, N) represents the total power consumption of the system, μ s ≥ 1 represents that each source node transmits The efficiency loss constant factor of the transmitter power amplifier device, μ r ≥ 1 represents the efficiency loss constant factor of the relay node transmitter power amplifier device, P s represents the constant fixed power consumption of each source node transmitter, P r represents the relay node transceiver constant fixed power consumption on each antenna of the machine;
所述步骤S2包括如下步骤:Described step S2 comprises the following steps:
6).由于步骤5)中目标函数的包含Sk,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,利用关于x的凸性和Jensen不等式,可以得到步骤4)中平均频谱效率Sk的下界,如下所示,6). Due to the inclusion of S k 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, use Regarding the convexity of x and Jensen's inequality, the lower bound of the average spectral efficiency S k in step 4) can be obtained as follows,
7).利用复逆Wishart矩阵的各阶矩性质,可以直接计算得到的解析表达式如下所示,7).Using the moment properties of each order of the complex inverse Wishart matrix, it can be directly calculated to get The analytical expression for is as follows,
其中, in,
8).考虑到中继节点部署的大规模天线数通常远大于用户数,即N>>K>1,并利用高信噪比条件,即γs>>1和γr>>1,将步骤7)中得到的解析表达式近似化简为如下形式,8). Considering that the number of large-scale antennas deployed by relay nodes is usually much larger than the number of users, that is, N>>K>1, and using the condition of high signal-to-noise ratio, that is, γ s >>1 and γ r >>1, the The analytical expression obtained in step 7) Approximate simplification to the following form,
9).基于步骤8)中的解析表达式将步骤5)中优化问题的目标函数进行近似替换,并代替步骤5)中优化问题的目标函数,转化为如下形式的优化问题,9). Based on the analytical expression in step 8) The objective function of the optimization problem in step 5) is approximately replaced, and the objective function of the optimization problem in step 5) is replaced, and transformed into an optimization problem of the following form,
10).步骤9)中目标函数EE(p,N)在给定天线数变量N的条件下,关于功率向量是严格拟凹的,并且存在唯一的最优发射功率组合满足能效最大化,且信源节点最优发射功率与中继节点最优发射功率所满足的关系式如下所示,10). In step 9), the objective function EE(p, N) is strictly quasi-concave with respect to the power vector under the condition of a given antenna number variable N, and there is a unique optimal transmit power combination The maximum energy efficiency is satisfied, and the relationship between the optimal transmit power of the source node and the optimal transmit power of the relay node is as follows,
步骤9)中目标函数EE(p,N)在给定功率变量的条件下,关于中继天线数是是严格拟凹的,且是先增后减的;In step 9), the objective function EE(p, N) is strictly quasi-concave with regard to the number of relay antennas under the condition of a given power variable, and it increases first and then decreases;
11).将步骤10)中最优发射功率关系式代入步骤9)中的目标函数,可简化为两变量优化问题,如下所示,11). Substituting the optimal transmit power relationship in step 10) into the objective function in step 9), it can be simplified as a two-variable optimization problem, as shown below,
其中, in,
所述步骤S3包括如下步骤:Described step S3 comprises the following steps:
12).根据分式规划性质,可将步骤11)中的优化问题等价的转换为带参数η的减法形式问题,如下所示,12). According to the nature of fractional programming, the optimization problem in step 11) can be equivalently transformed into a subtraction problem with parameter η, as shown below,
其中,η表示能效参量,求解中继最优发射功率与天线数参量以及最优能效值η*;Wherein, η represents the energy efficiency parameter, solves relay optimal transmitting power and antenna number parameter and optimal energy efficiency value η * ;
上述步骤中的符号及部分变量的含义如下:(·)H表示矩阵的共轭转置运算,ε{·}表示针对随机量(向量)的数学期望运算,tr{·}表示矩阵的迹,表示均值为μ方差为σ2的循环对称复高斯随机分布,||·||表示向量2范数运算,|·|表示实数绝对值运算或复数求模值运算,N是中继节点天线数,K是用户对总数。The meanings of the symbols and some variables in the above steps are as follows: (·) H represents the conjugate transpose operation of the matrix, ε{·} represents the mathematical expectation operation for random quantities (vectors), tr{·} represents the trace of the matrix, Indicates a circular symmetric complex Gaussian random distribution with mean value μ and variance σ2 , ||·||indicates vector 2 norm operation, |·|indicates real number absolute value operation or complex number modulo operation, and N is the number of relay node antennas , K is the total number of user pairs.
