Cédric Lévy-Bencheton #
email: cedric.levy-bencheton@insa-lyon.fr

Guillaume Villemaud
email: guillaume.villemaud@insa-lyon.fr

Power consumption optimization in multi-mode mobile relay

Multi-mode is a common feature in current generation terminals, enabling the user to stay connected at any time. By selecting an appropriate standard, multi-mode can reduce terminal power consumption. Software Defined Radio is an enabler towards multi-mode for the next generation of terminals. In such a radio, communication modes are implemented by a general processor through digital functions, instead of dedicated chips. Providing access to users in bad conditions through relays, is another solution to reduce power consumption. We look at multi-mode relaying, where a mobile terminal, connected to an UMTS base station, acts as an 802.11g-relay for those users. In this paper, we evaluate the algorithmic complexity of 802.11g and UMTS to estimate the power consumption of a Software Defined Radio. We propose a multi-mode relay scheme using such terminals, with the purpose of minimizing the global power consumption. Finally, we enounce different rules to maximize the local and global power gain by implementing multi-mode relays.

I. INTRODUCTION

Multi-mode is a key feature in all current mobile terminals. By enabling communication on different standards, such as UMTS or 802.11g, this property is a big step towards the unlimited connectivity requested by more users everyday. In Software Defined Radio (SDR), the increasing number of chips in current terminals is replaced by a single generic purpose processor running algorithms. Thus, a multi-mode SDR implements different standards as different algorithms. It brings the flexibility needed to guarantee an always available connection, while providing an adaptive and reconfigurable terminal. This reconfiguration is at the center of the IEEE SCC41 Working Group [START_REF]IEEE Standards Coordinating Committee 41 (Dynamic Spectrum Access Networks)[END_REF], via P1900.4 [START_REF] Holland | Development of a Radio Enabler for Reconfiguration Management within the IEEE P1900. 4 Working Group[END_REF].

Still, another problem remains. How can operators ensure an all time connectivity, without generating new costs? Relay usage is one possible answer. A relay is a device transmitting data from users in bad conditions to a base station. Such relays can be deployed by operators or be mobile, where users' terminals act as potential relays. Relaying enables a better efficiency on network coverage [START_REF] Cavalcanti | Connectivity opportunity selection in heterogeneous wireless multi-hop networks[END_REF], a greater capacity [START_REF] Nourizadeh | Performance evaluation of cellular networks with mobile and fixed relay station[END_REF] and reduces the transmission power [START_REF] Wang | Extending the lifetime of wireless sensor networks through mobile relays[END_REF]. Their implementation increases the network lifetime.

The decision for a terminal whether to act as a relay or to be relayed depends on a metric: for example transmission power reduction based on the channel conditions [START_REF] Madan | Energy-efficient cooperative relaying over fading channels with simple relay selection[END_REF], or network capacity improvement [START_REF] Seddik | Outage Analysis and Optimal Power Allocation for Multinode Relay Networks[END_REF]. Metrics are computed either locally by the terminal [START_REF] Ganesan | Cooperative Spectrum Sensing in Cognitive Radio, Part I: Two User Networks[END_REF], or globally by the operator [START_REF] Jiang | Self-organizing relay stations in relay based cellular networks[END_REF].

In our work, we consider mobile multi-mode relays: a terminal communicating with other users on one standard, and with the base station on another standard. Since mobile terminals are power-limited, we reduce the power consumption by taking advantage of multi-mode. Contrary to classical works in the relaying field, we focus on the physical layer power consumption, including not only the transmission power but also numerical and analogical power consumptions. The scope of this paper is the physical layer power consumption, and thus, we do not consider upper layers.

A SDR is a convenient way to implement multi-mode. Even though its power consumption is beyond classical radios, this drawback is largely compensated through reconfiguration, which allows the terminal to change mode following different criteria. Current works refer to channel conditions [START_REF] Debaillie | Energy-scalable ofdm transmitter design and control[END_REF]. We propose a new reconfiguration scheme based on power reduction. In order to evaluate a terminal power consumption for every mode, we separate the numerical power consumption (linked to the algorithmic complexity), and the radio power consumption (depending on the radio front-end and transmission power). Then, we compare all modes and reconfigure the terminal to the most power efficient one. Hence, the terminal power consumption is minimized at all time.

We detail the previous stages in Section II. Then, we compare a multi-mode relay with direct connections in order to reduce the network global power consumption in Section III. Finally, we express rules to minimize the global power consumption using a mobile multi-mode relay in Section IV.

II. TOWARDS A LOWER POWER CONSUMPTION

In Software Defined Radios (SDR), a physical layer is implemented through algorithms. Being multi-mode, the radio runs the different algorithms corresponding to the selected modes at the same time. We propose to communicate on the mode minimizing the SDR power consumption, which is composed of two parts: the numerical power consumption, and the radio power consumption.

A. Algorithmic complexity evaluation

In order to evaluate the numerical power consumption, we compute the algorithmic complexity per bit for every mode, by refering to Neel, Robert and Reed's work [START_REF] Neel | A formal methodology for estimating the feasible processor solution space for a software radio[END_REF]. This complexity per bit allows us to compare different standards.

We present the number of operations per bit for each mode (rounded to the upper integer) in IEEE 802.11g and UMTS (Table I). For a more detailed version, please refer to [START_REF] Lévy-Bencheton | Optimisation de la consommation dans les relais mobiles multi-modes[END_REF].

B. Numerical power consumption

Once we know the algorithmic complexities, we evaluate the numerical power consumption, P p (in Watt), following [START_REF] Wang | Energy-efficient dsps for wireless sensor networks[END_REF]:

P p = N * C * V 2 dd (1)
with N being the number of cycles, C the processor's switching capacitance (in Farad) and V dd the input voltage (in Volt). For a given processor, at fixed frequency, the number of cycles increases with the algorithmic complexity. This leads to a higher power consumption. Considering an ARM ARM 968E-S, we have V dd = 1.2V and C = 97.3pF.

In order to express P p in Watt per bit, we consider one operation per bit and set N to the number of operations per bit evaluated before. This result gives us the power required to transmit or receive one single data bit in the chosen mode. We call it the power cost per bit.

C. Radio power consumption

We separate the radio power consumption into two parts: the radio-frequency front-end power consumption, and the transmission power. We consider a multi-mode radio-frequency front-end, capable of receiving simultaneously an 802.11g and an UMTS signals, as presented in [START_REF] Burciu | A 802.11g and UMTS Simultaneous Reception Front-End Architecture using a double IQ structure[END_REF]. The front-end power consumption depends on the architecture and the activity (in transmission or reception). We evaluate the radio power consumption, P c (in Watt), using [START_REF] Shih | Physical layer driven protocol and algorithm design for energy-efficient wireless sensor networks[END_REF]:

P c = N T T on [P te + P O ] + N R R on P re ( 2
)
with P te and P re (in Watt) being the power consumption of the front-end components, respectively when emitting and receiving, P O the output signal power (in Watt), T on and R on defining transmission or reception, and N T and N R the amount of time the transmitter/receiver is switched on per period. Since a radio can either transmit or receive a signal at a given moment, for T on = 1, N T = 1 and N R = 0; reciprocally for R on = 1. We evaluate the power consumption during a single data bit and express P c in Watt per bit.

Yet, P O must be taken into account in transmission, since it depends on the channel conditions and the distance with the receiver. We explain how to evaluate P O in Section III-B.

Those hypothesis allow us to express the power cost per bit for all modes of our SDR on Fig. 1. In 802.11g, the numerical and radio power are almost identical to transmit and receive one data bit (Fig. 1a). The radio power mostly depends on the transmission power, adjusted according to the receiver's channel conditions.

In UMTS, the numerical and radio power decrease at high data rate, due to reduced complexity and sampling. Moreover, the numerical power represents approximately a quarter of the radio power at 384 kbps (Fig. 1b).

By taking into account those results, the fastest rate is not always the most power consuming. Thus, we use the fastest mode to reduce the power cost per bit. We consider an UMTS Base Station (BS) and two SDR terminals, one is a Primary User (PU) capable of becoming relay, the other is a Secondary User (SU). The terminals communicate at 54 Mbps in 802.11g with each other and at 384 kbps in UMTS with BS.

III. REDUCTION OF THE GLOBAL POWER CONSUMPTION

A. Case Comparison

We define the global power consumption as the sum of all terminals' power cost per bit. We compare the global power consumption, in Watt per bit, for the following cases:

1) PU direct : PU and SU communicate directly in UMTS with BS (Fig. 2a). 2) PU active relay : PU communicates in UMTS with BS and acts as a relay. SU's signal is relayed in 802.11g on another UMTS connection establised by PU (Fig. 2b).

3) PU inactive relay : PU is not in communication and acts as a relay. SU's signal is relayed in 802.11g on the UMTS connection established by PU. This case can also represent PU sharing its own connection, via multiplexing or aggregation techniques for example.

B. Channel conditions

The terminals control their transmission power by reducing P O to the minimum value allowing the receiver to decode data properly. The required radio power to transmit a single bit is obtained by integrating P O in (2).

