Tuan-Duc Nguyen

Olivier Berder

Olivier Sentieys

Energy efficient cooperative techniques for infrastructure to vehicle communications

In wireless distributed networks, cooperative relay and cooperative Multi-Input Multi-Output (MIMO) techniques can be used to exploit the spatial and temporal diversity gain in order to increase the performance or reduce the transmission energy consumption. The energy efficiency of cooperative MIMO and relay techniques is then very useful for the Infrastructure to Vehicle (I2V) and Infrastructure to Infrastructure (I2I) communications in Intelligent Transport Systems (ITS) networks where the energy consumption of wireless nodes embedded on road infrastructure is constrained. In this paper, applications of cooperation between nodes to ITS networks are proposed and the performance and the energy consumption of cooperative relay and cooperative MIMO are investigated in comparison with the traditional multi-hop technique. The comparison between these cooperative techniques helps us to choose the optimal cooperative strategy in terms of energy consumption for energy constrained road infrastructure networks in ITS applications.

I. INTRODUCTION

In future Intelligent Transport Systems (ITS), information and communication from the road infrastructure to vehicle (I2V) will play a key role in driving assistance, floating car data, and traffic management in order to make the road safer and more intelligent. The communications are supported by wireless nodes integrated in road signs (or traffic infrastructure along the road) and vehicles. While wireless nodes embedded in vehicles can take profit from their battery or can be regularly recharged, each road sign wireless node is usually powered by a small battery that may not be rechargeable or renewable for long term (or powered by a low power solar battery). Even if such networks are mainly concentrated in cities (but new applications appear for rural junctions too), many of the nodes are not necessarily connected to electrical power supply, due to the civil engineering cost. The energy consumption of road infrastructure wireless nodes is consequently one of the important constraints in order to increase the reliability and the lifetime of this network.

As the transmission power increases quickly as a K power function of the transmission distance (with typical path loss factor 2 < K < 6), the transmission energy consumption plays an important role for medium and long range transmission and represents the dominant part of the total energy consumption. In some ITS applications, energy efficient transmission techniques are very important for the communication from an energy constrained device like road infrastructure to a vehicle (I2V) or to another energy constrained device (I2I). In traditional approach, multi-hop transmission technique is used to reduce the transmission energy consumption by dividing the long transmission channel into multiple short transmissions.

The cooperative relay technique can exploit the spatial and temporal diversity gain in order to reduce the path loss effect in wireless channels. The result is that the system performance is improved or less energy is needed for data transmission. Relay techniques are recognized as a simple and energy efficient way to extend the transmission range due to their simplicity and their performance for wireless transmissions over fading channels [START_REF] Laneman | Energy-efficient antenna sharing and relaying for wireless networks[END_REF], [START_REF] Sendonaris | User cooperation diversity. Part I. System description[END_REF] and [START_REF] Laneman | Cooperative diversity in wireless networks: Efficient protocols and outage behavior[END_REF]. They have been recently studied in the context of Vehicle-to-Vehicle communications in [START_REF] Ilhan | Cooperative Diversity for Relay-Assisted Inter-Vehicular Communication[END_REF].

Beside the relay technique, some individual sensor nodes can cooperate at the transmission and the reception in order to deploy a cooperative Multi-Input Multi-Output (MIMO) transmission scheme [START_REF] Dohler | Space-time block codes for virtual antenna arrays[END_REF], [START_REF] Li | Energy efficient wireless sensor networks with transmission diversity[END_REF], [START_REF] Laneman | Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks[END_REF]. Classical MIMO transmission is investigated for V2V transmissions and should be proposed in the future 802.11.p standard. Unfortunately the nodes embedded in the road signs can not have more than one antenna because of the limitations in space, cost and energy consumption. Therefore classical MIMO can not be applied to I2I and I2V communications. On the other hand, cooperative MIMO can exploit the diversity gain of space-time coding technique to increase the system performance or to reduce the energy consumption. In [8] [9], it has been shown that cooperative MISO and MIMO systems are more energy-efficient than Single-Input Single-Output (SISO) and traditional multi-hop SISO systems for medium and long range transmission in wireless distributed sensor networks. Other recent works on MIMO STBC transmission in ITS applications can be found in [START_REF] Ito | A Novel MIMO-STBC Scheme for Inter-Vehicle Communications at Intersection[END_REF], [START_REF] Konkaew | The Impact of Path Loss on Cooperative MIMO Transmission Scheme for Intelligent Transport System[END_REF]. One the other hand, cooperation between nodes can also help to extend the transmission range (with the same output power of one wireless node), thus increasing the communication distance between two nodes or two groups of nodes.

In this paper, these cooperative techniques are adapted to ITS applications and characterized for I2V and I2I cooperative transmissions. The context of the study is the CAPTIV project (Cooperative strAtegies for low Power wireless Transmissions between Infrastructure and Vehicles) [START_REF] Berder | Cooperative communications between vehicles and intelligent road signs[END_REF], where the network composed of wireless nodes at a junction has to give to the arriving vehicles short term information for driving assistance and long term information for traffic management. It is shown that the cooperative MIMO and relay techniques are better than the Single-Input Single-Output (SISO) and SISO multi-hop technique in terms of performance and energy consumption. Both techniques are interesting in the energy constrained ITS applications and the advantages of each technique depend on the particular network structure or on the application. Based on a reference model, energy consumption calculations help us to choose the optimal cooperative strategy in terms of energy consumption for CAPTIV, with respect to the transmission distances between two junctions or between a junction and a vehicle.

