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
The invention discloses a kind of extensive antenna relay system of pairs of user optimal based on efficiency and its resource allocation methods, belong to wireless communication technology field.The system is made of multiple information source nodes, multiple information destination nodes and a relay node, information source node and information destination node correspond composition and communicate pair, relay node is amplified forwarding using Zero Forcing to the signal of information source node, and information is completed in two time slots and is transmitted.Single antenna, relay node configuration large-scale antenna array is configured in all information sources and information destination node in system.The method of the present invention is to maximize system energy efficiency as target, using three information source node transmission power, relay node transmission power and relay node antenna number system resource parameters as optimized variable founding mathematical models, again using alternating iteration optimization algorithm and the part convexity of object function and Lagrange duality method, obtain relay node optimum transmission power and relay the closed-form solution of optimal antenna number.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a paired user large-scale antenna relay system based on optimal energy efficiency and a resource allocation method thereof.
Background
In recent years, a massive multiple input multiple output (massive MIMO) technology has attracted more and more attention from the academic and industrial fields of wireless communication, and is widely considered as one of the key technologies of the fifth-generation mobile communication system. The massive MIMO technology is designed to provide massive antenna arrays at the base station end to serve multiple users with relatively small number at the same time, and it has been shown that many new characteristics relative to the conventional MIMO system can be obtained by mining available space resources using massive antenna arrays at the base station end, such as channel fast fading and thermal noise averaging (also called channel hardening), significantly reducing the transmit power at the base station end and the user end without affecting the achievable rate performance of the system, having ultrahigh spatial resolution for precise beam alignment, and being able to perfectly eliminate the interference between multiple users by simple linear processing.
Meanwhile, the multi-antenna relay communication system has been receiving wide attention from many research institutes and equipment manufacturers as an important component in future heterogeneous networks. By introducing the multi-antenna relay node, various performance improvements can be obtained in the aspects of cell coverage, edge user throughput, link reliability, transmission power consumption and the like. However, in the multi-user relay system, the inter-user interference has been a major factor limiting the performance of the multi-antenna relay system. To address this problem, the industry proposes two main types of solutions: one is that different users are scheduled on different time frequency resource blocks by utilizing the orthogonality of time frequency resources, and the interference among the users is inhibited by increasing the video resource consumption; and the other type is to jointly design a precoding module and a receiver module to achieve the aim of reducing the interference among users. However, although the first method can obtain a better effect of eliminating the inter-user interference, it consumes too many time-frequency resources of the system, and has a large negative impact on the overall spectrum efficiency performance of the system. The second method brings great difficulty in the aspect of implementation complexity, and the complexity of the algorithm of the joint design is usually too high, which puts higher requirements on hardware computing resources of the relay node and the sink node. In view of the characteristic that the large-scale MIMO technology can better eliminate the inter-user interference by adopting low-complexity linear processing, Himal a. suraweera et al propose to introduce the large-scale MIMO technology into a multi-user multi-antenna relay system for the first time in 2013, and solve the inter-user interference problem of a pair-user multi-antenna relay system by utilizing the multi-user interference suppression capability provided by the large-scale MIMO in multi-user communication, so that the system performance of the large-scale antenna relay has great growth potential, and meanwhile, the computing resource overhead of a relay node and a sink node can be greatly reduced by utilizing a simple linear processing mode of the large-scale MIMO technology.
It is noted that while introducing large-scale antenna arrays into relay nodes, several problems are also unavoidable. The use of the large-scale antenna array can reduce the transmission power of the source user and the transmission power of the relay node by times without influencing the spectrum efficiency of the system, which is beneficial to improving the transmission power efficiency of the system. However, the fixed power consumption of the radio frequency link closely related to the large-scale antenna array is increased by times along with the number of the antennas, and the increase of the total power consumption of the fixed circuit will certainly affect the overall energy efficiency performance of the relay communication system. Especially, when the total power consumption of the fixed circuit is much larger than the transmission power consumption, the total energy efficiency of the system does not increase or decrease due to the continuously increased number of the antennas. Therefore, the transmission power consumption can be reduced by increasing the number of the relay antennas, but the circuit power consumption of the radio frequency link can be increased, a compromise exists between the number of the relay antennas and the transmission power, the combined consideration of the resource distribution problems of the transmission power of the information source node, the transmission power of the relay node and the number of the relay antennas has very important practical significance and application background, particularly under the green communication concept, the distribution of the transmission power and the number of the antennas can directly influence the energy efficiency level of the system, and the problem is not referred to by researchers. In order to solve the problem of resource allocation in a large-scale antenna relay system, an information source node transmitting power, relay node transmitting power and relay node antenna number combined resource allocation optimization model based on energy efficiency maximization is provided, and due to the fact that an objective function in the model is too complex and an accurate analytical expression does not exist, the optimization problem solving process is very difficult.
