CN113923767B - Energy efficiency maximization method for multi-carrier cooperation non-orthogonal multiple access system - Google Patents
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
- H04W52/04—TPC
- H04W52/18—TPC being performed according to specific parameters
- H04W52/24—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters
- H04W52/241—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters taking into account channel quality metrics, e.g. SIR, SNR, CIR, Eb/lo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L5/00—Arrangements affording multiple use of the transmission path
- H04L5/0001—Arrangements for dividing the transmission path
- H04L5/0003—Two-dimensional division
- H04L5/0005—Time-frequency
- H04L5/0007—Time-frequency the frequencies being orthogonal, e.g. OFDM(A), DMT
- H04L5/001—Time-frequency the frequencies being orthogonal, e.g. OFDM(A), DMT the frequencies being arranged in component carriers
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
- H04W52/04—TPC
- H04W52/18—TPC being performed according to specific parameters
- H04W52/28—TPC being performed according to specific parameters using user profile, e.g. mobile speed, priority or network state, e.g. standby, idle or non transmission
- H04W52/282—TPC being performed according to specific parameters using user profile, e.g. mobile speed, priority or network state, e.g. standby, idle or non transmission taking into account the speed of the mobile
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- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
- H04W52/04—TPC
- H04W52/18—TPC being performed according to specific parameters
- H04W52/28—TPC being performed according to specific parameters using user profile, e.g. mobile speed, priority or network state, e.g. standby, idle or non transmission
- H04W52/283—Power depending on the position of the mobile
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- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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Abstract
The invention discloses a method for maximizing energy efficiency of a multi-carrier cooperation non-orthogonal multiple access system, belonging to the technical field of carrier cooperation non-orthogonal multiple access downlink systems. The method takes the base station transmitting power, the relay transmitting power and the lowest rate constraint condition of the user into consideration, and maximizes the total energy efficiency of the system by controlling the base station transmitting power, the relay transmitting power and the matching factor. According to the method, firstly, problems are decoupled into two sub-problems of sub-carrier user matching and power distribution, after a user sub-carrier matching algorithm is put forward based on a matching theory, transmission power and relay amplification power are distributed by using an alternate optimization variable algorithm, and the energy efficiency of a system is improved to the greatest extent. The method has the advantages of low calculation complexity, capability of strictly ensuring the minimum rate requirement of the user and improving the energy efficiency of the system, and is particularly suitable for the multi-carrier cooperation non-orthogonal multiple access downlink network.
Description
Technical Field
The invention belongs to the technical field of carrier cooperation non-orthogonal multiple access downlink systems, and particularly relates to a power control method for maximizing energy efficiency in a multi-carrier cooperation non-orthogonal multiple access downlink system.
Background
With the advent of the next generation mobile internet era, traffic congestion tends to be caused by access to massive internet of things devices, so that a Non-orthogonal multiple access (Non-orthogonal Multiple Access, NOMA) technology is used as a novel multiple access means to multiplex users in a power domain, transmit superposition coded signals in a physical layer, and finally decode information of each user at a receiving end through a serial interference cancellation (Successive Interference cancellation, SIC) technology, and compared with a traditional orthogonal multiple access technology (Orthogonal Multiple Access, OMA), the NOMA has higher spectral efficiency and energy efficiency, so that combining the NOMA technology with other technologies of traditional mobile communication has become a trend of domestic and foreign research.
The multi-carrier technology transmits information by dividing one sub-carrier into a plurality of sub-carriers, interference of users between the sub-carriers can be avoided, and thus system capacity can be improved under limited spectrum resources. The cooperative communication is widely applied in wireless communication, and the relay is additionally arranged in the source node and the destination node, so that the reliability and the capacity of the system are improved, multipath fading can be resisted, and the performance of the system is improved.
In the NOMA system, since information of different users needs to be superposition coded at the transmitting end, that is, users that are not used in the power domain are multiplexed to perform data transmission, how to allocate power is a critical factor affecting the performance of the system.
At present, most students analyze the power allocation problem in the NOMA system in a single carrier and traditional single hop network, and the NOMA resource allocation problem is not considered in combination with multi-carrier and cooperative communication. In practical wireless communication, relays are required to be erected according to the characteristics of the surrounding environment in different scenes, and meanwhile, the system performance can be fully improved under the condition of less frequency spectrum resources by adopting a multi-carrier technology.
