A cross-layer routing protocol method for underwater acoustic communication networks based on channel quality

Abstract

The present invention belongs to the field of underwater acoustic routing protocols, and relates to a cross-layer routing protocol method for an underwater acoustic communication network based on channel quality. The underwater acoustic communication network includes: a source node, a destination node and multiple relay nodes, and the method includes: step 1) the source node initiates the initialization of the underwater acoustic communication network; step 2) each node broadcasts a beacon to obtain the state of the neighboring node and calculates the channel quality evaluation index; step 3) the sending node determines the forwarding candidate set according to the node depth, the node remaining energy and the node buffer state; step 4) the sending node determines the reward function and calculates the Q value of all nodes in the forwarding candidate set; step 5) the sending node selects the node with the largest Q value as the next hop node and updates the V value, and continues to transmit the data packet; step 6) determines whether the destination node receives the data packet: if the destination node receives the data packet, it ends; if not, repeat steps 3) to 5) until the destination node receives the data packet.

Description

Technical Field

[0001] The invention relates to the field of underwater acoustic communication networks and underwater acoustic routing protocols, and relates to an underwater acoustic communication network cross-layer routing protocol method based on channel quality. Background Art

[0002] The ocean covers more than two-thirds of the earth's surface and plays a vital role in human survival and development. At present, underwater acoustic communication networks have become a research hotspot in the civil and military fields. Among them, network layer routing protocols are an important part of underwater acoustic communication network research.

[0003] The complexity of underwater acoustic channels far exceeds that of terrestrial wireless channels, mainly manifested in the fact that underwater acoustic channels have long propagation delays, limited bandwidth, and dynamic changes in the marine environment. These factors pose great challenges to the design of underwater acoustic routing protocols. Therefore, when designing routing protocols, the characteristics of underwater acoustic channels and underwater environments must be fully considered to ensure efficient and reliable underwater acoustic communications. In underwater acoustic communication networks, factors such as excessive amounts of transmitted data, interference or collisions between multiple paths, node failures, and limited sensor storage capacity may all lead to network congestion, which can make communications unstable and increase end-to-end delays. Due to the severe signal attenuation in the underwater environment, underwater acoustic communication equipment needs to consume a lot of energy to maintain communication quality. Therefore, the high energy consumption of the network is also one of the important factors that need to be considered in protocol design. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the prior art and propose a cross-layer routing protocol method for an underwater acoustic communication network based on channel quality, which avoids congested areas while selecting reliable links and improves the delivery success rate of data packets.

[0005] In order to achieve the above object, the present invention proposes a cross-layer routing protocol method for an underwater acoustic communication network based on channel quality, wherein the underwater acoustic communication network comprises: a source node, a destination node and a plurality of relay nodes, and the method comprises:

[0006] Step 1) The source node initiates the initialization of the underwater acoustic communication network;

[0007] Step 2) Each node broadcasts a beacon to obtain the status of neighboring nodes and calculate the channel quality assessment index;

[0008] Step 3) The sending node determines the forwarding candidate set according to the node depth, node remaining energy and node buffer status;

[0009] Step 4) The sending node determines the reward function and calculates the Q value of all nodes in the forwarding candidate set;

[0010] Step 5) The sending node selects the node with the largest Q value as the next hop node and updates the V value, and continues to transmit the data packet;

[0011] Step 6) Determine whether the destination node has received the data packet: if the destination node has received the data packet, the process ends; if not, repeat steps 3) to 5) until the destination node has received the data packet.

[0012] Preferably, both the source node and the relay node can be sending nodes.

[0013] Preferably, the initialization of step 1) includes: setting the coordinates, Q value, V value, communication range, maximum buffer length and initial energy parameters of each node in the network.

[0014] Preferably, the step 2) comprises:

[0015] The Bellhop ray model is used to simulate and determine the sound velocity profile, the multipath number Npa at the transmitting and receiving position, the amplitude and delay information of Npa*1 dimension, and the impulse response h(t) of the multipath channel is obtained as follows:

[0016]

[0017] Among them, A0 and τ0 are the amplitude and delay of the direct sound line at the receiving point, respectively. u and τ u are the amplitude and delay of the u-th sound line at the receiving point, t represents time, and δ is the unit pulse function:

[0018]

[0019] The time delay and amplitude information of the multipath channel is applied to the communication system to obtain the channel quality evaluation index CQ under the specific modulation mode and the determined transmission and reception position.

