A phase optimization method for RIS-aided internet of things uplink transmission

Abstract

The application discloses a RIS-assisted Internet of Things uplink transmission phase optimization method, specifically comprising the following steps: 1) all devices are divided into angle domain non-overlapping clusters; 2) a pilot multiplexing strategy is used to allocate pilots for devices in the cluster; 3) a base station obtains uplink channel estimation values according to received pilot signals; 4) the base station decomposes the channel amplitudes of different devices to RIS and devices to BS through a least square method; and 5) the base station optimizes RIS phase configuration by using estimated channels. The application reduces pilot overhead while improving channel estimation efficiency and accuracy.

Description

Technical Field

[0001] This invention belongs to the field of mobile communication technology, and in particular relates to a method for optimizing uplink transmission phase for RIS-assisted Internet of Things. Background Technology

[0002] The goal of next-generation mobile wireless communication is to achieve high-quality, high-speed broadband multimedia communication. Deploying high-frequency bandwidths such as millimeter waves and terahertz waves can effectively improve system capacity. However, in traditional methods, high-frequency communication between base stations and devices is easily affected by obstacles. Smart reflectors can reasonably adjust the reflection coefficient, and devices and base stations can communicate through reflective links constructed by RIS (Reflection Links). However, in existing technologies, the training overhead required for channel estimation increases linearly with the size of the RIS and the number of devices. When the RIS consists of a large number of reflective elements, the pilot overhead for channel estimation is enormous. Therefore, current methods cannot reduce the required pilot overhead while ensuring estimation accuracy. Summary of the Invention

[0003] Purpose of the invention: In order to overcome the shortcomings of the existing technology, the present invention discloses a method for optimizing uplink transmission phase of RIS-assisted Internet of Things.

[0004] Technical Solution: This invention discloses a method for optimizing uplink transmission phase in RIS-assisted Internet of Things (IoT) transmission, specifically including the following steps:

[0005] Step 1: Divide all K IoT devices into Z non-overlapping angular domains; each cluster from 1 to Zb contains Q IoT devices, and each cluster from Z-b+1 to Z contains Q-1 IoT devices; b = ZQ-K; Q is the number of available orthogonal pilots. Represents rounding up; combining K IoT devices into a set.

[0006] Step 2: Use pilot reuse strategy to allocate pilots to IoT devices. Configure Q orthogonal pilot sequences for each cluster. IoT devices within the same cluster are assigned different pilots, while IoT devices with the same index in different clusters use the same pilot. The IoT devices send pilot signals.

[0007] Step 3: Based on the channel matrix received by the base station when the q-th device in all clusters sends the l-th pilot signal. Obtain the amplitude estimate of the direct connection channel from the q-th IoT device in all clusters to the base station. The signal Y in the reflection link section from the IoT device to the base station l Y', q=1,2,…,Q; when q=Q, all clusters are the first 1~Zb clusters, and the least squares method is used to solve for Y. lObtain the estimated channel from the IoT device to the RIS. The amplitude of the direct connection channel from IoT devices using the same pilot frequency to the BS is decomposed based on the least squares principle. Obtain the estimated value of the direct connection signal from the q-th IoT device in cluster z to the base station. based on Obtain the estimated value of the signal from the q-th IoT device in cluster z to the RIS. Where z = 1, 2, ..., Z;

[0008] Step 4: Let k′ = (z-1)*Q + q. The k′-th IoT device retransmits the pilot signal to the base station, based on the estimated value of the direct connection signal from the k′-th IoT device to the base station. The estimated value of the signal from the k′-th IoT device to the RIS Iterative optimization of the RIS phase matrix Ψ.

