Pradel Marilys
email: marilys.pradel@istea.fr

Assessing fertilising practices with organic residues in agriculture: a life cycle assessment perspective

A large part of the environmental impacts in agriculture are due to the emissions of chemicals such as nitrous oxide (N 2 O), ammonia (NH 3 ) and nitrate (NO 3 ). As they generate such substances, sludges are often associated with environmental burdens and contribute to major environmental impacts (acidification, eutrophication and global warming). In this paper, we achieve a LCA study for 45 sewage sludge spreading scenarios. After assessing the system boundaries and the functional unit, inventory data were collected. Two impact assessment methods were chosen: Eco-indicator 99 and the CML baseline 2. An analysis of nitrogenous emission origins according to spreader technological performances was possible according to the first results. LCA results mainly show that pedoclimatic conditions have an influence on the environmental impacts of spreading scenarios especially for acidification, eutrophication, and global warming and that environmental impacts present significant difference between spreading machines.

Introduction

As they generate nitrous oxide (N 2 O), ammonia (NH 3 ) and nitrate (NO 3 ), manures, sludges and to a lesser extent mineral fertilisers are often associated with environmental burdens and contribute to major environmental impacts (acidification, eutrophication and global warming). Concerns over these emissions have led to the assessment of the environmental impact of fertilisation processes or to the reduction of these emissions through different application techniques, mainly for ammonia volatilisation and, to a lesser extent, for nitrate leaching and nitrous oxide emission. This paper presents a comparison of the environmental impacts of sewage sludge spreading scenarios involving different types of spreaders in different pedoclimatic conditions using Life Cycle Assessment. Life Cycle Assessment (LCA) is a common tool to assess environmental impacts of a product or a system. The process or product life cycle is assessed from raw material acquisition through production, use and disposal in a "cradle to grave" perspective. Each step of the life cycle consumes energy, depletes non renewable resources and produces air, soil and water emissions at different scales (local, regional or global scale). According to ISO14040 standards [START_REF] Afnor | Management Environnemental -Analyse du cycle de Vie -Principes et cadre[END_REF], Life Cycle Assessment is conducted through a four step procedure including (i) goal and scope definition, (ii) life cycle inventory, (iii) life cycle impact assessment and (iv) interpretation..

Material and Methods

System boundaries

The system boundaries are quite difficult to evaluate because spreading operations may be considered part of both the crop management and the sewage sludge disposal route. As our study is focused on the spreader environmental performances, the system boundaries are limited to the spreading operation as shown in Figure 1. The system takes into account the logistic phase and the spreading operation itself. The inputs include the environmental impact of the agricultural machinery used for spreading operations, in both logistic and spreading phases (manufacture and transport of agricultural machinery and shed, lorry transport operation), and the energy used for the agricultural machinery (fuel production). The outputs include emissions from the fuel combustion, for both tractor and lorry, the tyre abrasion of the agricultural machinery and the nitrogenous emissions related to the sewage sludge application in the soil. Emissions during the storage (at waste water treatment plant and intermediate storage) are left out of the system. All the sewage sludge production processes, such as the metallic trace elements (MTE) contained in the sludge and the energy used for the sludge treatment (thickening, dehydration…), are not taken into account in the system.

15th International Conference Ramiran, May 3-6, 2013, Versailles These assumptions have been made because spreading operation has absolutely no interaction with a possible reduction of the MTE environmental impacts and the sludge production process. Nevertheless, the MTE significantly impact the ecotoxicity and toxicity categories and remain the main environmental problem of sewage sludge production.

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36 S37 S38 S39 S40 S41 S42 S43 S44

Functional unit

Sewage sludge can be considered as a waste, as well as a fertiliser. If sludge is considered as a waste, the best functional unit will be the ton of sludge spread (dry or fresh matter). If sludge is considered as a fertiliser, the most suitable functional unit will be the quantity of nutritive element spread (N, P or K). However, spreading sludge is subject to legislation and should respect a fertilisation plan. Agronomic value of sewage sludge should be known to best fit the crop needs. The most relevant functional unit for our system will, thereby, be the dry matter ton of sewage sludge spread in the field, taking into consideration both the respect of legislation and an application rate calculated on the basis of the nutrient, which first fits the plant requirements.

Inventory data

Inventory data and scenarios construction are developed in [START_REF] Pradel | Valorisation of Organic Wastes Through Agricultural Fertilization: Coupling Models to Assess the Effects of Spreader Performances on Nitrogenous Emissions and Related Environmental Impacts[END_REF][START_REF] Pradel | Analyses du cycle de vie de chantiers d'épandage de boues de station d'épuration[END_REF].

Results

Nitrogenous emission origins according to spreader technological performances

According to the method proposed by [START_REF] Pradel | Valorisation of Organic Wastes Through Agricultural Fertilization: Coupling Models to Assess the Effects of Spreader Performances on Nitrogenous Emissions and Related Environmental Impacts[END_REF], we calculated the nitrogenous emissions produced by the different studied spreading operations (Figure 2). Results show that spreading liquid SS 1 with a splash plate produces more ammonia emissions than the other spreading techniques. While ammonia emissions are not linked with the spreader performances for other application techniques, the soil deposit and, to a lesser extent, the application rate measured for the slurry tanker equipped with a splash plate have an effect on ammonia emissions for liquid SS spreading (Figure 2a). In addition, using an injection technique reduces ammonia emission in comparison with splash plate technique. Nitrous oxide emissions are only produced in a pedoclimatic condition, where denitrification potential seems to be high and sensitive to soil compaction (Figure 2b). Finally, nitrate emissions are barely linked with spreader technological performances and depend mostly on soil and climatic conditions (Figure 2c).

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36 S37 S38 S39 S40 S41 S42 S43

Figure 2 (a, b, c). Nitrogenous emissions according to spreader technological performances