Therefore, in the NOMA system, it is necessary to study the power control method in the downlink system based on the multi-carrier cooperation non-orthogonal multiple access under the condition of ensuring the minimum rate requirement of the user.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. The method decomposes the energy efficiency problem into two sub-algorithms, firstly matches user carrier waves, then distributes power, and has the characteristics of low calculation complexity, less convergence times and suitability for a multi-carrier cooperation non-orthogonal multiple access system network. The technical scheme of the invention is as follows:
the energy efficiency maximization method of the multi-carrier cooperation non-orthogonal multiple access system comprises the following steps:
101. initializing the number of subcarriers and the number and positions of users, generating the positions of a base station and a relay, acquiring channel state information of the users by the base station and the relay, determining channel gain of each user, sequencing the users according to a descending order of the channel gain, and establishing an optimization problem;
102. generating a preference list of each user and each subcarrier according to the channel gain of the user, initializing a matching list and an unmatched list, wherein the matching list is used for recording the matching condition of the user on each subcarrier, and the unmatched list is used for recording the users which are not matched to the subcarriers;
103. executing a bilateral matching algorithm;
104. obtaining an energy efficiency expression of the whole system according to the matching result;
105. and carrying out user power and relay power distribution based on variable replacement, continuous convex approximation and a fractional programming method, and calculating a system energy efficiency value.
Further, in the step 101, the number of initialized users is K, the number of subcarriers is N, andrepresenting user set->Representing the subcarrier set, the information transmission needs to go through two stages, and in the first time slot, the base station transmits a broadcast signal: />In->Is the transmit power of user k on the carrier, +.>Is a data symbol and satisfiesThe channel between the base station and the relay is expressed as: h is a SR n The channel between the relay and the user is expressed as: g Rk n Thus, receiving a signal from a base station at a relay is: /> wherein Is additive white Gaussian noise, sigma 2 Is the variance of the noise;
in the second time slot, relay sends signals to the kth user using AF protocol, then the kth user receives signals on the nth sub-carrierThe method comprises the following steps: />
in the formula βn Representing the amplification factor relayed on subcarrier n, which is in conjunction withThe relationship of (2) is as follows:
in->Is the transmit power relayed on the nth subcarrier,is additive white gaussian noise on user k.
Further, assuming that the channels of K users are arranged in ascending order on the subcarrier n, the kth user can decode first, the information of the ith user is regarded as noise, after decoding is successful, the decoded information of the kth user is deleted from the received signal, and then the operation process is circulated until all user information is successfully decoded;
therefore, the SINR of user k on subcarrier n is:the sum rate achievable by user k on subcarrier n is: />Coefficient 1/2 is because two time slots are required for base station to user signaling, and the system sum rate is: /> wherein ,indicating whether subcarrier n matches to user k;
establishing an optimization problem:
s.t.
wherein ,is the power transmitted by the base station to the kth user on subcarrier n,/for the kth user>Power allocated to subcarrier n for the base station, +.>To match the factor, R n For the rate of subcarrier n +.>Signal-to-noise ratio of kth user on nth subcarrier;
wherein C1 is the maximum transmission power constraint of the base station, P smax Representing the maximum transmission power of the base station; c2 is the relay maximum transmit power constraint, P rmax Representing the maximum transmitting power when the relay performs the amplifying and forwarding protocol; c3 is the matching constraint of the set,representing a matching factor, i.e. 1 representing that user k occupies this subcarrier n,0 representing that user k does not occupy this subcarrier n; c4 is the maximum number of users that can be matched for each subcarrier is 2; c5 is the minimum rate requirement per userConstraint solving, R k min Representing a minimum rate requirement of the user; c6 is a non-negative constraint of all power.
Further, the step 102 generates a preference list of each user and each subcarrier according to the channel gain of the user, which specifically includes: first, the kth user is denoted as UT k The nth subcarrier is denoted as SC n Assuming that the number of subcarriers and the number of users satisfy k=2n, if UT k Is allocated to SC n Then describe UT k And SC (SC) n Mutually matched, based on perfect channel state information, the preference list of users and subcarriers is expressed as:
PF_UT＝[PF_UT(1),...,PF_UT(k),...,PF_UT(K)] T
PF_SC＝[PF_SC(1),...,PF_SC(n),...,PF_SC(N)] T
wherein PF_UT (k) and PF_SC (n) are user UTs, respectively k And subcarrier SC n If UT is preferred for list of preferences k At SC i Channel gain ratio at SC j Up high, UT k Preference for SC i Rather than SC j Expressed as: and />Respectively representing the channel gains relayed to the users.