[0009] Furthermore, step 1 specifically involves:

[0010] Step 1.1: Initialize the z-th cluster set Represent the empty set; calculate the angle φ from the k-th IoT device to the base station. k Calculate the distance d from the k-th IoT device to the base station. k Calculate the angle difference Δφ between any two IoT devices. ik Distance difference Δd ik and weighting index ε ik The subscript i represents the i-th device, i = 1, 2, ..., K, k = 1, 2, ..., K; ε ik The expression is as follows:

[0011]

[0012] Where, φ max Represents all φ k The maximum value in, d max For all d k The maximum value in the range, where α is the weight, α∈(0,1);

[0013] Step 1.2: When z = 1, in the set A random IoT device is selected as the central device and placed into the cluster head set. In the middle; and in the cluster head set Delete the device; z+1, and proceed to step 1.3;

[0014] Step 1.3: Calculation Remaining IoT devices and cluster heads Weighting indicators for all central devices, select set The IoT device corresponding to the highest weighted index is placed into the cluster head set as the new central device. In the middle, update the cluster head set In the set Delete the device, determine if z is greater than or equal to Z, if yes, go to step 1.4, otherwise z+1, and continue to execute step 1.3;

[0015] Step 1.4: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] The central equipment is distributed to different cluster sets, that is... express The z-th central device in;

[0016] Step 1.5: When z∈[1,Zb], for the z-th cluster set Compute set IoT devices and The weighted indicators are calculated and arranged in ascending order. The IoT devices corresponding to the top Q-1 weighted indicators are selected and placed into a cluster set. In; and in the set Remove these IoT devices;

[0017] When z∈[Z-b+1,Z], compute the set IoT devices and The weighted indicators are calculated and arranged in ascending order. The IoT devices corresponding to the top Q-2 weighted indicators are then placed into the cluster set. In; and in the set Remove these IoT devices;

[0018] Step 1.6: For any cluster The central device is assigned an index value of 1, and the remaining IoT devices are sorted in ascending order of their angle difference from the central device, and index values ​​are assigned accordingly.

[0019] Furthermore, step three specifically involves:

[0020] Step 3.1: The channel matrix received by the base station when the q-th IoT device in all clusters sends the l-th pilot signal. The expression is as follows:

[0021]

[0022] Among them, D h For the diagonal channel from BS to RIS for each element, D h =diag(h1,h2,...h N), diag(·) represents taking the diagonal matrix, θ l θ represents the l-th phase shift of the RIS when the IoT device sends the l-th pilot signal; l =[θ1,...,θ N ] T θ N The phase shift of the Nth reflector in the RIS is represented by T, which represents the transpose. Let be the channel from the q-th IoT device in the z-th cluster to the RIS; This is the sum of the signal amplitudes from the IoT device numbered q in all clusters to the base station; This is the steering vector of the base station antenna. j represents the imaginary unit, and λ is the wavelength. The angle of arrival (n) for IoT devices transmitting direct-link signals to the base station. l It is additive white Gaussian noise received by the base station. Representative dimension is A matrix of all 1s; for the clusters from 1 to Zb, For clusters from Z-b+1 to Z,

[0023] Step 3.2: Place L items Adding them together gives Y d According to Y d calculate

[0024]

[0025] Where H represents the conjugate transpose operation;

[0026] Step 3.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Subtract the amount Obtain the signal Y from the reflected link portion of the IoT device to the base station. l ′:

[0027]

[0028] Estimated channel from IoT devices to RIS The expression is as follows:

[0029]

[0030] Among them, ||·|| F This represents the F-norm operation, where M is the number of base station antennas.

[0031] Step 3.4: Estimation of the direct connection signal from the q-th IoT device in cluster z to the base station. The expression is:

[0032] in, It is the angle of arrival from the central device within cluster z to the base station. The guide vector, The amplitude of the signal transmitted by the q-th IoT device within cluster z, received by the base station;

[0033] The estimated value of the signal from the q-th IoT device in cluster z to the RIS. The expression is:

[0034]

[0035] in, For matrix The z-th element, α0 is the channel amplitude from RIS to the base station. h represents the channel from the base station to the RIS, a B (θ B ) represents the antenna steering vector of the base station. θ B Angle of arrival (Angle of arrival) is the signal reflected from the RIS to the base station, d is the antenna spacing between the base stations, and a is the angle of arrival. R (θ R ) is the direction vector of RIS, θ R The angle of arrival of the signal transmitted to the RIS. The antenna steering vector from the central device within cluster Z to the RIS. The angle of arrival for the signal transmitted by the device within cluster Z received by RIS.