Spreading scenario environmental impact analysis Do environmental impacts present significant differences between the spreading machines? Figure 3 presents the LCA results for spreading operation involving two pairs of "sewage sludge-spreading machine": (a) solid sewage sludge spread using an organic spreader with vertical rotors and (b) liquid sewage sludge injection. Mean and standard deviation values result from the impacts related to the different pedoclimatic conditions. Only spreading phases representing more than 5% for each impact are shown. Nitrogenous emissions mainly impact on eutrophication (almost 99%), acidification (between 75 to 95%) regardless of the spreading scenarios. Nitrogenous emissions contribute to around 35% of the GWP100 impact categories for all the scenarios, except for injection as it represents 90%. Solid and composted sludge transport from the storage place after treatment to an intermediate storage by a 16 ton lorry on 35 km is the most impacting element for almost all categories. However, sludge transport and organic spreader production equally impact on fresh water aquatic and human toxicity categories. In the same manner, transport equally impacts with nitrogenous emissions on GWP100. Pelleted sludge transport from the storage place after treatment to an intermediate storage by a 28 ton lorry on 100 km equally impacts on each category (except AP and EP). Spreader and tractor production and fuel emissions (during both production and combustion) have the same impact contribution (results not shown). As a conclusion, pelleted sludge transport (89% of dry matter per ton) on great distances with a high volume lorry (28 tons) has fewer impacts than solid and composted sludge transport (respectively 64 and 33% of dry matter par ton) on average distances with a low volume lorry (16 tons). Without sludge transport by lorry, agricultural material, spreader and tractor manufacturing affects most of the toxicity impact categories and, to a lesser extent, abiotic depletion. Fuel production and combustion in the tractor engine mainly impact on ozone layer depletion and 15th International Conference Ramiran, May 3-6, 2013, Versailles abiotic depletion. Photochemical oxidation is equally produced by spreader manufacturing and fuel production, as well as by combustion in the tractor engine. Cover crop transport and use for incorporation has a low impact for all sludge spreading scenarios. We also observed a high variability in GWP100 and acidification LCA results caused by a high variability in nitrous oxide and ammonia emissions, respectively. This high variability is strongly connected to the pedoclimatic conditions as reported by [START_REF] Pradel | Valorisation of Organic Wastes Through Agricultural Fertilization: Coupling Models to Assess the Effects of Spreader Performances on Nitrogenous Emissions and Related Environmental Impacts[END_REF] and illustrated in the previous section.

Do the pedoclimatic conditions have an influence on the environmental impact of spreading scenarios? Figure 4 represents a comparative LCA result between liquid sewage sludge spread with a splash plate and with injectors using Ecoindicator 99 method. Unlike Figure 3, which presents the mean and standard deviation values from the impacts of the nine pedoclimatic conditions, Figure 4 presents LCA results for each pedoclimatic conditions using Ecoindicator single score. These single scores are dimensionless and then can be summed up to present the total environmental burden of the studied scenarios. Generally, single scores are more important for liquid sludge spreading using splash plate regardless of the pedoclimatic conditions, as we considered an incorporation with cover crop while this step is not taken into account in liquid sludge spreading through injection. So, we observe that spreading liquid sewage sludge, whether using splash plate or injectors, is more impacting in Poitou Charentes pedoclimatic context than in other sites. This can be explained by the high denitrification potential of the local pedoclimatic conditions affecting climate change. According to the pedoclimatic conditions, spreading sludge using injector devices reduces impacts between 10 and 30 single scores (Pt) compared with spreading using splash plate devices.

Conclusion and perspectives

Our LCA study highlights that it is possible to accurately discriminate environmental performances integrating spreaders technological performances for several spreading operations. We also show the importance of the spreading operation phases (loading, transport, spreading) in terms of environmental impacts leading to a better understanding of the spreading operations and to a possible reduction of the main identified environmental impacts. The proposed method links nitrogenous emissions to the spreader technological performances so that the main spreader technological characteristics can be improved. This step is included within a bigger approach on the spreaders ecodesign. However, LCA results cannot be generalised to all the spreading operations because of both, the high variability in nitrogenous emissions strongly linked to the spreader performances and the specific conditions and assumptions established for scenarios construction, especially regarding sludge transport by lorry.

Figure 3 :

 3 Figure 3: Environmental impacts of sewage sludge spreading for two technologies using mean and standard deviation values from the impacts of the nine pedoclimatic conditions (CML 2 baseline 2000 V2.04 / characterisation)

soil, water Inputs Energy Raw materials Figure 1: Description of the sewage sludge spreading operation boundaries

	Exploration, processing and
	transportation of raw materials
	• Fossil fuel
	Production, maintenance and
	transportation of agricultural
	machinery and shed
	• Spreader
	• Tractor
	• Loader • Cover crop	Outputs
	Transport operation • Lorry production and maintenance	Emissions to air,
	• Road construction and maintenance
	• Lorry use
	Sewage sludge spreading
	• Agricultural machinery use
	during spreading
	• Agricultural machinery use
	during incorporation
	System boundaries
		kg NH3/ DMt spread
		Slurry tanker -splash	Slurry tanker -	Organic spreader -	Organic spreader -	Organic spreader -
		plate -liquid SS	injector -liquid SS	Moving rotor -Solid	Moving rotor -	discs -dry SS
				SS	Composted SS
		Without sludge spreading	With ideal sludge spreading
		Application Rate	Incorporation/soil deposit

Comparison of liquid sewage sludge spreading using slurry tanker equipped with splash plate or injectors (Eco-indicator 99 (E) V2.06 / single score)

	90.
	80.
	70.
	60.
	50.
	Pt
	40.
	30.
	20.
	10.
	0.
	Mt1 Mt2 Kl1 Kl2 Kl3 Ms1 Ms2 Pt1 Cx1 Mt1 Mt2 Kl2 Kl3 Ms1 Ms2 Pt1 Cx1
	Slurry tanker -splash plate	Slurry tanker -injector
	Carcinogens	Respiratory inorganics
	Climate change	Acidification/ Eutrophication
	Fossil fuels
	Figure 4:


Pradel Marilys
email: marilys.pradel@istea.fr

Pacaud Thomas

Cariolle Michel

Organic residues valorisation by fertilisation: Coupling models to assess the impact of spreader performances on nitrogenous emissions and related environmental impacts

This paper proposes a generic methodological framework to investigate the link between application technique performances and related nitrogen emissions in the field. Our approach is to couple biophysical models (of N emissions) and models used to assess machinery technological performances related to distribution, application rate efficiency and soil compaction through a four-step method. We highlighted that nitrate emissions cannot be directly linked to spreader distribution deficiencies but are more dependent on weather and soil conditions. On the contrary, ammonia volatilization can be directly linked to the type of spreading operation, especially for liquid sewage sludge. Nitrous oxide emissions are linked to the spreader weight as well as the weather and soil conditions. The methodological framework introduced in this paper highlights the feasibility of coupling real technological performances of spreaders and simulation models to assess the environmental impact of spreading practices.

