High-energy-efficiency relay selection method and device and electronic equipment
By applying the chaotic cosine search mechanism in a multi-user collaborative communication network, optimizing relay selection, the problem of low energy efficiency in the existing technology is solved, high-energy-efficient relay selection is achieved, and network performance and service quality are improved.
Patent Information
- Application Number
- CN202411033468.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-30
- Publication Date
- 2024-12-13
AI Technical Summary
The existing relay selection method is difficult to achieve high energy efficiency in multi-user scenarios, and the prior art has failed to effectively improve the energy efficiency of the collaborative communication network.
Using the relay selection method based on the chaotic cosine search mechanism, by establishing a network model of a collaborative multi-user multi-relay system, using chaotic cosine population and Logistic mapping to generate random sequences, update individual positions to optimize relay selection, and maximize network energy. efficiency.
It significantly improves the energy efficiency of multi-user collaborative communication networks, quickly converges and obtains high-efficiency relay selection solutions, saves hardware resources and energy resources, extends the service life of the system, and improves service quality.
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Figure CN119136274A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of wireless cooperative communication, and in particular relates to a high-energy-efficiency relay selection method, device and electronic equipment based on a chaotic sine-cosine search mechanism in this field. Background Art
[0002] With the rapid development of wireless communication technology, communication networks have higher requirements for transmission rate, transmission range and network energy efficiency. Relay technology, as an important component of wireless cooperative communication networks, has become the focus of researchers in recent years. Relay technology is of great significance in the field of communication. It can not only help signals enhance and expand coverage during transmission, thereby improving the coverage and reliability of communication networks, but also help signals compensate for signal attenuation and noise during transmission, ensure signal quality and improve communication stability. It is of great significance in expanding the coverage of communication networks and improving communication quality and stability.
[0003] Relay selection is an important part of communication network construction and optimization. Whether the selection is reasonable or not directly affects the performance and cost of the communication network. For multi-user scenarios, each user in the network selects a suitable relay node to cooperate with its information transmission. While considering the communication needs under different environmental conditions, the corresponding relay selection method is proposed. By comparing different relay selection methods, the stable operation of the communication network is ensured. In response to the existing research on cooperative communication relay selection, Rui Zhu et al. published "Relay Selection Scheme for AF System with Partial CSI and Optimal Stopping Theory" in "Tsinghua Science and Technology" (2020, vol. 25, no. 2, pp. 302-312), proposing a relay selection method with maximum spectrum efficiency and selection probability as the goals in a single-user scenario. The proposed method failed to be extended to multi-user scenarios and failed to achieve high energy-efficient relay selection; Xiaowei Wang published "Relay Selection Scheme for AF System with Partial CSI and Optimal Stopping Theory" in "IEEE Transactions on Vehicular Technology" (2019, vol. 68, no. 6, pp. 6212-6216), proposing a decision tree-based relay selection method, which can improve the average end-to-end transmission rate of the system to a certain extent, but it also cannot improve the energy efficiency of the relay cooperative communication system. In view of the problems existing in the current relay selection technology and the demand for improving energy efficiency in current network construction, it is necessary to design an energy-efficient relay selection solution. Especially for multi-user scenarios, relevant relay selection methods deserve further exploration. Summary of the invention
[0004] The technical problem to be solved by the present invention is to provide a high-energy-efficiency relay selection method, device and electronic device based on a chaotic sine and cosine search mechanism, with the aim of improving the system energy efficiency of the current collaborative relay network. The method can greatly improve the network energy efficiency of the wireless collaborative communication system by utilizing the designed chaotic sine and cosine (CSC) search mechanism to select relays in the collaborative communication network, thereby improving the network communication performance and service quality.