The invention discloses a resource allocation method for a paired user large-scale antenna relay system based on optimal energy efficiency. The system comprises a plurality of information source nodes, a plurality of information sink nodes and a relay node, wherein the information source nodes and the information sink nodes are in one-to-one correspondence to form a communication pair, the relay node adopts a zero forcing criterion to amplify and forward signals of the information source nodes, and information transfer is completed in two time slots. In the system, all information source nodes and information sink nodes are provided with single antennas, and the relay nodes are provided with large-scale antenna arrays. The method of the invention aims at maximizing system energy efficiency, and establishes a mathematical model by taking three system resource parameters of source node transmitting power, relay node transmitting power and relay node antenna number as optimization variables. Because the objective function in the optimization problem has no accurate analytic expression, an accurate lower-bound analytic expression of the objective function is solved by means of a Jensen inequality and the statistical property of an inverse Wishart matrix. And obtaining a mathematical relation of the optimal transmitting power of the information source node and the relay node by utilizing respective pseudo-concave characteristics of the analytical expression on the optimization variables, and converting the three-variable optimization problem into a two-variable optimization problem. And further, the original optimization problem is equivalently converted into a subtraction form by utilizing the fractional programming property, and an alternative iterative optimization algorithm is provided. And obtaining a closed form solution of the optimal transmitting power of the relay node and the optimal number of the relay antennas according to the partial convexity of the subtractive form objective function and a Lagrange dual method.
Disclosure of Invention
The invention provides a resource allocation method of a multi-user large-scale antenna relay system based on optimal energy efficiency for enabling a paired-user large-scale antenna relay system to obtain higher energy efficiency performance, and provides a closed form solution of relay node transmitting power and relay node antenna number obtained by an alternative iteration optimization algorithm.
The invention relates to a resource allocation method of a paired user large-scale antenna relay system based on optimal energy efficiency, wherein the relay system comprises K information source nodes, K information sink nodes and a relay node, the information source nodes and the information sink nodes are in one-to-one correspondence to form a communication pair, the relay node adopts a zero forcing criterion to amplify and forward signals of the information source nodes, and information transmission is completed in two time slots; the relay system adopts a time division duplex system, adopts a certain user scheduling strategy, places information source nodes or information sink nodes with the same large-scale fading in a time frequency resource block, and the channel obeys flat block fading, and is characterized by comprising the following steps:
s1, establishing a mathematical model which takes the total energy efficiency of a maximized system as a target and three system resource parameters of information source node transmitting power, relay node transmitting power and relay node antenna number as optimization variables;
s2, solving a lower bound analytical expression of the user spectrum efficiency by using a Jensen inequality and each step distance characteristic of an inverse Wishart matrix; the lower bound analytic expression is simplified approximately based on the fact that the number of large-scale antennas deployed by the relay node is far larger than the number of users, the lower bound analytic expression of the approximate simplification and the mathematical relation of the optimal transmitting power of the information source node and the relay node are substituted into the objective function of the original optimization problem;
s3, solving the optimal transmitting power of the relay node and the optimal number of the antennas of the relay node by using an alternative iterative algorithm; and
and S4, the relay node feeds back the optimal transmitting power value of the information source node to all the information source nodes, and adjusts the transmitting power of the relay node and the number of the relay node antennas to the optimal value obtained in S3.