Introduction

Since 1992, French and European regulations encouraged energetic recovery of waste as well as organic waste valorisation through land application. Land application is only possible if organic wastes bring enough nutrients to the crops and are harmless to both the crop and to the amended soils. As manures, sewage sludges and slurries contain great amounts of nitrogen, there is a growing issue about water and air pollution caused by their application in the field. Unfortunately, up to now, nitrogenous emissions are not well modelled in life cycle assessment methods. For instance, in databases attached to Life Cycle Assessment (LCA) inventories, the emission factors commonly used to quantify NO 3 and direct or indirect N 2 O emissions are global. They come from the IPCC guidelines (2006). They do not take into consideration neither the type and performance of the land application techniques nor the type of organic waste applied. However, average emission factors were proposed in the literature according to organic waste applied and the related application techniques. These factors were established on the basis that each application technique delivers the wanted application rate of organic waste homogeneously whereas it is a great challenge to spread liquid and solid organic fertilizers both accurately and evenly. The technological performances of the application technique -such as distribution homogeneity, respect of application rate and soil compaction -have barely been taken into account in impact computation. The aim of our research is to develop a generic methodological framework to investigate the link between application technique performances and the related nitrogen emissions in the field. Our approach is to couple biophysical models (of N emissions) and models used to assess machinery technological performances related to distribution, application rate efficiency and soil compaction in order to link nitrogenous emissions (NH 3 , NO 3 and N 2 O) with the spreading machine performances.

Material and Methods

The proposed methodology for assessing nitrogenous emissions based on technological performances of spreaders is done in a four-step method [START_REF] Pradel | Valorization of Organic Wastes Through Agricultural Fertilization: Coupling Models to Assess the Effects of Spreader Performances on Nitrogenous Emissions and Related Environmental Impacts[END_REF] (Figure 1). (a) The first step consists of creating scenarios that associate a cropping system (i.e. soil and climate conditions and a crop rotation), a spreading period and a technological couple "spreading machine/sewage sludge". Each scenario provides input data for the biophysical model.

(b) The second step consists of testing the technological performances of the spreaders. Spatial distribution and application rate efficiency are evaluated with a test bench. The test bench results are used as input data of a Matlab® simulation tool, named spreading simulator, to estimate the expected spatial distribution and application rate performances in the field. The effect of spreaders on soil compaction is assessed with the Compsoil model [START_REF] O'sullivan | A simplified method for estimating soil compaction[END_REF] which is parameterized with the technological characteristics of the spreaders. Through the simulation and the use of Compsoil model, respectively we will obtain (i) an application rate map and a histogram of application rate at the sub-field scale representing both the distribution and the application rate efficiency, i.e. the application rate really applied compared to the theoretical one, (ii) the bulk densities in compacted and non compacted areas representing the effect of the spreaders on soil compaction.

(c) The third step consists of simulating the nitrogenous emissions generated by different application rates, with biophysical models such as STICS [START_REF] Brisson | STICS: a generic model for the simulation of crops and their water and nitrogen balances. I. Theory and parameterization applied to wheat and corn[END_REF] and DEAC. Bulk densities in compacted and noncompacted areas which result from Compsoil simulations are used as input data in STICS model to model nitrogenous emissions in compacted and non compacted areas.

(d) Finally, the simulated nitrogen losses provided by the biophysical models are coupled with the levels of elementary spread amounts provided by the spreading simulator and with the proportion of areas compacted and non compacted. This allows calculating the various nitrogen losses of the spreader according to its performances on spatial distribution, on application rate efficiency and on soil compaction..

Results

Nitrogenous emissions for basal assessment (F0)

The basal emission assessment, using STICS and DEAC models for N-NH 3 , N-N 2 O and N-NO 3 emissions, is called F0. F0 is the value obtained for a 0% application rate, simulating the impact of no sewage sludge application for the 44 scenarios. There is an important effect of the reference site for all types of emissions, regardless of the spreading operation and the spreading machine. Total nitrogen emissions for each of these groups, resulting of the sum of N-NH 3 , N-NO 3 and N-N 2 O values, are respectively 32, 6.8, 49.8, 82, 93.5, 19.8, 32.7 and 27.8 kg N.ha-1. These emissions are due to nitrogen balance in soil coming from crop residues, nitrogen mineralization and mineral fertilizers application.

Figure 1 .

 1 Figure 1. General framework of the method

Nitrogenous emissions simulated under standard sewage sludge spreading (∆F1) ∆F1 is calculated by the difference between emissions obtained for a 100% application rate (Ft) and those obtained for a 0% application rate (F0), simulating the impact of sewage sludge spreading for the 44 scenarios. Results shown in Figure 2 represent the additional nitrogen emitted when the sewage sludge is applied, given that it is evenly distributed over the field at the optimal recommended application rate with no compacting effect of the spreading machine. Compared to the total amount of nitrogen supplied by the sewage sludge, N-NH 3 emissions vary from 0 to 8 % (from 0 to 10 kg of nitrogen per hectare), N-NO 3 emissions from -3 to 8 % (from -3 to 10 kg of nitrogen per hectare) and N-N 2 O emissions from -3 to 6 % (from -2 to 4 kg of nitrogen per hectare). Variability of nitrogenous emissions related to spatial distribution and application rate. The additional nitrogen flow due to the spatial distribution heterogeneity is less than 4% total N applied for N-NH 3 emissions in most of the 44 scenarios (Figure 3). N-NO 3 emissions are very low, excepted for LS spreading in one weather and soil situation (19 % total N applied). Extra denitrification induced by spreading heterogeneity is not significant. This result is explained by the limited sensitivity of models to the sewage sludge application rate, by the relatively small proportion of surface concerned by higher application rates and by the compensatory phenomenon induced by surfaces receiving lower application rates.

Nitrogenous emissions variability related to soil compaction

Our results show that soil compaction induced by the spreading machine had no significant impact on ammonia volatilization (Figure 4). Indeed, the compaction effect of the machine does not lead to a sufficient reduction of the infiltration for the liquid sewage sludge and has no effect for non-liquid 15th International Conference Ramiran, May 3-6, 2013, Versailles, France sludges. Soil compaction has a logical negative effect on nitrate leaching. In compacted areas, a part of the nitrates are likely to be removed with runoff. Besides, denitrification losses (represented by nitrous oxide emissions) are the most affected ones by soil compaction; especially in sensitive locations where the water filled pore space (WFPS) often reaches the trigger threshold for activate the denitrification process.

Conclusion and perspectives

The aim of this paper was to propose a methodological framework to refine the inventory of nitrogenous emissions linked to sewage sludge spreading, by introducing in particular spreading and spreaders' characteristics. The methodological framework introduced in this paper highlights the feasibility of coupling real technological performances of spreaders and simulation models to assess the environmental impact of spreading practices.

Our method can be used to assess the environmental impacts of the organic waste valorisation through land spreading operation and to assess the impact of spreader performances in different conditions. This method can help spreader manufacturers in improving the technological performances of their spreader through ecodesign or in providing farmers with advices on the better use of their spreader depending on the conditions of use. Finally, as it highlights the variability in nitrogenous emissions, this method can also be used to assess the variability in Life Cycle Assessment Inventories of spreading operations. Indeed, environmental assessment of agricultural practices implying fertilization and spreading processes through Life Cycle Assessment generally comes up against difficulties in estimating nitrogenous emissions. As a simplification, it is common to use standard emissions factors (IPCC-tiers 1 or data coming from the literature). The limits of this simple approach result in standardization of the LCA results as well as a standardization of the recommendations to improve the fertilization and spreading practices. Giving a range of nitrogenous emissions values instead of using one single value based on emission factors such as IPCC-tiers 1 ones will allow recommendations in fertilization and spreading practices improvement adapted to the local weather and climate conditions. As a perspective, this method can also be used to conduct spatialized LCA of fertilizing and spreading operations.