The rest of the paper is organized as follows. The principle of cooperative strategies for the energy consumption optimization are presented in Section II. In Section III, the energy calculation model is proposed and simulation results on the energy consumption comparison of cooperative techniques in CAPTIV are presented in Section IV. Finally, conclusions and discussion are given in Section V.

II. COOPERATIVE TRANSMISSIONS AND CAPTIV

CONTEXT A scientific coordination group devoted to Intelligent Transportation Systems, called GIS ITS Bretagne, has been set up in the Brittany region of France, to investigate this research area. One of its projects, CAPTIV, aims at using existing infrastructure, i.e. road signs but also every infrastructure along the road, to transmit information inside a wireless network including equipped vehicles, as illustrated by Fig. 1. The first applications offered by CAPTIV are road signs anticipated displays (including dynamic situations as temporary works on the road) and arriving vehicle indications (in order to help a driver at a stop to start or not on the main road in case of smog, heavy rain or snow, for example). In such a network, every kind of information can be transmitted, leading then to more advanced applications which integrate live data and feedback from a number of other sources, such as parking guidance and information systems, weather information, and so on.

In the CAPTIV system, information is transmitted, thanks to vehicles and existing infrastructure, within a network whose typical size is metropolitan. The communications can occur from road infrastructure to vehicle (I2V), road infrastructure to road infrastructure (I2I), vehicle to road infrastructure (V2I) or a vehicle to vehicle (V2V). The energy constraint for road sign infrastructure is very important due to the fact that batteries in traffic road signs can not be replaced for a long time.

A. Relay and Cooperative MIMO Techniques

The traditional model for relay diversity technique with one relay node shown in Fig. 2, consists in a source node S, a destination node D and a relay node R. The relay transmission from S to D can be performed by a two-time slot transmission. In the first time slot, signals are transmitted by the source S to the destination node D and the relay node R at the same time. In the second time slot, the relay node retransmits the information previously received. At node D, the receiver combines received signals by using a diversity combination technique (MRC, EGC...) before symbol detection. In relay cooperative networks, the received signal comes from different independent fading channels, so that the probability of deep fading is minimized. This diversity gain helps to decrease the error rate, or to decrease the transmission power for the same required error rate. Relay techniques can be classified according to their forwarding strategy. There are three main methods for the relay node to transmit the received frame to the destination node: Amplify and Forward, Decode and Forward, and Re-encode and Forward.

Multi-Input Multi-Output (MIMO) technique can exploit the diversity gain of space-time coding technique in order to increase the system performance or to reduce the transmission consumption for the same Bit Error Ratio (BER) requirement. The principle of cooperative MIMO transmission using space-time block codes (STBC) was presented in [START_REF] Cui | Energy-efficiency of MIMO and cooperative MIMO techniques in sensor networks[END_REF]. As illustrated by Fig. 3, the cooperative MIMO transmission (with N cooperative transmission and M cooperative reception nodes) from source node S to destination node D over a transmission distance d is composed of three phases: Local data exchange, cooperative MIMO transmission and cooperative reception. In the local data exchange at the transmission side, the source node S must cooperate with its neighbors and exchange its data in order to perform a MIMO transmission in the next phase. Node S can broadcast the transmission bits to the other N -1 cooperative transmission nodes. The distance between cooperating nodes d m is usually much smaller than the transmission distance d. In cooperative MIMO transmission phase, after N -1 neighbor nodes receive the data from source node S, N cooperative transmission nodes will modulate and encode their received bits to the QPSK STBC symbols and then transmit simultaneously to the destination node (or multi-destination nodes) like a traditional MIMO systems (each cooperative node plays role of one antenna of the MIMO system). In finally in the cooperative reception phase at the reception side, cooperative neighbor nodes of destination node D receive the MIMO modulated symbols, then sequentially retransmit them to the destination node D for joint MIMO signals combination and data decoding. In a cooperative MIMO system, the decoder at destination node D requires the analog value of received signals at all cooperative nodes for the space time combination. Therefore, each cooperative node must transmit their received value trough a wireless channel to the destination node D. Three cooperative reception technique: Quantization, Combineand-Forward or Forward-and-Combine can be used for this retransmission procedure [START_REF] Nguyen | Impact of Transmission Synchronization Error and Cooperative Reception Techniques on the Performance of Cooperative MIMO Systems[END_REF].