Since, P O depends on the channel conditions, we model the 802.11g and UMTS channels independently. We use an ITU-R office indoor channel model for 802.11g [START_REF]Recommendation ITU-R P.1238-1 : Propagation data and prediction models for the planning of indoor radiocommunication systems and radio local area networks in the frequency range 900 MHz to 100 GHz[END_REF]:

L = 20log 10 (f ) + 30log 10 (d) -28 + L f (n) (3)
with L being the pathloss (in dB), f the carrier frequency (in MHz), d the distance between two terminals (in m), 28 the freespace loss coefficient and L f (n) the floor penetration loss factor with n the number of floors penetrated. Here, L f (n) = 15 + 4(n -1) for n = 2.

We use the following Outdoor-to-Indoor empirical channel model in UMTS [START_REF] Kürner | Prediction of outdoor and outdoor-to-indoor coverage in urban areas at 1.8 GHz[END_REF]:

L in,LOS,K = 32.4 + 20log 10 (f ) + 20log 10 (S + d in ) +L perp + L par (1 - D S ) 2 (4)
with L in,LOS,K the pathloss with line of sight (in dB), f the carrier frequency (in MHz), d in the distance between the terminal and the outdoor (in m), S and D the distances between the base station and the building (in m), respectively in line of sight and parallel to the ground, L perp and L par the wave penetration factors into the building (in dB), respectively for a perpendicular incidence and the line of sight angle. We take L perp = 10dB, L par = 40dB, D S = 0.4, and the mobile terminal inside the building, d in = 10m from the walls.

We apply a Rice fading to both signals, since the terminals are in line of sight. PU moves in straight line from d BS-P U = 800m to SU, fixed at distance d BS-SU = 1, 000m. We compare the global power consumption for all three previous cases on Fig. 3.

C. Mobile relay

When PU and SU are far from each other, PU active relay is more efficient than direct connections. However, when PU is getting closer to SU, relaying becomes more expensive: the power cost per bit of two UMTS connection plus an 802.11g relay is approximately the same as two direct UMTS connections. At that point (30m< d P U -SU < 80m), PU enters a "No-Relay Zone": a zone where relaying has no major gain compared to direct connections. When PU and SU are too close (d P U -SU < 30m), direct connections should to be privileged.

We also notice that PU inactive relay always gives the lowest global power consumption. This behaviour comes from the highest power cost per bit in UMTS: when PU and SU become closer, PU only maintains one UMTS connection and an 802.11g link for the relay. Compared to two UMTS connections at long range, and due to the fact that the power cost per bit is much lower in 802.11g than in UMTS, the global power consumption is minimized when PU shares its UMTS connection. PU and SU move together in straight line from BS to d BS-P U = 1, 000m. We fix d P U -SU = 50m to study the persistence of the "No-Relay Zone", at any distance from BS. The global power consumption is depicted on Fig. 4.

D. Fixed relay

Near BS, PU active relay is not interesting. For 200m< d BS-P U < 300m, the gain is neglectable. Far from BS, direct connections are privileged. Meanwhile, PU inactive relay is always interesting for the same reason as above.

E. Multi-users mobile relay

We now evaluate the gain of relaying N SUs on PU active relay , with PU moving in straight line from d BS-P U = 800m to d BS-SU = 1, 000m on 5. With PU far from SU, the global power consumption of N SUs directly connected in UMTS is approximately the same as PU relaying N + 2 SUs. When PU gets closer to SU, direct connections become more efficient. Moreover, PU inactive relay is always interesting. Based on the previous results, the following rules allow to minimize the global power consumption (Fig. 6).

• Terminals far from BS are relayed by PU closer to BS (Fig. 6 , ). • In the "No-Relay Zone", a terminal relaying has no impact on the global power consumption. Terminals connect directly to BS in UMTS (Fig. 6 ). • When PU and SU are too close from each other, they contact BS directly (Fig. 6 , ). • For multi-users, PU shares its connections when approaching SUs (Fig. 6 ). All other approaches aiming at power reduction only consider the transmission power and forget the numerical power consumption. We have shown how important the numerical power consumption is in multi-mode, and have minimized the global power consumption using multi-mode relay.

By adding mobility, the terminal acting as a PU will relay for a certain period, before entering the "No-Relay Zone". At that moment, PU stops relaying. Later, that terminal can become a new SU and be relayed by a new PU. This way, by reducing a terminal power consumption, we minimize the global power consumption.

V. CONCLUSION AND FUTURE WORK

In this paper, we have shown how to minimize a network global power consumption by using a Software Defined Radio as a multi-mode mobile relay. We have expressed the need to evaluate a terminal power consumption, and have calculated the complexity of two standards and their associated power cost per bit. We have determined the gain provided by such terminal, acting as a multi-mode mobile relay, on the global power consumption. Finally, we have presented different rules to establish a relay in order to reduce the global power consumption.

We will continue to explore this reconfiguration scheme in a multicast streaming network and study the benefits for operators and users at the same time. We will also study the minimization of power consumption with mobile SUs and multiple relays, and evaluate the impact of a realistic MAC layer using network simulation.

Fig. 1 .

 1 Fig. 1. Power cost per bit (W/bit) in (a) 802.11g (b) UMTS. For the radio part, the distance between the emitter and the receiver is 100 m.

Fig. 2 .

 2 Fig. 2. (a) Two terminals are directly connected to an UMTS Base Station (BS). (b) A Secondary User (SU) connects to a Primary User (PU) in 802.11g. The latter establishes a secondary UMTS connection to transmit SU data.

Fig. 3 .

 3 Fig. 3. Global Power Consumption in Watt per bit (Normalized by direct connections) with a Primary User (PU) acting as a mobile relay for a fixed Secondary User (SU).

  BS-PU (m) Normalized Power Consumption (W/bit) Global Power Consumption for PU-SU = 50m (Normalized by direct connections) 802.11g Relay + 2 PU UMTS 802.11g Relay + 1 PU UMTS 2 Direct UMTS Connections

Fig. 4 .

 4 Fig. 4. Global Power Consumption in Watt per bit (Normalized by direct connections) with a Primary User (PU) acting as a fixed relay for a Secondary User (SU) at 50m. PU and SU move away together from the base station. The results for direct connections and PU active relay overlap each other.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Global Power Consumption in Watt per bit (Normalized by direct connections) with a Primary User (PU) acting as a mobile relay for N fixed Secondary User (SU). PU maintains N + 1 UMTS connections with the base station (N SUs and its own).


Ioan Burciu
email: ioan.burciu@insa-lyon.fr

Jacques Verdier
email: jacques.verdier@insa-lyon.fr

Guillaume Villemaud
email: guillaume.villemaud@insa-lyon.fr

Low Power Multistandard Simultaneous Reception Architecture

Keywords: double orthogonal frequency translation, multistandard simultaneous reception, power consumption, complexity

In this paper, we address the architecture of multistandard simultaneous reception receivers and we aim at improving both the complexity and the power consumption of the analog front-end. To this end we propose an architecture using the double orthogonal translation technique in order to multiplex two received signals. A study case concerning the simultaneous reception of 802.11g and UMTS signals is developed in this article.

I. INTRODUCTION

In the wireless telecommunications embedded domain, we can observe a request of multiple functionalities expected from the devices also impacting on the classical constraints of power consumption and complexity. Several new services have appeared such as video streaming and high-speed data transfer. They either use already existing wireless standards or need new dedicated ones. Because of the need for using simultaneously different services and therefore different standards, the transceivers able of processing simultaneously several standards have to be developed.

In this paper we focus on the reception part of a multistandard simultaneous processing transceiver. The present state of the art is using stacked-up dedicated frontends in order to simultaneously receive several standards. One of its major drawbacks is the bad performance-powercomplexity trade-off due to the parallelization of the processing stages.

In order to obtain a better trade-off, we propose a new architecture for multistandard simultaneous reception inspired by the image rejection double IQ architecture [START_REF] Rudell | A 1.9GHz Wide-Band IF Double Conversion CMOS Integrated Receiver for Cordless Telephone Applications[END_REF]. It uses a single front-end capable of multiplexing the two input signals, once separately filtered and amplified, of translating the resulting signal in the baseband domain and then of demultiplexing the two signals in the digital domain.

This paper consists of three parts. Following this introduction, section II describes this novel architecture and shows simulated results of the simultaneous 802.11g/UMTS reception, further details have been already published [START_REF] Burciu | A 802.11g and UMTS Simultaneous Reception Front-End Architecture using a double IQ structure[END_REF]. In section III a comparative power consumption study between the proposed architecture and the state of the art is presented. It consists in a theoretical study using power models for each block [START_REF] Li | A System Level Energy Model and Energy-Quality Evaluation for Integrated Transceiver Front[END_REF] and a state of the art of analogical circuits used by the two architectures [START_REF] Siddiqi | 2.4 GHz RF down-conversion mixers in standard CMOS technology[END_REF]- [START_REF] Arias | Low-Power Pipeline ADC for Wireless LANs[END_REF]. Finally, conclusions of this study are drawn.

II. DOUBLE IQ MULTISTANDARD SIMULTANEOUS RECEPTION

ARCHITECTURE In wireless telecommunications, the integration of IQ baseband translation structures in the receiver chain has become a common procedure. The simple IQ architecture is usually used in the receiver front-end design in order to reduce the bandwidth of baseband signals treated by the ADC.

Meanwhile, the orthogonal frequency translation technique is also used to eliminate the image frequency during the translation steps of heterodyne front-end architectures [START_REF] Rudell | A 1.9GHz Wide-Band IF Double Conversion CMOS Integrated Receiver for Cordless Telephone Applications[END_REF]. The image frequency rejection technique consists in using two orthogonal frequency translations. After the double orthogonal translation, a signal processing block uses the four baseband signals to eliminate the image frequency signal.