Mazoyer Jacky
email: jacky.mazoyer@irstea.fr

Pradel Marilys

Overview of the organic spreaders stock in France: state of the art and performance assessment

The French stock of organic spreader evolves and presents differences by their users. Cuma and agricultural work companies are the main operators which buy machines and provide spreading services for farmers. Individual sales are currently at a low level. The market decreases in units sold but prices increase. In this context, operators renew spreaders after 7-8 years and over 10 years for tankers, replacing small machines with bigger ones. Cuma use mostly vertical rotors spreaders for solid organic fertilisers and big slurry tankers for liquid organic fertilisers. Application rate equipment is at a level of confidential use. Agricultural work companies, when they are specialized in spreading, use mostly spreading table spreader, the biggest slurry tankers on the market and also all type of selfpropelled machines. They adopt more easily application rate equipment as they have to respect more constraints for spreading than farmers and the possibility to get easier cost amortization due to a high intensive activity.

Introduction

The stock of organic spreaders is currently barely known in France. Public institutions have very little information on this equipment and are in demand of such data to improve either legislation or provide subsidies for farmers. Since 20 years, spreaders with vertical rotors are very used for manure spreading. Slurry tankers have increased their capacity following the farm areas evolution. In the largest farms with cultivated land, some self-propelled spreaders are used. A study was conducted in order to answer several questions [START_REF] Mazoyer | Etude du parc des matériels d'épandage de matière organique en France[END_REF]. What kinds of equipment are in use for solid and liquid spreading? What are there capacities? What is the different application rate equipment used?

Material and Methods

The different type of spreader in use Organic spreaders can be divided in two types, for solid organic fertilisers such as manure or residual waste and for liquid ones such as slurries [START_REF] Rousselet | Evaluation des performances des épandeurs de fumier : premiers résultats selon la norme NF EN 13080[END_REF][START_REF] Thirion | Epandage des boues résiduaires et effluents organiques -Matériels et pratiques[END_REF]. Regarding the solid product spread, the main type used in France is spreaders with two vertical rotors (Photo 1). These spreaders are mainly used for cattle manure which is the most common matter encountered in spreading practices. These spreaders are robust and especially destined for raw products. The common application rate for these spreaders is between 20 and 30 t/ha. For other solid product, such as compost, broiler manure and other byproducts, the spreaders with spreading table (Photo 2) are also used. These spreaders with large capacities allow small application rate (between 3 t/ha and 15 t/ha). Liquids are commonly spread with slurry tankers. The most common spreading equipment is a simple splash plat. But recent models, with largest capacities receive better spreading equipment as trailing hoses (Photo 3) and injectors (Photo 4).

15th International Conference Ramiran, May 3-6, 2013, Versailles

Survey of the main operators

Different operators represented at the national level were surveyed. Three types of groups were identified: the cooperatives for the use of agricultural equipment (CUMA) i.e. groups of farmers buying together agricultural equipment for a common use. In the CUMA Network, organic spreading is a main activity with approximately 9.000 spreaders in use in 2009. By contacting Cuma in most of the departments (67), we collected data on a large sample of machines. Finally, almost 6.400 spreaders and 3.400 tankers are taken in account. The localisation in the country is presented Table 1.

Technical characteristics

Three technical characteristics were studied to have a look of the stock: (i) The kind of spreading equipment use (vertical rotors or spreading tables for solid products, splash plates, multi nozzle spreader bars, trailing hoses or injectors for liquid products), (ii) The spreader capacities divided in different classes announced in m 3 , (iii) The type of application rate equipment used like proportional flow rate speed, flow rate meter (for liquid spreaders only) and weighing systems, following shutter, edge shutter (for solid spreaders only). Complementary information as the year of purchase and localisation in the country were also studied.

Results

Spreaders of Cuma

For solid organic fertilisers, most of the spreader (sample of approximately 6000 units) have been bought since 6 years ago. Spreaders are intensively used, generally more than 500 loads per year and the wear is important. Models with vertical rotors are the reference for Cuma (Figure 1). Spreader capacity is between 10 and 15 m 3 in 60 % of cases. Since 2006, increase in sales of bigger capacities spreaders (more than 15 m 3 ) was observed. Application rate equipment just appears recently in the Cuma. This equipment is used in little number. The flow rate proportional to the speed (DPAE) system is the most disseminated (Figure 2). For liquid organic fertilisers (sample of approximately 3 000 units), slurry tankers are also recent (20 % of the sample more than 10 years). The half of tankers bought since 20 years have a capacity of 10 to 15 m 3 . Smaller models represent the third. Since 2006, sales of tankers having a 15 to 20 m 3 capacity also increase. The simple splash plate is used in an overwhelming majority of the spreading equipment. If the use of others solutions increases, notably the multi nozzle spreader bars, this represents a little part yet (Figure 3). Application rate equipment is very few used with a little number of units (Figure 4). Since 2006, flowmeters are often mounted on big capacity models.

Spreaders of agricultural work companies

For the solid organic spreading (sample of 152 spreaders), companies use mostly spreading table (Figure 5), with a capacity over 15 m 3 in half of cases. Application rate equipment is more used, especially DPAE and edge shutter. For the liquid organic fertilisers (sample of 101 tankers), different spreading systems are used in same proportion (Figure 6). The splash plate is only used for 28 % of cases. Application rate equipment is well disseminated in the studied sample. In our sample, 40 % of de tankers have DPAE. Generally, application rate equipment is recent and get up on big tankers (over 15m 3 )

Figure 5. Spreading system for solid spreaders Figure 6. Spreading system for liquid spreaders

Self-propelled spreaders are also used by companies. In our sample, we have found 81 machines. These spreaders use only spreading table for solid organic fertilisers spreading. The capacity of selfpropelled machines is less high than towed ones but there level of application rate equipment is higher (GPS, DPAE, weighing system in any case). These machines have the particularity to be loaded in the field; no transport is done with such machines. ,. In our sample, most of liquid machines use multi nozzle spreader bar and there is a common use of DPAE as application rate equipment and a beginning for flowmeter.