Further, the step 103 executes a bilateral matching algorithm, which specifically includes:
each user sends a matching request to the sub-carrier which is selected most preferably according to the preference list, and then the sub-carrier is used for selecting the user; if the number of the matching lists of the sub-carriers is less than 2, the sub-carriers add the user to the matching list; if the number of the matching list of the subcarriers is equal to 2, byIn->Representing the energy efficiency value, P, of user 1 and user 2 on that subcarrier 1 n ＝P 2 n ＝1/2P n Is the power the base station transmits on subcarrier n for two users, < >>Power allocated to subcarrier n for the base station, +.>For matching factor, ++>Signal-to-noise ratio of kth user on nth subcarrier; respectively calculating energy efficiency values of three users paired to the carrier wave in pairs, and when calculating the energy efficiency values, distributing the same power P to each subcarrier wave n ＝P smax /N，P r n ＝P rmax/N, in the formula Pr n Representing the power allocated to subcarrier n by relay, P rmax The maximum value of the power which can be distributed to all the subcarriers by the relay is represented, the user combination of the maximum energy efficiency value is selected by the subcarriers as a matching list of the subcarriers, and the matching list is updated and the unmatched list is updated; two users successfully matched to subcarrier n aliquoting power P 1 n ＝P 2 n ＝1/2P n The rejected user deletes the subcarrier from its preference list; if the number of the users of the preferred sub-carriers exceeds 3, the method is still used for comparing the energy efficiency values of the sub-carriers matched with any two users, and the users matched with the sub-carriers are selected by the method; and each other subcarrier is matched with the rest users according to the method until all the users are successfully matched with the subcarriers, and the matching algorithm is finished.
Further, in step 104, an energy efficiency expression of the whole system is written according to the matching result, specifically:
the energy efficiency expression is expressed as:
s.t.
wherein ,is the power transmitted by the base station to the kth user on subcarrier n,/for the kth user>Power allocated to subcarrier n for base station, R n For the rate of subcarrier n +.>Signal-to-noise ratio of kth user on nth subcarrier;
solving the discrete variable constraint by a bilateral matching algorithm, wherein the signal-to-noise ratio in the formula is rewritten as: wherein A1 ,A 2 And a are respectively represented as:
let->Therefore constraints C2 and C3 can be rewritten as +.>Then, an exponential function substitution variable is introduced, let ∈ ->Thus-> And can be rewritten to +.> and /> wherein Let->The optimization problem is rewritten as:
s.t.
introduction of Taylor expansionThe above problem is rewritten as the lower bound of the problem:
s.t.
in the formula , wherein ,/>Respectively represent the power allocated by the relay and the base station,representing the signal-to-noise ratio of the user, respectively +.>Is the initial point of the q-th iteration.
Further, in the step 105, user power and relay power are allocated based on variable replacement, continuous convex approximation and a split planning method, and a system energy efficiency value is calculated, which specifically includes:
firstly, the form of an optimization problem is known, the problem is a convex constraint multi-ratio problem of a numerator concave and a denominator convex, and a variable lambda is introduced based on a partitional programming theory n The objective function is rewritten as:
s.t.
wherein ,λ n in order to introduce the auxiliary variable(s),representing the power allocated by the relay and the base station, respectively, +.>Respectively representing the signal-to-noise ratio of the user,
initializing an iteration tolerance factor epsilon and a maximum iteration number q max Setting the initial value of power allocation to 0, calculating the energy efficiency value each time and updating lambda n Up toThe difference between the unit modulus values of the two iterations is smaller than the iteration tolerance factor or reaches the maximum iteration number, and the power value is output.