This monostandard image rejection architecture relies on the advantage of orthogonalizing the useful signal and the signal occupying its image frequency band. Even though the spectrums of the two signals are completely overlapped after the first frequency translation, this orthogonalization allows the baseband processing to theoretically eliminate the image frequency component while reconstructing the useful one.

This paper assesses the use of the double orthogonal translation technique to develop a multistandard simultaneous reception front-end [START_REF] Burciu | A 802.11g and UMTS Simultaneous Reception Front-End Architecture using a double IQ structure[END_REF]. The main idea is to consider that the signal from the image band becomes another useful signal. The architecture and the spectrum evolution of such a receiver, able of treating simultaneously two standards, are developed in Fig. 1. The parallelization of the input stages of the frontend imposes the use of two dedicated antennas, two dedicated RF band filters and two dedicated LNAs. The gain control stage is realized by the input stages, each LNA being dedicated to the gain control of one of the signals. Once the two signals are well filtered and amplified, an addition of the two outputs is made. The resulting signal is then processed by a double orthogonal translation structure. The frequency of the oscillator used by the first stage is ably chosen in such a manner that each of the two useful signals occupies a spectrum in the image band of the other. This implies a complete overlapping of the spectrums of the two signals in the intermediate frequency domain. After the second orthogonal frequency translation and after the digitalization of the four resulting signals, two parallel processing are implemented, each of them composed of a series of basic operations. Each of them reconstructs one of the two useful signals, while rejecting the other. As a result, the output signals of this final block are the two useful signals translated in baseband.

The choice of the standards used for our study case is WLAN (802.11g) and WCDMA-FDD because of their growing importance. Several simulation of the structure presented in Fig. 1 were performed using the ADS software provided by Agilent Technologies. One of this series of simulations concerns the BER (Bit Error Rate) evolution of the two study case standards when being simultaneously received by a structure using the state of the art front-end stack-up architecture and the proposed double IQ architecture.

In order to achieve a good performance comparison between the multistandard single frond-end receiver and the front-end stack-up, the blocks used during the simulation have the same typical metrics (gain, noise figure, 1 dB compression point, third order interception point) in both cases. As it can be seen from Fig. 2 the performance of the two architectures during the simultaneous reception of the two standards is almost identical. Meanwhile, these simulations do not take into account the orthogonal mismatches of the IQ translation blocks. An additional study concerning this issue has been made and will be presented in an extended version of this paper. The conclusions impose a basic digital algorithm (Least Mean Squares) in order to mitigate the impact of these mismatches on the signal quality. For our study case the results obtained by using this adaptive algorithm show a complete mitigation of the IQ mismatches. In the same time, the same study concludes that the power consumption of this algorithm is not significant compared to that of the whole receiver composed of the analog front-end described here and of the digital signal processing part.

III. POWER AND COMPLEXITY ISSUES

When designing an embedded front-end, the main issues to be considered are the power consumption and the complexity of the structure. Generally these two issues are related: the growing complexity involves the use of spare elements which increases the power consumption. In this paper we propose an innovating architecture which allows the reduction of the analogical front-end power consumption and complexity during a multistandard simultaneous reception. In order to reveal these reductions, this section presents a study comparing the proposed structure to the state of the art of the multiband simultaneous reception architecture -the front-end stack-up.

While evaluating the performances of the proposed structure, it can be seen that it has the same advantages and the same drawbacks as the stack-up structure using two heterodyne front-end. Therefore the comparison will be made between the double IQ structure presented in Fig. 1 and the stacked-up heterodyne dedicated front-end architecture presented in Fig. 3.

The theoretical part of the power comparison study relies on energy models of each type of block used in the two architectures. These energy models are presented in [START_REF] Li | A System Level Energy Model and Energy-Quality Evaluation for Integrated Transceiver Front[END_REF], along with a system level energy evaluation. In order to realize a global evaluation of the power consumption of the two structures, the theoretical study takes into account the state of the art of each block used by the two structures, in terms of performance-power trade-off.

A. Filters

There are several analog filters in the analog part of a receiver. These include the RF band select filter, used to suppress the wideband interference signal, the IF filter, used to suppress the interference signal from the image frequency band, and the baseband low-pass filter, used to suppress inband interference while also helping with the anti-aliasing

B. LNA and Mixers

The power consumption model of the mixers used in the two structures, it is a function of the noise figure NF and the gain K:

NF K k P mixer mixer / ⋅ = . ( 1
)
In the followings we consider that all the mixers used in the two architectures have the same performances constrains in terms of gain and noise figure and therefore have the same power consumption. One of the better suited mixers offering an excellent performance-power trade-off is presented in [START_REF] Siddiqi | 2.4 GHz RF down-conversion mixers in standard CMOS technology[END_REF]. It has a power consumption of 5.6 mW.

The power model of the LNA is similar to that of the mixers as it also depends on the noise figure NF and on the gain A:

NF A k P LNA LNA / ⋅ = . ( 2
)
For our study case the two structures use the same couple of dedicated LNAs. The state of the art show a power consumption of 8.04 mW for the WLAN dedicated LNA [START_REF] Cheng | A 1 V switchable CMOS LNA for 802.11A/B WLAN applications[END_REF] and of 7.2 mW for the UMTS dedicated LNA [START_REF] Alam | A 2 GHz variable gain low noise amplifier in 0.18-µm CMOS[END_REF]. In this study we assume that the power control is performed by the LNAs. This assumption doesn't influence the power study as the LNAs' highest consumption level appears when it operates in the high gain mode.

C. Baseband Amplifier

The baseband amplifier (BA) is used to amplify the signal before conversion. It improves the SNR (Signal to Noise Ratio) of the signal, allowing a better BER. Its power consumption depends on its gain and on its bandwidth:

LNA a BW k P ⋅ ⋅ = (3)
where the k coefficient depends on the device dimensions and other process parameters. a BA is the baseband amplifier gain and is assumed to be a BA = 5. Here we assume that the UMTS dedicated BA consumes 5mW [START_REF] Li | A System Level Energy Model and Energy-Quality Evaluation for Integrated Transceiver Front[END_REF] and the WLAN dedicated BA consumes 10 mW as it has a two times larger bandwidth. For the proposed structure, the BAs are assumed to consume 10 mW.

D. Frequency Synthesizer

Concerning the frequency synthesizer's power consumption, it has a model composed of two separate components: the power consumed by the VCO (Voltage Controlled Oscillator) and that consumed by the PLL (Phase Lock Loop). The consumption of the phase lock loop has a model depending on the reference frequency F ref , on the RF frequency F LO , on the total capacitances C 1 and C 2 loading the RF circuits and on supply voltage V dd :

ref dd LO dd PLL F V C b F V C b P ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ = 2 2 2 2 1 1 (4)
An LC tank-based VCO has a power model depending on the values of the elements of the LC tank R, L, C, on the noise excess factor NEF along with the phase shift where it is measured ∆ω, on the phase noise power spectral density S Φ , on the temperature T and on the Boltzmann constant K:

( ) 2 3 1 ω ∆ ⋅ ⋅ ⋅ ⋅       ⋅ = Φ S T k NEF L R C P VCO (5)
The central frequencies of the state of the art synthesizers used by the two architectures are practically the same, as well as the other metrics. A well suited element is presented in [START_REF] Fu | Fully integrated frequency synthesizer design for wireless network application with digital programmability[END_REF]. It consumes 42 mW for an output frequency between 2.6 GHz and 2.9 GHz and a phase noise of -115dBc/Hz @1MHz.

E. Analog to Digital Converters

The analog to digital converters, along with the number of frequency synthesizers, are the key elements of this power consumption comparative study. In fact, except for the ADC and the baseband amplifiers, all the elements used by the two architectures need to fulfill the same performance constrains.

The power model of the ADCs can be defined by: ( )

) 838 . 4 1525 . 0 ( min 2 1 10 + ⋅ - + ⋅ ⋅ = N signal sample dd ADC f f L V P (6)
where N 1 is the resolution of the A/D converter and L min is the minimum channel length of the used CMOS technology. For our study case, the f sample for the UMTS is the same as that of the WLAN, even if the signal has a bandwidth two times smaller, because of the over-sampling that has to be done for this standard. Concerning the ADCs used by the proposed structure, the sampling frequency is equal to that of the WLAN dedicated ADC as the bandwidths of the signals to be digitized in the two cases are equal.

In a receiving front-end architecture, the ADCs' resolution requests depend on several metrics such as the performances offered by the power control stage, but also on the PAPR (Peak to Average Power Ratio) of the signal to be digitized. While the power control stage is the same for the two architectures, we have to evaluate the PAPR evolution when adding an UMTS and a WLAN signal. A theoretical and simulation study was separately done and it reveals a worse case scenario where the final signal's PAPR increases of only 2 dB compared to that on the WLAN input signal. Therefore, while comparing the two structures and for the same power control performances (dedicated LNAs), we considered that the resolution of the ADC used by the proposed architecture is the same as that used in the WLAN dedicated front-end in the stacked-up front-end architecture.

The performance-power trade-off state of the art of ADC dedicated to the UMTS and WLAN are presented in [START_REF] Farahani | A low power multi-standard sigma-delta ADC for WCDMA/GSM/Bluetooth applications[END_REF] and respectively in [START_REF] Arias | Low-Power Pipeline ADC for Wireless LANs[END_REF]. Their power consumption is of 11 mW and 12 mW.