S D MIMO Transmission

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B. Performance comparison of cooperative techniques

As the cooperative relay and cooperative MIMO technique can exploit the diversity gain to increase the performance, the performance of both techniques is much better than the SISO technique and the needed Signalto-Noise Ratio (SNR) is smaller for the same error rate requirement. Fig. 4 represents the Frame Error Rate (FER) performance comparison of the relay (Decodeand-Forward and Amplify-and-Forward techniques) and the cooperative MISO techniques for two transmit nodes with the traditional SISO technique. As needed SNRs of the cooperative MISO and relay techniques are smaller than the SISO technique, the two cooperative techniques can help to reduce the transmission energy consumption for the same transmission reliability in an energy constrained traffic-signs wireless network. This energy efficiency of cooperative MIMO and relay techniques is very useful for a typical medium to long distance transmission in ITS application where the transmission energy consumption dominates the total consumption of a wireless node.

The nature of STBC [START_REF] Alamouti | A simple transmit diversity technique for wireless communications[END_REF][15] considers that the signals from different transmit antennas must be received synchronously at each cooperative node to perform the orthogonal combination. Furthermore, the clock of each wireless node can be drifted during transmission times and the transmission delay can vary for each MIMO channel. Consequently, it is impossible to have a perfectly synchronized transmission in distributed wireless nodes, leading to a unsynchronized received signal at the reception node. The effect of the transmission synchronization error is the superposition of the signal pulses from each node, shifted by the corresponding time delay, at the receiver. After the synchronization and the signal sampling process, Inter Symbol Interference (ISI) between the unsynchronized sequences appears and the space-time sequences from the different nodes are no longer orthogonal. The orthogonal combination of space time codes can not be performed, which leads to the amplitude decrease of the desired signal and generates more interferences in final estimated symbols [START_REF] Jagannathan | The effect of time synchronization errors on the performance of cooperative MISO systems[END_REF].

The effect of transmission synchronization in the performance of cooperative MIMO technique for the case of two transmit node is presented in Fig. 5. The performance degradation increases with the transmission synchronization error range. The cooperative MIMO system is rather tolerant for small range of transmission synchronization error and the degradation is negligible for synchronization error range as small as 0.25T s (and small for error range as small as 0.5T s ). For small transmission synchronization error ranges, the performance degradation is small enough to keep the energy efficiency advantage of cooperative MIMO system over SISO and multi-hop SISO techniques. However, the performance degradation is significant for transmission synchronization errors as large as 0.75T s . In this case, a more complex distributed space time code or a efficient space-time combination technique can be used in order to retain the performance of cooperative MIMO in the presence of transmission synchronization error.

C. Cooperative Transmission Schemes in CAPTIV project

In plenty of communication scenarios in ITS, the transmission between the infrastructure and the vehicles are usually from a medium to long distance and a direct transmission, if possible, would need too much transmission energy. A traditional multi-hop routing technique can be used for such transmissions but it is not efficient enough in terms of energy consumption in many cases. By exploiting the diversity transmission to reduce the transmission energy consumption, relay and cooperative MIMO techniques are the better strategies in terms of energy efficiency.

Considering that the circle and the rectangle stand respectively for the road sign and the vehicle in the transport system, some cooperative transmission strategies, illustrated in the following figures, have been proposed for energy efficiency transmissions in CAPTIV.

1) SISO multi-hop transmission:

The most simple cooperation scheme is the multi-hop SISO transmission, as shown by Fig. 6. Instead of the transmission over a long distance from source node S to the destination node D, a message from a road sign (source node S) at a junction can be transmitted through multiple road signs (cooperation nodes) to a vehicle (destination node D). Multi-hop transmission can save significantly the transmission energy consumption with the cost of more circuit energy consumption. 2) Relay transmission: In Fig. 7, a message from the road sign can be transmitted to the vehicle (destination node D) and another road sign (relay node R). Then, the message is relayed from this relay road sign to the vehicle for signal combination. Transmission diversity gain of relay technique helps to decrease the transmission power for the same error rate requirement, so that reduce the transmission energy consumption. This technique is more energy efficient than multi-hop SISO for medium range transmission. Cooperative MIMO technique exploits the diversity gain of the MIMO space-time coding technique in distributed wireless networks in order to reduce the transmission energy consumption. Depending on the system topology (the available nodes) and the transmission distance, the optimal selection of transmit and receive nodes number can be chosen in order to minimize the total energy consumption. As shown by Fig. 9, the road sign node S and the vehicle node D can cooperate with their respective neighbor road signs to employ a cooperative MIMO transmission over a long distance. As the vehicles do not have the surface and energy consumption constraints, multiple antennas can be easily integrated in a vehicle to deploy the cooperative MIMO schemes without the need of the cooperative reception phase [START_REF] Nguyen | Cooperative MIMO schemes optimal selection for wireless sensor networks[END_REF].

S D MI SO Tra nsm iss ion

Another example of cooperative MIMO transmission in CAPTIV is shown in Fig. 10, where the road sign node S can cooperate with other road signs in one junction to transmit the message by using a cooperative MIMO technique to the cooperative reception road signs in the other junction.

4) Multi-hop cooperative MIMO transmission: For a long distance communication, the cooperative MIMO technique with the number of transmit and receive nodes greater than 2 has energy consumption advantages [START_REF] Nguyen | Cooperative MIMO schemes optimal selection for wireless sensor networks[END_REF], but this scenario can not be always employed because of the lack of available nodes at the junctions. In this condition, a multi-hop technique using cooperative MIMO for each transmission hop is a suitable solution. As an example, for a communication between two crossroads with a distance greater than 1km in Fig. 11, two road signs in the middle of the transmission line can be employed (and cooperate together) to perform a multihop cooperative MIMO transmission.