[0036] Furthermore, step four utilizes a convex optimization method to solve the following objective function to obtain the optimal value of the RIS phase Ψ:

[0037]

[0038] Where max represents the maximum value, ω k' Let σ be the weight of the k'-th IoT device. 2 For noise power, h is the channel from the base station to the RIS, Ψ=[ψ1,ψ2,…,ψ N ] T , ψ N The phase shift of the Nth reflector in RIS is represented by T, where T represents transpose and P represents the phase shift of the Nth reflector. k' P represents the transmit power of the k'-th IoT device. max γ represents the maximum transmit power. k' For iterative optimization of variables, γ k' The expression is:

[0039]

[0040] A computer device includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to implement the steps of the RIS-assisted Internet of Things uplink transmission phase optimization method.

[0041] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the RIS-assisted Internet of Things uplink transmission phase optimization method.

[0042] Beneficial effects: This invention uses a pilot reuse strategy to allocate the same orthogonal pilots to different clusters, uses the least squares method to estimate the direct channel and the reflection link channel in sequence, and decomposes the amplitude of the device signal using the common pilot in different clusters based on the known angle of arrival of the transmitted signals from the IoT devices to the RIS and the base station. Finally, it uses the Lagrange dual transform to optimize the RIS phase, further improving the accuracy of channel estimation and pilot overhead. Attached Figure Description

[0043] Figure 1 This is a system model diagram of the RIS-assisted MISO network of the present invention;

[0044] Figure 2 This is a flowchart of the present invention. Detailed Implementation

[0045] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0046] This invention provides a pilot multiplexing and phase optimization method for RIS-assisted IoT uplink transmission. This method uses pilot multiplexing and parameterized channel estimation knowledge to effectively reduce pilot overhead and computational complexity.

[0047] like Figure 1 As shown, in the RIS-assisted IoT uplink transmission scenario, there is a base station BS equipped with M antennas, a smart reflector RIS equipped with N reflective elements, and K single-antenna devices, with Q available orthogonal pilots.

[0048] In one embodiment, such as Figure 2 As shown, this invention provides a pilot multiplexing and phase optimization method for RIS-assisted IoT uplink transmission, which includes the following steps:

[0049] Step 1: Divide all K devices into Z non-overlapping angular domain clusters. Each cluster contains Q or Q-1 devices. When the channels of different IoT devices can be strictly separated in the angular domain, pilot interference emitted by devices between clusters will no longer have an impact.

[0050] Step 2: Use pilot reuse strategy to assign pilots to devices, that is, devices in the same cluster are assigned different orthogonal pilots, and devices with the same number in different clusters use the same pilot sequence;

[0051] Step 3: The base station eliminates the channel at the RIS end based on the pilot signals received multiple times, performs channel estimation on the direct channel, estimates the channel from the device to the RIS end based on the estimated direct channel, and finally uses the least squares method to decompose and obtain the channel amplitude between different devices to the RIS and between the device and the base station.

[0052] Step 4: Optimize RIS phase configuration based on the estimated channel.

[0053] In one embodiment, step one divides all IoT devices into Z non-overlapping angular domain clusters, as detailed below:

[0054] Step a: Initialize Z clusters as z = 1, 2, ..., Z, where This represents rounding up; initialize the set of K IoT devices as U = {u1, u2, ..., u...} K Let φ k Let d be the angle from device k to the base station. k Let φ be the distance from device k to the base station. max Represents all φ k The maximum value in, d max For all d k The maximum value in the set. Define the set. The angle difference between any two devices i and k is Δφ ik =|φ i -φ k |, Distance difference Δd ik =|d i -d k |, weighting index is Where α∈(0,1) are the weight values. From the set Randomly select one device, whose index value is Add to cluster head set In, that is And remove the device from the original set, i.e. Let z = 2, then proceed to step b.

[0055] Step b: Calculate the set Internal remaining equipment and cluster head assembly Weight metrics for all devices in the set The device corresponding to the highest weighted index in the cluster; as the new cluster head, update In the set Delete the central device, z = z + 1. If z < Z, repeat step b; otherwise, go to step c.