Conclusion and perspectives

Since twenty years, spreaders have become huge machines, with a high productivity and also a more intensive using. Cuma mainly spread cattle manure and so use vertical rotors spreaders. Models with spreading tables are more in use in agricultural work companies which spread a larger variety of organic fertilisers. Slurry tankers are bigger and the renewal is less than manure spreaders. Spreading in France is evolving with more professional actors. Units sold decrease each year but medium prices increase. Application rate equipment's have for the moment a confidential using. A progress in their use is possible because the stock is insufficiently equipped. The study identified different levels of application rate equipment. All these equipment need to be qualified in a test bench to assess their performances. With these results, it will be possible to communicate for users and manufacturers to develop a more high-performance stock.

Figure 1 .Figure 2 .

 12 Figure 1. Proportion of spreader models Figure 2. Application rate equipment for solid spreaders

Figure 3 .Figure 4 .

 34 Figure 3. Proportion of spreading system for liquid spreaders

Photo 1. Spreaders with two vertical rotors Photo 2. Spreader with spreading table Photo 3. Trailing hoses Photo 4. High capacity tanker with injectors

Table 1 . Number of machines by region

 1

	Localisation	Manure spreader	Slurry tanker
	West	1824	1201
	North east	1536	836
	Centre	925	274
	South east	771	451
	South west	1357	666
	Agricultural work companies represented by their national federation (FNEDT) can provide different
	agricultural services including organic spreading. The national federation has selected a sample about
	a hundred of companies specialized in organic spreading. All companies of this sample were localised
	in north east, west and centre French regions. Finally, the sample takes into account 150 manure
	spreaders, 100 slurry tankers and 80 self-propelled spreaders.
	The French syndicate (Axema) representing the industry of agricultural equipment in France
	collaborates also to this study. The French market of manure spreader decreases since 15 years: the

number of machines was over 4 000 in 2000 and near 2 000 right now. Their capacities are nevertheless largest and the value of the market is stable. For slurry tankers, a collapse of the market divided sells by 3 in 15 years. The large capacities (over 14 m 3 ) are in expansion.

15th International Conference Ramiran, May 3-6, 2013, Versailles


Kun Wei

Guoqiang Mao

Wuxiong Zhang

Yang Yang

Zihuai Lin

Chung Shue Chen

Optimal Microcell Deployment for Effective Mobile Device Energy Saving in Heterogeneous Networks

Keywords: Heterogeneous network, energy efficiency, microcell planning, power saving

 is considered as an energy efficient system structure to alleviate the problem of rapidly increasing power consumption in the wireless communication system. Significant research on HetNet energy efficiency has been conducted. However, most of them only consider power consumption of Base Stations (BSs) while ignoring influence on energy efficiency of Mobile Devices (MDs) brought by new BSs deployment. In this work, we propose a novel power saving metric for HetNet. Under the coexisting scenario of a single macrocell and a single microcell, we analyze the changes in power consumption at both the BSs side and the MDs side with the deployment of a micro BS. Optimum microcell radii for maximum power saving at the MDs sides and for highest network energy efficiency are obtained through analytical studies. It is found that total power saving for microcell MDs is close to 18% with a proper deployment of a microcell. Finally, extensive simulations have been provided to establish the accuracy of our theoretical analyses.

I. INTRODUCTION

To address the challenge of rapidly increaing mobile broadband traffic, mobile network service providers have to continuously deploy new BSs. However, the increasing number of BSs will result in higher power consumption, which is becoming a major concern for network service providers due to both economical and environmental considerations. To conquer these challenges, 3GPP suggests the deployment of HetNet as a cost-efficient way to deal with the surging traffic demand and increasing power consumption. HetNet is a network with complex interoperation among macrocell, microcell, picocell, femtocell and WiFi networks, which together provide a mosaic of coverage with handoff capability between network elements [START_REF] Damnjanovic | A survey on 3GPP heterogeneous networks[END_REF]. It has been demonstrated both experimentally and theoretically that HetNet provides both a cost-effective and an energy-efficient solution to capacity shortage [START_REF] Hu | HetNets -a new paradigm for increasing cellular capacity and coverage[END_REF].

This research is partially supported by the NSFC under the grant 61231009, the MOST under grant 2014AA01A707, National Science and Technology Major Project under grant 2011ZX03005-002, Shanghai Municipal Commission of Economy and Informatization R&D Program-Wireless Communication Technology Test Platform with Shanghai Urban Pattern, Science and Technology Commission of Shanghai Municipality under grant 11JC1412300, and Australian Research Council Discovery projects DP110100538 and DP120102030, and European Celtic project "Operanet2".

In addition to the energy efficiency of the BSs, power consumption reductions of MDs are also increasingly important considerations. More specifically, there are more than six billion mobile phones all over the world, including about one billion smartphones and five billion non-smartphones [START_REF]Measuring the information society[END_REF]. It is roughly estimated that the total power consumption of these mobile phones easily exceeds 5 billion kWh/annum. Further, due to the limitation of the battery capacity and the fact that smart phones are much more power consuming, the smart phone usage time is far from satisfactory for most users. A smart phone customer satisfaction studies demonstrated that up to 60 percent of mobile users in China complained short battery usage time as the greatest problem while using 3G services [START_REF] Feng | A survey of energy-efficient wireless communications[END_REF]. The energy efficiency of MDs hence becomes one of the most important considerations for user experience. Therefore an energy efficient network design should not only consider the energy efficient operations of BSs but also take the energy efficiency of MDs into account.

Much prior work has studied the energy efficiency of HetNet, in which different metrics have been defined to measure the energy efficiency of HetNet. The metric area power consumption, which is defined as the average power consumed in a cell divided by the corresponding average size of cellular coverage area, defined by Richter in [START_REF] Richter | Energy efficiency aspects of base station deployment strategies for cellular networks[END_REF]. Wang and Shen introduced the metric area energy efficiency (with a unit of bit/Joule/km 2 ), which is defined as the number of bits transmitted per joule of energy consumed and per unit area, to measure the energy efficiency of HetNet [START_REF] Wang | Energy efficiency of heterogeneous cellular network[END_REF]. This metric has incorporated the impact of the size of cellular coverage area in the analysis of the energy efficiency. In [START_REF] Soh | Energy efficient heterogeneous cellular networks[END_REF], [START_REF] Quek | Energy efficiency analysis of two-tier heterogeneous networks[END_REF], the authors used the value of area energy efficiency divided by the average power consumption of the BSs which is shown in [START_REF] Quek | Energy efficiency analysis of two-tier heterogeneous networks[END_REF] to assess the energy efficiency of HetNet.