F. Overall power and complexity evaluation

In order to make a comparative overall power consumption evaluation between the two architectures, a complexity study has to be made in order to evaluate the number of elements that have to be used for each structure. Table 1 summaries the elements used by each of the two architectures, as well as their individual power consumption along with their supply voltage.

As shown here, the proposed architecture needs less components than the state of the art front-end stack-up as it doesn't need image rejection filters and it uses less frequency synthesizers. Therefore, the complexity comparison is favorable to the proposed structure, especially because the image rejection filters are not on-chip integrated elements.

For our study case and for the power consumption levels in Table 1 the overall power consumption comparison shows that the proposed structure consumes 216 mW while the state of the art architecture uses 284 mW. This means a 20 % of gain in favor of the single front-end structure assessed in this paper. In order to better understand this power gain, Fig. 4 shows the power consumed by every type of block used by the two architectures. This power gain comes essentially from the use of two times less frequency synthesisers, while using the same number of other components.

IV. CONCLUSIONS

In this article, a novel multistandard simultaneous reception architecture was presented. Expected performance of its implementation has been presented for a particular study case -simultaneous reception of two signals using the 802.11g and UMTS standards. The signal processed by the analog part of the receiver presents an excellent spectral efficiency as the two standards spectrums are overlapped after the first IQ stage. Compared to the state of the art represented by the stack-up dedicated front-ends structure, the proposed architecture offers a much better performance-complexity-power trade-off. In fact it is less complex as it uses less electronic blocks (external image rejection filters and frequency synthesizers) for the same performance. In addition to the reduced complexity, the overall power study shows a 20% power gain.

Fig. 3

 3 Fig. 3 State of the art of simultaneous reception -Stacked-up heterodyne dedicated front-end architecture.

Fig. 1 Fig. 2

 12 Fig. 1 High complementary standard rejection multistandard simultaneous reception architecture.

Fig. 4

 4 Fig. 4 Consumption of the different block types used by the two architectures.

ACKNOWLEDGMENT

The authors wish to acknowledge the assistance and support of the Orange Labs Grenoble.


EROI

Energy as a limiting factor of economic growth: the profit rate channel

Alban Pellegris -Working Paper

Introduction

Neoclassical economists do not consider energy as an important driver of economic growth. In their perspective, economic growth comes from the accumulation of different capitals: technical capital, human capital, technological capital or public capital. Energy resources are also a capital: they belong to the so called natural capital. However, this capital is not specific so that, in the long run, it appears to be substitutable by other capitals [START_REF] Solow | The Economics of Resources or the Resources of Economics[END_REF][START_REF] Stiglitz | Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths[END_REF].

Ecological economists have vigorously opposed these views in many ways. Two major contribution are the neo-thermodynamic theory of growth developed by Robert Ayres and Benjamin Warr [START_REF] Ayres | The economic growth engine: how energy and work drive material prosperity[END_REF] and the biophysical approach developed by [START_REF] Cleveland | Energy and the U.S. Economy: A Biophysical Perspective[END_REF][START_REF] Husson | Relating Financial and Energy Return on Investment[END_REF].

For Ayres and Warr and their followers [START_REF] Santos | Useful Exergy Is Key in Obtaining Plausible Aggregate Production Functions and Recognizing the Role of Energy in Economic Growth: Portugal 1960-2009[END_REF], the measurement of energy from useful exergy allows the Solow residual to disappear. Thus energy would explain most of the 20 th century economic growth. However, the fragility of this approach lies precisely in the analytical framework in which it is situated. It falls under the same post-Keynesian criticism formulated during the Cambridge controversy towards Agregate Production Function [START_REF] Felipe | The Aggregate Production Function: 'Not Even Wrong[END_REF][START_REF] Robinson | The Production Function and the Theory of Capital[END_REF][START_REF] Sraffa | Production of commodities by means of commodities: prelude to a critique of economic theory[END_REF]. In other words, the physical and monetary dimensions of production are not distinguished but rather confused [START_REF] Hornborg | Ecological economics, Marxism, and technological progress: Some explorations of the conceptual foundations of theories of ecologically unequal exchange[END_REF][START_REF] Pellegris | Le découplage entre la consommation d'énergie et le PIB : questionnements théoriques et évaluations empiriques du rôle de l'énergie dans le processus de croissance économique. Pirgmaier, E[END_REF].

Faced with these limitations, the biophysical approach may appear more robust. According to these authors, economic development depends on the energy surplus, which directly rely on the EROI. To prove this, they establish a relationship between the EROI, the price of energy, the energy bill and thus the GDP. The mechanism can be summarized in the following figure: According to these economists, the EROI determines the price of energy [START_REF] Heun | Energy return on (energy) invested (EROI), oil prices, and energy transitions[END_REF] while the price of energy would, for a given energy intensity of GDP, affect the weight of the energy bill1 . Finally, an increasing energy bill would subtract sums used for consumption or investment and reduce the rate of economic growth [START_REF] Bashmakov | Three laws of energy transitions[END_REF][START_REF] Fizaine | Energy expenditure, economic growth, and the minimum EROI of society[END_REF][START_REF] Murphy | Energy return on investment, peak oil, and the end of economic growth: EROI, peak oil, and the end of economic growth[END_REF]. For example, in the US case, [START_REF] Fizaine | Energy expenditure, economic growth, and the minimum EROI of society[END_REF] estimate that the maximum bill to expect positive economic growth is 11%, which would correspond to an EROI of 11:1. However, this litterature has two limitations. Firstly, this work is (implicitly) based on the energy theory of value [START_REF] Costanza | Embodied Energy and Economic Valuation[END_REF][START_REF] Farber | Economic and ecological concepts for valuing ecosystem services[END_REF]. Although not always explicitly claimed (Pirgmaier, 2021), the EROI does correspond to the energy embodied in energy production. Yet this theory of value has been criticised for its substantialism and reductionism [START_REF] Hornborg | Ecological economics, Marxism, and technological progress: Some explorations of the conceptual foundations of theories of ecologically unequal exchange[END_REF].

Secondly, this work is questionable in terms of the method used. While the channel identified is a demand channel (the weight of the bill affects consumption and investment), the model used by Court and Fizaine (2016) take capital and labour, two supply variables, as the control variables. The model used does not therefore allow for a proper test of the hypothesis, which weakens the significance of the results.

In this paper, we argue that these difficulties can be overcome by turning to another paradigm: Marxist political economy. Thus, this paper can be understood as part of a collective movement to restore the Marxist perspective within the ecological economics [START_REF] Burkett | Marx's reproduction schemes and the environment[END_REF][START_REF] Foster | Ecological Economics and Classical Marxism: The "Podolinsky Business[END_REF]Pirgmaier, 2021). To show this we proceed in three steps. Section 2 shows that the Marxist framework allows us to theoretically identify a profit rate channel through which energy exerts a limiting character on the growth process. Sections 3 and 4 propose an empirical evaluation of this channel: section 3 presents our method while section 4 presents and discusses the results. Section 5 concludes.

The theoretical existence of a profit rate channel

Three elements structure the Marxist framework: (1) the adherence to the labour theory of value (2) the importance of the rate of profit in the economic dynamic, especially (3) the equalization of profit rate among industries. Let us see how these concepts are articulated to think about the limiting character of energy on the growth process.

The labor theory of value

Summarized briefly, the labour theory of value considers that the relative prices of goods are given by the quantities of labour (direct and indirect) that the goods incorporate. This theory therefore makes room for natural constraints: the more difficult goods are to produce, the higher the relative price will tend to be. From this point of view, the labour embodied in the production of energy is therefore a possible alternative to the EROI (embodied energy) to account for the price of energy.

Contrary to the energy theory of value, the labor theory of value is still discussed and some recent work have shown its relevance [START_REF] Cockshott | Testing Marx: Some new results from UK data[END_REF][START_REF] Cockshott | Robust correlations between prices and labour values: a comment[END_REF][START_REF] Tsoulfidis | Price-value deviations: further evidence from input-output data of Japan[END_REF][START_REF] Wright | Marx's transformation problem and Pasinetti's vertically integrated subsystems[END_REF][START_REF] Zachariah | value and equalisation of profit rates: a multi-country study[END_REF] to analyze relative prices dynamics.

The rate of profit

The rate of profit is a fundamental variable that determines the rate of accumulation, i.e. the rate of growth. Marx analyses the rate of profit as the ratio between two variables:  the rate of exploitation, which relates the amount of profits (P) to the wage bill (W)  the organic composition of capital (OCC), which relates the value of constant capital (that is machines and raw materials, C) to the value of variable capital (that is the value of the worforce, W).

𝑃𝑟𝑜𝑓𝑖𝑡 𝑅𝑎𝑡𝑒 = 𝑃 𝑊 𝐶 𝑊 + 1
The organic composition of capital is not a purely technical indicator, as prices will influence this ratio. Nevertheless, there is a technical component that Marx calls the technical composition of capital (TCC) which relates the quantity of machines (c) to the quantity of workers (L).

𝑇𝐶𝐶 = 𝑐 𝐿

If we add to the analysis, pc the unit price of capital and w the individual wage, the OCC can be expressed by the following equation:

𝑂𝐶𝐶 = 𝑐 𝐿 * 𝑝𝑐 𝑤 𝑂𝐶𝐶 = 𝑇𝐶𝐶 * 𝑝𝑐 𝑤
Thus, because it is a component of constant capital, when the price of energy increases, all else being equal, the price of constant capital (pc) increases. The organic composition increases, especially in the sectors where the technical composition (CTC) is the highest.