Further, the step S1 includes the following steps:
1) the relay node obtains ideal channel state information from the relay node to all source nodes and sink nodes through channel estimation, namely a channel matrixAndwherein h iskRepresenting the kth source node to the relay nodeAnd obey a complex gaussian distribution Representing a large scale fading factor from the source node to the relay node,representing the channel vector of the relay node to the kth sink node and obeying a complex Gaussian distribution Representing a large-scale fading factor from the relay node to the sink node; assuming 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; supposing that a system adopts a certain user scheduling strategy, and placing information source nodes (information sink nodes) with the same large-scale fading in a time-frequency resource block;
2) k source nodes transmit information symbols simultaneously to the relay node in the first slot, the received signal vector r at the relay node can be represented in the form,
wherein s ═ s1,s2,...,sK]T，sk(K ═ 1, 2.. times.k) denotes a transmission symbol of the kth source node andnrrepresents additive white noise of the first time slot at the relay node and satisfies a complex Gaussian distributionρsRepresenting an average transmission power variable of each source node;
3) in the second time slot, the relay node adopts zero-forcing receiving and zero-forcing precoding to amplify and forward the received signal r, and the processing matrix isFormed forwarded signal vector ytAs will be shown below, in the following,
yt＝Dyr
where ψ is a power normalization factor to satisfy an average total transmit power constraint ρ at the relay noderThat is to say that,
then the process of the first step is carried out,the relay node then transmits the signal ytTo all the sink nodes, the signal received by the k-th sink node can be represented in the form,
wherein n iskRepresents additive white noise at the kth sink node and satisfies a complex Gaussian distribution
4) Based on the received signal expression of the sink node in step 3), the received signal to interference plus noise ratio expression of the kth sink node can be obtained as shown below,
so that the average spectral efficiency of the kth sink node 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) based on the average spectral efficiency expression in step 4), establishing at the relay node to maximize the total system energy efficiency function η (ρs,ρr) Targeting the source node transmit power ρsAnd relay node transmit power ρrFor a mathematical optimization model of the variables, as shown below,
wherein EE (P, N) represents an energy efficiency function, S (P, N) represents the total spectral efficiency of the system, Ptot(p, N) represents the total power consumption of the system, μsMore than or equal to 1 represents the constant factor of the efficiency loss of each source node transmitter power amplifier, murMore than or equal to 1 represents the efficiency loss constant factor, P, of the power amplifier device of the relay node transmittersRepresenting a constant fixed power consumption, P, of each source node transmitterrRepresents a constant fixed power consumption on each antenna of the relay node transceiver;
the step S2 includes the following steps:
6) due toInclusion of S in the objective function in step 5)kAnd the accurate analytical expression is difficult to obtain, which is not beneficial to solving the subsequent optimization problem. Here, use is made ofWith respect to the convexity and Jensen inequality of x, the average spectral efficiency S in step 4) can be obtainedkThe lower bound of (a), as shown below,
7) by utilizing the property of each order moment of the complex inverse Wishart matrix, the complex inverse Wishart matrix can be directly calculatedThe analytical expression of (a) is as follows,
wherein,
8) consider that the number of large-scale antennas deployed at a relay node is usually much larger than the number of users, i.e., N > K > 1, and utilize the condition of high signal-to-noise ratio, i.e., γs> 1 and γr> 1, using the analytical expression obtained in step 7)The approximation is simplified to the form that,
9) based on the analytical expression in step 8)Approximately replacing the objective function of the optimization problem in the step 5), converting the objective function into the following form of optimization problem,
10) step 9) the objective function EE (p, N) is strictly pseudo-concave with respect to the power vector and there is a unique optimum transmit power combination, given the variable N of the number of antennasThe energy efficiency maximization is satisfied, and the relation formula satisfied by the optimal transmitting power of the information source node and the optimal transmitting power of the relay node is shown as follows,
in the step 9), the objective function EE (p, N) is strictly pseudo-concave with respect to the number of relay antennas and is increased and then decreased under the condition of a given power variable;
11) substituting the optimal transmit power relation in step 10) into the objective function in step 9) can be simplified into a two-variable optimization problem, as shown below,
wherein,
the step S3 includes the following steps:
12) the optimization problem in step 11) can be equivalently converted into a subtractive form problem with parameters η, according to the nature of the fractional programming, as shown below,
η represents energy efficiency parameters, and the relay optimal transmitting power, antenna number parameters and optimal energy value η are solved＊；
The symbols and some variables in the above steps have the following meanings: (.)HRepresents the conjugate transpose operation of the matrix,. epsilon. {. cndot.represents the mathematical expectation operation on the random quantity (vector), tr {. cndot.represents the trace of the matrix,mean is μ and variance is σ2The method comprises the following steps of (1) circularly symmetric complex Gaussian random distribution, | | | represents vector 2 norm operation, | represents real absolute value operation or complex modulo value operation, | represents relay node antenna number, and K represents user pair total number.