S D

MIMO Transmission MIMO Transmission

Fig. 11. Multi-hop cooperative MIMO transmission between infrastructure and vehicle

III. ENERGY EFFICIENCY OF COOPERATIVE STRATEGIES

A. Energy consumption model

For a traditional MIMO system (non-cooperative MIMO system) with N transmit and M receive antennas (N transmit antennas and M receive antennas are integrated in one transmitter and one receiver), the typical RF system block of transmitters and receivers is shown in Fig. 12. The total power consumption of a typical MIMO system consists of two components: the transmission power P pa of the power amplifier and the circuit power P c of all RF circuit blocks.

P pa depends on the output transmission power P out . If the channel is square law path loss (power loss factor K = 2), the needed transmission power can be calculated as

P out (d) = Ēb R b × (4πd) 2 G t G r λ 2 M l N f ( 1
)
where Ēb is the mean required energy per bit for ensuring a given error rate requirement, R b is the bit rate, d is the transmission distance. G t and G r are the transmission and reception antenna gain, λ is the carrier wave length, M l is the link margin, N f is the receiver noise figure defined as N f = M n /N 0 with N 0 is the single-side thermal noise Power Spectral Density (PSD) and M n is the PSD of the total effective noise at receiver input.

Depending on the number of transmit and receive antennas (N and M ), and the Power Spectral Density (PSD) of thermal noise N 0 , the Ēb can be calculated based on SN R value given by Tab. I for error rate requirement F ER = 10 -3 and the performance result in Fig. 4. The power consumption P pa can be approximated as

SN R N = 1 N = 2 N = 3 N = 4 M = 1
P pa = (1 + α)P out (2)
where α = ξ η -1 with η the drain efficiency of the RF power amplifier and ξ the Peak-to-Average Ratio (PAR) which depends on the modulation scheme and the associated constellation size. Indeed, the power consumption of the amplifier is always higher than the effective output power.

The total circuit power consumption of N transmit and M receive antennas is given by P c ≈ N (P DAC + P mix + P f ilt + P syn ) +M (P LN A + P mix + P IF A + P f ilr + P ADC + P syn ) [START_REF] Laneman | Cooperative diversity in wireless networks: Efficient protocols and outage behavior[END_REF] where P DAC , P mix , P LN A , P IF A , P f ilt , P f ilr , P ADC , P syn stand respectively for the power consumption values of the digital-to-analog converter, the mixer, the low noise amplifier, the intermediate frequency amplifier, the active filter at the transmitter and receiver, the analogto-digital converter and the frequency synthesizer. The power consumption of signal processing blocks in transmitter and receiver is typically much smaller than the consumption of RF blocks. It is considered omitted in this estimation for the simplicity.

The energy consumption of the traditional MIMO system E M IM O can be obtained as

E M IM O = (P pa + P c ) N b R b (4)
The energy consumption of the SISO technique or one hop of SISO technique is the case that N = M = 1. The energy consumption of one transmission phase (from S node to R node and from R node to D node) of the relay technique can be calculated like in the SISO technique case.

For a cooperative MIMO system with N transmit and M receive nodes , there are three communication phases: data exchange, MIMO transmission and cooperative reception phases. The energy consumption of the MIMO transmission phase can be calculated like the non-cooperative MIMO case. The total energy consumption must include the energy consumption of cooperative data exchanges and cooperative reception phases. The extra cooperative energy consumption at the transmission side E coopTx and at the reception side E coop R x can be calculated based on the non-cooperative energy consumption model [START_REF] Nguyen | Cooperative MIMO schemes optimal selection for wireless sensor networks[END_REF].

The total energy consumption of a cooperative MIMO system with N transmit and M receive nodes is

E total = E coopTx + E M IM O + E coopRx (5)
For the case of cooperative MISO transmission (M = 1), there are just two first communication phase which means the energy consumption of reception phase E coopRx is zero.

B. Energy Consumption Comparison

For energy consumption estimation, evaluation and comparison purposes, the reference energy model in [START_REF] Cui | Modulation optimization under energy constraints[END_REF] with the system parameters in Table II is used in this paper. More details on the energy consumption calculation using this reference model can be consulted in [START_REF] Nguyen | Cooperative MIMO schemes optimal selection for wireless sensor networks[END_REF]. The following figures represent the total energy consumption to transmit 10 7 bits with the error rate requirement F ER = 10

1) Multi hop SISO vs. cooperative MISO Techniques:

The energy consumption comparison between multi-hop SISO and the cooperative MISO is presented on Fig. 13 with the optimal hop distance d hop = 25m. At the transmission distance d = 100m (4 hops), the multi-hop technique can save 53% of the total energy consumption of the SISO system.