The equalization of profit rates among industries

This has two consequences: the most capital-intensive branches experience a fall in their profit rate, which drives the average profit rate of the economy down. However, this situation is not sustainable: in order for the capitalists in these industries to continue to produce, a change in relative prices must take place, otherwise they would have an interest in investing in industries with a less capital-intensive technical composition, as the rate of profit is currently higher there. Through this mechanism of capital reallocation, producing relative price movements, profit rates tend to equalize among industries. At the end of this process, all industries, whether intensive or not, gradually tend to align themselves with the new et lower (average) macroeconomic profit rate. The fall in the macroeconomic rate of profit is thus spread and borne by all branches of production

Methods

In order to test the existence of the profit channel, we develops an econometric analysis of the relationship between the relative price of energy and the profit rate based on a panel of 16 countries over the period 1995-2019. Our starting hypothesis is that there is a significant and negative relationship between the relative price of energy and the profit rate of an economy.

Variables

We retain four variables to carry out this econometric work: a dependent variable that we seek to explain, the profit rate, and three explanatory variables. Among these three variables, we find, first of all, the relative price of energy, which is the variable of interest to us and whose influence on the profit rate we are trying to understand. To this variable, we have added two control variables, which are highly likely to influence the rate of profit according to the Marxist perspective mentioned above: the exploitation rate and the technical composition of capital. First, the exploitation rate, since this is the numerator of the rate of profit formula (see above). A fall in the rate of profit can be compensated by an increase in the exploitation of workers, that is, in the share of value added accruing to capitalists. This is one of the counter-tendencies identified by Marx to the tendency of the rate of profit to fall (Marx, Cohen-Solal and Badia, 1959). Second, the technical composition is also important as suggested in section 2: the effect of the energy price on the profit rate depend on how capital intensive is the industry or the country under study.

Data

All the data come from the OCDE database. Following the example of other Marxist works [START_REF] Basu | Quantitative empirical research in marxist political economy: a selective review[END_REF], the rate of profit series were obtained by relating the net operating surplus to the net value of capital. For the relative price of energy, we relate the energy price index to the consumer price index. When the energy price increases faster than the consumer index, the relative price of energy increases. For the exploitation rate, we relate the net operating surplus to the payroll.

The main innovation in terms of indicators relates to the technical composition of capital. Following [START_REF] Giampietro | The Metabolic Pattern of Societies: Where Economists Fall Short[END_REF], we considere that the capital intensity of an industry can be observed from the energetic metabolic rate (EMR) which relates the quantity of (primary) energy to the hours of work mobilized. Such a ratio offers the advantage to be truly technical in the sense that it does not rely on monetary aggregates but only on physical aggregates.

Linear regressions and estimators

Once the data are computed, we test the stationarity of our variables (see appendix 6.1.) before running multivariate linear regressions. We first run different models in order to confirm the number of explanatory variables to use (table 1). The result of these four pool OLS confirm the relevance of model D with all three explanatory variables (table 2). In a second step, we consider four econometric regressions that complement the last one (Pool OLS) that we have just presented. These new regressions allow us to confirm the robustness of our approach, as do Carpenter and [START_REF] Guariglia | Cash flow, investment, and investment opportunities : new tests using UK Panel data[END_REF]for an estimation of fixed capital accumulation on panel data. In the end, we report in Table 3 the following 5 regressions for our tri-variate equation:

1-A pool model with an OLS estimator (Pool Ordinary Least Square) where all our data are treated as a single geographic set. This model has already been estimated since it is the result of equation D, a model that will be called "Pool" in the following. 2-A country fixed effect model with within estimator ("Country" model) where the regression is conducted for each of the 16 countries. A fixed effect model means that "the difference between individuals can be captured by the constant" (Greene et al., 2011, p.345). Here, the estimated model will therefore have a different constant for each of the 16 countries. 3-A time fixed effect model with OLS estimator ("time" model) where the regression is conducted for each year. Example: we compile all the data from all the countries for the year 1995 and we look at the relationship that emerges. Unlike the previous model, there is not a constant for each country but for each year selected. 4-A model with country and time fixed effects with OLS estimator ("two effects" model) which combines the two previous models since we control here both the country and the year. 5-A random model with a random estimator: like a fixed-effect model, a random model will consider that being in country A, rather than in country B, will affect the relationship between profit and energy price. However, unlike the fixed-effect model, the random-effect model considers that it is possible for countries to respond differently to a change in energy price. In statistical terms, the relationship is not just affected by a different constant. We can first note that, with the exception of the "two-effects" model, whatever the model chosen, our variables are all significant. For all these other models, our independent variables are not only significant, but above all the coefficients are compatible with our hypotheses:  The increase in the price of energy tends to negatively affect the profit rate ("country," "time,"

Results

Results of multivariate regressions

"random" and "pool" models)  The exploitation rate tends to affect the profit rate positively (all models)  The increase in the technical composition of capital tends to affect the rate of profit negatively ("pool" and "time" models) or positively ("random", "country", and "two effects" models)

To choose between these different models, we run several tests (see appendix 6.2.). First, we distinguish a pool OLS pool from a country fixed effect model. In our case, it seems reasonable to consider a country fixed effect. Indeed, we can estimate that there are unobservable variables, specific to each of the countries studied. For example, some countries have a particular position in the value chain that allows for a higher profit rate than elsewhere, as the analysis of profit rates has revealed. The use of a Fisher test confirms this intuition and highlights significant effects linked to heterogeneity between countries.

We then determine whether a country fixed effect model should be preferred to a random effect model. To do this, we perform a Haussman test. With a p value < 0.05, this test leads us to prefer the fixed effect model. Finally, we need to decide whether the country fixed effects should be combined with a year fixed effect ("two way fixed" model). Here again, there is a test to guide us: the Lagrange multiplier test for time effect (Breusch-Pagan) for cylindrical panels. With a p-value > 0.05, this test leads us to prefer the model with only a country fixed effect. Finally, a last comparison must be made: that between a model with time fixed effects and a model with country fixed effects. The Fisher test allows us to decide in favor of the country fixed effects model. Finally, we test different characteristics that can modify the robustness of the selected model. Our data exhibits heteroskedaticity, serial correlation and cross sectional dependence (see appendix 6.3.). According to [START_REF] Baltagi | Econometric Analysis of Panel Data[END_REF], autocorrelation and cross-sectional dependence can be problematic for macroeconomic panels with large time series (beyond 20 to 30 years). Since our study covers a 24year period and our data are macroeconomic, we consider a procedure to take care of their presence. Heteroscedasticity also makes the estimates provided by the least squares method questionable (our various estimators are all derived from this method). The econometric literature suggests two different ways to take into account the behavior of model errors.

The first solution consists in keeping a model using the least squares method (Ordinary Least Square) but with robust standard errors [START_REF] Bai | Feasible Generalized Least Squares for Panel Data with Crosssectional and Serial Correlations[END_REF]. In the case where heteroscedasticity, autocorrelation and dependence between sections are present, [START_REF] Hoechle | Robust Standard Errors for Panel Regressions with Cross-Sectional Dependence[END_REF] recommends using the Driscoll-Kraay estimator.

The second solution proposed by [START_REF] Bai | Feasible Generalized Least Squares for Panel Data with Crosssectional and Serial Correlations[END_REF] is to use an FGLS (Feasible Generalized Least Square) model when the number of years T is greater than the number of individuals N, which corresponds to our situation (T= 25 and N=16). This type of model allows estimation in the presence of autocorrelation, dependence between sections within the panel and heteroscedasticity across the panel.

Interpretation

The estimation of the two models is consistent with our hypotheses. The relative price of energy appears to be negatively correlated with the profit rate. The coefficient is -3.4. This means that when the relative energy price index increases by one unit, then the profit rate decreases by 3.4 percentage points. The interpretation of one unit of relative price is not immediately obvious. To understand it, we need to recall the values of relative prices: the relative price of energy ranges from about 0.75 to 1.10, between 1995 and 2019, for all countries combined. The change in the relative price of energy over the period is therefore less than one unit. The increase of one unit represents, in the case of a relative price of 0.75, an increase of 130%. Over the period studied, the energy price index increased by only 0.35 units, or about 46%. If we accept a rough calculation, it turns out that the increase in the relative price of energy would have cost 0.46*3.4 = 1.19 points of profit rate between 1995 and 2019. The effect therefore appears to be substantial over the period.

We can say that this empirical work largely validates the hypotheses formulated by the Marxist analytical framework. The latter thus appears heuristic in order to understand the way in which energy, an indispensable use value in the economy, exerts its effects on the dynamics of growth. In particular, we highlight a profit rate channel that, until now, seems to have been neglected by the literature in ecological economics which prefers the weight of the energy bill. Controlling for the exploitation rate and technical composition of capital, the effect of the relative price of energy is significant on the rate of profit, confirming the hypothesis of an action through the organic composition of capital.

Energy bill as part of the profit rate channel

It is possible to put this opposition between the rate of profit and the weight of the energy bill into perspective. Indeed, if we examine the formula of the weight of the energy bill in GDP, it is possible by rearranging the equation to include the variables we have used in our regression. The profit rate channel exhibits two control variables that are part of the definition of the energy bill. This could explain why, in the case of France, Marxist authors like [START_REF] Husson | Relating Financial and Energy Return on Investment[END_REF] observe a high correlation between the energy bill and the profit rate (fig. 3). It also confirms that the energy bill can be used in a supply channel (the profit rate channel) rather than a demand channel (as suggested by the biophysical approach).