Further, to solve the relay optimal transmitting power and antenna parameters and the optimal energy value η＊The method can be realized by using a Dinkelbach method for alternate iteration. The method comprises the following specific steps:
12.1), setting iteration termination epsilon, setting an iteration number variable m to be 0, and setting an energy efficiency parameter initial value η(0)≥0；
12.2) utilization of η(m)Solving the optimization problem with respect to the relay transmit power and the number of relay antennas, as shown below,
12.3) when (N-K) ρrWhen the value is more than or equal to (1+ ξ) K/v, the target function is convex in the step 12.2), and the partial convexity of the target function is utilized to make the target function to rhorAnd N separately find the first order partial derivatives and make them as0, a closed form solution of the optimal transmit power of the relay node and the optimal number of antennas of the relay node can be obtained, as shown below,
wherein,
12.4) updating energy efficiency parametersAnd an iteration number variable m is m + 1;
12.5) judgmentThen stopping iterative operation and outputting optimum resource variable combinationAnd an optimum energy value ηopt＝η(m)(ii) a If the termination condition is not met, returning to the step 12.2) to repeat iteration again;
12.6) the optimum number of antennas in step 12.5) is usually a fraction taken as NoptAnd calculating corresponding energy efficiency values of the two nearest integer values, wherein the antenna value with the larger energy efficiency value is the optimal antenna value.
The invention also provides a paired user large-scale antenna relay system based on optimal energy efficiency, which comprises K information source nodes, K information sink nodes and a relay node, wherein the information source nodes and the information sink nodes are in one-to-one correspondence to form a communication pair, the relay node adopts a zero forcing criterion to amplify and forward signals of the information source nodes, and information transmission is completed in two time slots; the relay system adopts a time division duplex system, adopts a certain user scheduling strategy, places information source nodes or information sink nodes with the same large-scale fading in a time frequency resource block, and channels obey flat block fading.
The invention provides a resource allocation method for a paired user large-scale antenna relay system based on optimal energy efficiency, which is used for deducing a mathematical relation between an information source node and the optimal transmitting power of a relay node and directly solving the optimal solution of the closed form of the transmitting power of the relay node and the number of the antennas of the relay node by using an alternative iteration algorithm. By distributing the optimal transmitting power to the information source node and the relay node and allocating the optimal number of the antennas at the relay node, the large-scale antenna relay system can obtain the benefits brought by the large-scale antenna array, and simultaneously avoid the influence of more circuit power consumption caused by the large number of the antennas, so that the total energy efficiency of the system can reach the highest level. The method adopts a mature and efficient Dinkelbach iterative optimization method, and obtains a closed form optimal solution of the transmission power of the relay node and the number of the relay node antennas by using a standard convex optimization scheme, so that the optimal energy value can be converged through a small amount of iterative operation, and the algorithm complexity is relatively low.
Drawings
FIG. 1 is a system model of the method of the present invention;
FIG. 2 is a basic flow chart of the algorithm of the present invention;
FIG. 3 is a graph comparing a lower bound analytical expression of spectral efficiency and Monte Carlo simulation results under different information source-information sink node pair number K scenarios;
FIG. 4 is a diagram illustrating the energy efficiency performance of the alternative iterative resource allocation algorithm proposed in the present patent varying with the number of signal source-signal sink node pairs under different circuit power consumption conditions;
fig. 5 is a convergence trajectory diagram of the alternative iteration algorithm proposed by this patent.