The invention has the advantages and beneficial effects as follows:
the invention is based on a matching theory and a split planning method under the condition of considering multi-carrier cooperation NOMA, the traditional method is to convert the matching problem into a discrete variable constraint problem, but the invention adopts a method based on Gale-shape matching theory to solve, firstly, users and sub-carriers are respectively listed according to channel gain preference lists, the users and the sub-carriers are paired, and if the number of the matching lists of the sub-carriers is less than 2, the sub-carriers add the users to the matching lists; if the number of the matching list of the subcarriers is equal to 2, byIn->Representing the energy efficiency value, P, of user 1 and user 2 on that subcarrier 1 n ＝P 2 n ＝1/2P n Is the power the base station transmits on subcarrier n for two users, < >>Power allocated to subcarrier n for the base station, +.>Signal-to-noise ratio of kth user on nth subcarrier; respectively calculating energy efficiency values of three users paired on the carrier wave in pairs, selecting a user combination with the largest energy efficiency value as a matching list of the subcarrier wave by the subcarrier wave, updating the matching list, and updating a non-matching list; two users successfully matched to subcarrier n aliquoting power P 1 n ＝P 2 n ＝1/2P n The rejected user deletes the subcarrier from its preference list; if the number of users of the preferred sub-carriers exceeds 3, the method is still used for comparing the energy efficiency values of any two of the users matched with the sub-carriers, and the method is used for selecting the matched sub-carriersA carrier matched user; each of the remaining sub-carriers is matched with the remaining users according to the method until all the users are successfully matched with the sub-carriers, and finally, the energy efficiency value on each sub-carrier is calculated>The constraint is then transformed into a convex set by a series of variable rewrites, thus into an equivalence problem
s.t.
in the formula wherein />
Then the objective function is rewritten into a numerator concave and denominator convex constraint multi-ratio problem by a split programming method, the power distribution is innovatively carried out by adopting a theory based on split programming, and a variable lambda is introduced n The objective function is rewritten as:
s.t.
wherein ,λ n in order to introduce the auxiliary variable(s),representing the power allocated by the relay and the base station, respectively, +.>Respectively representing the signal-to-noise ratio of the user, finally, the method provided by the invention has the characteristics of low complexity and less convergence times, and compared with other schemes, the method provided by the invention can maximize the energy efficiency of the system on the basis of guaranteeing the minimum rate requirement of the user, is particularly suitable for a downlink multi-carrier cooperation NOMA network, and has better feasibility and practicability.
Drawings
Fig. 1 is a diagram of a multi-carrier cooperative non-orthogonal multiple access downlink system model in accordance with a preferred embodiment of the present invention;
FIG. 2 is a diagram showing the effect of the transmit power of a base station on the energy efficiency of the system according to the present invention;
FIG. 3 illustrates the effect of user minimum rate requirements and system energy efficiency in the present invention;
FIG. 4 is a graph showing the effect of constant circuit loss on system power consumption in accordance with the present invention;
FIG. 5 is a flow chart of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and specifically described below with reference to the drawings in the embodiments of the present invention. The described embodiments are only a few embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
the invention discloses an energy efficiency maximization method of a multi-carrier cooperation non-orthogonal multiple access downlink system, which comprises the following steps:
initializing the number of users and the number of subcarriers, acquiring channel state information of the users by a base station and a relay, determining channel gain of each user, sequencing the users according to a descending order of the channel gain, and establishing an optimization problem; a preference list is generated for each user and each subcarrier based on the channel gains of the users. Initializing a matching list and an unmatched list, wherein the matching list is used for recording the matching condition of users on each subcarrier, and the unmatched list is used for recording users which are not matched to the subcarriers; executing a bilateral matching algorithm; writing an energy efficiency expression of the whole system according to the matching result; and carrying out user power and relay power distribution based on a split planning theory. Compared with other schemes, the method provided by the invention can maximize the energy efficiency of the system on the basis of ensuring the user rate requirement, is suitable for a downlink multi-carrier collaborative NOMA network, and has better feasibility and practicability.
The implementation is an energy efficiency maximization method of a multi-carrier cooperation non-orthogonal multiple access downlink system, wherein the multi-carrier cooperation non-orthogonal multiple access downlink system comprises a base station and a relay, K users and N subcarriers are distributed randomly in a service range with a radius of 130 meters, signals are sent to the relay by the base station, and the relay adopts an amplification and forwarding protocol to send the signals to the users. The base station to relay channel gain can be expressed as:the gain of the relay to the user can be expressed as: /> wherein fSR and fRk Is the Rayleigh Li Cuila coefficient, d SR and dRk The distances between the base station to the relay and the relay to the user are indicated, respectively, and α is a path loss factor, set to 2. Beta SR and βRk Respectively at d SR and dRk The channel gains at 1 meter are all 0.1. The system bandwidth B is 5 MHz, and the energy spectrum density of the additive Gaussian white noise energy is-174 dBm/Hz. An iteration tolerance factor epsilon of 10 -6 Maximum number of iterations q max 100 times.