Multi-hop technique is more efficient than SISO transmission. However, the multi-hop SISO system is 69% less energy-efficient than the cooperative 2-1 MISO system. At distance d = 100m, 85% energy is saved by using 2-1 cooperative MISO strategy instead of SISO. One should note that the total energy consumption is the consumption of all nodes, not only one source node. 69% or 85% is the total energy saving for the whole network by using cooperative techniques. The transmission energy consumption (which is always greater than reception energy consumption for long distance) is shared by all cooperative transmission nodes. Moreover, as the multi-hop system needs four hops for signal transmission to the destination node, the transmission delay of the multi-hop technique is much more than the cooperative MISO technique which cost typically two phases of transmission. As the performance gain increases with the number of cooperative transmission nodes in cooperative MIMO techniques, the cooperative MISO 3-1 or MISO 4-1 is more efficient than the cooperative MISO 2-1 or MISO 3-1 at d = 180m or d = 300m respectively as shown in Fig. 14.

If all the RF parameters and the transmission distance are fixed, the transmission energy consumption depends on the required energy per bit E b and the power path-loss factor of the channel (as shown in Eq. 1). If the required error rate F ER increases (less reliable transmission), the required SNR and transmission energy consumption will decrease, reducing the energy efficiency advantage of the cooperative MIMO over SISO and SISO multihop techniques. Otherwise, if the path-loss factor K increases (e.g. in a urban environment), the transmission energy consumption increases quickly (as a power function of the path-loss factor K). As cooperative MIMO technique helps to reduce efficiently the transmission energy, the advantage of cooperation increases. As far as the frequency band is concerned, if the frequency f c = 5.8GHz (which was elected by the European Union for ITS applications and is used in Delicate Short Range Communication technology) is considered instead of a reference model frequency 2.5GHz used in this paper, the transmission energy consumption increases ( 5.8 2.5 ) K times, and the cooperative MIMO technique will probably be more efficient.

Since the nodes are physically separated in a cooperative MIMO system, their different respective clocks lead to de-synchronized transmission and reception. That generates Inter-Symbol Interference (ISI), decreases the desired signal amplitude at the receiver and makes it more difficult to estimate the Channel State Information (CSI). At the reception side, each cooperative node has to forward its received signal through the wireless channel to the destination node for signal combination, which leads to additional noise in the final received signal. The effect of synchronization error at the transmission side and this additive noise at the cooperative reception side lead to some performance degradations of cooperative MIMO system [START_REF] Nguyen | Impact of Transmission Synchronization Error and Cooperative Reception Techniques on the Performance of Cooperative MIMO Systems[END_REF]. The transmission energy needs to be increased for the same error rate requirement, which will lead to an increase in the transmission energy and the total energy consumption. 2) Cooperative MIMO vs. Cooperative MISO Techniques: Fig. 16 shows the energy consumption comparison between the cooperative MIMO system with two receive nodes and the cooperative MISO systems 3-1 and 4-1. The Forward-and-Combine, Combine-and-Forward cooperative reception (with the amplification factor K c = √ 4) [START_REF] Nguyen | Impact of Transmission Synchronization Error and Cooperative Reception Techniques on the Performance of Cooperative MIMO Systems[END_REF] and Quantization reception are used in the cooperative reception phase of cooperative MIMO technique and the transmission synchronization error range is consider as ∆T s = 0.25T s .

The energy consumption of the cooperative MIMO 2-2 using Forward-and-Combine cooperative reception technique is always smaller than the cooperative MISO 4-1 consumption, and smaller than cooperative MISO 3-1 consumption for distances d > 130m. At d = 500m, 25% energy is saved by using the cooperative MIMO 2-2 technique instead of the cooperative MISO 4-1 technique.

For each range of transmission distance d, based on the energy calculation result, we can find the best N -M antenna selection strategy of the cooperative MIMO technique in term of the energy consumption, as shown in Fig. 17. One should note that given the transmission distance and other parameters such as the quality of service (eg. FER, the propagation channel), the global energy consumption must be calculated for every possible N -M configuration of cooperative MIMO by the analytic formula to perform the selection.

3) Cooperative MISO vs. Relay Techniques: The performance of relay techniques is limited by the decoding (or signal processing) process at the relay nodes. The error bit (or amplification noise) occurring at the relay node can not be always corrected at the destination node. Although with the same diversity gain, the performance of relay is always lower than MISO space time coding techniques. Therefore, in many cases, the total energy consumption of the relay technique is higher than the cooperative MISO technique. Fig. 18 shows the energy consumption of relay technique in comparison with SISO technique and cooperative MISO 2-1 technique. However, in the presence of transmission errors, the performance of cooperative MISO technique decreases, leading to the increase of transmission energy consumption. The energy consumption of cooperative MISO 2-1 as a function of transmission synchronization error range is illustrated in Fig 19 . For a small synchronization error range, the degradation is negligible but it becomes significant for a large error range, leading to a more required transmission energy [START_REF] Nguyen | Impact of Transmission Synchronization Error and Cooperative Reception Techniques on the Performance of Cooperative MIMO Systems[END_REF] and less energy efficiency as The advantage of relay technique over cooperative is that relay is not affected by the un-synchronized transmission. Fig. 20 shows the energy consumption comparison of cooperative 2-1 and relay techniques with the path loss factor K = 3 and the transmission synchronization error range ∆T syn is as large as 0.5T s . In this condition, the relay is clearly better than the cooperative MISO in terms of energy consumption. In the case that the number of cooperative transmission nodes N is greater than two (e.g. three or four transmit nodes), the relay technique typically needs N transmis-sion phases to transmit all signals from N -1 relay nodes to the destination node (if orthogonal frequency channels are not considered). But a cooperative MISO technique needs typically 2 transmission phases (data exchange and MISO transmission phases). The transmission delay of the relay technique is longer than the cooperative MISO technique. However, the complexity of the relay is less than the cooperative MISO.