[0020] Preferably, the channel quality assessment indicator CQ is one or more of a bit error rate, a bit error rate and a packet error rate.

[0021] Preferably, the step 3) comprises:

[0022] Filter out the neighbor node subset Subest1 that meets the depth requirements:

[0023]

[0024] where n i is the current sending node, Neighbor i n i The set of neighbor nodes, n j is a neighbor node, depth indicates the node depth;

[0025] Filter out the neighbor node subset Subset2 that meets the energy requirements:

[0026]

[0027] Among them, E res Represents the remaining energy of the node, E init is the initial energy of the node;

[0028] Filter out the neighbor node subset Subset3 that meets the buffer requirements:

[0029]

[0030] in For node n j The current buffer length, For node n j Maximum buffer length;

[0031] The forwarding candidate set candidateSet is obtained by the intersection of Subset1, Subset2 and Subset3.

[0032] Preferably, the reward function R in step 4) is ij For node n i Transmit to node n j The reward function satisfies the following formula:

[0033]

[0034] Among them, CQ is the channel quality assessment indicator, is the reward function for successful transmission, is the reward function for transmission failure, which satisfies the following formula:

[0035]

[0036] Among them, g0 is the constant overhead, is the channel quality overhead weight, are the delay and congestion overhead weights, is the residual energy sensitivity, is the energy distribution sensitivity, c(q) is the communication channel quality overhead, c(t) is the delay and congestion overhead, b(n i ),b(n j ) are node n i and node n j The remaining energy cost, d(n i ),d(n j ) are node n i and node n jThe residual energy distribution overhead of , c′(t) is the delay and congestion related overhead of transmission failure, and c′(q) is the channel quality related overhead of transmission failure.

[0037] Preferably, the Q value Q in step 4) is * (s i ,a i ) is calculated according to the following formula:

[0038] Q * (s i ,a i )=R ij +γ×((1-CQ)×V * (s j )+CQ×V * (s i ))

[0039] Where γ is the discount factor, V * (s i )) means n i The V value of the node, V * (s j ) is n j The V value of the node.

[0040] Compared with the prior art, the advantages of the present invention are:

[0041] 1. The present invention provides a cross-layer routing protocol CLCQ for underwater acoustic communication network based on channel quality, which realizes information interaction between different layers;

[0042] 2. Simulate the multipath effect of underwater acoustic channels and apply the results to OFDM communication systems or other communication systems to obtain channel quality evaluation indicators and apply them to cross-layer routing protocols;

[0043] 3. Designed a reinforcement learning reward function that comprehensively considers channel quality, node buffer status, and remaining energy to improve the success rate of data packet delivery;

[0044] 4. A forwarding candidate set selection method considering node depth, node residual energy and node buffer status is proposed to improve the efficiency of reinforcement learning algorithm;

[0045] 5. The cross-layer routing protocol method of the present invention uses information from other layers of the protocol stack to make more intelligent routing decisions. Through cross-layer design, the performance indicators of the network can be better optimized, such as reducing latency, reducing packet loss rate, etc. It can also be dynamically adjusted according to the actual network conditions, and can better adapt to different network environments and application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1is a flow chart of a cross-layer routing protocol of an underwater acoustic communication network based on channel quality in an embodiment;

[0047] Figure 2 is a diagram of the structure of an underwater acoustic communication network in an embodiment;

[0048] Figure 3 is the sound velocity profile of a certain sea area in winter in the embodiment;

[0049] Figure 4 It is the multipath channel response of a point-to-point link with a transmitting depth of 1000m, a receiving depth of 950m and a distance of 1000m under the sound velocity profile in a certain sea area in winter in the embodiment;

[0050] Figure 5 This is the implementation process of the OFDM underwater acoustic communication system in the embodiment;

[0051] Figure 6 It is a two-dimensional bit error rate diagram of the transmitting depth of 800m, different receiving depths and different receiving distances in the embodiment;