The following describes the method for maximizing energy efficiency in the multi-carrier cooperative non-orthogonal multiple access downlink system in detail with reference to the specific example:
(1) Assuming that the user minimum rate requirement is satisfied in the case of ideal channel state information, the optimization problem that maximizes the system energy efficiency is expressed as follows:
s.t.
wherein C1 is the maximum transmission power constraint of the base station, P smax Representing the maximum transmission power of the base station; c2 is the relay maximum transmit power constraint, P rmax Representing the maximum transmitting power when the relay performs the amplifying and forwarding protocol; c3 is the matching constraint of the set,representing the matching factor, i.e. 1 representing that user k occupies this subcarrier n,0 representing that user k does not occupy this subcarrierA carrier n; c4 is the maximum number of users that can be matched for each subcarrier is 2; c5 is a minimum rate requirement constraint per user, R k min Representing a minimum rate requirement of the user; c6 is a non-negative constraint of all power.
(2) And decoupling the established optimization problem into two parts, wherein the first part is a matching problem between the subcarrier and the user. First, the kth user is denoted as UT k The nth subcarrier is denoted as SC n Assuming that the number of subcarriers and the number of users satisfy k=2n, if UT k Is allocated to SC n Then describe UT k And SC (SC) n Mutually matched, based on perfect channel state information, the preference list of users and subcarriers is expressed as:
PF_UT＝[PF_UT(1),...,PF_UT(k),...,PF_UT(K)] T
PF_SC＝[PF_SC(1),...,PF_SC(n),...,PF_SC(N)] T
wherein PF_UT (k) and PF_SC (n) are UT, respectively k and SCn If UT is preferred for list of preferences k At SC i Channel gain ratio at SC j Up high, UT k Preference for SC i Rather than SC j Expressed as:
for example, consider 4 users and 2 subcarriers whose channel gain matrix is:
H＝[0.227,0.335；0.767,0.590；0.684,0.458；0.195,0.658]
where the row index represents the user and the column index represents the subcarrier, thus yielding a preference list for the user:
PF_UT(1)＝[2 1] T ；PF_UT(2)＝[1 2] T ；PF_UT(3)＝[1 2] T ；PF_UT(4)＝[2 1] T 。
each user sends a matching request to the sub-carrier that is most selected by the user according to the preference list of the user, and then the sub-carrier is used for selecting the user. If the number of the matching lists of the sub-carriers is less than 2, the sub-carriers add the user to the matching list; if the sub-carriers matchWhen the number of the list is equal to 2, respectively calculating the energy efficiency values of the three users paired on the carrier wave in pairs, and when the energy efficiency values are calculated, distributing the same power P to each subcarrier n ＝P smax /N，P r n ＝P rmax and/N, selecting the user combination with the maximum energy efficiency value as the matching list of the subcarrier, updating the matching list, and updating the unmatched list. Two users successfully matched to subcarrier n aliquoting power P 1 n ＝P 2 n ＝1/2P n The rejected user deletes the subcarrier from its preference list.
(3) And after the matching process of the sub-carrier and the user is finished, performing a power distribution part. The problem is first expressed as:
s.t.
wherein the expressions of C1, C2, C3 and C4 are the same as the corresponding meanings in step 101, the discrete variable constraint is solved by the above-mentioned bilateral matching algorithm. The optimization problem is rewritten as follows through variable replacement and rewrite:
s.t.
/>
in the formula , wherein ,/> Is the initial point of the q-th iteration.
First, as known from the form of an optimization problem, the problemThe problem is that the convex constraint of a numerator concave and a denominator convex is a multi-ratio problem. Based on the split programming theory, variable lambda is introduced n The objective function is rewritten as:
s.t.
initializing an iteration tolerance factor epsilon and a maximum iteration number q max . Setting the initial value of power allocation to 0, updating lambda n Until the difference between the unit modulus values of the two iterations is smaller than the iteration tolerance factorOr the maximum number of iterations q is reached max Output power value->And calculates an energy efficiency value.
The algorithm ends.