IV. CONCLUSION

Cooperative techniques can exploit the transmission diversity gain in order to increase the performance or to reduce the transmission energy consumption of the system. Some cooperative strategies, based on the multihop, cooperative relay and cooperative MIMO techniques, have been proposed in order to deploy energy efficient transmissions between the road infrastructures and vehicles in CAPTIV.

In this paper, it is shown that cooperative MISO and MIMO techniques are more energy-efficient than SISO and traditional multi-hop SISO techniques for medium and long range transmissions. An optimal cooperative MIMO scheme selection is also presented in order to find the optimal N -M antenna configuration for a given transmission distance.

Cooperative relay techniques provide attractive benefits for wireless distributed systems when the temporal and spatial diversity can be exploited to reduce the transmission energy consumption. Relay techniques are more efficient than the SISO technique, but still less efficient than cooperative MISO techniques in terms of energy consumption. The performance of relay techniques is not as good as cooperative MISO techniques for the same SNR. However, relay techniques are not affected by the un-synchronized transmission scheme. When the transmission synchronization error becomes significant, the performance of relay is better than the performance of cooperative MISO, leading to a better energy efficiency.

Fig. 1 .

 1 Fig. 1. Infrastructure-to-Infrastructure and Infrastructure-to-Vehicle wireless communications in the CAPTIV, Intelligent Transport System Project.

Fig. 2 .

 2 Fig. 2. Three terminal relay diversity scheme.

Fig. 3 .

 3 Fig. 3. Cooperative MIMO transmission scheme from S to D with N cooperative transmission nodes (S, CT,1, CT,2..CT,N-1) and M cooperative reception nodes (D, CR,1, CR,2..CR,M-1).

Fig. 4 .

 4 Fig. 4. FER of relay technique vs. cooperative MISO technique with two transmission nodes, non-coded QPSK modulation over a Rayleigh channel, 120 bits/frame, source-relay distance d1 = d/3, and power path-loss factor K=2.

Fig. 5 .

 5 Fig.5.Effect of the transmission synchronization error on the performance of cooperative MISO systems with two transmit nodes N = 2, Alamouti STBC over a Rayleigh fading channel.

Fig. 6 .

 6 Fig. 6. Multi-hop SISO transmission between infrastructure and vehicle

Fig. 7 .

 7 Fig. 7. Relay transmission between infrastructure and vehicle

Fig. 8 .Fig. 9 .DFig. 10 .

 8910 Fig. 8. Cooperative MISO transmission between infrastructure and vehicle

Fig. 12 .

 12 Fig. 12. Transmitter and receiver blocks with N transmit and M receive antennas.

fc = 2 . 5 1 BP

 251 GHz η = 0.35 GtGr = 5 dBi σ 2 = N 0 2 = -174 dBm/Hz B = 10 Khz β = 1 Pmix = 30.3 mW Psyn = 50 mW Pb = 10 -3 Ts = f ilt = P f ilr = 2.5 mW PLNA = 20 mW N f = 10 dB ML = 40 dB

  -3 from a source node S to a destination node D separated by a distance d (over a Rayleigh fading channel). The local distance between cooperative nodes in cooperative MIMO techniques is d m = 5m and the source-relay distance in relay techniques is d 1 = d/3.

Fig. 13 .

 13 Fig. 13. Energy Consumption of SISO vs. cooperative MISO technique with two transmission nodes, power path-loss factor K = 2, F ER = 10 -3 , Rayleigh fading channel.

Fig. 14 .

 14 Fig. 14. Energy Consumption of cooperative MISO technique with two, three and four transmission nodes, power path-loss factor K = 2, F ER = 10 -3 , Rayleigh fading channel.

Fig. 15 . 1 Fig. 16 .

 15116 Fig. 15. Energy consumption of the cooperative MISO 2 -1 with different cooperative transmission distances dm = 5, 10 and 20m, F ER = 10 -3 requirement, Rayleigh block fading channel with power path-loss factor K = 2.

Fig. 17 .

 17 Fig. 17.Optimal N -M transmit and receive antennas set selection as a function of transmission distance, ∆Tsyn = 0.25Ts, F ER = 10 -3 requirement, Rayleigh fading channel with power path-loss factor K = 2.

Fig. 18 .

 18 Fig. 18. Energy Consumption of relay technique vs. cooperative MIMO technique with two transmission nodes, error rate F ER = 10 -3 , power path-loss factor K = 2, source-relay distance d1 = d/3.

  illustrated in Fig 19.