[0052] Figure 7 : is a comparison diagram of source node V values ​​of the present invention and the QELAR protocol in the embodiment;

[0053] Figure 8 is a schematic diagram of comparison results of simulation of total energy consumption of the protocol proposed in the present invention, the QELAR protocol and the GEDAR protocol under different numbers of nodes in the embodiment;

[0054] Fig. 9 is a schematic diagram of the comparison results of the simulation of the residual energy variance of the protocol proposed in the present invention, the QELAR protocol and the GEDAR protocol under different numbers of nodes in the embodiment;

[0055] Fig.10 It is a schematic diagram of the comparison results of the simulation of the data packet delivery success rate of the protocol proposed in the present invention, the QELAR protocol and the GEDAR protocol under different numbers of nodes in the embodiment. DETAILED DESCRIPTION

[0056] According to the present invention, a cross-layer routing protocol for underwater acoustic communication network based on channel quality comprises the following steps:

[0057] 1. Initialize the network: set network node coordinates, Q value, V value, communication range, maximum buffer length, initial energy and other parameters;

[0058] 2. Broadcast beacon: obtain the location information, remaining energy, current buffer status of neighboring nodes and calculate channel quality assessment indicators;

[0059] The calculation of the channel quality assessment index includes the following steps:

[0060] (2.1) Simulating the multipath effect of underwater acoustic channels: The Bellhop ray model is used to simulate and obtain the multipath number Npa, the amplitude and delay information of Npa*1 dimension, which determines the sound velocity profile and the transmitting and receiving positions. The impulse response of the multipath channel is:

[0061]

[0062] Among them A u and τ u are the amplitude and delay of the u-th sound line at the receiving point respectively.

[0063] (2.2) Apply the delay and amplitude information of the multipath channel obtained in step (2.1) to the OFDM communication system to obtain a channel quality evaluation index for a specific modulation mode and a specific transmission and reception position. It should be noted that this embodiment takes the OFDM communication system as an example, but is not limited thereto. Other underlying communication systems may also be used, such as single carrier modulation, direct sequence spread spectrum, chaotic spread spectrum, etc.

[0064] 3. Determine the forwarding candidate set: Consider the node depth, node remaining energy and node buffer status for selection;

[0065] Step 3 includes the following steps:

[0066] (3.1) Filter out the neighbor node subset Subset1 that meets the depth requirements:

[0067]

[0068] where n i is the current node, Neighbor i n i The set of neighbor nodes, n j is a neighbor node, and depth indicates the node depth.

[0069] (3.2) Filter out the neighbor node subset Subset2 that meets the energy requirements:

[0070]

[0071] Where E res represents the remaining energy of the node, E init is the initial energy of the node.

[0072] (3.3) Filter out the neighbor node subset Subset3 that meets the buffer requirements:

[0073]

[0074] Buff now is the current buffer length, Buffmax is the maximum buffer length.

[0075] (3.4) The forwarding candidate set is the intersection of Subset1, Subset2 and Subset3:

[0076] candidateSet=Subset1∩Subset2∩Subset3

[0077] The candidateSet is the final candidate forwarding set of the current node.

[0078] 4. Calculate the Q value of all nodes in the forwarding candidate set;

[0079] Step 4 includes the following steps:

[0080] (4.1) Determine the reward function:

[0081] Data packet from node n i Transfer to n j , the reward function for successful transmission is calculated as follows:

[0082]

[0083] Among them, g0 is the constant overhead, is the channel quality overhead weight, are the delay and congestion overhead weights, is the residual energy sensitivity, is the energy distribution sensitivity, c(q) is the channel quality overhead, c(t) is the delay and congestion overhead, b(n i ),b(n j ) is the remaining energy consumption, d(n i ),d(n j ) is the remaining energy distribution overhead.

[0084] Data packet from slave node n i Transfer to n j , the reward function for transmission failure is calculated as follows:

[0085]

[0086] Where c′(t) is the delay and congestion-related overhead of transmission failure, and c′(q) is the channel quality-related overhead of transmission failure.

[0087] The direct reward function for packet transmission is calculated as follows:

[0088]

[0089] Wherein, CQ is the channel quality evaluation index obtained in step (2.2). The smaller the CQ, the better the channel quality. CQ can be the bit error rate, or the bit error rate or the packet error rate.