[0005] The present invention adopts the following technical solution:
[0006] A high energy efficiency relay selection method, the improvement of which is that it includes the following steps:
[0007] Step 1: Establish a cooperative multi-user multi-relay system network model:
[0008] A cooperative multi-user multi-relay communication scenario, assuming that the network consists of Q users and M candidate relays, each user includes a sender and a receiver, and the relay adopts a decode-and-forward method;
[0009] The cooperative transmission is divided into two stages. In stage 1, the qth transmitter sends a signal to the corresponding receiver and the corresponding candidate relay, q = 1, 2, ..., Q; in stage 2, the relay sends a signal to the corresponding receiver, and the receiver performs maximum ratio combining on the signals received in the two stages;
[0010] Define the channel gain from the qth transmitter s to the mth relay r in phase 1 as The channel gain from the qth transmitter s to the jth receiver d is Define the channel gain from the mth relay r to the jth receiver d in phase 2 as
[0011] The transmission power of the qth transmitter s is The transmission power of the mth relay r is
[0012] The signal interference noise ratio between the transmitter and the receiver in phase 1 is:
[0013]
[0014] In the above formula, w represents the Gaussian white noise power;
[0015] The signal interference noise ratio of the transmitter to the relay is:
[0016]
[0017] The signal interference noise ratio between the relay and the receiver in phase 2 is:
[0018]
[0019] The total throughput of the network is:
[0020]
[0021] In the above formula, B is the available bandwidth of the system;
[0022] Use n=[n 1 ,n 2 ,...,n Q ] represents the relay selection scheme, where n q represents the relay selection scheme for the qth user, q = 1, 2, ..., Q;
[0023] Assuming that a relay can cooperate with at most one user for information transmission, the energy efficiency of the entire cooperative multi-user multi-relay system network is:
[0024]
[0025] For the cooperative multi-user multi-relay system, the relay selection problem with the optimization goal of maximizing network energy efficiency is proposed as follows:
[0026]
[0027] Step 2, initialize the chaotic sine and cosine population and parameters:
[0028] Assume that the t-th generation chaotic sine-cosine population contains H individuals, and the dimension of each individual is Q, which is the dimension of the optimization problem. The position of the i-th individual in the t-th generation is expressed as: In the above formula is the lower bound of the q-th dimension position, is the upper bound of the q-th dimension position;
[0029] Map the position of the i-th individual to an integer solution. The specific rules are: ceil(.) represents the upward rounding function, so the position of the i-th individual Mapping to integer solutions The integer solution for each individual position corresponds to a relay selection scheme for a cooperative multi-user multi-relay system;
[0030] Step 3, calculate the fitness of all individuals in the chaotic sine and cosine population:
[0031] Substitute the integer solution of the individual position of the chaotic sine and cosine population into the fitness function to calculate the fitness of all individuals in the chaotic sine and cosine population. The greater the fitness, the greater the network energy efficiency of the cooperative multi-user multi-relay system. The position of the individual with the largest fitness until the tth generation is recorded as the global optimal position.
[0032] Step 4: Update individual positions according to the sine and cosine laws and chaotic sequences:
[0033] Use Logistic mapping to generate a set of random sequences as chaotic sequences. The sequence mapping function is defined as:
[0034] ω k+1 =τ·ω k (1-ω k )
[0035] In the above formula, ω kis the kth chaotic variable of the chaotic sequence, k=1,2,3,..., τ is the Logistic parameter;
[0036] According to the changing rules of sine and cosine functions and chaotic sequences, the position of each individual is updated to guide the search process in a better direction. The specific evolution formula is:
[0037]
[0038] In the above formula, c 1 is the control parameter, c 2 is the amplitude of the sine function, c 3 is the amplitude of the cosine function, and is a uniform random number between [0,2π], a∈{1,2,...,H}, b∈{1,2,...,H}, a≠b≠i, is a uniform random number between [0,1], κ 1 is the evolution probability;
[0039] Step 5, check and process the boundary conditions of all updated individuals in the chaotic sine and cosine population. If the q-th dimension position of the updated i-th individual exceeds the value range, reassign the individual position that exceeds the value range, and let: In the above formula, Represents a uniform random number between [0,1];
[0040] Step 6: Map the updated individual positions to integer solutions and calculate the fitness of the updated individuals. According to the greedy selection strategy, if make Update the global optimal position by comparing the fitness of all individuals in the chaotic sine and cosine population;
[0041] Step 7, if the number of iterations is less than the preset maximum number of iterations, set t=t+1 and return to step 4; otherwise terminate the iteration, output the global optimal position of the chaotic sine and cosine population, and obtain the relay selection scheme of the corresponding cooperative multi-user multi-relay system according to the mapping rule.