Fig. 19 .

 19 Fig. 19. Energy Consumption of cooperative MISO technique in function of transmission synchronization error range, two transmission nodes, error rate F ER = 10 -3 requirement, Rayleigh fading channel with the power path-loss factor K = 2

Fig. 20 .

 20 Fig. 20. Energy consumption of relay technique vs. cooperative MISO technique with two transmission nodes N = 2, power pathloss factor K = 3, error rate F ER = 10 -2 transmission synchronization error range ∆Tsyn = 0.5Ts and source-relay distance d1 = d/3.


Abdullah Almaksour

Eric Anquetil

Réjean Plamondon

Christian O'reilly

Synthetic Handwritten Gesture Generation Using Sigma-Lognormal Model for Evolving Handwriting Classifiers

HAL is

Introduction

Motivated by the increasing spread of many types of devices equipped by pen-based interfaces, such as PDAs, ebook, Tablet PCs, Whiteboards ... etc, more emphasis is placed on the development of efficient recognition systems that can correctly interpret the gestures sketched by the user and then translate them either into computerized text or into some specific commands. Nowadays, the used recognition systems are always pre-trained on a fixed, predefined and almost limited group of gestures, which usually contains the Latin letters and a few specific gestures. These systems do not allow users to add new gestures in order to assign them to new commands or shortcuts, or to replace default gestures assigned to existing commands. In order to meet this important functionality, the static handwriting recognition systems that had been used so far must be replaced by new dynamic ones where the knowledge base can endlessly evolve during the use of the system. The evolving nature comes from the fact that the system must be able to integrate in any moment a new unseen class (gesture in our context), and must also continue the learning of the existing classes using the new available learning data. The latter property is very important because learning a new class can never be perfect using the very few learning samples that the user is ready to provide. So the idea is to start the learning using this few data, and then when the user starts using the system, he will be asked to validate or not the recognition system's responses In this way, new learning data samples become available and the classifier must take advantage of them to enhance its performance.

Therefore, the recognition system must be learned in incremental, online and lifelong mode. In incremental learning, the system (the classifier) must keep learning from any new available data samples without neither restarting the learning process from zero nor requiring access to preceding data samples. We present in this paper a handwriting classification system that satisfies the aforementioned needs. The challenge is to learn new unseen gestures on-the-fly, from scratch and using very few samples. Furthermore, the classification system has to remain robust and has to maintain its knowledge about the existing gestures, when introducing new unseen ones anytime during the lifelong learning process. However, the online nature of the incremental learning process requires that the classification performance of the system must be acceptable as much as possible even when adding new classes. A high performance is very hard to reach using the very few data samples that are available in the beginning of learning a new class. To cope with this problem, we integrate in our method a handwriting generation technique by which many synthetic learning data samples can be generated starting from the original real data. The handwriting generation is based on the Sigma-Lognormal representation of handwritten strokes. In this paper, we briefly describe our evolving classifier structure and learning algorithm in section 2. A short description of the Sigma-Lognormal model is presented in section 3. Then, integrating synthetic data based on Sigma-Lognormal model in the incremental learning process is explained in section 4. We present our experimental results in section 5 before concluding in section 6.

1

Our system is based on first-order Takagi-Sugeno (TS) fuzzy inference system. It consists of a set of fuzzy rules of the following form:

Rule i : IF x is close to P i THEN y 1 i = l 1 i ( x), ..., y k i = l k i ( x) (1)
where l m i ( x) is the linear consequent function of the rule i for the class m:

l m i ( x) = π m i x = a m i0 + a m i1 x 1 + a m i2 x 2 + ... + a m in xn (2)
where n is the size of the input vector. The Prototype P is defined by a center and a fuzzy zone of influence. To find the class of x, its membership degree β i ( x) to each fuzzy prototype is first computed. After normalizing these membership degrees, the sum-product inference is used to compute the system output for each class:

y m ( x) = r i=1 βi ( x) l m i ( x) (3)
where r is the number of fuzzy rules in the system. The membership degree is computed by the prototype center µ i and its variance-covariance matrix A i using the multivariate Cauchy probability distribution.:

β i ( x) = 1 2π |A i | 1 + ( x -µ i ) t A -1 i ( x -µ i ) -n+1 2 (4)
The incremental learning algorithm of our model consists of three different tasks: the creation of new rules, the adaptation of the existing rule's premises, and the tuning of the linear consequent parameters. These three tasks must be done in an online incremental mode and all the needed calculation must be completely recursive.