[0056] Step c: [The sentence is incomplete and requires more context to be translated accurately.] The central equipment is allocated to different clusters, that is Compute set Internal and central equipment Weighting indicators.

[0057] Step d: For each central device When z∈[1,Zb], from the set Select with The Q-1 devices with the smallest weight difference are assigned to the cluster. And select the Q devices from the set Excluded from the middle;

[0058] When z∈[Z-b+1,Z], from the set Select with The Q-2 devices with the smallest weight difference are assigned to the cluster. In; and select Q-2 devices from the set Excluded from the list.

[0059] Step e: For each cluster First, the central equipment Assign index value 1; then other devices in the cluster will follow the same path as the central device. Sort the angle differences from smallest to largest and assign index values.

[0060] In step two, the length of the available orthogonal pilots is Q. A pilot reuse strategy is used to send pilots to all devices within a cluster. Devices within the same cluster are assigned different pilots, while devices with the same index in different clusters use the same pilot sequence. The pilot signal is defined as follows:

[0061]

[0062] Where x i Let P be the pilot signal assigned to the i-th device within the cluster, and let P represent the transmit power of each device. δ(·) is the Kronecker function, defined as...

[0063] A pilot reuse strategy is employed to transmit pilots to all devices within a cluster. Specifically, the base station uniformly configures Q orthogonal pilot sequences for each cluster. In practice, the Q pilots are first sequentially allocated to each device within the cluster according to their index values, ensuring that different devices within the same cluster always use non-overlapping pilot resources. For devices with the same index value in different clusters, the base station allocates the same pilot sequence; that is, devices within a single cluster are allocated different pilots, and devices with the same index in each cluster are allocated the same pilot sequence. Because the pilot sequences are reused between clusters, and the angle domains between clusters do not overlap, pilot interference is avoided, reducing the pilot overhead required for channel estimation by a factor of Z.

[0064] In one embodiment, step three is divided into the following sub-steps:

[0065] Step a: The device sends L pilot signals to the base station, and the RIS adjusts the phase L accordingly. The l-th phase shift configuration is represented as follows: Utilizing the principle of pilot orthogonality, when the q-th device in all clusters transmits the l-th pilot, the channel matrix received by the BS is expressed as:

[0066]

[0067] Among them, D h For the diagonal channel from BS to RIS for each element, D h =diag(h1,h2,...h N ), diag(·) represents taking the diagonal matrix, θ l θ represents the l-th phase shift of the RIS when the IoT device sends the l-th pilot signal; l =[θ1,...,θ N ] T θ N The phase shift of the Nth reflector in the RIS is represented by T, which represents the transpose. Let be the channel from the q-th IoT device in the z-th cluster to the RIS; This is the sum of the signal amplitudes from the IoT device numbered q in all clusters to the base station; This is the steering vector of the base station antenna. j represents the imaginary unit, and λ is the wavelength. The angle of arrival (n) for IoT devices transmitting direct-link signals to the base station. l It is additive white Gaussian noise received by the base station. Representative dimension is A matrix of all ones. For the clusters from 1 to Zb, For clusters from Z-b+1 to Z,

[0068] Step b: Place L items Adding them together approximately eliminates the influence of the RIS reflection link.

[0069]

[0070] in

[0071] Step c: Based on the above steps, obtain the amplitude estimate of the direct connection channel from the q-th IoT device in all clusters to the BS.

[0072] Step d: Through the channel matrix Subtract the direct connection portion estimated in step c Obtain the signal from the reflected link portion of the IoT device to the base station:

[0073]

[0074] Using the least squares algorithm, the estimated channel from the IoT device to the RIS is finally obtained as follows:

[0075]

[0076] in Operator (·) H The operator ||·|| represents the conjugate transpose operation. F This represents the F-norm operation.

[0077] Next, the least squares algorithm is used to decompose the direct channel amplitude from IoT devices using the same pilot to the BS. Let the sum of the direct link channels from the q-th IoT device in all clusters to the BS be... in It is the angle of arrival from the central device within cluster z to the BS. The guide vector, Let be the amplitude of the signal transmitted by the q-th IoT device within cluster z, received by the base station.