With the metrics above, researchers analyzed the energy efficiency of various HetNet BS deployment strategies. In [START_REF] Soh | Energy efficient heterogeneous cellular networks[END_REF], Soh et al. found that the use of small cells generally led to higher energy efficiency but this gain saturated as the density of small cells increases beyond a threshold. In [START_REF] Quek | Energy efficiency analysis of two-tier heterogeneous networks[END_REF], Quek et al. showed that there exists an optimal pico-macro density ratio that maximizes the overall energy efficiency of HetNet. In another work [START_REF] Richter | Energy efficiency aspects of base station deployment strategies for cellular networks[END_REF], Richter et al. found that in saturated traffic load scenarios, the use of micro BSs had a rather moderate effect on the area power consumption of HetNet.

All of the above metrics and associate research focused on studying the energy efficiency of HetNet from service provider's perspective. Comparatively, much less work studied the power consumption of MDs in HetNet and almost all of the work largely ignored the energy efficiency changes of MDs caused by the deployment of new BSs in HetNet. In fact, when new sites are deployed under HetNet, on one hand, the power consumption of MDs will benefit from the increasing number of BSs due to the following two reasons: first, with the increase in the capacity of the HetNet, the MDs will accomplish data transmissions using less amount of time, thus reducing the duration of data transmission which in turn results in reduced power consumption; second, with the increase in the density of BSs, transmission power required by the MDs to reach their respective associate BSs will reduce, which also leads to reduced power consumption. On the other hand, even if the new sites are low-power devices, the overall power consumption of HetNet BSs may increase [START_REF] Corliano | Energieverbrauch der mobilen kommunikation[END_REF]. Therefore, from the point of view of power consumption, the increase in the number of BSs in HetNet has two opposite effects on the BSs and on the MDs respectively. When studying the energy efficiency of HetNet, it is important to jointly consider both of the effects to gain a complete understanding of the energy efficiency of the overall system.

In this paper, we study the energy efficiency of HetNet from a more comprehensive and systematic perspective. Specifically, by considering a HetNet with a single macro BS and a single micro BS, we analyze the power consumption of both at the BSs side and at the MDs side in HetNet system. Based on the analyses, schemes of energy efficient planning of a micro BS are investigated. In summary, contributions of this paper are as follows:

1) A novel power saving metric which considers the power consumption of both BSs and MDs is proposed. The metric helps us to gain a more complete understanding on the energy efficiency of HetNet system. 2) Power consumption of both BSs and MDs under different micro BS deployment strategies is analyzed. Optimum coverage radii of a micro BS are obtained to maximize the power saving on MDs and to maximize the overall HetNet energy efficiency respectively. The rest of the paper is organized as follows. In Section II, our system model and the power saving metric are introduced. In Section III, the analyses of power consumption of MDs with and without a microcell BS and the optimum radius of microcell are provided. Section IV verifies our analyses with extensive simulations. Section V concludes the paper and discusses future research directions.

II. SYSTEM MODEL AND POWER SAVING METRIC

A. System Model

In this paper, we consider a HetNet model illustrated in Fig. 1 (similar to [START_REF] Lee | A probabilistic call admission control algorithm for WLAN in heterogeneous wireless environment[END_REF]). Specifically, we consider a HetNet with a single macrocell and a single microcell. The coverage area of the macrocell is modeled by a disk with a radius of R, one used by the macrocell and the other used by the microcell, is adopted in this work [START_REF] Damnjanovic | A survey on 3GPP heterogeneous networks[END_REF]. We further assume that all active MDs are allocated with equal bandwidth resources at different carrier frequencies. Therefore there is no interference among MDs. If an MD is located in the coverage area of the micro BS, the MD will be associated with the micro BS; otherwise, the MD will be associated with the macrocell BS.

In addition, a standard power loss propagation model with path loss exponent γ (γ ≥ 2) and path loss constant L 0 (typically about (4π/ν) 2 , where ν is the wavelength) at reference distance r 0 = 1m is adopted [START_REF] Jo | Heterogeneous cellular networks with flexible cell association: A comprehensive downlink SINR analysis[END_REF]. The noise power is assumed to be additive and constant with value σ 2 . So the Signal to Noise Ratio (SNR) at an MD which is x meters away from the BS is

SN R = P tx L 0 x -γ σ 2 , ( 1
)
where P tx is the transmission power of the BS. We assume the channel model of macrocell and microcell are the identical as the micro BS in this paper indicates a full functional BS set up in the outdoor area with less coverage size than that of macrocell and larger coverage size than that of picocell for traffic offloading of the network. The transmission rate of the MD obeys the Shannon's law. Thus if bandwidth for the MD is B and signal to noise ratio is SN R, then transmission rate is

Rate = B • log 2 (1 + SN R).
(

) 2
There is a striking contrast in power consumption among different types of MDs [START_REF] Zhang | Accurate online power estimation and automatic battery behavior based power model generation for smartphones[END_REF]. On the basis of the model in [START_REF] Zhang | Accurate online power estimation and automatic battery behavior based power model generation for smartphones[END_REF], the power consumption of MDs is modeled as

P ph = pP i + (1 -p)P w , (3)
where P i is the power consumption when the MD is in the idle state and P w is the power consumption when the MD is active (i.e., downloading). The p is the probability that the MD is in the idle state.

For base station power consumption, since the power consumption of BS can be approximate as independent of the instantaneous traffic load [START_REF] Corliano | Energieverbrauch der mobilen kommunikation[END_REF], the consumption models of macrocell and microcell BSs are

P ma = a 1 P tma + P mma , (4)
P mi = a 2 P tmi + P mmi , (5)
respectively [START_REF] Etsi | Environmental Engineering (EE); Principles for Mobile Network level energy efficiency[END_REF], where a 1 and a 2 are decided by the efficiency of radio power amplifiers. P tma and P tmi are transmission powers of the macro BS and micro BS. P mma and P mmi summarize independent components of transmission power such as signal processing, battery backup, and also parts of the cooling unit.

B. The Power Saving Metric

Previous work on energy efficiency of HetNet mainly focuses on only one side of the networks (the BSs or the MDs), and the energy efficiency metrics therefore do not give a complete picture of the overall energy efficiency. In fact, power consumption of both BSs and MDs are both essential. When studying the energy efficiency of HetNet, neither side of the two should be neglected. We proposed a novel power saving metric in [START_REF] Soh | Energy efficient heterogeneous cellular networks[END_REF] to capture the energy efficiency of the entire network, including the benefit and cost of deploying new BSs, which is an integration of MDs power consumption and the BSs power consumption. The power saving indicator Ψ is defined as follows: When new BSs are deployed, the difference between the power saved (benefit) at the MDs (P save ) and a weighted power consumption (cost) increase on the BSs (P mi ) compared with the situation without the new BSs are used for measuring the energy efficiency. The weight β is the importance ratio between the power cost and power benefit from mobile network operator's standpoint. As the battery energy for MDs is quite limited and MD usage time is of great significance to user's experience, we think β should be less than one to reflect the situation that network operator may accept increased power consumption to improve their user experience.