The importance of a given new sample in an incremental clustering process can be evaluated by its potential value. The potential of a sample is defined as inverse of the sum of distances between a data sample and all the other data samples. A recursive method for the calculation of the potential of a new sample hes been introduced in [START_REF] Angelov | An approach to online identification of takagi-sugeno fuzzy models[END_REF]. The recursive formula avoids memorizing the whole previous data but keeps -using few variables -the density distribution in the feature space based on the previous data (see [START_REF] Almaksour | Improving premise structure in evolving takagi-sugeno neuro-fuzzy classifiers[END_REF] for more details). A Premise adaptation process allows to incrementally update the prototype centers coordinates according to each new available learning data, and to recursively compute the prototype covariance matrices in order to give them the rotated hyper-elliptical form. For each new sample, the center and the covariance matrix of the prototype that has the highest activation degree are updated recursive manner [START_REF] Almaksour | Improving premise structure in evolving takagi-sugeno neuro-fuzzy classifiers[END_REF]. The tuning of the linear consequent parameters in a first-order TS model can be done by the weighted Recursive Least Square method (wRLS). More details are available in [START_REF] Almaksour | Improving premise structure in evolving takagi-sugeno neuro-fuzzy classifiers[END_REF].

Sigma-Lognormal Model

The Sigma-Lognormal [START_REF] Plamondon | A multi-level representation paradigm for handwriting stroke generation[END_REF] model consider the neuromuscular system as a cascaded network of a large number of subsystems coupled through a proportionality law. Applying the central limit theorem to this representation shows that such a system will produce elementary movement units having a lognormal speed profile [START_REF] Plamondon | A kinematic theory of rapid human movement. part iv: a formal mathematical proof and new insights[END_REF]. Such a unit, referred to as a neuromuscular component, is scaled and time-shifted by values labeled respectively as D and t 0 , and has a lognormal shape characterized by the time delay (µ) and the response time (σ) of the neuromuscular system involved in its production. Moreover, for planar motions, it is hypothesized that each neuromuscular component is made along a fixed pivot and hence, has a circle-arc trajectory starting at an angle θ s and ending at an angle θ e .

The speed profile and the angular variation of a component are described by ( 5) and ( 6) where P j is the vector of Sigma-Lognormal parameters of the j th component (i.e. P j = [t 0j D j σ j µ j θ sj θ ej ]).

vt(t; P

j ) = D j σ j (t -t 0j ) √ 2π e -[ln(t-t0j)-µj] 2 2σ 2 j
(5)

φ(t; P j ) = θ sj + θ ej -θ sj D j t 0 vt(τ ; P j )dτ (6)
The Sigma-Lognormal model generates complex motions by a vectorial summation of time overlapping neuromuscular components. Once a parameter set is defined, velocity in Cartesian space can be computed using (7). v x (t; P ) = j v tj (t; P j )cos(φ j (t; P j )) , v y (t; P ) = j v tj (t; P j )sin(φ j (t; P j )) Even with a good incremental learning algorithm and an elastic classifier structure, the lack of available learning data in online learning methods remains as important restriction especially in our application where the user needs to use the new added gestures and to get an acceptable classification accuracy as fast as possible. For this reason, we focused on the idea of generating synthetic data samples in order to boost the learning process. Artificial handwriting generation had been already approached, but the deformations on the handwritten shape were always applied on coordinate's level, which produces unrealistic shapes in many cases. Obviously, applying deformations on sigma-lognormal profiles level allows obtaining mush more realistic synthetic data. The idea is to extract the sigma-lognormal profiles of a real handwritten gesture provided by the user. Then, we apply some variation on the extracted parameters within some specific ranges, and we regenerate artificial gestures using the modified profiles. Real and artificial gestures are both used in the incremental learning of our evolving classifier (see Figure 1).

Experimental results

We led the experiments on a dataset of on-line handwritten gestures. It is composed of 11 different gestures drawn by 7 right-handed writers on a Tablet PC. Each writer has drawn 100 samples of each gesture, i.e. 1,100 gestures in each writer specific dataset. Each gesture is described by a set of 10 features. The presented results are the average of results of 7 different tests for the 7 writers. In order to get the results unbiased by the data order effect, we repeat the experiment for each writer 40 times with different random data orders and the mean results are considered. We used about 40% of the dataset for the incremental learning process and the rest is used to estimate the evolution of the performance during the learning process. We generate 10 synthetic samples (gestures) for each real learning sample. Results are shown in Figure 2. By comparing the performance obtained when considering synthetic data samples in the learning process against the one with only the few real samples, we note that the recognition error rate decreases by about 50% thanks to synthetic data samples. Figure 2 shows also that using synthetic samples, the classifier resists better when introducing new classes and it is able to re-estimate rapidly all its parameters and to improve rapidly the recognition performance for the old and the new gestures.

Conclusion

In an online incremental learning of handwriting classifier, the lack of learning data represents an important challenge that can sometime lead to unacceptable performance and make the application difficult to use by the user. Thanks to the Sigma-lognormal representation of handwritten gestures, we could use synthetic gestures in the learning process to enhance the prediction capacity of the classifier. Experimental results shows that the deformed samples help to significantly improve the classification performance if our system in an incremental learning scenarios. One of our perspectives is to replace the predefined static variation ranges that we used to generate artificial samples by an automatic mechanism that can (incrementally) estimate the best variation ranges for each parameter and for each user.

Figure 1 :

 1 Figure 1: (a) Integrating data generation in the incremental learning process (b) some examples of generated gestures

Figure 2 :

 2 Figure 2: (a)(b) Performance evaluation during the incremental learning process (c) Variation ranges of sigmalognormal parameters and impact of each parameter variation on classification performance.