The specific implementation mode is as follows:
the method for allocating resources to a paired user large-scale antenna relay system based on optimal energy efficiency according to the present invention is specifically described with reference to the algorithm flowchart shown in fig. 2, and includes the following steps:
1) establishing a transmission power vector p ═ rho [ rho ] at the relay node with the aim of maximizing the total energy efficiency function EE (p, N) of the systems,ρr]And a mathematical optimization model with the number of relay node antennas N as variables, as shown below,
wherein EE (P, N) represents an energy efficiency function, S (P, N) represents the total spectral efficiency of the system, Ptot(p, N) represents the total power consumption of the system, μsMore than or equal to 1 represents the constant factor of the efficiency loss of each source node transmitter power amplifier, murMore than or equal to 1 represents the efficiency loss constant factor, P, of the power amplifier device of the relay node transmittersRepresenting a constant fixed power consumption, P, of each source node transmitterrRepresenting constant fixed power consumption, S, on each antenna of a relay node transceiverk(p, N) represents the average spectral efficiency of the kth sink node, as shown below,
wherein, γkRepresenting the received signal to interference plus noise ratio of the kth sink node.
3) By usingThe Jensen inequality and each moment characteristic of the complex inverse Wishart matrix are considered, and the large-scale antenna number and the high signal-to-noise ratio interval are considered, namely N > K,Andthe spectral efficiency S in the step 2) can be obtainedkIn simplified form, as shown below,
4) based on the approximate expression of spectral efficiency in step 3)Replacing the objective function of the optimization problem in the step 2), approximately converting the objective function into the following form of optimization problem,
5) substituting the mathematical relation between the optimal transmitting power of the source node and the optimal transmitting power of the relay node into the objective function in the step 4) to simplify the original problem into a two-variable optimization problem, as shown below,
wherein,
6) based on the optimization problem in the step 5), an alternating iteration method is adopted to solve the optimal transmitting power value, and the specific steps are as follows:
6.1) settingThe iteration is terminated epsilon, the variable m of the iteration number is equal to 0, and the initial value η of the energy efficiency parameter is given(0)≥0；
6.2) utilization of η(m)Solving the optimization problem with respect to the relay transmit power and the number of relay antennas, as shown below,
6.3) when (N-K) ρrWhen the value is more than or equal to (1+ ξ) K/v, the target function is convex in the step 12.2), and the partial convexity of the target function is utilized to make the target function to rhorAnd N respectively find the first order partial derivatives and make them be 0, so that a closed form solution of the optimal transmission power of the relay node and the optimal number of antennas of the relay node can be obtained, as shown below,
wherein,
6.4) updating energy efficiency parametersAnd an iteration number variable m is m + 1;
6.5) judgmentThen stopping iterative operation and outputting optimum resource variable combinationAnd an optimum energy value ηopt＝η(m)(ii) a If the termination condition is not met, returning to the step 12.2) to repeat iteration again;
6.6) the optimum number of antennas in step 6.5) is usually a fraction taken from NoptCalculating corresponding energy efficiency values of the two nearest integer values, wherein the antenna value with the larger energy efficiency value is the optimal antenna value;
wherein, (.)H-representing the conjugate transpose operation of the matrix,. epsilon. {. for a mathematical expectation operation on a random quantity (vector), tr {. for the trace of the matrix,-mean value μ variance σ2The method comprises the following steps of (1) circularly symmetric complex Gaussian random distribution, | | | represents vector 2 norm operation, | represents real absolute value operation or complex modular value operation, N is the number of relay node antennas, and K is the total number of user pairs.
FIG. 3 shows the transmission power ρ in different user pair number scenariosr＝ρsWhen the number of the relay node antennas is 20dB, along with the increase of the number of the relay node antennas, a comparison curve of a lower bound analytical expression of the spectrum efficiency and a Monte Carlo numerical simulation result is provided. As can be seen from the figure, the analytic approximation expression provided by the patent has a very good approximation effect, and the difference between the analytic approximation expression and the Monte Carlo numerical simulation curve is almost negligible, which shows that the analytic approximation expression provided by the patent has a good effect. FIG. 4 shows that when the fixed power consumption of the source node antenna and the fixed power consumption of the relay node antenna satisfy Ps＝PrWhen the energy efficiency value obtained by the iterative resource allocation algorithm is equal to-20 dB and-15 dB, the energy efficiency value changes along with the number of the source-sink node pairs. Fig. 5 shows the convergence speed and the convergence trajectory of the alternating iterative optimization algorithm proposed by the present patent to converge to the optimal energy efficiency value. As can be seen from the figure, the optimal energy value can be converged after about 6 iterations, and the convergence process is fast.