[0090] (4.2) According to the reward function, determine the Q value of each node:

[0091] The Q value is calculated as follows:

[0092] Q * (s i ,a i )=R ij +γ×((1-CQ)×V * (s j )+CQ×V * (s i ))

[0093] Where γ is the discount factor, V * (s i )) represents n i The V value of the node, V * (s j ) is n j The V value of the node.

[0094] 5. Select the node with the largest Q value as the next hop node and update the V value to continue transmitting the data packet;

[0095] 6. Determine whether the destination node has received the data packet: If the destination node has received the data packet, the process ends; otherwise, repeat steps 3 to 5 until the destination node has received the data packet.

[0096] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0097] Example 1

[0098] refer to Figure 1 A protocol flow chart of a cross-layer routing protocol for an underwater acoustic communication network based on channel quality, the method of the present invention comprises the following steps:

[0099] 1. Initialize the network: The source node initiates network initialization and sets the coordinates, Q value, V value, communication range, maximum buffer length, initial energy and other parameters of all network nodes;

[0100] 2. Broadcast beacon: Each node broadcasts a beacon to obtain the location information, remaining energy, current buffer status of neighboring nodes and calculate channel quality assessment indicators;

[0101] 3. Determine the forwarding candidate set: The sending node determines the forwarding candidate set considering the node depth, node remaining energy and node buffer status;

[0102] 4. The sending node calculates the Q value of all nodes in the forwarding candidate set;

[0103] 5. The sending node selects the node with the largest Q value as the next hop node and updates the V value, and continues to transmit the data packet;

[0104] 6. Determine whether the destination node has received the data packet: If the destination node has received the data packet, the process ends; if not, repeat steps 3 to 5 until the destination node has received the data packet.

[0105] Specifically:

[0106] 1. Initialize the network

[0107] The model used in this embodiment is as follows Figure 2 As shown in the figure. In this network model, information is generated by underwater source nodes and transmitted upward to the destination node via relay forwarding. A large number of underwater sensor nodes are randomly distributed in a three-dimensional underwater network. Assume that the energy of the destination node is not limited and can obtain its own location information through GPS, all underwater nodes can obtain their own location information through positioning algorithms, and all nodes can obtain their own buffer status.

[0108] The simulation model of this embodiment is a network structure including a source node, a destination node and multiple relay nodes. The three-dimensional coverage area is 3000m x 3000m x 1000m, and the relay nodes are randomly arranged. In order to avoid data packet conflicts, the handshake-based multiple access protocol Slotted FAMA is used as the MAC protocol. The data packet is generated by the source node, and one data packet is sent in one handshake. The parameter settings are shown in Table 1:

[0109] Table 1 Simulation parameter settings

[0110]

[0111]

[0112] 2. Broadcast Beacon

[0113] Obtain the location information, remaining energy, and current buffer status of neighboring nodes and calculate the bit error rate, using the bit error rate as a channel quality assessment indicator. Use the BELLHOP ray model, introduce the sound velocity profile data to calculate the actual propagation loss and delay, apply the generated channel impulse response to the multipath channel model of the network, and give the bit error rate of the underwater acoustic channel under a specific modulation mode and a specific marine environment. This embodiment uses Figure 3 The winter sound velocity profile of a certain sea area shown in the figure describes the sound velocity distribution of the deep-sea sound channel, and obtains the amplitude and delay information of the multipath number Npa, Npa*1 dimension, which determines the transmission depth and the receiving position. The impulse response h(t) of the multipath channel is defined as:

[0114]

[0115] Among them A u and τ u are the amplitude and delay of the u-th sound line at the receiving point respectively. Figure 4 The figure shows the multipath amplitude and delay at a transmitting depth of 1000m, a receiving depth of 950m, and a distance of 1000m in the winter sound speed profile of a certain sea area.