[0042] A high energy efficiency relay selection device, the improvement of which comprises:
[0043] Modeling module: used to establish a collaborative multi-user multi-relay system network model;
[0044] Initialization module: used to initialize chaotic sine and cosine populations and parameters;
[0045] Calculation module: used to calculate the fitness of all individuals in the chaotic sine and cosine population;
[0046] Update module: used to update individual positions according to the sine and cosine laws and chaotic sequences;
[0047] Checking and processing module: used to check and process the boundary conditions of all updated individuals in the chaotic sine and cosine population;
[0048] A mapping module for mapping updated individual positions to integer solutions;
[0049] Judgment module: If the number of iterations is less than the maximum number of iterations, set t=t+1 and return to step 4; otherwise terminate the iteration, output the global optimal position of the chaotic sine and cosine population, and obtain the relay selection scheme of the corresponding cooperative multi-user multi-relay system according to the mapping rule.
[0050] An electronic device, the improvement of which lies in: comprising a memory and a processor, wherein the memory is used to store a program; the processor is coupled to the memory and is used to execute the program stored in the memory to implement the steps in the above-mentioned high-energy-efficiency relay selection method.
[0051] The beneficial effects of the present invention are:
[0052] The present invention solves the problem of high-energy-efficiency relay selection in existing multi-user cooperative communication networks, designs a relay selection method based on chaotic sine and cosine search mechanism, and can obtain a multi-relay selection scheme with the goal of maximizing energy efficiency, greatly improving the energy efficiency of multi-user cooperative communication networks, and conforming to the current green communication concept. The proposed relay selection method has fast convergence speed and stable performance, and a high-energy-efficiency relay selection scheme can be obtained in a short time.
[0053] In response to the problem of low energy efficiency of existing relay cooperative communication networks in multi-user transmission scenarios, the high-efficiency relay selection method proposed in the present invention can increase the amount of data transmitted per unit energy, save the system's hardware resources and energy resources, extend the system's service life, and improve the multi-user service quality of the cooperative communication network.
[0054] The present invention organically combines the chaotic mechanism with the sine-cosine search, designs a chaotic sine-cosine search strategy to solve the energy-efficient relay selection problem, breaks through the application limitations of existing integer optimization methods, and can provide new ideas for solving other engineering problems. BRIEF DESCRIPTION OF THE DRAWINGS
[0055] Figure 1 It is a schematic flow diagram of the method of the present invention;
[0056] Figure 2 It is a curve diagram showing the energy efficiency of the relay selection method using chaotic sine-cosine search mechanism and particle swarm mechanism as a function of the number of iterations;
[0057] Figure 3 It is a curve graph showing the energy efficiency of the relay selection method using chaotic sine-cosine search mechanism and particle swarm mechanism as the number of relays changes. DETAILED DESCRIPTION
[0058] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.
[0059] Embodiment 1, this embodiment discloses a high energy efficiency relay selection method, such as Figure 1 As shown, the following steps are included:
[0060] Step 1: Establish a cooperative multi-user multi-relay system network model:
[0061] A collaborative multi-user multi-relay communication scenario. Assume that the network consists of Q users and M candidate relays. Each user includes a transmitter and a receiver to send and receive signals, and the relay adopts a decoding and forwarding method. Considering most situations in actual communication scenarios, M is usually greater than Q.