Ψ = P save -β • P mi . (6)
It can be seen that the larger the Ψ is, the more significant the benefit brought by the deployment of a new micro BS will be. So Ψ provides a useful guidance on the optimum deployment of the new BS is from "power consumption" point of view.

In fact, Ψ is positively correlated with some energy efficiency metrics, such as the widely used metric in [START_REF] Soh | Energy efficient heterogeneous cellular networks[END_REF] E ef f = Area Spectral Ef f iciency Average N etwork P ower Consumption .

Firstly, high area spectral efficiency will reduce MDs download time, and thus save MDs power, so P save increases with the increase of Area Spectral Efficiency. Deployment of new BSs with power consumption P mi will increase the Average Network Power Consumption. Compared with the metric E ef f , we consider more factors, such as the difference of MD power consumption under different networks and different working status.

III. ENERGY EFFICIENCY ANALYSES WITH THE DEPLOYMENT OF A MICROCELL

In this section, we firstly analyze the power consumption before and after the deployment of the microcell, then we obtain the optimal value of microcell radius to get the maximum MDs power saving and to reach the best performance.

A. Power Consumption without a Microcell

Under a single macrocell scenario, the number of macrocell MD is M a = λ • πR 2 , and thus bandwidth per MD is:

B mauser = Bma
Ma , where B ma is the total bandwidth of the macrocell.

According to the channel model mentioned in Section II, if minimum SNR required at the edge of the macrocell is SN R R , the macrocell BS transmission power is

P tma = SN R R • σ 2 L -1 0 R γ . ( 8
)
Then the received SNR at a distance of r meters from the BS is

SN R(r) = P tma L 0 r -γ σ 2 = SN R R • ( R r ) γ . (9)
The probability density that an MD is located at r meters from the BS is

p ma (r) = 2r R 2 r < R. ( 10
)
Transmission duration of an MD which is r meters away from the macro station is t ma (r) = S Rama(r) , in which Ra ma (r) equals to [START_REF] Jo | Heterogeneous cellular networks with flexible cell association: A comprehensive downlink SINR analysis[END_REF] where η r represents the spectrum efficiency when an MD is located at r meters from the macro BS, namely, η r = log 2 (1+ SN R(r)).

Ra ma (r) = B mauser • log 2 (1 + SN R r (r)) = B u • η r ,
Combining ( 9), ( 10) and ( 11), the average transmission duration of all MDs is

T ma = ˆR 0 S Ra ma (r) • p ma (r)dr = ˆR 0 S B mauser • η r • 2r R 2 dr. ( 12
)
The total power consumption of MDs is

P mauser = M a [P w • T ma + P i • (1 -T ma )]. (13)

B. Power Consumption With a Microcell

For the single macrocell / single microcell HetNet scenario, the active number of macrocell MD is given by M a = λπ(R 2 -D 2 ) and the active number of microcell MD is given by M i = λπD 2 . Accordingly, bandwidth of macrocell and microcell MD are B mauser = Bma M a and B miuser = Bmi Mi . Here, B mi is the total bandwidth of microcell.

Similar as [START_REF] Wang | Energy efficiency of heterogeneous cellular network[END_REF], the minimum required SNR at the edge of the microcell is SN R D . The microcell BS transmission power is

P tmi = SN R D • σ 2 L -1 0 D γ . ( 14
)
Received SNR at distance r from the macro BS is the same as [START_REF] Richter | Energy efficiency aspects of base station deployment strategies for cellular networks[END_REF]. Received SNR at a distance r meters from the micro BS is

SN R(r ) = P tmi L 0 r -γ σ 2 = SN R D • ( D r ) γ . ( 15
)
As MDs in the coverage of the microcell will associate with the microcell instead after the deployment of microcell, the active macrocell MD distribution will change. When an MD is located in Area 1 and Area 3 shown in Fig. 1, the probability density that the MD is r meters from the BS is

P {r|M D is in Area 1} = 2r (d -D) 2 , ( 16
)
P {r|M D is in Area 3} = 2r R 2 -(d + D) 2 , (17)
respectively. In Area 2, for MDs located r meters from the macro station, arccos{ (d 2 +r 2 -D 2 ) /2dr} π proportion of the MDs will associate with micro station. So the probability density that a macrocell MD located at the place that is r meters from the macro BS is

P {r|M D is in area 2} = π -arccos (d 2 +r 2 -D 2 ) /2d•r π × 2r (d + D) 2 -(d -D) 2 d -D < r < d + D. ( 18
)
So from the whole system point of view, in the macrocell, the probability density of active MD as a function of r is given by

p ma (r) =          2r (R 2 -D 2 ) r < d -D, r > d + D π-arccos{ (d 2 +r 2 -D 2 ) /2dr} π • 2r (R 2 -D 2 ) d -D < r < d + D . (19)
The probability density that a microcell MD is located at distance r meters from the micro BS is

p mi (r ) = 2r D 2 r < D. ( 20
)
As the transmission rates of both macrocell and microcell MDs (R mauser ,R miuser ) obey the Shannon's law (2), the average transmission duration of macrocell and microcell MDs can be derived as

T ma (r) = ˆR 0 S R mauser (r) • p ma (r)dr, (21)
T mi (r ) = ˆD 0 S R miuser (r ) • p mi (r )dr . ( 22
)
The sum of macrocell and microcell MDs power consumption can be expressed as

P user = M a [P w • T ma + P i • (1 -T ma )]+ M i [P w • T mi + P i • (1 -T mi )] . ( 23
)
Then total power saving for MDs is given in Eq. ( 24) on the next page.

In Equation.( 24), η r represents the spectrum efficiency when a microcell MD is located at r meters from the micro BS, namely, η r = log 2 (1 + SN R(r )).

To make (24) more tractable, we propose an approximation that uses the transmission rate of a certain place, analogous to the well-known "typical node (place)" in stochastic geometry, to represent the average transmission rate of the whole microcell or macrocell MDs. Denote d equal as the distance from the place to its associated BS and denote α= d equal R . Through simulations, we found, just as Fig. 2 shows, with different size of coverage, α changed little. Another approximation is that the average transmission rate when the microcell MDs are served by the macrocell before the microcell deployment can be approximated as the transmission rate of the place that is (d + 0.1D) meters from the macro BS. So, denote

η Rα = log 2 (1+SN R R •(α) -γ ) and η Dα = log 2 (1+SN R D •(α) -γ ), (24)
can be approximated as

Psave ≈ λ 2 π 2 S(Pw -P i ) D 2 R 2 Bmaη Rα - D 4 B mi η Dα + D 2 (R 2 -D 2 ) Bmalog 2 (1+SN R R •( d+0.1•D R ) -γ ) . ( 25
)
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 6.76 6.77 6.78 6.79