[0116] Then add the delay and amplitude information of the multipath channel calculated by BELLHOP to Figure 5 The OFDM simulation model of the physical layer is shown in FIG. The OFDM system of this embodiment adopts LDPC code for channel coding, the modulation and demodulation mode is QPSK, and the channel estimation and equalization based on pilot are adopted. In order to eliminate the Doppler effect of the underwater acoustic channel, the Doppler estimation of the time domain correlation method and the Doppler compensation of the interpolation method are performed. According to the position information of the transmitting node and the receiving node, the bit error rate for determining the transmission depth, the receiving depth and the distance can be obtained, and the channel quality between the nodes is evaluated based on the bit error rate. Figure 6 It is the two-dimensional bit error rate at different receiving depths and different receiving distances when the transmitting depth is 800m.

[0117] 3. Determine the forwarding candidate set

[0118] The steps for this part are as follows:

[0119] (3.1) Filter out the neighbor node subset Subset1 that meets the depth requirements:

[0120]

[0121] where n i is the current node, Neighbor i n i The set of neighbor nodes, n j is a neighbor node, and depth indicates the node depth.

[0122] (3.2) Filter out the neighbor node subset Subset2 that meets the energy requirements:

[0123]

[0124] Where E res Represents the remaining energy of the node, E init is the initial energy of the node.

[0125] (3.3) Filter out the neighbor node subset Subset3 that meets the buffer requirements:

[0126]

[0127] Buff now is the current buffer length, Buff max is the maximum buffer length.

[0128] (3.4) The forwarding candidate set is the intersection of Subset1, Subset2 and Subset3:

[0129] candidateSet=Subset1∩Subset2∩Subset3

[0130] The candidateSet is the final candidate forwarding set of the current node.

[0131] 4. Calculate the Q value of all nodes in the forwarding candidate set

[0132] Calculate the Q value of all nodes in the candidate set and select the node with the largest Q value as the next hop node. The calculation of the Q value includes the following steps:

[0133] (4.1) Determine the reward function:

[0134] Data packet from node n i Transfer to n j , the reward function for successful transmission is calculated as follows:

[0135]

[0136] Among them, g0 is the constant overhead, is the channel quality overhead weight, are the delay and congestion overhead weights, is the residual energy sensitivity, is the energy distribution sensitivity, c(q) is the communication channel quality overhead, c(t) is the delay and congestion overhead, b(n i ),b(n j ) is the remaining energy consumption, d(n i ),d(n j ) is the remaining energy distribution overhead.

[0137] Data packet from node n i Transfer to n j , the reward function for transmission failure is calculated as follows:

[0138]

[0139] Where c′(t) is the delay and congestion-related overhead of transmission failure, and c′(q) is the channel quality-related overhead of transmission failure.

[0140] The direct reward function for packet transmission is calculated as follows:

[0141]

[0142] Among them, BER ij is the bit error rate calculated in step 2. In this embodiment, the bit error rate is used as a standard to evaluate the channel quality between nodes.

[0143] (4.2) According to the reward function, determine the Q value of each node:

[0144] The Q value is calculated as follows:

[0145] Q * (s i ,a i )=R ij +γ×((1-BER ij )×V * (s j )+BER ij ×V * (s i ))

[0146] Where γ is the discount factor, V * (s i )) means n i The V value of the node, V * (s j ) is n j The V value of the node.

[0147] 5. Select the node with the largest Q value as the next hop node and update the V value

[0148] The V value update formula is as follows:

[0149]

[0150] 6. Determine whether the destination node has received the data packet: If the destination node has received the data packet, the process ends; if not, repeat steps 3 to 5 until the destination node has received the data packet.

[0151] Figure 7 3 is a comparison diagram of the source node V value of the present invention and the QELAR protocol in the embodiment. It can be seen from the simulation results that the convergence speed of the protocol of the present invention is faster than that of QELAR.

[0152] Figure 8 3 is a schematic diagram of the comparison results of the simulation of the total energy consumption of the protocol proposed in the present invention, the QELAR protocol and the GEDAR protocol under different numbers of nodes. It can be seen from the simulation results that when the number of nodes is greater than 60, the energy consumption advantage of the protocol begins to emerge.

[0153] Fig. 9 It is a schematic diagram of the comparison results of the simulation of the residual energy variance of the protocol proposed in the present invention, the QELAR protocol and the GEDAR protocol under different numbers of nodes. It can be seen from the results that as the number of nodes increases, the residual energy variance of the protocol becomes smaller and smaller, and it has more advantages in energy balance.