进一步地,为了求解中继最优发射功率与天线数参量以及最优能效值η*,可采用利用Dinkelbach方法进行交替迭代的方法实现。具体步骤如下:Further, in order to solve the parameters of the optimal transmission power and the number of antennas of the relay and the optimal energy efficiency value η * , it can be realized by using the Dinkelbach method to perform alternate iterations. Specific steps are as follows:
12.1).设定迭代终止ε,迭代次数变量m=0,给定能效参量初始值η(0)≥0;12.1). Set the iteration termination ε, the iteration number variable m=0, and give the initial value of the energy efficiency parameter η (0) ≥ 0;
12.2).利用η(m),求解关于中继发射功率和中继天线数的最优化问题,如下所示,12.2). Use η (m) to solve the optimization problem about the relay transmission power and the number of relay antennas, as shown below,
12.3).当(N-K)ρr≥(1+ξ)K/ν时,步骤12.2)中目标函数是凸的。利用该目标函数的部分凸性,令其对ρr和N分别求一阶偏导并使其为0,可以得到中继节点最优发射功率和中继节点最优天线数的闭合形式解,如下所示,12.3). When (NK)ρ r ≥ (1+ξ)K/ν, the objective function in step 12.2) is convex. Taking advantage of the partial convexity of the objective function, let it calculate the first-order partial derivatives for ρr and N respectively and make them 0, and then obtain the closed-form solution of the optimal transmit power of the relay node and the optimal number of antennas of the relay node, As follows,
其中, in,
12.4).更新能效参量和迭代次数变量m=m+1;12.4). Update energy efficiency parameters And the number of iterations variable m=m+1;
12.5).判断时,终止迭代运算,输出最优资源变量组合以及最优能效值ηopt=η(m);若不满足终止条件,返回步骤12.2)重新进行迭代;12.5). Judgment When , the iterative operation is terminated and the optimal resource variable combination is output And the optimal energy efficiency value ηopt =η (m) ; if the termination condition is not met, return to step 12.2) to re-iterate;
12.6).步骤12.5)中的最优天线数通常为小数,取与Nopt最近的两个整数值,计算其对应的能效值,取能效值较大的天线数值即为最优天线数值。12.6). The optimal number of antennas in step 12.5) is usually a decimal number. Take the two closest integer values to N opt and calculate the corresponding energy efficiency value. The antenna value with a larger energy efficiency value is the optimal antenna value.
本发明还提出了一种基于能效最优的成对用户大规模天线中继系统,包括K个信源节点、K个信宿节点和一个中继节点,所述信源节点与信宿节点一一对应,组成通信对,所述中继节点采用迫零准则对信源节点的信号进行放大转发,在两个时隙内完成信息传递;所述中继系统采用时分双工制式,采用了一定的用户调度策略,将具有相同大尺度衰落的信源节点或信宿节点放在一个时频资源块中,且信道服从平坦块衰落,其特征在于,所述中继系统采用上述的资源分配方法配置信源节点发射功率、中继节点的发射功率和中继节点的天线数量。The present invention also proposes a large-scale antenna relay system for paired users based on optimal energy efficiency, including K source nodes, K sink nodes and a relay node, and the source nodes correspond to the sink nodes one by one , forming a communication pair, the relay node adopts the zero-forcing criterion to amplify and forward the signal of the source node, and completes the information transmission within two time slots; the relay system adopts the time division duplex system, and adopts a certain Scheduling strategy, put the source node or sink node with the same large-scale fading in a time-frequency resource block, and the channel obeys flat block fading, characterized in that the relay system uses the above resource allocation method to configure the source The transmit power of the node, the transmit power of the relay node, and the number of antennas of the relay node.