Concluding remarks

In this article, we have shown the heuristic character of the Marxist framework to show how energy acts as a limiting factor in the growth process. This framework makes it possible to identify a supply channel, the rate of profit channel, which appears more robust than a demand channel, the energy bill channel, highlighted by the authors of the biophysical approach. Indeed, the statistical work conducted on data from a panel of 16 OECD countries confirms the existence of this channel over the period 1995-2019. In contrast to the work of the biophysical approach, the control variables used are consistent with the hypothesis tested. Moreover, the reformulation of the energy bill (as a product of three factors: the relative price of energy, the technical composition and real labor productivity), suggests that the energy bill can also be interpreted in the context of a supply channel.

An interesting extension of this work would be to compare the results in terms of labor embodied in energy production with those in terms of energy embodied in energy production (EROI).

Heteroskedaticity, auto-correlation and cross sectionnal dependance

Objectif

Fig 1 .

 1 Fig 1. Energy surplus as a limiting factor to economic growthSource: author

Figure 2

 2 Figure2summarize what we call the profit rate channel:

  bill/GDP nGDP : nominal GDP ; rGDP : real GDP Pe : energy price; P : price; Pe/P : energy relative price Qe : energy quantity; h : hours worked ; Qe/h : technical composition of capital rGDP/h : real productivity of labor

Fig. 3

 3 Fig.3 Energy bill (as % of GDP) and the profit rate, France (1949-2006). Taux de profit = profit rate; consommation d'énergie en valeur (% du PIB) = energy bill (% of GDP) Source : Husson 2009

Table 1 .

 1 Different equations estimatedWith α, a constant ; β1, β2 et β3 coefficients of the explanatory variables explicatives and ε the error term. PR_NRJ = relative price of energy; Expl = exploitation rate; TCC = technical composition of capital. Source : auteur

	Model	Equation
	A	𝑃𝑟𝑜𝑓𝑖𝑡𝑅𝑎𝑡𝑒 = 𝛼 + 𝛽1𝑃𝑅 𝑁𝑅𝐽 + 𝜀
	B	𝑃𝑟𝑜𝑓𝑖𝑡𝑅𝑎𝑡𝑒 = 𝛼 + 𝛽1𝑃𝑅 𝑁𝑅𝐽 + 𝛽2𝐸𝑥𝑝𝑙 + 𝜀
	C	𝑃𝑟𝑜𝑓𝑖𝑡𝑅𝑎𝑡𝑒 = 𝛼 + 𝛽1𝑃𝑅 𝑁𝑅𝐽 + 𝛽2𝑇𝐶𝐶 + 𝜀
	D	𝑃𝑟𝑜𝑓𝑖𝑡𝑅𝑎𝑡𝑒 = 𝛼 + 𝛽1𝑃𝑅 𝑁𝑅𝐽 + 𝛽2𝐸𝑥𝑝𝑙 + 𝛽3𝑇𝐶𝐶 + 𝜀
		Modèles

Table 2 . Pool OLS with the different explanatory variables.

 2

Source : auteur.

Table 3 . Results of multivariate regression of the rate of profit on the relative price of energy, the operating rate and the technical composition of capital.

 3

	Models

Table 4 . Results of 3 models : fixed effect, Discroll & Kray and FGLS.

 4 It is clear that taking into account autocorrelation, heteroscedasticity and dependence between sections does not change our results. Both methods (Discroll & Kray and FGLS) give us significant coefficients (table 4)

			Models
		« Country »	« Discroll &	« FGLS »
			Kray »
	Relative price of energy	-3.4 ***	-3.4*	-3.4***
	Exploitation rate	0.09 ***	0.09*	0.09***
	Technical composition of	0.21***	0.21***	0.21***
	capital
	R²	0.50	0.50	0.39
	Adj. R²	0.48	0.48
	Number of observations	400	400	400
		*** p < 0.001 ; ** p<0.01 ; * p<0.05
		Source : author

Table . 7 Testing for heteroscedasticity, autocorrelation and cross-sectional dependence.

 .

		Test	H0	Result	Interpretation
	Heteroskedaticity	Breush-	Homoskedaticity	88.522***	Heteroskedaticity
		Pagan		(BP)
	Auto-correlation	Breush-	No auto-	264,89***	Auto-correlation
		Goodfrey-	corrélation	(chisq)
		Woolridge
	Cross-sectionnal	Breush-	No dependance	586,4***	Cross-sectionnal
	dependance	Pagan LM		(chisq)	dependance
	Cross-sectionnal	Pesaran CD	No dependance	5,544***	Cross-sectionnal
	dependance			(z)	dependance
			*** p < 0.01 ; ** p<0.05 ; * p<0.1

Source : author

Indeed, the energy bill in relation to GDP can be expressed as the product of the energy price (p) and the energy intensity (E/GDP). Energy bill/GDP = p * E/GDP

Energy price Energy bill/GDP

GDP growth

Appendix

Unit root tests


P F Morlat

A Luna

X Gallon

G Villemaud

J M Gorce

Structure and Implementation of a SIMO Multi-Standard Multichannel SDR Receiver

Keywords: SIMO processing, WLAN standard, SDR receiver, multi-channel multi-standard receiver

This article presents the structure of a multiantenna multi-channel and multi-standard receiver based on Software Defined Radio (SDR) concept. At this time our work is focused on 802.11g and 802.11b signals cohabiting in a 40 MHz frequency bandwidth around the 2.4 GHz RF carrier frequency. Using classical Single Input Multiple Output (SIMO) processing, these incoming signals are combined to increase transmission performances and to mitigate fading effect. Simulated and measured results of our structure are given and a description of the real proposed architecture is detailed.

I. INTRODUCTION

The future of wireless communications can be view as numerous standards operating together. Reconfigurable receiver is an important feature in the solution of providing interoperability of transceivers in a number of different wireless systems. The ideal universal receiver sampling the incoming signals just after a RF stage is very seducing but not realistic at this time due to limitations in sampling capabilities for high frequency systems. In this context, Software-defined radio (SDR) [START_REF] Mitola | The software radio architecture[END_REF][START_REF] Rhiemeir | Modular Software-Defined Radio[END_REF] principles have attracted more and more attention. We can then imagine reconfigurable receiver able to deal with predefined transmission standards. An important number of contributions on SDR can be found in the literature and several key-items of different aspects of the signal processing chain are discussed: sample rate adaptation [START_REF] Brandolini | Toward Multistandard Mobile Terminals-Fully integrated Receivers requirements and architectures[END_REF], RF front end design [START_REF] Hentschel | Sample Rate conversion for software radio[END_REF] as example, and several SDR test bed platforms are described [START_REF] Miranda | A self reconfigurable receiver architecture for software radio systems[END_REF][START_REF] Xu | Analysis and implementation of software defined Radio receiver platform[END_REF].

Our work combines several attractive and relevant principles in order to increase data rate, quality of service and flexibility in the same architecture. First of all, based on SDR concept we propose a multi-standard approach. Indeed, the receiver we describe is able to deal with WLAN 802.11g and 802.11b standards. In this way, each technology will no longer relies on a particular chip, but on a software package, allowing dynamical changes and also parallel decoding. Then a particular attention should be paid on calculation resources, assuming a maximum reuse of basic functions for all standards (FFT, filtering) and a precise dimensioning to achieve real time operations.

Moreover, it is well known that multiplying antennas, even from the only receiver point of view offers a high potential to compensate radio channel fading and interference. That is why 4 receiving antennas are used by our receiver. Several copies of the same emitted signal are available and using SIMO processing a great benefit could be taken from spatial diversity, especially in large angular spread configuration which corresponds to the working environment of WLAN transmissions. At this time SIMO algorithms we use are based on the classical and well known Minimum Mean Square Error (MMSE) criterion; because of its low complexity and its good adaptation to WLAN transmissions using training sequences at the beginning of each frame. But depending on the treated signal and the propagation channel, different alternatives of the same algorithm are used in order to have the better trade off complexity -performances increasing for each WLAN standard. [START_REF] Morlat | Performance Validation of a multi-standard and multiantenna receiver[END_REF] describes classical SIMO processing we use, applied in the case of 802.11g and 802.11b transmissions.

Another particularity of the proposed structure is the multi-channel approach. Classical receivers, after selection of its allowed channel for communication, operate a frequency tuning in its RF part to only filter this chosen band, naturally operating an adjacent channel rejection. 802.11 transmission based on 84 MHz large band shared between up to 14 overlapping 20 MHz channels is a very relevant example of this phenomena. That is why designing a receiver sampling a 40 MHz bandwidth instead of a bandwidth corresponding to only one communication channel seems to be interesting. This allows taking advantage of larger numerical information of the desired signal together with interferes. Then different techniques of interference mitigation, channel rejection [START_REF] Mary | Performance Analysis of Mitigated Asynchronous Spectrally-Overlapping WLAN Interfernce[END_REF], or parallel decoding can be involved.

All of those multi-* approaches are combining in the same test platform composed by antenna and RF frontend, numerical processing stage with DSP and FPGA, and a PC to combine received signals thanks SIMO processing and compute transmission BER. This article is structured as follow: first part describes results obtained by simulation and measure using software demonstrator developed with ADS from Agilent Technologies [9] in different working conditions. Then, the second part presents the structure developed platform.