[0062] The cooperative transmission is divided into two stages, stage 1 and stage 2. In stage 1, the qth transmitter sends a signal to the corresponding receiver and the corresponding candidate relay, q = 1, 2, ..., Q; in stage 2, the relay sends a signal to the corresponding receiver, and the receiver performs maximum ratio combining on the signals received in the two stages;
[0063] Define the channel gain from the qth transmitter s to the mth relay r in phase 1 as The channel gain from the qth transmitter s to the jth receiver d is Define the channel gain from the mth relay r to the jth receiver d in phase 2 as
[0064] The transmission power of the qth transmitter s is The transmission power of the mth relay r is
[0065] The signal interference noise ratio between the transmitter and the receiver in phase 1 is:
[0066]
[0067] In the above formula, w represents the Gaussian white noise power;
[0068] The signal interference noise ratio of the transmitter to the relay is:
[0069]
[0070] The signal interference noise ratio between the relay and the receiver in phase 2 is:
[0071]
[0072] The total throughput of the network is:
[0073]
[0074] In the above formula, B is the available bandwidth of the system;
[0075] Use n=[n 1 ,n 2 ,...,n Q ] represents the relay selection scheme, where n q represents the relay selection scheme for the qth user, q = 1, 2, ..., Q;
[0076] Assuming that a relay can cooperate with at most one user for information transmission, the energy efficiency of the entire cooperative multi-user multi-relay system network is:
[0077]
[0078] For the cooperative multi-user multi-relay system, the relay selection problem with the optimization goal of maximizing network energy efficiency is proposed as follows:
[0079]
[0080] Step 2, initialize the chaotic sine and cosine population and parameters:
[0081] Assume that the t-th generation chaotic sine-cosine population contains H individuals, and the dimension of each individual is Q, which is the dimension of the optimization problem. The position of the i-th individual in the t-th generation is expressed as: In the above formula is the lower bound of the q-th dimension position, is the upper bound of the q-th dimension position;
[0082] Map the position of the i-th individual to an integer solution. The specific rules are: ceil(.) represents the upward rounding function, so the position of the i-th individual Mapping to integer solutions The integer solution for each individual position corresponds to a relay selection scheme for a cooperative multi-user multi-relay system;
[0083] Step 3, calculate the fitness of all individuals in the chaotic sine and cosine population:
[0084] Substitute the integer solution of the individual position of the chaotic sine and cosine population into the fitness function to calculate the fitness of all individuals in the chaotic sine and cosine population. The greater the fitness, the greater the network energy efficiency of the cooperative multi-user multi-relay system. The position of the individual with the largest fitness until the tth generation is recorded as the global optimal position.
[0085] Step 4: Update individual positions according to the sine and cosine laws and chaotic sequences:
[0086] Use Logistic mapping to generate a set of random sequences as chaotic sequences. The sequence mapping function is defined as:
[0087] ω k+1 =τ·ω k (1-ω k )
[0088] In the above formula, ω k is the kth chaotic variable of the chaotic sequence, k=1,2,3,..., τ is the Logistic parameter;
[0089] According to the changing rules of sine and cosine functions and chaotic sequences, the position of each individual is updated to guide the search process in a better direction. The specific evolution formula is:
[0090]
[0091] In the above formula, c 1 is the control parameter, c 2 is the amplitude of the sine function, c 3 is the amplitude of the cosine function, and is a uniform random number between [0,2π], a∈{1,2,...,H}, b∈{1,2,...,H}, a≠b≠i, is a uniform random number between [0,1], κ 1 is the evolution probability;
[0092] Step 5, check and process the boundary conditions of all updated individuals in the chaotic sine and cosine population. If the q-th dimension position of the updated i-th individual exceeds the value range, reassign the individual position that exceeds the value range, and let: In the above formula, Represents a uniform random number between [0,1];
[0093] Step 6: Map the updated individual positions to integer solutions and calculate the fitness of the updated individuals. According to the greedy selection strategy, if make Update the global optimal position by comparing the fitness of all individuals in the chaotic sine and cosine population;
[0094] Step 7, if the number of iterations is less than the preset maximum number of iterations, set t=t+1 and return to step 4; otherwise terminate the iteration, output the global optimal position of the chaotic sine and cosine population, and obtain the relay selection scheme of the corresponding cooperative multi-user multi-relay system according to the mapping rule.
[0095] Next, the beneficial effects of the present invention are further illustrated by simulation experiments:
[0096] For the cooperative multi-user multi-relay system, Q = 10, M = 20, nodes are randomly distributed in the range of 100m × 100m, the transmission power of the user sender is set to 10W, the transmission power of the relay is [5,15]W, the system bandwidth B = 10MHz, and the Gaussian white noise power of all nodes is 10 -4 W. The parameters of the relay selection method for cooperative multi-user multi-relay system based on chaotic sine-cosine search mechanism are set as follows: H = 20, the maximum number of iterations is 1000, c 1 As the number of iterations decreases from 0.95 to 0.01, c 2 =3, c 3 =3,κ 1 =0.5,τ=3.57,ω 1 =0.1. In order to obtain the optimal relay selection scheme for the cooperative multi-user multi-relay system, the dimension of individuals in the chaotic sine-cosine population is Q, In order to compare the performance of the proposed chaotic sine-cosine search mechanism, the particle swarm mechanism is applied to the relay selection of the cooperative multi-user multi-relay system, and the population size and maximum number of iterations of the two are set to the same value. All experimental results are the average of 200 simulation experiments. The other parameter settings of the particle swarm mechanism refer to the paper "Relay Node Selection Strategy for Wireless Sensor Networks Based on Particle Swarm Algorithm" published by Zhao Suping et al. in the Journal of Sensor Technology (2022, vol. 35, no. 12, pp. 1712-1716).
