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SHANGHAI UNIVERSITY 毕业设计（论文）UNDERGRADUATE PROJECT (THESIS)论文题目基于连续隐马尔科夫模型的语音识别学院机自专业自动化学号03122669学生姓名金微指导教师李昕起讫日期2007 3.20—6.6目录摘要---------------------------------------------------------------------------2 ABSTRACT ------------------------------------------------------------------------2绪论---------------------------------------------------------------------------3第一章语音知识基础---------------------------------------------------------------6 第一节语音识别的基本内容-------------------------------------------6第二节语音识别的实现难点-------------------------------------------9第二章HMM的理论基础--------------------------------------------------------10 第一节HMM的定义----------------------------------------------------10第二节隐马尔科夫模型的数学描述---------------------------------10第三节HMM的类型----------------------------------------------------12第四节HMM的三个基本问题和解决的方-----------------------15第三章HMM算法实现的问题----------------------------------------------21 第一节HMM状态类型及参数B的选择---------------------------21第二节HMM训练时需要解决的问题-----------------------------23第四章语音识别系统的设计---------------------------------------------------32 第一节语音识别系统的开发环境-----------------------------------32第二节基于HMM的语音识别系统的设计------------------------32第三节实验结果---------------------------------------------------------49第五章结束语-------------------------------------------------------------------67致谢------------------------------------------------------------------------------68参考文献------------------------------------------------------------------------69摘要语音识别系统中最重要的部分就是声学模型的建立，隐马尔可夫模型作为语音信号的一种统计模型，由于它能够很好地描述语音信号的非平稳性和时变性，因此在语音识别领域有着广泛的应用。

Application of the Soil and Water Assessment Tool (SWAT)to predict the impact of alternative management practices on water quality and quantityAntje Ullrich *,Martin VolkHelmholtz Centre for Environmental Research –UFZ,Department of Computational Landscape Ecology,Permoserstr.15,D-04318Leipzig,Germany1.IntroductionDue to insufficient water quality of European streams environmental programs such as the European Water Framework Directive (WFD)were implemented to achieve good ecological and chemical conditions of water quality of groundwater and surface water bodies (EC,2000;Rekolainen et al.,2003).Main nutrient input comes from nonpoint source pollution,mainly forced by intensive agricultural activities (Behrendt et al.,1999).Therefore,alternative land management practices are increasingly used to reduce nonpoint source pollution.Reduction of soil tillage intensity positively affects numerous soil properties,such as aggregate stability,macroporosity,and saturated hydraulic con-ductivity and consequently increases infiltration rates and reduces surface runoff,nutrient loss,and soil erosion (Jones et al.,1969;Pitka¨nen and Nuutinen,1998;Schmidt et al.,2001;Kirsch et al.,2002;Pandey et al.,2005;Tripathi et al.,2005).Alternative land management practices may include reduced tillage such asconservation tillage (e.g.without deep ploughing,field preparation just before planting)or no-tillage (direct drilling)(Sullivan,2003;LfULG,2006).In Germany the implementation of alternative tillage systems is increasingly supported by agro-environmental pro-grams.In the German State of Saxony,for instance,conservation tillage and mulch seeding on arable land has increased from <1%to about 27%during 1994–2004with support from the Saxonian Program for Environmental Agriculture (LfL,2006).A number of field studies have illustrated the positive effects of conservation tillage and no-tillage practices on water and material fluxes at the field local level (e.g.Sloot et al.,1994;King et al.,1996;Schmidt et al.,2001),but this effect needs to be assessed on the watershed level to guide river basin management programs as WFD claimed (Kirsch et al.,2002;Chaplot et al.,2004;Pandey et al.,2005;Behera and Panda,2006;Bracmort et al.,2006).Therefore,watershed models are useful tools and have been used for decades to evaluate nonpoint source pollution and the short-and long-term impacts of alternative management practices.In order to fulfill the objectives of the WFD,we have chosen the semi-distributed river basin model,Soil and Water Assessment Tool (SWAT)2005(Neitsch et al.,2002;Arnold and Fohrer,2005)to examine the impact of alternative management practices on waterAgricultural Water Management 96(2009)1207–1217A R T I C L E I N F O Article history:Received 3September 2008Accepted 6March 2009Keywords:SWATTillage management practice Conservation tillage Water balance Nutrient ModellingA B S T R A C TAlternative land management practices such as conservation or no-tillage,contour farming,terraces,and buffer strips are increasingly used to reduce nonpoint source and water pollution resulting from agricultural activities.Models are useful tools to investigate effects of such management practice alternatives on the watershed level.However,there is a lack of knowledge about the sensitivity of such models to parameters used to represent these conservation practices.Knowledge about the sensitivity to these parameters would help models better simulate the effects of land management.Hence,this paper presents in the first step a sensitivity analysis for conservation management parameters (specifically tillage depth,mechanical soil mixing efficiency,biological soil mixing efficiency,curve number,Manning’s roughness coefficient for overland flow,USLE support practice factor,and filter strip width)in the Soil and Water Assessment Tool (SWAT).With this analysis we aimed to improve model parameterisation and calibration efficiency.In contrast to less sensitive parameters such as tillage depth and mixing efficiency we parameterised sensitive parameters such as curve number values in detail.In the second step the analysis consisted of varying management practices (conventional tillage,conservation tillage,and no-tillage)for different crops (spring barley,winter barley,and sugar beet)and varying operation dates.Results showed that the model is very sensitive to applied crop rotations and in some cases even to small variations of management practices.But the different settings do not have the same sensitivity.Duration of vegetation period and soil cover over time was most sensitive followed by soil cover characteristics of applied crops.