Psave = Puser -P user = λπR 2 (Pw -Pi) ´R 0 S Bma λπR 2 •ηr • 2r R 2 dr -λπ(R 2 -D 2 )(Pw -Pi) • ´d-D 0 S Bma λπ(R 2 -D 2 )
•ηr

• 2r (R 2 -D 2 ) dr + ´d+D d-D S Bma λπ(R 2 -D 2 ) •ηr • π-arccos (d 2 +r 2 -D 2 )/2dr 2π • 2r (R 2 -D 2 ) dr + ´R d+D S Bma λπ(R 2 -D 2 )
•ηr

• 2r (R 2 -D 2 ) dr -λπD 2 (Pw -Pi) • ´D 0 S B mi λπD 2 •η r • 2r D 2 dr = λ 2 π 2 D 2 (Pw -Pi) ´R 0 S Bma •ηr • 2rdr + (R 2 -D 2 )(Pw -Pi) • ´d+D d-D S Bma •ηr • arccos (d 2 +r 2 -D 2 )/2dr π • 2rdr -D 2 (Pw -Pi) • ´D 0 S B mi •η r • 2r dr (24)
Denote the term λ 2 π 2 S(P w -P i ) by K,

1 η Rα by T M a , 1 η Dα by T M i , 1 log 2 (1+SN R R •( d+0.1•D R ) -γ ) by T d , the power saving is Psave = K D 2 R 2 Bma • Tma - D 4 B mi T mi + D 2 (R 2 -D 2 ) Bma • T d . ( 26
)
From the expression above, we can get some interesting conclusions:

1) Power saving on the MDs side P save is linearly correlated with the square of the active MD density, down load data size, and the difference of working power and idle power of the MDs. 2) High macrocell capability (B ma ) will impair the benefit of microcell deployment. 3) High microcell capability (B mi ) will save more power on the MDs side. 4) From the parameter T d in the expression, we can see that P save increases with the increase of distance between the microcell and the macrocell.

C. The Optimal Microcell Radius to Maximize MDs' Power Saving

Through (26), we can get the optimal value of D delivering the maximum saving power for the MDs by letting the dPsave dD = 0. Ignoring the effect of the 0.1D in T d , we can get the optimum value of D as

D = R √ 2 Tma + T d Bma B mi T mi + T d . (27)
Some interesting results can easily be observed from (27):

1) The optimum D increases linearly with the increase of the macrocell radiusR.

2) The optimum D is positively correlated with the bandwidth ratio of microcell and macrocell ( Bmi Bma ). That is to say, more capable micro BS fits bigger coverage size.

3) The further the microcell is from the macrocell, the bigger the optimum D should be.

D. The Optimal Microcell Radius for The Highest Power Saving

According to the definition of the power saving metric in (6), Ψ can be expressed as follows

Ψ = Psave -β • P mi = K D 2 R 2 Bma • Tma -D 4 B mi T mi + D 2 (R 2 -D 2 ) Bma • T d - D γ (β • a • SN R D • σ 2 L -1 0 ) + β • Pm mi . (28)
a•SN R D •σ 2 KL0
by ρ, then the optimal value of D to balance the energy efficiency of both BSs and MDs will be obtained by setting dΨ dD = 0:

d K D 2 R 2 Bma •Tma-D 4 B mi Tmi+ D 2 (R 2 -D 2 ) Bma •T d dD - d{Kβ•ρD γ +β•a•Pm mi } dD = 0. (29)
When γ = 2, the optimal value of D is

D = R 2 B mi (Tma + T d ) -BmaB mi βρ 2(BmaT mi + B mi T d ) . (30)
It can be seen that the importance of the power consumption on the BS (β) is negatively correlated with the the size of D.

IV. NUMERICAL RESULTS

To verify the accuracy of our analytical results, extensive simulations with the deployment of a microcell with different size and at different location are provided in this section. The simulation parameters are summarized in Table I.

With respect to BS power consumption, some typical parameter values for macrocell and microcell in (4) and ( 5) are chosen as follows: a macro = 3.8, P mma = 68.8W , a micro = 5.5 and P mmi = 38W respectively [START_REF] Wang | Energy efficiency of heterogeneous cellular network[END_REF]. For all the simulations, the coverage of the microcell is assumed to be within that of the macrocell.

A. Numerical Results

The relationship of power saving at MDs with different microcell size D and different distance between macrocell and microcell d are shown in Fig. 3. In this figure, small circles stand for simulation results and solid lines are analytical results according to (26). It can be seen that the two curves are very close to each other. The larger d is, the more power saving can be achieved under the same configurations. This finding coincides with our analytical results in (24) of Section III. For the given configurations, power saving for microcell MDs is close to 18%, compared with the scenario with no microcell deployments. Meanwhile, deployment of microcell also brings about 4% of power saving for the entire active MDs. If more data are downloaded by MDs, the power saving gain will be more significant. Fig. 4 shows the power saving indicator of the system measured by the metric in [START_REF] Soh | Energy efficient heterogeneous cellular networks[END_REF]. The weight β of the power consumption for the mobile network operator is 0.5. When the D is less than a threshold, about 1400 meters in the figure, with the increasing of D, better service of microcell will be of benefit to more and more mobile devices, so the power saving is increasing. However when the microcell radius exceeds the threshold, too many mobile devices are in the microcell, and the inappropriate user assiment will lead to poor performance of the microcell. Thus the power saving will be decreasing with the increasing D. If the power saving indicator is larger than 0, the deployment of a microcell is beneficial from power consumption perspective. Observing from the Fig. 4, with further distance from the macro BS to the micro BS, the power saving improvement by deployment of the micro BS will be more significant.

V. CONCLUSION

In this paper, we analyzed the energy efficiency of HetNets from a more comprehensive and systematic perspective. We proposed an power saving metric which considers the power consumption of both BSs and MDs. Under a single macrocell and a single micro BS scenario, the power saving of the HetNet was analyzed. Approximate expressions which better reveal the relationship of the power consumption at the MDs side as well as the optimum microcell radii with different system parameters of the system were provided. It was shown that the total power saving for microcell MDs is close to 18% with a proper deployment of a microcell. This work could provide a useful guidance for energy efficient planning of micro BSs. In the future, more practical MD distribution model and more efficient resource allocation algorithm will be taken into consideration so as to obtain more realistic performance analyses.

Fig. 1 .

 1 Fig. 1. An Illustration of a HetNet with One Macrocell and One Microcell

Fig. 2 .

 2 Fig. 2. Equivalent Point (α) over Cell Radius

Fig. 3 .

 3 Fig. 3. Power Saving at MDs over Coverage Radius of the Microcell

Fig. 4 .

 4 Fig. 4. Power Saving Indicator over Coverage Radius of the Microcell