[0097] Figure 2 , Figure 3 The results of the energy efficiency of the relay selection method for a cooperative multi-user multi-relay system using chaotic sine-cosine search mechanism and particle swarm mechanism varying with the number of iterations and the number of relays are given.
[0098] Figure 2 The energy efficiency of the relay selection method of the cooperative multi-user multi-relay system using the chaotic sine-cosine search mechanism and the particle swarm mechanism varies with the number of iterations. From the simulation results, it can be seen that the particle swarm mechanism falls into local convergence, while the optimization ability of the chaotic sine-cosine search mechanism is significantly better than that of the particle swarm mechanism. The relay selection method using the chaotic sine-cosine search mechanism can obtain greater energy efficiency and improve the overall performance of the cooperative communication network.
[0099] Figure 3 The energy efficiency of the relay selection method of the cooperative multi-user multi-relay system using the chaotic sine-cosine search mechanism and the particle swarm mechanism varies with the number of relays. In the simulation, the number of relays increases from 15 to 40. From the simulation results, it can be seen that the energy efficiency of the cooperative multi-user multi-relay system increases with the increase of the number of relays. In addition, for different numbers of relays, the energy efficiency obtained by the relay selection method using the chaotic sine-cosine search mechanism is always better than the relay selection method using the particle swarm mechanism, which proves the effectiveness of the designed method.
[0100] This embodiment also discloses a high energy efficiency relay selection device, including:
[0101] Modeling module: used to establish a collaborative multi-user multi-relay system network model;
[0102] Initialization module: used to initialize chaotic sine and cosine populations and parameters;
[0103] Calculation module: used to calculate the fitness of all individuals in the chaotic sine and cosine population;
[0104] Update module: used to update individual positions according to the sine and cosine laws and chaotic sequences;
[0105] Checking and processing module: used to check and process the boundary conditions of all updated individuals in the chaotic sine and cosine population;
[0106] A mapping module for mapping updated individual positions to integer solutions;
[0107] Judgment module: If the number of iterations is less than the maximum number of iterations, set t=t+1 and return to step 4; otherwise terminate the iteration, output the global optimal position of the chaotic sine and cosine population, and obtain the relay selection scheme of the corresponding cooperative multi-user multi-relay system according to the mapping rule.
[0108] This embodiment also discloses an electronic device, including a memory and a processor, wherein the memory is used to store programs; the processor is coupled to the memory and is used to execute the programs stored in the memory to implement the steps in the above-mentioned high-efficiency relay selection method.