ß2009Elsevier B.V.All rights reserved.*Corresponding author.Tel.:+493454722602;fax:+493412351939.E-mail address:antje.ullrich@ (A.Ullrich).Contents lists available at ScienceDirectAgricultural Water Managementj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /a g w a t0378-3774/$–see front matter ß2009Elsevier B.V.All rights reserved.doi:10.1016/j.agwat.2009.03.010quantity and quality.Gassman et al.(2007)point out that‘‘a key strength of SWAT is aflexible framework that allows the simulation of a wide variety of conservation practices and other BMP,such as fertiliser and manure application rate and timing, cover crops(perennial grasses),filter strips,conservation tillage, irrigation management,flood prevention structures,grassed waterways,and wetlands.The majority of conservation practices can be simulated in SWAT with straightforward parameter changes’’.Many studies have used SWAT(Saleh et al.,2000; Shanti et al.,2001;Vache et al.,2002;Shanti et al.,2003;Chaplot et al.,2004;Pandey et al.,2005;Tripathi et al.,2005;Arabi et al., 2006;Behera and Panda,2006;Rode et al.,2008;Volk et al.,2009) and EPIC(Sloot et al.,1994;King et al.,1996)to evaluate the effects of land use scenarios and management practices.Several studies have analysed the long-term effects of structural Best Management Practices(BMP)on water quality(e.g.Kirsch et al.,2002;Chaplot et al.,2004;Tripathi et al.,2005;Pandey et al.,2005or Behera and Panda,2006;Bracmort et al.,2006).Arabi et al.(2007)investigated the impact of modelling uncertainty on evaluation of management practices using a Monte Carlo-based probabilistic approach.The SWAT model was developed for application to large complex watersheds over long periods of time(Neitsch et al., 2002).Working on the watershed-scale means that required input data are often aggregated in terms of temporal scale(e.g.daily climate data).In contrast,land management parameters(tillage, fertilisation,crop rotation,etc.)can be included in high resolution and detail,due to its modular structure and its historical development based on the EPIC(Erosion Productivity Impact Calculator)model(Benson et al.,1988;Neitsch et al.,2002;Arnold and Fohrer,2005;Gassman et al.,2007).Furthermore,modelling evaluations of conservation management effects at the watershed-scale are limited by the lack of management operation data.Thus, knowledge is needed of the sensitivity of such models to conservation management parameters and practice to improve the efficiency of model parameterisation and the quality of model calibration.Furthermore,potential simulation uncertainties based on ranges of realistic parameter values and on influences of scale need to be understood because simulated effects often drive financial and political decisions(Onatski and Williams,2003).As a result,the main objective of this study is to analyse the sensitivity of the SWAT model to selected conservation manage-ment parameters and practices to improve model parameterisa-tion and calibration.To the best of our knowledge,a sensitivity analysis of the model to conservation management parameters and practices has not yet been conducted.But in our opinion this is essential for a more efficient use of models for the implementation of land management practices as tools to improve water quantity and quality.We used a so-called semi-virtual watershed for which we combined topography and climate information of an existing watershed(Parthe watershed,Saxony,Germany)but with homo-geneous land use and soil information.Homogeneous land use and soil information were utilised because the resulting data sets are concise and manageable and calculation time is reduced. Recommendations are given for the parameterisation of tillage operations under certain conditions.2.Materials and methods2.1.Model descriptionThe SWAT model is considered as one of the most suitable models for predicting long-term impacts of land management measures on water,sediment,and agricultural chemical yield (nutrient loss)in large complex watersheds with varying soils,land use,and management conditions(Arnold and Fohrer,2005;Behera and Panda,2006;Gassman et al.,2007).The model has been gained international acceptance as a robust interdisciplinary watershed modelling tool(Gassman et al.,2007).SWAT is a physically based, conceptual,continuous-time river basin model with spatial distributed parameters operating on a daily time step.It is not designed to simulate detailed,single-eventflood routing(Neitsch et al.,2002).The relationship between input and output variables is described by regression equations.The SWAT model integrates all relevant eco-hydrological processes including waterflow, nutrient transport and turn-over,vegetation growth,and land use and water management at the subbasin