本发明提出了一种基于能效最优的成对用户大规模天线中继系统资源分配方法,推导得出了信源节点与中继节点最优发射功率的数学关系,并利用交替迭代算法直接求得中继节点发射功率和中继节点天线数的闭合形式最优解。通过给信源节点和中继节点分配最优发射功率,并在中继节点配备最优天线数,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,避免了庞大天线数所产生的较多电路功耗影响,从而使得系统总能效达到最高水平。本专利算法采用成熟且高效的Dinkelbach迭代优化方法,并利用标准的凸优化方案得到了中继节点发射功率和中继节点天线数的闭合形式最优解,因而,经过少量迭代运算即可收敛到最优能效值,算法复杂度相对较低。The present invention proposes a method for resource allocation of a large-scale antenna relay system for paired users based on optimal energy efficiency, deduces the mathematical relationship between the optimal transmission power of the source node and the relay node, and uses an alternate iterative algorithm to directly obtain The closed-form optimal solution of the transmit power of the relay node and the number of antennas of the relay node is obtained. By allocating the optimal transmission power to the source node and the relay node, and configuring the optimal number of antennas on the relay node, the large-scale antenna relay system can obtain the benefits of large-scale antenna arrays while avoiding the need for large-scale antennas. The impact of more circuit power consumption generated by the number, so that the overall energy efficiency of the system reaches the highest level. This patent algorithm adopts the mature and efficient Dinkelbach iterative optimization method, and uses the standard convex optimization scheme to obtain the closed-form optimal solution of the transmit power of the relay node and the number of antennas of the relay node. Therefore, after a small number of iterative operations, it can converge to The optimal energy efficiency value, the algorithm complexity is relatively low.
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为在不同的信源-信宿节点对数目K场景下,本专利所提出的频谱效率下界解析表达式与蒙特卡洛仿真结果对比图;Figure 3 is a comparison diagram of the spectral efficiency lower bound analytical expression proposed in this patent and the Monte Carlo simulation results under different source-sink node pairs K scenarios;
图4为本专利所提出的交替迭代资源分配算法在不同的电路功耗条件下的能效性能随信源-信宿节点对个数的变化情况;Fig. 4 shows the variation of the energy efficiency performance of the alternate iterative resource allocation algorithm proposed in this patent under different circuit power consumption conditions with the number of source-sink node pairs;
图5为本专利所提出的交替迭代算法的收敛轨迹图。Fig. 5 is a graph of the convergence trajectory of the alternate iterative algorithm proposed in this patent.
具体实施方式:Detailed ways:
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成对用户大规模天线中继系统资源分配方法作具体说明,包括如下步骤:In conjunction with the algorithm flow chart shown in Figure 2, a method for resource allocation of a large-scale antenna relay system for paired users based on optimal energy efficiency of the present invention is specifically described, including the following steps:
1).在中继节点处建立以最大化系统总能效函数EE(p,N)为目标,以信源-中继节点发射功率向量p=[ρs,ρr]和中继节点天线数N为变量的数学优化模型,如下所示,1). Establish at the relay node to maximize the total system energy efficiency function EE(p, N) as the goal, with the source-relay node transmit power vector p = [ρ s , ρ r ] and the number of relay node antennas N is the mathematical optimization model of the variable, as shown below,
其中,EE(p,N)表示能效函数,S(p,N)表示系统的总频谱效率,Ptot(p,N)表示系统的总功率消耗,μs≥1表示每个信源节点发射机功放器件的效率损耗常量因子,μr≥1表示中继节点发射机功放器件的效率损耗常量因子,Ps表示每个信源节点发射机的常量固定功率消耗,Pr表示中继节点收发机每根天线上的常量固定功率消耗,Sk(p,N)表示第k个信宿节点的平均频谱效率,如下所示,Among them, EE(p, N) represents the energy efficiency function, S(p, N) represents the total spectral efficiency of the system, P tot (p, N) represents the total power consumption of the system, μ s ≥ 1 represents that each source node transmits The efficiency loss constant factor of the transmitter power amplifier device, μ r ≥ 1 represents the efficiency loss constant factor of the relay node transmitter power amplifier device, P s represents the constant fixed power consumption of each source node transmitter, P r represents the relay node transceiver The constant fixed power consumption on each antenna of the machine, S k (p,N) represents the average spectral efficiency of the kth sink node, as shown below,
其中,γk表示第k个信宿节点的接收信干噪比。Among them, γ k represents the received signal-to-interference-noise ratio of the kth sink node.