Claims
1. A high energy efficiency relay selection method, characterized in that: The steps include: Step 1: Establish a cooperative multi-user multi-relay system network model: A cooperative multi-user multi-relay communication scenario, assuming that the network consists of Q users and M candidate relays, each user includes a sender and a receiver, and the relay adopts a decode-and-forward method; The cooperative transmission is divided into two stages. In stage 1, the qth transmitter sends a signal to the corresponding receiver and the corresponding candidate relay, q = 1, 2, ..., Q; in stage 2, the relay sends a signal to the corresponding receiver, and the receiver performs maximum ratio combining on the signals received in the two stages; Define the channel gain from the qth transmitter s to the mth relay r in phase 1 as The channel gain from the qth transmitter s to the jth receiver d is Define the channel gain from the mth relay r to the jth receiver d in phase 2 as The transmission power of the qth transmitter s is The transmission power of the mth relay r is The signal interference noise ratio between the transmitter and the receiver in phase 1 is: In the above formula, w represents the Gaussian white noise power; The signal interference noise ratio of the transmitter to the relay is: The signal interference noise ratio between the relay and the receiver in phase 2 is: The total throughput of the network is: In the above formula, B is the available bandwidth of the system; With n=[n1,n2,...,n Q ] represents the relay selection scheme, where n q represents the relay selection scheme for the qth user, q = 1, 2, ..., Q; Assuming that a relay can cooperate with at most one user for information transmission, the energy efficiency of the entire cooperative multi-user multi-relay system network is: For the cooperative multi-user multi-relay system, the relay selection problem with the optimization goal of maximizing network energy efficiency is proposed as follows: Step 2, initialize the chaotic sine and cosine population and parameters: Assume that the t-th generation chaotic sine-cosine population contains H individuals, and the dimension of each individual is Q, which is the dimension of the optimization problem. The position of the i-th individual in the t-th generation is expressed as: In the above formula q=1,2,...,Q, is the lower bound of the q-th dimension position, is the upper bound of the q-th dimension position; Map the position of the i-th individual to an integer solution. The specific rules are: ceil(.) represents the upward rounding function, so the position of the i-th individual Mapping to integer solutions The integer solution for each individual position corresponds to a relay selection scheme for a cooperative multi-user multi-relay system; Step 3, calculate the fitness of all individuals in the chaotic sine and cosine population: Substitute the integer solution of the individual position of the chaotic sine and cosine population into the fitness function to calculate the fitness of all individuals in the chaotic sine and cosine population. The greater the fitness, the greater the network energy efficiency of the cooperative multi-user multi-relay system. The position of the individual with the largest fitness until the tth generation is recorded as the global optimal position. Step 4: Update individual positions according to the sine and cosine laws and chaotic sequences: Use Logistic mapping to generate a set of random sequences as chaotic sequences. The sequence mapping function is defined as: oh k+1 =t·h k (1-h k ) In the above formula, ω k is the kth chaotic variable of the chaotic sequence, k=1,2,3,..., τ is the Logistic parameter; According to the changing rules of sine and cosine functions and chaotic sequences, the position of each individual is updated to guide the search process in a better direction. The specific evolution formula is: In the above formula, c1 is the control parameter, c2 is the amplitude of the sine function, and c3 is the amplitude of the cosine function. and is a uniform random number between [0,2π], a∈{1,2,...,H}, b∈{1,2,...,H}, a≠b≠i, is a uniform random number between [0,1], κ1 is the evolution probability; Step 5, check and process the boundary conditions of all updated individuals in the chaotic sine and cosine population. If the q-th dimension position of the updated i-th individual exceeds the value range, reassign the individual position that exceeds the value range, and let: In the above formula, Represents a uniform random number between [0,1]; Step 6: Map the updated individual positions to integer solutions and calculate the fitness of the updated individuals. According to the greedy selection strategy, if make Update the global optimal position by comparing the fitness of all individuals in the chaotic sine and cosine population; Step 7, if the number of iterations is less than the preset maximum number of iterations, set t = t + 1 and return to step 4; Otherwise, the iteration is terminated, the global optimal position of the chaotic sine and cosine population is output, and the relay selection scheme of the corresponding cooperative multi-user multi-relay system is obtained according to the mapping rule.
2. A high energy efficiency relay selection device, characterized in that: include: Modeling module: used to establish a collaborative multi-user multi-relay system network model; Initialization module: used to initialize chaotic sine and cosine populations and parameters; Calculation module: used to calculate the fitness of all individuals in the chaotic sine and cosine population; Update module: used to update individual positions according to the sine and cosine laws and chaotic sequences; Checking and processing module: used to check and process the boundary conditions of all updated individuals in the chaotic sine and cosine population; A mapping module, for mapping updated individual positions to integer solutions; Judgment module: If the number of iterations is less than the maximum number of iterations, set t = t + 1 and return to step 4; Otherwise, the iteration is terminated, the global optimal position of the chaotic sine and cosine population is output, and the relay selection scheme of the corresponding cooperative multi-user multi-relay system is obtained according to the mapping rule.
3. An electronic device, characterized in that: It comprises a memory and a processor, wherein the memory is used to store a program; the processor is coupled to the memory and is used to execute the program stored in the memory to implement the steps in the energy-efficient relay selection method as described in claim 1 above.