scale.Consequently, the watershed is subdivided into subbasins based on the number of tributaries.Size and number of subbasins is variable,depending on stream network and size of the entire watershed.Subbasins are further disaggregated into classes of Hydrological Response Units (HRU),whereby each unique combination of the underlying geographical maps(soils,land use,etc.)forms one class.HRU are the spatial unit where the verticalflows of water and nutrients are calculated,which are then aggregated and summed for each subbasin.Water and material from HRU in sub-watersheds are routed to the sub-watershed outlet.The HRU in SWAT are spatially implicit,their exact position in the landscape is unknown,and it might be that the same HRU covers different locations in a subbasin(Neitsch et al.,2002;Di Luzio et al.,2005).The water balance for each HRU is represented by the four storages snow,soil profile,shallow aquifer and deep aquifer.The soil profile can be subdivided in up to ten soil layers.Soil water processes include evaporation,surface runoff,infiltration,plant uptake,lateralflow and percolation to lower layers(Arnold and Allen,1996;Neitsch et al.,2002).The surface runoff from daily rainfall is estimated with a modification of the SCS curve number method from United States Department of Agriculture-Soil Conservation Service(USDA SCS) (Arnold and Allen,1996;Neitsch et al.,2002).Nitrogen movement and transformation are simulated as a function of the nitrogen cycle(Neitsch et al.,2002;Jha et al.,2004). The SWAT model monitorsfive different pools of nitrogen in the soils:two inorganic(ammonium(NH4+)and nitrate(NO3À))and three organic(fresh organic nitrogen(associated with crop residue and microbial biomass)and active and stable organic nitrogen (associated with the soil humus)).Nitrogen is added to the soil by fertiliser,manure or residue application,fixation by bacteria,and rain(Neitsch et al.,2002).Nitrogen losses occur by plant uptake, surface runoff in the solution and the eroded sediment(Neitsch et al.,2002;Jha et al.,2004).Background for the crop growth and the management practices is the EPIC crop growth model,which is a comprehensivefield scale model.EPIC was originally developed to simulate the impact of erosion on crop productivity and has now evolved into a comprehensive agricultural management,field scale,nonpoint source loading model(Benson et al.,1988;King et al.,1996; Neitsch et al.,2002).The management practices are defined by specific management operations(e.g.the beginning and end of growing season,timing of tillage operations as well as timing and amount of fertiliser,pesticide,and irrigation application).These management operations take place in every HRU.The operations in turn are defined by specific management parameters(e.g. tillage depth,biological soil mixing efficiency,etc.)(Neitsch et al., 2002).2.2.Input dataWe used a semi-virtual watershed.Therefore we combined topography and climate information of an existing watershed with virtual land use and soil information.The Parthe watershed was chosen as study area.It is located in the State of Saxony in Central Germany and drains an area of about315km2(Fig.1).It is aA.Ullrich,M.Volk/Agricultural Water Management96(2009)1207–1217 1208subbasin of the Weiße Elster catchment in the Elbe River system. The topography of the area isflat with altitudes between106and 230m above sea level.The mean annual precipitation is about 570mm.The model input data are shown in Table1.For the sensitivity analysis,we assumed‘‘arable land’’to be homogeneous land use without any further differentiation.A typical soil profile was used from a soil map(1:25,000)of the Parthe watershed.The use of homogeneous land use and soil(semi-virtual catchment)is advantageous because the resulting data sets are concise and manageable and calculation time is reduced.Daily precipitation data and other climate data are from one weather station in the watershed.This station is part of the environmental monitoring network of the Environmental Operation Agency of the Saxon State Agency for the Environment,Agriculture and Geology.2.3.Sensitivity analysisModel sensitivity analysis regarding selected management practices was donefirstly by varying the most important tillage and management parameters:tillage depth,mechanical mixing efficiency,biological mixing efficiency,curve number,and Man-ning’s roughness coefficient for overlandflow,USLE support practice factor,andfilter strip width.Secondly,management practices were parameterised and varied for different crops and dates of operation. Subsequently,the influence of varying these practices on water balance components and nutrients was evaluated.2.4.Management parametersThe applied tillage operation(plough,stubble cultivation, harrow,etc.)is defined by the parameters tillage depth(DEPTIL) and mechanical soil mixing efficiency(EFFMIX).These parameters also define the fraction of crop residue,nutrients,pesticides,and bacteria for each soil horizon,which are redistributed within the mixed soil depth(Neitsch et al.,2002).The biological soil mixing efficiency(BIOMIX)defines the activity of soil organisms,such as earthworms as representatives of macrofauna,which influence soil porosity and waterfluxes by their grubbing activity(Kladivoka, 2001;Neitsch et al.,2002).The biological soil mixing efficiency can be defined for each HRU.The SCS curve number(CN)defines soil permeability based on soil characteristics and land cover(land use).This parameter routes the process