II. SIMO MULTI-STANDARD MULTI-CHANNEL RECEIVER PERFORMANCES

As presented before, combining multi-antenna, multichannel and multi-standard principles in the same receiver seem to be a very promising issue to increase wireless transmission performances. However, several parameters like antenna coupling, channel correlation and also propagation channel properties have an important influence on SIMO performances [START_REF] Dietze | Analysis of a two-ranches maximal ratio and selection diversity system with unequal SNRs and correlated inputs for a Rayleigh fading Channel[END_REF]. That is why a software demonstrator simulating the running of a 4 antennas receiver and able to deal with 802.11g/b signals in a 40 MHz bandwidth was developed using ADS software. Different SIMO algorithms, configurations of running (space between two interest communication channels), and propagation channel characteristics could be chosen to have a better estimation of the performances of our system in realistic working conditions. Moreover, thanks the compatibility with Agilent equipment, a complete multi-antenna (2x2) test bed radio platform was installed in order to rapidly test and evaluate performances of any stage of wireless transmission [START_REF] Morlat | Global System evaluation scheme for multiple antennas adaptive receivers[END_REF]. Due to the current capacity of our platform, it is possible to record only 2 incoming signals simultaneous. However it is sufficient to introduce channel correlation and antenna coupling in our measure. That is why, even if the developed demonstrator is able to run with 4 receiving antennas, only 1x2 SIMO performances are presented. 1 gives measured and simulated performances of an 11 Mbps 802.11b transmission in different working conditions. Firstly a very good match between AWGN theoretical, simulated, and measured Bit Error Rate (BER) curves is observed. Furthermore, about 5 dB of gain could be also observe in the case of a transmission under a fast fading multi-path propagation channel between the single antenna receiver and the 2 antennas structure using SIMO processing to combine received signals.

Finally, table 1 presents BER values in the case of the terminal is dealing with two recorded signals of each standard after propagation under a measured AWGN channel. Both signals are emitted to a sufficient level to guaranty no transmission error in the case of a mono standard communication. As it could be expected, the more channels are spaced, the better are transmission performances. With these results, we can observe a great performances increasing using a 1x2 SIMO architecture even if only spatial diversity processing are used. On the other hand, in the case of two channels are 25% overlapped (channel spacing of 15 MHz), no transmission error is obtained, even if a single antenna receiver is used.

III. THE SDR RECEIVER STRUCTURE

This parts describes different operating stage we develop in order to treat RF incoming signals to the BER of the transmission computation.

A. RF stage

A 2 patches antenna spaced by a distance of 6 cm and providing each 2 channels of orthogonal polarization is used. So, we have 4 incoming signals to treat. This antenna is designed for 2.4 GHz transmissions, and connected to the RF stage which allows the down conversion, and also an 80 MHz sampling and a 10 bits coding of the complex signal. Mo/s connection is possible. However, rate of the incoming data from the RF stage to the FPGA, due to the sampling and the bit coding is 800 Mo/s. An important data rate decreasing must be applied in the FPGA. Part D will describe functions of different numerical processing components. At the end, each DSP is connected to a 600 Mo/s internal bus to access to SDRAM, Flash Memory and also the PCI gateway. Finally, the coding rate used with this TS-C43 board is 8 bits.

B. Numerical Processing

C. PC connection

Thanks the 528 Mo/s PCI connection, numerical data are send to a dual-processor 3 GHz PC with a 4 Go RAM running Linux. The PC is used to combine the 4 numerical channels using different SIMO processing, and also to demodulate signals in order to compute BER of the transmission. At this stage of treatment, real time processing is not a really important parameter. Let us now list the most important functions used in the numerical processing stage.

D. Numerical functions

Each TS-C43 board has to deal with 2 reception channels. Remembering that our receiver must be able to deal with 2 802.11 communications at the same time, one DSP has to permit the global signal processing for 1 incoming signal.

The major aim of the FPGA is to ensure an important data rate decreasing to make transmission to DSP possible. That is why the FPGA has to detect signal presence in the 40 MHz bandwidth of interest, detect the WLAN channel (carrier frequency) used and apply a 11 MHz filter around this carrier frequency on both complex channels (I and Q), which corresponds to a 22 MHz channel bandwidth. That way, the data rate is 44 Mo/s and there is no problem for transmission to the DSP.

After a standard characterization and an adapted sampling according to the detected standard, numerical processing is applied to the signal. Fig. 3. Description of numerical functions Fig. 3 describes the different numerical functions implemented on each one of eight DSP. The Channel Impulse Response (CIR) for 802.11g transmissions is computed in frequency domain by the PC, before SIMO processing. In the case of 802.11b transmission, barker dispreading is applied after the optimal SIMO coefficients computation. Thanks the several algorithms implemented, the data rate in the PCI transmission to PC is sufficient low.

At this time 802.11b and 802.11g processing have been tested with Matlab and implemented and tested with VC++ software. 802.11b receiver architecture is implemented on DSP and validated, but a lot work taking into account real time constraint has to be done. SDR concept combined with SIMO processing and multi-channel approach is a very promising issue to develop future wireless terminals ensuring robust and flexible transmissions. The aim of this work is to propose a SDR receiver architecture including these different approaches. RF properties, real time digital processing and also global system considerations have to be taken into account in order to propose a suitable architecture. Even if the SDR terminal structure and the role of different equipments of our platform depending on their computing capacities, are well defined at this time, a lot of work on the DSP implementation optimization has to be done in order to permit a real time processing.

Fig. 1 .

 1 Fig. 1. BER vs. Eb/No for 802.11b transmission

  The numerical processing is computed using two TS-C43 PMC from VSystems[12]. Each board (fig.2) comprises 4 clustered TigerSHARC DSP allowing a 300 MHz processing, a Xilinx Virtex-II FPGA and a 528 Mo/s PCI connection.

Fig. 2 .

 2 Fig. 2. The TS-C43 PMC board FPGA and the RF stage are connected together by an external I/O connection of 100 pins, each one allowing a 100 MHz connection. Between FPGA and DSP, a 150Mo/s connection is possible. However, rate of the incoming data from the RF stage to the FPGA, due to the sampling and the bit coding is 800 Mo/s. An important data rate decreasing must be applied in the FPGA. Part D will describe functions of different numerical processing components. At the end, each DSP is connected to a 600 Mo/s internal bus to access to SDRAM, Flash Memory and also the PCI gateway. Finally, the coding rate used with this TS-C43 board is 8 bits.

ACKNOWLEDGEMENT

The authors wish to acknowledge France-Telecom R&D who supports this work.


P F Morlat

X Gallon

G Villemaud

J M Gorce

MEASURED PERFORMANCES OF A SIMO MULTI-STANDARD RECEIVER

Keywords: SIMO processing, measure validation, SDR receiver, WLAN

SIMO algorithms ensure important increasing of radio communications robustness, but their performances strongly depend on channel propagations conditions and antenna characteristics. This article presents performances of different SIMO treatments applied on WLAN (802.11b and 802.11g) transmissions in a multi-standard and multi-channel context. These performances are obtained by measure, under different propagation channels and for realistic working conditions.

Introduction

Combining different standards communication in the same receiver structure, based on concept of Software Defined Radio (SDR) is a very promising issue for future wireless systems [START_REF] Xu | Analysis and implementation of software defined radio receiver platform[END_REF][START_REF] Harada | Software Defined Radio Prototype toward Cognitive Radio Communication Systems[END_REF]. Moreover using SIMO (Single Input Multiple Output) processing improves wireless systems performances. Furthermore, a multi channel receiver seems to be an interesting evolution with the arrival of communication standard defined on overlapping channels, such as 802.11 systems. Thus a software demonstrator simulating the running of a multi-channel multi-standard and multi-antenna receiver was developed using Advanced Design Systems (ADS) from Agilent Technologies [START_REF] Morlat | Performance Validation of a multi-standard and multi-antenna receiver[END_REF]. At this time we focused our study on a 4 arms receiver capable to deal with 802.11g and 802.11b cohabiting signals in a 36 MHz bandwidth. However in order to have a better estimation of SIMO processing performances, an evaluation oh those algorithms in real working conditions is necessary. Indeed, antenna coupling, channel correlation and channel propagation properties have an important influence on those performances. Based on capacities of our 2x2 radio platform using the Agilent connected solution equipments [START_REF] Morlat | Global system evaluation scheme for multiple antennas adaptative receivers[END_REF], our work presents measured performances of a SIMO multi-standard multichannel receiver.