In this embodiment, fig. 1 provides an example multi-carrier cooperative non-orthogonal multiple access downlink system link model for the present invention. Fig. 2 illustrates the effect of the transmit power of a base station on the energy efficiency of the system according to the present invention. FIG. 3 illustrates the impact of user minimum rate requirements and system energy efficiency in the present invention. FIG. 4 is a graph showing the effect of constant circuit loss and system power consumption in the present invention. As can be seen from fig. 2, compared with the three comparison schemes, the system energy efficiency obtained by the proposed scheme of the algorithm increases with the increase of the maximum transmission power of the base station, and the energy efficiency is higher than that of the three comparison schemes. As can be seen from fig. 3, the proposed scheme of the algorithm results in a system with reduced energy efficiency as the minimum rate requirement of the user increases, compared to the three comparison schemes, and the energy efficiency is higher than the three comparison schemes. As can be seen from fig. 4, compared with the three comparison schemes, the system energy efficiency obtained by the proposed scheme of the algorithm decreases with the increase of the loss of the circuit in the system, and the energy efficiency is higher than that of the three comparison schemes.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or apparatus that comprises the element.
The above examples should be understood as illustrative only and not limiting the scope of the invention. Various changes and modifications to the present invention may be made by one skilled in the art after reading the teachings herein, and such equivalent changes and modifications are intended to fall within the scope of the invention as defined in the appended claims.
Claims (1)
1. The energy efficiency maximization method of the multi-carrier cooperation non-orthogonal multiple access system is characterized by comprising the following steps of:
101. initializing the number of subcarriers and the number and positions of users, generating the positions of a base station and a relay, acquiring channel state information of the users by the base station and the relay, determining channel gain of each user, sequencing the users according to a descending order of the channel gain, and establishing an optimization problem;
102. generating a preference list of each user and each subcarrier according to the channel gain of the user, initializing a matching list and an unmatched list, wherein the matching list is used for recording the matching condition of the user on each subcarrier, and the unmatched list is used for recording the users which are not matched to the subcarriers;
103. executing a bilateral matching algorithm;
104. obtaining an energy efficiency expression of the whole system according to the matching result;
105. user power and relay power are distributed based on variable replacement, continuous convex approximation and a split planning method, and a system energy efficiency value is calculated;
in the step 101, the number of initialized users is K, the number of subcarriers is N, anda set of users is represented and,representing the subcarrier set, the information transmission needs to go through two stages, and in the first time slot, the base station transmits a broadcast signal: />In->Is the transmit power of user k on the carrier, +.>Is a data symbol and satisfies->The channel between the base station and the relay is expressed as: h is a SR n The channel between the relay and the user is expressed as: g Rk n Thus, receiving a signal from a base station at a relay is: /> wherein />Is additive white Gaussian noise, sigma 2 Is the variance of the noise;
in the second time slot, relay sends signals to the kth user using AF protocol, then the kth user receives signals on the nth sub-carrierThe method comprises the following steps: />
in the formula βn Representing the amplification factor relayed on subcarrier n, which is in conjunction withThe relationship of (2) is as follows:
in->Is the transmit power relayed on the nth subcarrier, ">Is additive white gaussian noise on user k;
assuming that the channels of the K users are arranged in ascending order on the subcarrier n, the kth user can decode first, the information of the ith user is regarded as noise, after the decoding is successful, the decoded information of the kth user is deleted from the received signal, and then the operation process is circulated until all user information is successfully decoded;
therefore, the SINR of user k on subcarrier n is:the sum rate achievable by user k on subcarrier n is: />Coefficient 1/2 is because two time slots are required for base station to user signaling, and the system sum rate is: /> wherein ,indicating whether subcarrier n matches to user k;
establishing an optimization problem:
s.t.