Claims (5)
1. A resource allocation method for a paired user large-scale antenna relay system based on optimal energy efficiency is disclosed, wherein the relay system comprises K information source nodes, K information sink nodes and a relay node, the information source nodes and the information sink nodes are in one-to-one correspondence to form a communication pair, the relay node adopts a zero forcing criterion to amplify and forward signals of the information source nodes, and information transmission is completed in two time slots; the relay system adopts a time division duplex system, adopts a certain user scheduling strategy, places information source nodes or information sink nodes with the same large-scale fading in a time frequency resource block, and the channel obeys flat block fading, and is characterized in that the method comprises the following steps:
s1, establishing a mathematical model which takes the total energy efficiency of a maximized system as a target and three system resource parameters of information source node transmitting power, relay node transmitting power and relay node antenna number as optimization variables;
s2, solving a lower bound analytical expression of the user spectrum efficiency by using a Jensen inequality and each step distance characteristic of an inverse Wishart matrix; the lower bound analytic expression is simplified approximately based on the fact that the number of large-scale antennas deployed by the relay node is far larger than the number of users, the lower bound analytic expression of the approximate simplification and the mathematical relation of the optimal transmitting power of the information source node and the relay node are substituted into the objective function of the original optimization problem;
s3, solving the optimal transmitting power of the relay node and the optimal number of the antennas of the relay node by using an alternative iterative algorithm; and
and S4, the relay node feeds back the optimal transmitting power value of the information source node to all the information source nodes, and adjusts the transmitting power of the relay node and the number of the relay node antennas to the optimal value obtained in S3.
2. The paired subscriber large scale antenna relay system resource allocation method according to claim 1, wherein said step S1 includes the steps of:
1) the relay node obtains ideal channel state information from the relay node to all source nodes and sink nodes through channel estimation, namely a channel matrixAndwherein h iskRepresenting the channel vector from the kth source node to the relay node and obeying a complex Gaussian distribution Representing a large scale fading factor from the source node to the relay node,representing the channel vector of the relay node to the kth sink node and obeying a complex Gaussian distribution Representing a large-scale fading factor from the relay node to the sink node;
2) k source nodes transmit information symbols simultaneously to the relay node in the first slot, the received signal vector r at the relay node can be represented in the form,
wherein s ═ s1,s2,...,sK]T，sk(K ═ 1, 2.. times.k) denotes a transmission symbol of the kth source node andnrrepresents additive white noise of the first time slot at the relay node and satisfies a complex Gaussian distributionρsRepresenting an average transmission power variable of each source node;
3) in the second time slot, the relay node adopts zero-forcing receiving and zero-forcing precoding to amplify and forward the received signal r, and the processing matrix isFormed forwarded signal vector ytAs will be shown below, in the following,
yt＝Dyr
where ψ is a power normalization factor to satisfy an average total transmit power constraint ρ at the relay noderThat is to say that,
then the process of the first step is carried out,the relay node then transmits the signal ytTo all the sink nodes, the signal received by the k-th sink node can be represented in the form,
wherein n iskRepresents additive white noise at the kth sink node and satisfies a complex Gaussian distribution
4) Based on the received signal expression of the sink node in step 3), the received signal to interference plus noise ratio expression of the kth sink node can be obtained as shown below,
the average spectral efficiency of the kth sink node can thus be obtained:
wherein, represents the spectral efficiency loss generated by taking the occupied two time slot resources into account;
5) based on the average spectral efficiency expression in step 4), establishing at the relay node to maximize the total system energy efficiency function η (ρs,ρr) Targeting the source node transmit power ρsAnd relay node transmit power ρrFor a mathematical optimization model of the variables, as shown below,
wherein EE (P, N) represents an energy efficiency function, S (P, N) represents the total spectral efficiency of the system, Ptot(p, N) represents the total power consumption of the system, μsMore than or equal to 1 represents the constant factor of the efficiency loss of each source node transmitter power amplifier, murMore than or equal to 1 represents the efficiency loss constant factor, P, of the power amplifier device of the relay node transmittersRepresenting a constant fixed power consumption, P, of each source node transmitterrRepresents a constant fixed power consumption on each antenna of the relay node transceiver;
the step S2 includes the steps of:
6) the average spectral efficiency S in step 4) can be obtained according to the Jensen inequalitykThe lower bound of (a), as shown below,
7) directly calculating by using the property of each order moment of the complex inverse Wishart matrix to obtain the characteristic of each order moment in the step 6)The analytical expression of (a) is as follows,
wherein,
8) consider that the number of large-scale antennas deployed at a relay node is usually much larger than the number of users, i.e., N > K > 1, and utilize the condition of high signal-to-noise ratio, i.e., γs> 1 and γr> 1, using the analytical expression obtained in step 7)The approximation is simplified to the form that,
9) based on the analytical expression in step 8)Approximately replacing the objective function of the optimization problem in the step 5), converting the objective function into the following form of optimization problem,
10) step 9) the objective function EE (p, N) is strictly pseudo-concave with respect to the power vector and there is a unique optimum transmit power combination, given the variable N of the number of antennasThe energy efficiency maximization is satisfied, and the relation formula satisfied by the optimal transmitting power of the information source node and the optimal transmitting power of the relay node is shown as follows,
in the step 9), the objective function EE (p, N) is strictly pseudo-concave with respect to the number of relay antennas and is increased and then decreased under the condition of a given power variable;
11) substituting the optimal transmit power relation in step 10) into the objective function in step 9) can be simplified into a two-variable optimization problem, as shown below,
wherein,
the step S3 includes the steps of:
12) the optimization problem in step 11) is equivalently converted into a subtractive form problem with parameters η, according to the fractional programming nature, as shown below,
η represents energy efficiency parameters, and the relay optimal transmitting power, antenna number parameters and optimal energy value η are solved＊；
The symbols and some variables in the above steps have the following meanings: (.)HRepresents the conjugate transpose operation of the matrix,. epsilon. {. cndot.represents the mathematical expectation operation on the random quantity (vector), tr {. cndot.represents the trace of the matrix,mean is μ and variance is σ2The cyclic symmetry complex Gaussian is randomly distributed, | | | represents vector 2 norm operation, | represents real absolute value operation or complex modulo operation, and N is the number of the relay node antennas.
3. The resource allocation method for paired-user large-scale antenna relay system of claim 2, wherein in the step 12), the method of performing alternate iteration by using the Dinkelbach method is used to solve the optimal transmission power and the antenna number parameter of the relay and the optimal energy value η＊Then (c) is performed.
4. The paired-user large-scale antenna relay system resource allocation method according to claim 2 or 3, wherein the step 12) includes the steps of:
12.1), setting iteration termination epsilon, setting an iteration number variable m to be 0, and setting an energy efficiency parameter initial value η(0)≥0；
12.2) utilization of η(m)Solving the optimization problem with respect to the relay transmit power and the number of relay antennas, as shown below,
12.3) when (N-K) ρrWhen the value is more than or equal to (1+ ξ) K/v, the target function is convex in the step 12.2), and the partial convexity of the target function is utilized to make the target function to rhorAnd N respectively find the first order partial derivatives and make them be 0, so that a closed form solution of the optimal transmission power of the relay node and the optimal number of antennas of the relay node can be obtained, as shown below,
wherein,
12.4) updating energy efficiency parametersAnd an iteration number variable m is m + 1;
12.5) judgmentThen stopping iterative operation and outputting optimum resource variable combinationAnd an optimum energy value ηopt＝η(m)(ii) a If the termination condition is not met, returning to the step 12.2) to repeat iteration again;
12.6) the optimum number of antennas in step 12.5) is usually a fraction taken as NoptAnd calculating corresponding energy efficiency values of the two nearest integer values, wherein the antenna value with the larger energy efficiency value is the optimal antenna value.
5. A paired user large-scale antenna relay system based on optimal energy efficiency comprises K information source nodes, K information sink nodes and a relay node, wherein the information source nodes and the information sink nodes are in one-to-one correspondence to form a communication pair, the relay node adopts a zero forcing criterion to amplify and forward signals of the information source nodes, and information transfer is completed in two time slots; the relay system adopts a time division duplex system, adopts a certain user scheduling strategy, places information source nodes or information sink nodes with the same large-scale fading in a time frequency resource block, and channels obey flat block fading, and is characterized in that the relay system adopts the resource allocation method as claimed in claims 1-4 to configure the transmitting power of the information source nodes, the transmitting power of the relay nodes and the number of antennas of the relay nodes.
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