The Measurement procedure 2.1 Description of the platform

A complete test bed platform was installed, using Agilent Technologies equipments and ADS software (Fig. 1). This

Description of the measure

Our aim is to study SIMO performances under realistic working conditions. In this context, antenna coupling, channel correlation, and also different propagation conditions must be introduced in the measurement system. Depending on the current capabilities of our platform only 1x2 SIMO configuration is possible. Correlation of received signals and antenna coupling introduce loss of information diversity, and then a reduction of SIMO performances. Envelope correlation ρ between two signals x and y is compute according to (1) [START_REF] Dietze | Analysis of a two-ranches maximal ratio an selection diversity system with inequal SNRs and correlated Inputs for a Rayleigh Fading Channel[END_REF] [ ] ( ) ( )

2 2 ) ( ) ( ) ( ) ( y y E x x E y y x x E - ⋅ - - ⋅ - = ρ (1)
where E(.) denotes the expected value and

dv v dy y BER N X X v X v         - ⋅                 - - = - ∞ - + - - ∫ ∫ 2 1 2 2 2 exp 2 exp 2 1 1 π (2) Where No Eb X ⋅ = 2
and N=8 in the case of an 11 Mbps transmission. Figure 3 presents BER variation for a 36 Mbps 802.11g transmission under different channel propagation conditions. A very good match between simulated and measured AWGN results can be observed (only 1 dB of deviation, but measures were no realized in anechoic chamber). Simulated performances of the mono-antenna 802.11g receiver for propagation under the ETSI-A channel are also presented. An important deviation (about 4 dB) between these simulated results and BER variation under the measured multi-path channel is observed. That is due to the fact that only two echoes are detected during the characterization of the propagation channel used for measure, while 18 taps model for the ETSI-A channel. Of this fact, it is normal to observe better performances of the channel equalizer for propagation under the measured channel than under the simulated ETSI-A channel. It is important to note that at this time, BER variations are obtained in the case of a static channel and that no fast fading is introduced to validate our platform and measurement system. Introduction of fast fading will be described in the next section.

1x2 SIMO measure

SIMO performances strongly depend on channel correlation, and also antenna coupling [START_REF] Shiu | Fading correlation and its effect on the capacity of MEA systems[END_REF]. That is why studying SIMO processing introducing channel correlation and also antenna coupling is relevant. All of SIMO algorithms used to increase 802.11b and 802.11g transmissions are described in [START_REF] Morlat | Performance Validation of a multi-standard and multi-antenna receiver[END_REF]. Only 1 dB of gain thanks SMI processing is obtained compared to a single antenna receiver dealing with the best signal recorded (switch antenna selection). It is due to the fact that difference of received signals power on both antennas was very important during these measures. However, using SF-MMSE algorithm to combine different incident signals ensure an increasing of system performances of 3 dB. But propagation under static multi-path channel do not really corresponds to realistic working conditions, that is why to have a more precise estimation of our system's performances, it is necessary to introduce fast fading in the measurement procedure. In this context, speed was imposed to the antenna during measurement. In order to choose the maximum imposed speed, we must keep in mind that the propagation channel has to stay constant during the time of one frame. In the demonstrator developed with ADS and running with Ptolemy tool , speed of the terminal is fixed to 10 km/hr, i.e. 2.78 m/s, which results in a maximum Doppler shift of 22 Hz. The Doppler spread and coherence time are inversely proportional to each other, yielding a coherence time of 45 ms. Duration of a 802.11g or 802.11b frame depends on the data rate and also on data size to transmit. In our conditions of work, the longest frames are obtained for 11 Mbps 802.11b transmissions. Packet size of these frames is 100 octets, so the duration of one frame is 290 usec. So, channel could be considered constant. Figure 6 presents BER performances of the single antenna receiver and the 1x2 SIMO receiver running with signals recorded at the same time after propagation under the multipath channel by the moving terminal in the case of a 36 Mbps 802.11g transmission. The SIMO processing used is the SMI, and BER curves of the single antenna receiver were obtained with one of the two recorded signals. Indeed, in this case of measure, signal power level on each arm of the SIMO receiver are quite equivalent. In these conditions of work, estimate Eb/No at the input of the receiver is quite difficult due to the fast variation of the signal power level. That is why BER curves are not so smooth as usual. About 5 dB of gain is observed thanks SMI processing for a BER value of 10 -2 . We also observe an important variation of the curve's slope. The well know result that with SIMO processing under fast fading propagation, BER decreases more quickly than in the case of a single antenna reception is verify.

Multi-standard configuration

Nowadays, with the growth of number of communication standard, users would like to have only one terminal to achieve multiple wireless standards. The most promising technology to achieve such receiver is SDR technology, which allows users to switch communication systems by changing software alone. At this time we focus our study on a system able to run with 802.11g and 802.11b transmission.

Cohabitation between these two standards seems to be relevant to study because they share the same RF carrier and are defined on overlapping channels. In this context, designing a receiver based on SDR concept and sampling a frequency band wider than those of a single communication channel seems to be a relevant study. This allows taking advantage of the knowledge of adjacent channel interferes and to increase transmission performances. [START_REF] Morlat | Global system evaluation scheme for multiple antennas adaptative receivers[END_REF] describes the architecture of the multi standard (802.11b/g) multi channel (40 MHz of bandwidth reception) SDR terminal we propose. This part of the article presents performances of a multistandard multi-channel terminal using 1x2 SIMO processing able to run with two 802.11 signals cohabiting at the same time. SIMO algorithms ensure to combat fading and multipath effect, but we will show that these algorithms also ensure mitigation of interferences. Others adjacent channel cancellation processing exist [START_REF] Suthaharan | Joint interference cancellation and decoding scheme for next generation wireless LAN systems[END_REF]. Performances of these algorithms will be probably studied later.

An important parameter to study the comportment of the multi-channel terminal is the number of communications channels between the two signals of interest.

The first tested configuration is the cohabitation of two 36 Mbps 802.11g emitted throw an AWGN propagation channel on different carrier frequencies. Incoming works are dealing with more analysis and estimation of WLAN performances in a multi-channel configuration. Studies about implementation of more efficient multi-antenna algorithms in order to permit better interferers mitigation could also be interesting.

  platform is made of one arbitrary waveform generator (ESG 4438C) and a vector spectrum analyzer (VSA 89641) with two RF inputs. These equipments are connected to a PC running with the ADS software. With this platform, any signals of a maximum RF frequency of 6 GHz could be generated by ADS and emitted to a real propagation channel. Our platform ensures a reception bandwidth of 40 MHz, that is why it is possible to make cohabit two 20 MHz WLAN signals, emitted on two different carrier frequencies spaced by 20 MHz. The recorded signals are transferred to the software and all of the baseband processing are applied in order to combine the different received signals (SIMO processing) and to demodulate the data.

Figure 1 :

 1 Figure 1: 2x2 MIMO transmission with the radio platform

Figure 3 :

 3 Figure 3: 36 Mbps 802.11g SISO performances

Figure 5 :

 5 Figure 5: 802.11g BER performances

Figure 6 :

 6 Figure 6: 802.11g BER performances

3 Measured performances 3.1 Validation for a SISO configuration

						x =	E	(x	)	.
	Table 1 presents correlation value in function of the antenna
	spacing d (a fraction of wave length λ) in the case of a NLOS
	(Non Line of Sight) transmission configuration. For each
	distance value, we also give the BER (Bit Error Rate) value
	obtained thanks SIMO processing applied to the two recorded
	signals used to compute the correlation.
	d	0.3	0.5	0.75	1	1.25	1.5
	ρ	0.45	0.43	0.02	0.07	0.1	0.12
	BER 0.02	0.03	0.03	0.01	0.02	0.01
	Table 1: Correlation value in function of antenna spacing
	A very low envelope correlation (ρ<0.7) is observed. A quite
	constant BER is also obtained, proving that for all distance
	between the two antennas, correlation has no influence on
	system's performances.
	For different antenna spacing, coupling between the two arms
	is compute and the maximum value, obtained for a distance of
	0.3 λ is equal to -20 dB. That is why, coupling effect between
	receiving antennas could be considered as negligible.
	Finally, characterisation of the propagation channel was
	realized. The measured NLOS channel used has a delay
	spread much less important (about 76 ns, τ rms = 35 ns) than
	the often used channel model ETSI-A for office environment
	(delay spread = 390 ns, τ rms = 50ns) [6].
	At first, in order to validate the structure of our radio
	platform, first tests were realized in a SISO configuration
	under AWGN and multi path propagation. Figure 2 presents
	results we obtained for an 11 Mbps AWGN 802.11b
	transmission.
	1,0E+00
							theoritical BER
	1,0E-01						measured BER simulated BER
	1,0E-02
	BER
	1,0E-03
	1,0E-04
	1,0E-05
		0	2	4	6	8		10	12
				Eb/No -dB

Figure 2: 11 Mbps 802.11b SISO performances

For each Eb/No, 10 000 frames of 100 octets are emitted and demodulated to accurately estimate the corresponding BER. The theoretical 11 Mbps 802.11b BER variation was computed according to (2)

[START_REF] Borgo | Analysis of the hidden terminal effect in multi-rate IEEE 802.11b networks[END_REF]

Table 2

 2

	presents

Table 3 :

 3 multi-standards multi-channel performancesWith table 3, we can also observe the contribution of SMI processing to mitigate interference effect and to decrease transmission error. In the case of two channel 25% overlapped, even if the terminal uses a single antenna, no transmission error is obtained. SDR concept combined with multi-channel and SIMO processing in the same terminal is a very promising issue to develop future wireless receivers ensuring high data rate and robust transmissions. The aim of this work was to expose performances results of several SIMO processing applied to real communication standards in realistic working conditions. Theses results were obtained by measure, taking so into account a most realistic as possible propagation channel, antenna coupling, channel correlation and fast fading. We have first presented results obtained in a single user transmission to detail effect of different propagation parameters and then in the second part of this article, several results obtained by measures simulating the running of a 40 MHz dealing with different 802.11 signals are given. With theses results we can study the effect of adjacent channel interference in the case of WLAN communication for different value of the channel spacing between the two signals of interest. Results are also given to prove the utility of spatial diversity to mitigate not only fading channels but also interference channels.

	4 Conclusions