wherein ,is the power transmitted by the base station to the kth user on subcarrier n,/for the kth user>Power allocated to subcarrier n for the base station, +.>To match the factor, R n For the rate of subcarrier n +.>Signal-to-noise ratio of kth user on nth subcarrier;
wherein C1 is the maximum transmission power constraint of the base station, P smax Representing the maximum transmission power of the base station; c2 is the relay maximum transmit power constraint, P rmax Representing the maximum transmitting power when the relay performs the amplifying and forwarding protocol; c3 is the matching constraint of the set,representing a matching factor, i.e. 1 representing that user k occupies this subcarrier n,0 representing that user k does not occupy this subcarrier n; c4 is the maximum number of users that can be matched for each subcarrier is 2;c5 is a minimum rate requirement constraint per user, R k min Representing a minimum rate requirement of the user; c6 is a non-negative constraint of all power;
step 102 generates a preference list of each user and each subcarrier according to the channel gain of the user, which specifically includes: first, the kth user is denoted as UT k The nth subcarrier is denoted as SC n Assuming that the number of subcarriers and the number of users satisfy k=2n, if UT k Is allocated to SC n Then describe UT k And SC (SC) n Mutually matched, based on perfect channel state information, the preference list of users and subcarriers is expressed as:
PF_UT＝[PF_UT(1),...,PF_UT(k),...,PF_UT(K)] T
PF_SC＝[PF_SC(1),...,PF_SC(n),...,PF_SC(N)] T
wherein PF_UT (k) and PF_SC (n) are user UTs, respectively k And subcarrier SC n If UT is preferred for list of preferences k At SC i Channel gain ratio at SC j Up high, UT k Preference for SC i Rather than SC j Expressed as: and />Respectively representing channel gains relayed to users;
step 103 executes a bilateral matching algorithm, which specifically includes:
each user sends a matching request to the sub-carrier which is selected most preferably according to the preference list, and then the sub-carrier is used for selecting the user; if the number of the matching lists of the sub-carriers is less than 2, the sub-carriers add the user to the matching list; if the number of the matching list of the subcarriers is equal to 2, byIn->Representing the energy efficiency value, P, of user 1 and user 2 on that subcarrier 1 n ＝P 2 n ＝1/2P n Is the power transmitted by the base station to two users on subcarrier n, P r n Power allocated to subcarrier n for the base station, +.>For matching factor, ++>Signal-to-noise ratio of kth user on nth subcarrier; respectively calculating energy efficiency values of three users paired to the carrier wave in pairs, and when calculating the energy efficiency values, distributing the same power P to each subcarrier wave n ＝P smax /N，P r n ＝P rmax/N, in the formula Pr n Representing the power allocated to subcarrier n by relay, P rmax The maximum value of the power which can be distributed to all the subcarriers by the relay is represented, the user combination of the maximum energy efficiency value is selected by the subcarriers as a matching list of the subcarriers, and the matching list is updated and the unmatched list is updated; two users successfully matched to subcarrier n aliquoting power P 1 n ＝P 2 n ＝1/2P n The rejected user deletes the subcarrier from its preference list; if the number of the users of the preferred sub-carriers exceeds 3, the method is still used for comparing the energy efficiency values of the sub-carriers matched with any two users, and the users matched with the sub-carriers are selected by the method; each other subcarrier is matched with the rest of users according to the method until all the users are successfully matched with the subcarriers, and the matching algorithm is completed;
step 104, writing an energy efficiency expression of the whole system according to the matching result, specifically:
the energy efficiency expression is expressed as:
s.t.
wherein ,is the power transmitted by the base station to the kth user on subcarrier n, P r n Power allocated to subcarrier n for base station, R n For the rate of subcarrier n +.>Signal-to-noise ratio of kth user on nth subcarrier;
solving the discrete variable constraint by a bilateral matching algorithm, wherein the signal-to-noise ratio in the formula is rewritten as: wherein A1 ,A 2 And a are respectively represented as:
order theTherefore constraints C2 and C3 can be rewritten as +.>Then, an exponential function substitution variable is introduced, let ∈ ->Thus-> And can be rewritten to +.> and /> wherein
Reams theThe optimization problem is rewritten as:
s.t.
introduction of Taylor expansionThe above problem is rewritten as the lower bound of the problem:
s.t.
in the formula , wherein ,/>Respectively represent the power allocated by the relay and the base station,representing the signal-to-noise ratio of the user, respectively +.>Is the initial point of the q-th iteration;
step 105, performing user power and relay power allocation based on variable replacement, continuous convex approximation and a split planning method, and calculating a system energy efficiency value, wherein the method specifically comprises the following steps:
first, the optimization problem is known as a convex constraint multiple ratio of a numerator concave and a denominator convexThe rate problem is based on the split programming theory, and a variable lambda is introduced n The objective function is rewritten as:
s.t.
wherein ,λ n for the auxiliary variables introduced ∈ ->Representing the power allocated by the relay and the base station, respectively, +.>Respectively representing the signal-to-noise ratio of the user,
initializing an iteration tolerance factor epsilon and a maximum iteration number q max Setting the initial value of power allocation to 0, calculating the energy efficiency value each time and updating lambda n And outputting a power value until the difference between the unit modulus values of the two iterations is smaller than an iteration tolerance factor or the maximum iteration number is reached.
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