of infiltration and generation of surface runoff.The parameter CN can generally be defined on the HRU level and more detailed based on tillage operations data(Neitsch et al.,2002).The Manning’s roughness coefficient for overlandflow(OV_N)is a parameter toestimateFig.1.Location of the study area in Germany.Table1Input data.Topography Land use Soil WeatherDEM Homogeneous Homogeneous Daily values-Area:315km2-Arable land-Cambisol-Precipitation[mm]-Grid cell size:30m-Mean wind speed(recorded in2.5m height)[m/s]-Max.and min.air temperature[8C]-total solar radiation(calculated using global radiation)[MJ/m2]-Mean relative humidity(recorded in0.5and2m height)[%]A.Ullrich,M.Volk/Agricultural Water Management96(2009)1207–12171209overlandflow velocity,which depends on characteristics of the land surface.This parameter can be defined for each HRU(Neitsch et al.,2002).The management parameter USLE support practice factor(USLE_P)defines the ratio of soil loss with a specific support practice(such as contour tillage,strip cropping,and terraces)to the corresponding loss with up-and-down the cultivation.The parameter USLE_P can also be defined on the HRU level(Neitsch et al.,2002).The width of edge offieldfilter strip(FILTERW)defines filter strips with a specific width in meters.Thefilter strips are not differentiated any further.Sediment and nutrient loads in surface runoff and subsurfaceflow are reduced as it passes through the strip.Filter strips can be defined for each HRU(Neitsch et al.,2002).For each simulation only one parameter was varied within a realistic range(see Table2).The value ranges defined for each model parameter are based on literature studies(Neitsch et al., 2002).SWAT also supplies the user with default parameters values. For the basic settings we used these default values,as we are not working with real conditions where these values would have to be adjusted to.The advantage of this method is that the effect on model output is related to the variability of only the selected parameter,but it does not consider the dependency on settings chosen for the other parameters(Arabi et al.,2007).For sensitivity analysis a basic management scenario was used. This is a generalised Agricultural Land Close Grown(AGRC) scenario,which uses values for winter wheat.One fertiliser application(70kg N/ha)just after seeding,and one tillage operation(deep ploughing)just after harvesting,was implemen-ted.This basic scenario was not changed during sensitivity analysis of management parameters.The model output parameters investigated are surface runoff,baseflow,total water yield,total sediment loading,organic nitrogen,organic phosphorus,nitrate in surface runoff,nitrate,and phosphorus leached.The results(see Fig.2)indicate SCS curve number as a very sensitive parameter for water balance components and nutrient and sediment load.This observation is confirmed by Neitsch et al. (2002)as well as by other studies,such as Sloot et al.(1994), Heuvelmans et al.(2004),Bracmort et al.(2006),and Arabi et al. (2007).The CN is most sensitive for values above65.For example surface runoff increased from almost zero up to more than100mm between CN65to95.At the same time,corresponding surface runoff organic nitrogen,organic phosphate,nitrate in surface runoff and total sediment loading increased.In contrast,based on the decrease of baseflow,nitrate and phosphate leached decreased.Biological soil mixing efficiency and Manning’s roughness coefficient for overlandflow do only moderately affect water balance components.The values vary less than5mm for applied parameter ranges.For the value range of biological soil mixing efficiency(0–1)the results for organic nitrogen(simulated range between0.225kg/ha and0.55kg/ha),organic phosphate(0.034–0.069kg/ha),and total sediment loading(0.057–0.318t/ha)increased while phosphate leached(0.318–0.145kg/ha)decreased. For the watershed area(315km2)this represents load values for organic nitrogen between7.1t and17.3t,organic phosphate between1.1t and2.2t,phosphate leached between10t and4.6t, and total sediment loading between1795t and10,017t.Based on these results we assume biological mixing efficiency to be a sensitive parameter regarding the above described nutrient components.Manning’s roughness coefficient for overlandflow affected organic nitrogen(simulated range between0.248kg/ha and 0.135kg/ha;7.8–4.3t for watershed area)followed by sediment loading(0.088–0.048t/ha; 2.8–1.5t for watershed area)and organic phosphorus(0.038–0.02kg/ha; 1.2–0.6t for watershed area).Therefore,we assume this parameter to be sensitive with respect to the described nutrients and sediment load.Both the USLE support practice factor and the width of edge of fieldfilter strip do not influence water balance components.But USLE support practice factor is very sensitive to total sediment loading(simulated range between0.007t/ha and0.067t/ha;220–2110t for watershed area),organic nitrogen(0.019–0.187kg/ha, 0.6–5.9t for watershed area),and organic phosphorus(0.003–0.027kg/ha;0.09–0.9t for watershed area)while the width of edge offieldfilter strip affected organic nitrogen and decreased from 0.187kg/ha to0.076kg/ha(see Fig.3).This means that with an extension of thefilter strip width from0.5m to5m the organic nitrogen loss related to the watershed area decreased about50% (from5.9t to2.4t).Furthermore,with increasing width of edge of fieldfilter strip organic phosphate(simulated values:0.027kg/ha and0.011kg/ha;0.85t and0.35t),nitrate load in surface runoff (0.047–0.019kg/ha;1.5–0.6t)and total sediment loading0.067–0.027t/ha;2110–850t)decreased.In this study the variation of tillage depth and mechanical soil mixing efficiency did not influence neither water cycle components nor nutrient and sediment cycle components.2.5.Management practicesWith respect to the management parameters’sensitivity,the tillage operations subject to management practices(conventional (CVT),conservation(CST)and no-tillage(NOT))were parameterised exemplary(see Table3).Here,conventional tillage primarily is distinguished dependent on tillage practices applied after harvest-ing including deep ploughing,previous stubble cultivation and following harrow operation before seeding/planting.For conserva-tion management a multiplicity of measures can be taken.For tillage practice we chose altogether three variations:(a)deep ploughing operation is replaced by a less intensive operation(CST_A),(b)deep ploughing operation is left out and not replaced(CST_B)and(c) harrow operation is applied only(CST_C).Parameters were set as follows.Differentiated by applied tillage operation,we parameterised curve number(CN)values in detail. The curve number adjustment is strongly linked to the soil dependent basic curve number identified within calibration process,planted crop(grain and root crop),applied tillage operation,and residue coverage(defined by applied management practice).The allocation of the SCS curve number is based on the parameterisations suggested by Neitsch et al.(2002)and continuative on the comments of Rawls and Richardson(1983). Rawls and Richardson(1983)recommend lowering the SCS curve number by2%for soils with poor hydrological conditions when applying conservation tillage(compared to conventional tillage). Forfields with good hydrological conditions,the SCS curve number should be lowered by4%compared to conventional tillage.King et al.(1996)applied EPIC using curve number values of87and82 for conventional tillage and for no-tillage practices respectively representing the soil hydrological group D(clay soil).Sloot et al. (1994)used the initial curve numbers:A value of84forTable2Basic parameter settings and variation ranges.Parameter Basic setting Parameter rangeSCS curve number(CN)7535–95 Biological soil mixingefficiency(BIOMIX)0.20–1.0Manning’s roughnesscoefficient for overlandflow(OV_N)0.140.01–0.5Tillage depth(DEPTIL)[cm]300–95 Mechanical soil mixingefficiency(EFFMIX)0.50–1.0USLE support practicefactor(USLE_P)1.00.1–1.0Width of edge offieldfilter strip(FILTERW)[m]0.00–5.0A.Ullrich,M.Volk/Agricultural Water Management96(2009)1207–12171210conventional tillage,83for minimum tillage(conservation tillage) and82for no-tillage.Here,the initial CN representing the soil hydrological group A(for soils with good hydrological conditions) was used.Biological soil mixing efficiency is a sensitive parameter and was parameterised in detail depending on the intensity of the applied management practice.As a result,the biological mixing activity decreases with increasing tillage intensity.Theparameter Fig.2.Sensitivity of SWAT model to tillage parameters:CN,BIOMIX andOV_N.Fig.3.Sensitivity of SWAT model to management practice parameters USLE_P and FILTERW.A.Ullrich,M.Volk/Agricultural Water Management96(2009)1207–12171211values for biological soil mixing efficiency used in this study were discussed with local farmers.Manning’s roughness coefficient for overland flow was defined subject to management practise and changing residue cover (Sloot et al.,1994;Neitsch et al.,2002).The parameter increases with increasing soil coverage according to decreasing tillage intensity.We defined only one tillage depth and mixing efficiencies for one main tillage operation (as applied crop-dependent on the field in reality;Abraham et al.,2004).The timing of tillage operations affects soil coverage (residue decomposition).For example,fall tillage operation reduces residue over the winter and spring period.The timing of tillage and theTable 3Parameterisation of tillage operations within management practices.ScenarioTillage operationDEPTIL a (cm)EFFMIX bBIOMIX cOV_N dCN*e GrainsRow cropsConventional tillage (CVT)CVT Cultivation stubble120.450.10.0976Plough (bare soil)250.8577Harrow 70.3Plant 6367Harvest 74Conservation tillage (CST)CST_A Cultivation stubble120.450.20.1376Harrow 70.3Plant 6266Harvest74CST_B 0.30.19CST_C Harrow70.30.40.374Plant 6165Harvest 73No-tillage (NOT)Plant 0.40.36064Harvest73a Abraham et al.(2004)—based on practical experience.b Neitsch et al.(2002).c Discussed with local farmers.d Neitsch et al.(2002).eNeitsch et al.(2002)–CN is exemplarily used representatively for soil hydrological group A –soil with good hydrological conditions.Table 4Tillage scenarios based on tillage practices;(P)plough,(St)stubble cultivation,(H)harrow,(S)seed (dates by Abraham et al.,2004).Dates of operation Fall tillageSpring tillage Spring barley 03.August 10.October 01.March 05.March 10.March15.MarchWinter barley 12.August 20.August 01.September 05.September Sugar beet08.October 11.October 26.March 01.April 05.April 10.April Conventional tillage CVTSt P ––H S CVT_1St P –––S CVT_2–P ––H S CVT_3–P –––S CVT_4St ––P H S CVT_5St ––P –S CVT_6––St P H S CVT_7––St P –S Conservation tillage CST_A St St ––H S CST_A1St St –––S CST_A2St ––St H S CST_A3St ––St –S CST_A4––St St H S CST_A5––St St –S CST_B St –––H S CST_B1St ––––S CST_B2–St ––H S CST_B3–St –––S CST_B4–––St H S CST_B5–––St –S CST_B6––St –H S CST_B7––St ––S CST_C ––––H S No-tillage NOT–––––SA.Ullrich,M.Volk /Agricultural Water Management 96(2009)1207–12171212choice of tillage operation depend on the crop being planted and the chosen management practice (Kirsch et al.,2002).Therefore differences between spring and winter crops as well as between grains and root crops are expected.Hence we applied commonly planted crops:spring barley (Hordeum vulgare )—representative for grains planted in early spring;winter barley (Hordeum vulgare var.a genuinum )—representative for grains planted in early fall and sugar beet (Beta vulgaris )—representative for root crops planted in early spring.For each crop depending on management practice basic scenarios were defined (see Table 4).Conventional and conservation tillage are primarily distinguished by tillage practices applied directly after harvesting (deep ploughing,previous stubble cultivation).The harrow operation is applied for all scenarios just before seeding/planting.Following sub-scenarios for conventional and conservation tillage (CVT_1,CVT_2,etc.)we defined where,e.g.tillage operations,were applied at different dates (for springplanted crops spring tillage instead of autumn tillage)to identify the sensitivity of SWAT model to the timing of the tillage operations.Management practices related tillage operations are chronolo-gical (e.g.conventional tillage:stubble cultivation/deep ploughing/harrowing).Thus,the harrow operation is least intensive operation.In the following,varying tillage operation combinations were applied to find out if it is necessary to parameterise a less intensive operation which follows a more intensive operation (e.g.harrowing after ploughing).If the effect on model output parameters is only marginal the less intensive operation could be left out.Additionally,the conservation management practice contour-ing and implementation of filter strips was applied to the base tillage scenarios of conservation tillage CST_A and CST_B (e.g.CST_Aa)and no-tillage practise (see Table 5).Finally,a catch crop (red clover)scenario was implemented (CST_CC)for green manuring (only applied for conservation tillage basic scenario with sugar beet).3.Results and discussionGenerally,our results confirm the outcome of studies under-taken by Kirsch et al.(2002),Chaplot et al.(2004),Pandey et al.(2005),Tripathi et al.(2005),and Behera and Panda (2006)that conventional tillage practices need to be replaced by less intensiveTable 5Parameter settings for contouring and filter stripes.ScenarioParameter USLE_PFILTERW (m)_a 0.60_b 1.02_c0.62Fig.4.Percentage deviation of modelling results regarding to application of basic management scenarios with a)sugar beet,b)spring barley and c)winter barley on water balance components,nutrients and sediment loading.A.Ullrich,M.Volk /Agricultural Water Management 96(2009)1207–12171213。

Adaptive OFDM Modulation for Underwater Acoustic Communications:Design Considerations andExperimental ResultsAndreja Radosevic,Student Member,IEEE,Rameez Ahmed,Tolga M.Duman,Fellow,IEEE,John G.Proakis,Life Fellow,IEEE,and Milica Stojanovic,Fellow,IEEEAbstract—In this paper,we explore design aspects of adaptive modulation based on orthogonal frequency-division multiplexing (OFDM)for underwater acoustic(UWA)communications,and study its performance using real-time at-sea experiments.Our design criterion is to maximize the system throughput under a target average bit error rate(BER).We consider two different schemes based on the level of adaptivity:in thefirst scheme,only the modulation levels are adjusted while the power is allocated uniformly across the subcarriers,whereas in the second scheme, both the modulation levels and the power are adjusted adaptively. For both schemes we linearly predict the channel one travel time ahead so as to improve the performance in the presence of a long propagation delay.The system design assumes a feedback link from the receiver that is exploited in two forms:one that conveys the modulation alphabet and quantized power levels to be used for each subcarrier,and the other that conveys a quantized estimate of the sparse channel impulse response.The second approach is shown to be advantageous,as it requires significantly fewer feedback bits for the same system throughput.The effectiveness of the proposed adaptive schemes is demonstrated using computer simulations,real channel measurements recorded in shallow water off the western coast of Kauai,HI,USA,in June2008, and real-time at-sea experiments conducted at the same location in July2011.We note that this is thefirst paper that presents adaptive modulation results for UWA links with real-time at-sea experiments.Index Terms—Adaptive modulation,feedback,orthogonal frequency-division multiplexing(OFDM),underwater acoustic (UWA)communication.Manuscript received February26,2012;revised October17,2012and Feb-ruary12,2013;accepted March12,2013.Date of publication May24,2013; date of current version April10,2014.This work was supported by the Multidis-ciplinary University Research Initiative(MURI)of the U.S.Office of Naval Re-search(ONR)under Grants N00014-07-1-0738/0739,N00014-10-1-0576,and N00014-09-1-0700.Associate Editor:S.Zhou.A.Radosevic is with Qualcomm Technologies Inc.,San Diego,CA92122 USA(e-mail:radosevica@).R.Ahmed and M.Stojanovic are with the Department of Electrical and Com-puter Engineering,Northeastern University,Boston,MA02115USA(e-mail: rarameez@;millitsa@).T.M.Duman is with the Department of Electrical and Electronics En-gineering,Bilkent University,Bilkent,Ankara06800,Turkey(e-mail: duman@.tr).J.G.Proakis is with the Department of Electrical and Computer Engi-neering,University of California at San Diego,La Jolla,CA92093USA (e-mail:jproakis@).Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/JOE.2013.2253212I.I NTRODUCTIONU NDERWATER ACOUSTIC(UWA)channels are con-sidered as some of the most challenging communication media,generally characterized by low propagation speed of sound in water(nominally1500m/s),limited bandwidth,and randomly time-varying multipath propagation which results in frequency-selective fading[1].Delay spreading in an UWA channel can occur over tens of milliseconds;however,the channel impulse response often has a sparse structure,with only a few propagation paths carrying most of the channel energy.Orthogonal frequency-division multiplexing(OFDM)has re-cently emerged as a promising alternative to single-carrier sys-tems for UWA communications because of its robustness to channels that exhibit long delay spreads and frequency selec-tivity[2]–[14].However,applying OFDM to UWA channels is a challenging task because of its sensitivity to frequency offset that arises due to motion.In particular,because of the low speed of sound and the fact that acoustic communication signals oc-cupy a bandwidth that is not negligible with respect to the center frequency,motion-induced Doppler effects result in major prob-lems such as nonuniform frequency shift across the signal band-width and intercarrier interference(ICI)[15],[16].Time-varying multipath propagation and limited bandwidth place significant constraints on the achievable throughput of UWA communication systems.To support high spectral efficiencies over long intervals of time in a nonstationary environment such as the UWA channel,we consider commu-nication systems employing adaptive modulation schemes. While adaptive signaling techniques have been extensively studied for radio channels[17]–[21],only preliminary results for UWA channels are reported in[22]–[26],where simulations and recorded data are used to demonstrate the effectiveness of the proposed adaptation metrics.The performance of an adaptive system depends on the trans-mitter’s knowledge of the channel which is provided via feed-back from the receiver.Since sound propagates at a very low speed,the design and implementation of an adaptive system es-sentially relies on the ability to predict the channel at least one travel time ahead.This is a very challenging task for communi-cations in the range of several kilometers which imposes signifi-cant limitations on the use of feedback.However,our prior work has shown that channel prediction is possible over such intervals of time using a low-order predictor[27].Crucial to successful0364-9059©2013IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.See /publications_standards/publications/rights/index.html for more information.Fig.1.The adaptive system with the important functional blocks.channel prediction is motion compensation that stabilizes the nonuniform Doppler shift and enables (sparse)channel estima-tion.The so-obtained channel estimates contain only a few sig-ni ficant coef ficients that are shown to be stable enough to sup-port prediction several seconds into the future.In this paper,we design an adaptive OFDM system and study its performance using recorded test channels and real-time at-sea experiments.Our approach and contributions are the following.•We estimate small Doppler rates (less than 10)that cor-respond either to drifting of the instruments,or residuals after initial resampling in mobile systems (e.g.,systems using autonomous underwater vehicles).Proper Doppler compensation ensures stability over intervals of time that are long enough to support channel prediction several sec-onds ahead.•We exploit the sparse multipath structure of the channel impulse response to estimate the most signi ficant channel paths and simplify the prediction problem.Speci fically,we estimate only a few signi ficant paths of the channel within a possibly large overall delay spread.We treat the statistical properties of the underlying random process of the channel fading as unknown,and compute the parameters of a linear predictor adaptively,by applying a recursive least squares (RLS)algorithm [28].•We develop two modulation schemes,distinguished by the level of adaptivity:Scheme 1adjusts only the modula-tion level and assumes a uniform power allocation,while scheme 2adjusts both the modulation level and the power allotted to each subcarrier.Both schemes are based on a greedy algorithm whose optimality was discussed in [20].•We propose a new design criterion for an adaptive OFDM system based on the information that is fed back to the transmitter.Speci fically,we consider two cases.In the first case,the information about the modulation alphabet and the quantized power level for each subcarrier is computed at the receiver and fed back to the transmitter.In the second case,the quantized channel estimates are fed back,and the adaptive algorithm for bit loading and power allocation is implemented at the transmitter.