[0154] Fig.10 It is a schematic diagram of the comparison results of the simulation of the data packet delivery success rate of the protocol proposed in the present invention, the QELAR protocol and the GEDAR protocol under different numbers of nodes. It can be seen that the data packet delivery success rate using the method of the present invention is the highest.

[0155] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A cross-layer routing protocol method for an underwater acoustic communication network based on channel quality, the underwater acoustic communication network comprising: A source node, a destination node and a plurality of relay nodes, the method comprising: Step 1) The source node initiates the initialization of the underwater acoustic communication network; Step 2) Each node broadcasts a beacon to obtain the status of neighboring nodes and calculate the channel quality assessment index; Step 3) The sending node determines the forwarding candidate set according to the node depth, node remaining energy and node buffer status; Step 4) The sending node determines the reward function and calculates the Q value of all nodes in the forwarding candidate set; Step 5) The sending node selects the node with the largest Q value as the next hop node and updates the V value, and continues to transmit the data packet; Step 6) Determine whether the destination node has received the data packet: if the destination node has received the data packet, the process ends; if not, repeat steps 3) to 5) until the destination node has received the data packet; The step 2) comprises: The Bellhop ray model is used to simulate and determine the sound velocity profile, the multipath number Npa at the transmitting and receiving position, the amplitude and delay information of Npa*1 dimension, and the impulse response h(t) of the multipath channel is obtained as follows: Among them, A0 and τ0 are the amplitude and delay of the direct sound line at the receiving point, respectively. u and τ u are the amplitude and delay of the u-th sound line at the receiving point, t represents time, and δ is the unit pulse function: Apply the delay and amplitude information of the multipath channel to the communication system to determine the channel quality evaluation index CQ under the specific modulation mode and the transmission and reception position; The reward function R in step 4) ij For node n i Transmit to node n j The reward function satisfies the following formula: Among them, CQ is the channel quality assessment indicator, is the reward function for successful transmission, is the reward function for transmission failure, which satisfies the following formula: Among them, g0 is the constant overhead, is the channel quality overhead weight, are the delay and congestion overhead weights, is the residual energy sensitivity, is the energy distribution sensitivity, c(q) is the communication channel quality overhead, c(t) is the delay and congestion overhead, b(n i ),b(n j ) are node n i and node n j The remaining energy cost, d(n i ),d(n j ) are node n i and node n j The remaining energy distribution overhead, c′(t) is the delay and congestion related overhead of transmission failure, and c′(q) is the channel quality related overhead of transmission failure; The Q value Q in step 4) * (s i ,a i ) is calculated according to the following formula: Q * (s i ,to i )=R ij +γ×((1-CQ)×V * (s j )+CQ×V * (s i )) Where γ is the discount factor, V * (s i )) represents n i The V value of the node, V * (s j ) is n j The V value of the node.

2. The cross-layer routing protocol method for underwater acoustic communication network based on channel quality according to claim 1 is characterized in that: Both source nodes and relay nodes can be sending nodes.

3. The cross-layer routing protocol method for underwater acoustic communication network based on channel quality according to claim 1 is characterized in that: The initialization of step 1) includes: setting the coordinates, Q value, V value, communication range, maximum buffer length and initial energy parameters of each node in the network.

4. The cross-layer routing protocol method for underwater acoustic communication network based on channel quality according to claim 1 is characterized in that: The channel quality evaluation indicator CQ is one or more of a bit error rate, a bit error rate and a packet error rate.

5. The cross-layer routing protocol method for underwater acoustic communication network based on channel quality according to claim 1 is characterized in that: The step 3) comprises: Filter out the neighbor node subset Subset1 that meets the depth requirements: Among them, n i is the current sending node, Neighbor i n i The set of neighbor nodes, n j is a neighbor node, depth indicates the node depth; Filter out the neighbor node subset Subset2 that meets the energy requirements: Among them, E res Represents the remaining energy of the node, E init is the initial energy of the node; Filter out the neighbor node subset Subset3 that meets the buffer requirements: in, For node n j The current buffer length, For node n j Maximum buffer length; The forwarding candidate set candidateSet is obtained by the intersection of Subset1, Subset2 and Subset3.

Images