3).利用Jensen不等式和复逆Wishart矩阵的各阶矩特性,并考虑大规模天线数与高信噪比区间,即N>>K、和可获得步骤2)中频谱效率Sk的下界闭合表达式简化形式,如下所示,3).Using Jensen's inequality and the moment characteristics of each order of the complex inverse Wishart matrix, and considering the large-scale number of antennas and the high signal-to-noise ratio interval, that is, N>>K, and The simplified form of the lower bound closed expression of the spectral efficiency S k in step 2) can be obtained, as shown below,
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,
5).将信源节点与中继节点最优发射功率的数学关系式代入步骤4)中的目标函数,将原问题简化为两变量优化问题,如下所示,5). Substitute the mathematical relationship between the source node and the relay node's optimal transmit power into the objective function in step 4), and simplify the original problem into a two-variable optimization problem, as shown below,
其中, in,
6).基于步骤5)中的优化问题,采用交替迭代方法求解最优发射功率值,具体步骤如下:6). Based on the optimization problem in step 5), an alternate iterative method is used to solve the optimal transmit power value. The specific steps are as follows:
6.1).设定迭代终止ε,迭代次数变量m=0,给定能效参量初始值η(0)≥0;6.1). Set the iteration termination ε, the iteration number variable m=0, and give the initial value of the energy efficiency parameter η (0) ≥ 0;
6.2).利用η(m),求解关于中继发射功率和中继天线数的最优化问题,如下所示,6.2). Use η (m) to solve the optimization problem about the relay transmission power and the number of relay antennas, as shown below,
6.3).当(N-K)ρr≥(1+ξ)K/ν时,步骤12.2)中目标函数是凸的。利用该目标函数的部分凸性,令其对ρr和N分别求一阶偏导并使其为0,可以得到中继节点最优发射功率和中继节点最优天线数的闭合形式解,如下所示,6.3). When (NK)ρ r ≥ (1+ξ)K/ν, the objective function in step 12.2) is convex. Taking advantage of the partial convexity of the objective function, let it calculate the first-order partial derivatives for ρr and N respectively and make them 0, and then obtain the closed-form solution of the optimal transmit power of the relay node and the optimal number of antennas of the relay node, As follows,
其中, in,
6.4).更新能效参量和迭代次数变量m=m+1;6.4). Update energy efficiency parameters And the number of iterations variable m=m+1;
6.5).判断时,终止迭代运算,输出最优资源变量组合以及最优能效值ηopt=η(m);若不满足终止条件,返回步骤12.2)重新进行迭代;6.5). Judgment When , the iterative operation is terminated and the optimal resource variable combination is output And the optimal energy efficiency value ηopt =η (m) ; if the termination condition is not met, return to step 12.2) to re-iterate;
6.6).步骤6.5)中的最优天线数通常为小数,取与Nopt最近的两个整数值,计算其对应的能效值,取能效值较大的天线数值即为最优天线数值;6.6). The optimal number of antennas in step 6.5) is usually a decimal number, and the two nearest integer values to N opt are used to calculate the corresponding energy efficiency value, and the antenna value with a larger energy efficiency value is the optimal antenna value;
其中,(·)H—表示矩阵的共轭转置运算,ε{·}—针对随机量(向量)的数学期望运算,tr{·}—矩阵的迹,—表示均值为μ方差为σ2的循环对称复高斯随机分布,||·||—表示向量2范数运算,|·|—表示实数绝对值运算或复数求模值运算,N—中继节点天线数,K—用户对总数。Among them, (·) H —represents the conjugate transposition operation of the matrix, ε{·}—mathematical expectation operation for random quantities (vectors), tr{·}—the trace of the matrix, —Represents a circular symmetric complex Gaussian random distribution with a mean of μ and a variance of σ2 , ||·||—represents a vector 2 norm operation, |·|—represents a real number absolute value operation or a complex number modulus operation, N—relay The number of node antennas, K—the total number of user pairs.
图3给出了不同的用户对个数场景下,发射功率ρr=ρs=20dB时,随着中继节点天线数的增长,本专利所给出的频谱效率下界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给出了当信源节点天线固定功耗和中继节点天线固定功耗满足Ps=Pr=-20dB和-15dB时,本专利所给出的迭代资源分配算法获得的能效值随信源-信宿节点对个数的变化情况。图5给出了本专利所提出的交替迭代优化算法收敛到最优能效值的收敛速度与收敛轨迹。从图中可以看出,经过大约6次迭代即可收敛到最优能效值,收敛过程较快。Fig. 3 shows different scenarios of the number of user pairs, when the transmission power ρ r = ρ s = 20dB, with the increase of the number of relay node antennas, the analytical expression of the lower bound of the spectrum efficiency given in this patent and the Monte Carlo The comparison curve of the numerical 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 that when the fixed power consumption of the source node antenna and the fixed power consumption of the relay node antenna satisfy P s =P r =-20dB and -15dB, the energy efficiency value obtained by the iterative resource allocation algorithm given in this patent varies with Changes in the number of source-sink node pairs. Fig. 5 shows the convergence speed and the convergence track of the alternate iterative optimization algorithm proposed in this patent converging to the optimal energy efficiency value. It can be seen from the figure that the optimal energy efficiency value can be converged after about 6 iterations, and the convergence process is fast.
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