[0078] According to the least squares principle, the amplitude of the signal transmitted by the q-th IoT device within cluster z received by the base station is... Finally, the direct connection signal from the q-th IoT device within cluster z to the BS is obtained as follows:

[0079] Similarly, the amplitude of the transmitted signal from the q-th device to the BS via the RIS reflection link can be obtained. Where α0 is the channel amplitude from RIS to BS, and h is the channel amplitude from base station to RIS. in Let θ be the antenna steering vector of BS, d be the antenna spacing distance of the base station, and θ be the antenna steering vector of BS. B Let a be the angle of arrival of the signal reflected from the RIS to the BS. R (θ R ) is the direction vector of RIS, θ R Ψ is the angle of arrival of the signal transmitted to the RIS, and Ψ is the phase of the RIS. The antenna steering vector from the central device within cluster Z to the RIS. The angle of arrival for the signal transmitted by the device within cluster Z received by RIS.

[0080] Finally, the signal from the q-th device within cluster z to the RIS can be obtained as follows:

[0081] In step four, the IoT device retransmits the pilot signal to the base station, utilizing the estimated channel. and Iterative optimization of the RIS phase matrix Ψ, using Lagrange dual transformation to simplify the optimization problem, includes the following steps:

[0082] 1) Let k′=(j-1)*Q+q, so that k′ can be specifically mapped to a certain device in a certain cluster; then set the initial phase of RIS Ψ=Ψ0;

[0083] 2) Update and iterate to optimize variables

[0084] 3) Solve the following problems using convex optimization methods.

[0085]

[0086] in ω represents the transmit power of each device. k' Let σ be the weight of the k'-th IoT device. 2 For noise power, Assume the solution obtained through optimization is Ψ * Update Ψ=Ψ * Perform steps 2) and 3) until convergence, and output Ψ as the final solution.

[0087] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be covered by the protection of the present invention.

Claims

1. A method for optimizing uplink transmission phase in RIS-assisted Internet of Things (IoT), characterized in that, Specifically, the steps include the following: Step 1: Divide all K IoT devices into Z non-overlapping angular domains; each cluster from 1 to Zb contains Q IoT devices, and each cluster from Z-b+1 to Z contains Q-1 IoT devices. ; Q is the available orthogonal pilot number. It represents rounding up; Group K IoT devices into a set ; Step 2: Use pilot reuse strategy to allocate pilots to IoT devices. Configure Q orthogonal pilot sequences for each cluster. IoT devices in the same cluster are assigned different pilots, and IoT devices with the same index in different clusters use the same pilot. IoT devices send pilot signals; Step 3: Based on the channel matrix received by the base station when the nth device in all clusters sends the lth pilot signal. This yields the amplitude estimate of the direct connection channel from the q-th IoT device in all clusters to the base station. Signal from IoT devices to the base station via the reflected link , ;when When all clusters are the first 1 to Zb clusters, the least squares solution is used. Obtain the estimated channel from the IoT device to the RIS Decompose the direct channel amplitude from IoT devices using the same pilot to the BS based on the least squares principle. The estimated value of the direct connection signal from the q-th IoT device in cluster z to the base station is obtained. ;based on Obtain the estimated value of the signal from the q-th IoT device in cluster z to the RIS. ;in ; Step 4: Let , No. The IoT device resends the pilot signal to the base station, based on the first... Estimated value of direct signal from an IoT device to a base station and the Estimated signal from an IoT device to the RIS ; Iterative optimization of RIS phase matrix ; Step four uses convex optimization to solve the following objective function to obtain the RIS phase. The optimal value: ； in, Indicates the maximum value. For the first The weight of each IoT device For noise power, , For the channel from the base station to the RIS, , This represents the phase shift of the Nth reflector in the RIS, where T denotes transpose. Indicates the first The transmit power of an IoT device This indicates the maximum transmit power. To iteratively optimize variables, The expression is: 。 2. The method for optimizing uplink transmission phase in RIS-assisted IoT as described in claim 1, characterized in that, Step 1 is as follows: Step 1.1: Initialize the z-th cluster set , Represent the empty set; calculate the angle from the k-th IoT device to the base station. Calculate the distance from the k-th IoT device to the base station. Calculate the angle difference between any two IoT devices. Distance difference and weighting indicators The subscript i indicates the i-th device. , ; The expression is as follows: ； in, Representing all The maximum value in, For all The maximum value in, As weight, ; Step 1.2: When z=1, in the set A random IoT device is selected as the central device and placed into the cluster head set. In the middle; and in the cluster head set Delete the device; z+1, and proceed to step 1.3; Step 1.3: Calculation Remaining IoT devices and cluster heads Weighting indicators for all central devices, select set The IoT device corresponding to the highest weighted index is placed into the cluster head set as the new central device. In the middle, update the cluster head set and in the set Delete the device, determine if z is greater than or equal to Z, if yes, go to step 1.4, otherwise z+1, and continue to execute step 1.3; Step 1.4: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require The central equipment is distributed to different cluster sets, that is... , express The z-th central device in; Step 1.5: When At that time, for the z-th cluster set Calculate the set IoT devices and The weighted indicators are calculated and arranged in ascending order. The IoT devices corresponding to the top Q-1 weighted indicators are selected and placed into a cluster set. In; and in the set Remove these IoT devices; when When calculating the set IoT devices and The weighted indicators are calculated and arranged in ascending order. The IoT devices corresponding to the top Q-2 weighted indicators are then placed into the cluster set. In; and in the set Remove these IoT devices; Step 1.6: For any cluster The central device is assigned an index value of 1, and the remaining IoT devices are sorted in ascending order of their angle difference from the central device, and index values ​​are assigned accordingly.

3. The method for optimizing uplink transmission phase in RIS-assisted IoT as described in claim 1, characterized in that, Step three specifically involves: Step 3.1: The channel matrix received by the base station when the nth IoT device in all clusters sends the lth pilot signal. The expression is as follows: ； in, For each element from BS to RIS, the diagonal channel, , This represents taking a diagonal matrix. , This indicates the l-th phase shift of the RIS when the IoT device sends the l-th pilot signal; , The phase shift of the Nth reflector in the RIS is represented by T, which represents the transpose. , Let be the channel from the ith IoT device in the z-th cluster to the RIS; This is the sum of the signal amplitudes from the IoT device numbered q in all clusters to the base station; This is the steering vector of the base station antenna. j represents the imaginary unit. For wavelength, The angle of arrival for IoT devices to transmit direct-link signals to the base station. It is additive white Gaussian noise received by the base station. Representative dimension is A matrix of all ones; for the first 1 to Zb clusters, For clusters from Z-b+1 to Z, ; Step 3.2: Place L items Adding them together gives ,according to calculate : ； Where H represents the conjugate transpose operation; Step 3.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Subtract the amount Obtain the signal from the reflected link portion of the IoT device to the base station. : ； Estimated channel from IoT devices to RIS The expression is as follows: ； in, This represents the F-norm operation, where M is the number of base station antennas. ; Step 3.4: Estimation of the direct connection signal from the q-th IoT device in cluster z to the base station. The expression is: ； in, It is the angle of arrival from the central device within cluster z to the base station. The guide vector, The amplitude of the signal transmitted by the q-th IoT device within cluster z, received by the base station; The estimated value of the signal from the q-th IoT device in cluster z to the RIS. The expression is: ； in, For matrix The z-th element, , The channel amplitude from RIS to the base station. , For the channel from the base station to the RIS, This is the antenna steering vector for the base station. , Let be the angle of arrival of the signal reflected from the RIS to the base station, and d be the antenna spacing distance of the base station. Here is the direction vector of RIS. The angle of arrival of the signal transmitted to the RIS. The antenna steering vector from the central device within cluster Z to the RIS. The angle of arrival for the signal transmitted by the device within cluster Z received by RIS.

4. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the RIS-assisted Internet of Things uplink transmission phase optimization method as described in any one of claims 1 to 3.

5. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the RIS-assisted Internet of Things uplink transmission phase optimization method as described in any one of claims 1 to 3.

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