•We demonstrate the effectiveness of the proposed adap-tive schemes using computer simulations,test channels recorded during the Kauai Acoustic Communications Mul-tidisciplinary University Research Initiative (MURI)2008(KAM08)experiment in shallow water off the westerncoast of Kauai,HI,USA,in June 2008,and real-time at-sea experiments conducted during the Kauai Acoustic Com-munications MURI 2011(KAM11)experiment at the same location in July 2011.The numerical and experimental re-sults show that the adaptive modulation scheme can pro-vide signi ficant throughput improvements as compared to conventional,nonadaptive modulation for the same power and target bit error rate (BER).The paper is organized as follows.In Section II,we describe the system and the channel model that characterizes an UWA channel.In Section III,we introduce a linear RLS predictor for the channel tap coef ficients.In Section IV,we introduce the rules for selection of the modulation levels,the information that is fed back to the transmitter,and the adaptive OFDM schemes.In Section V,we demonstrate the performance of the proposed adaptive schemes using numerical and experimental results that are based on recorded test channels and real-time at-sea trials,respectively.In Section VI,we provide concluding remarks.II.S YSTEM AND C HANNEL M ODELLet us consider an OFDM system with subcarriers,where the th block of the input data symbols ,,is modulated using the inverse fast Fourier transform (IFFT).The block of input data consists of information-bearing sym-bols and pilots,with corresponding sets denoted as and ,respectively.We assume that the information symbols are inde-pendent,while candidate modulation schemes are binary phase-shift keying (BPSK),quadrature phase-shift keying (QPSK),8phase-shift keying (8PSK),and 16-quadrature amplitude mod-ulation (16QAM)with 2-D Gray mapping.In other words,for the th subcarrier,where ,and the th block,the modu-lation level ,and if no data are transmitted.It is assumed that the pilot symbols takevalues from the QPSK modulation alphabet.For each modula-tion alphabet,we assume a uniform distribution of the constel-lation points with a normalized average power.The transmitter sends frames of OFDM blocks,such that one OFDM block oc-cupies an interval ,where and are the symbol duration and the guard time interval,respectively.We denote by the total bandwidth of the system,by the fre-quency of the first subcarrier,by the central frequency,and by the subcarrier separation.In this paper,we consider an adaptive system illustrated in Fig.1.The different functional blocks of the system,such as channel and Doppler estimation,channel prediction,adaptiveRADOSEVIC et al.:ADAPTIVE OFDM MODULATION FOR UNDERWATER ACOUSTIC COMMUNICATIONS359allocation,and feedback information,are discussed in the rest of the paper.A.Channel ModelLet us now define the impulse response of the overall channel(1) where is the number of distinct propagation paths,is the delay variable,and is the time at which the channel is ob-served.Coefficient represents the real-valued gain of the th path,and represents the corresponding delay.Here, we emphasize that the channel model(1)includes the initial re-sampling operation at the receiver by a common Doppler factor. Assuming a high bandwidth(sufficient resolution in the delay variable),the set of coefficients offers a good representation of the actual propagation paths.The re-ceived signal is given as(2) where is the transmitted signal and represents the ad-ditive white Gaussian noise(AWGN)process with zero mean and power spectral density normalized to unity.1If we also de-fine the equivalent baseband signals and with respect to the frequency,such that(3) we then obtain(4)where(5) and is the equivalent baseband noise.Equation(4)implies the equivalent baseband channel response(6)B.Modeling of the Time-Varying Path DelayFollowing the approach from our previous work[27],we model the time-varying path delays as(7)1The AWGN assumption incurs no loss of generality of the proposed adaptive scheme even though acoustic noise is not white.where is the Doppler scaling factor,which is some func-tion of time.This model includes thefixed term,which describes the nominal propagation delay corresponding to the system geometry at the time of transmission,and an additional term that describes the effect of motion at the time of either due to drifting of the instruments(Doppler rates less than10)in stationary systems,or residuals after initial resampling in mobile systems(e.g.,systems using au-tonomous underwater vehicles).The system motion during a period of time corresponding to a few seconds(or several data packets)is modeled by velocity and acceleration terms which lead to a linear Doppler rate.A more accurate model could include higher order terms;however,experimental results con-firm that this is not necessary.Specifically,we model as a piecewise linear function(8) where,and are the Doppler scaling factors evaluated at time instances.This channel model is deemed suitable for the time scales of interest to an adaptive UWA communication system,since pro-viding a reliable predicted channel state information(CSI)de-pends on the availability of a stable signal reference that can be obtained through accurate motion compensation.For example, for a2-km link and the center frequency20kHz,a small Doppler rate can cause the phase of in (5)to change up to radians during a time interval of1.33s that corresponds to the propagation delay of one travel time.2 Such a phase shift can considerably degrade the performance of channel prediction and the reliability of the corresponding CSI. In other words,proper Doppler compensation ensures stability over intervals of time that are long enough to support channel prediction several seconds ahead.Model(7)allows one to decouple phase into two terms:one that is not related to motion,and another that is re-lated to motion.While thefirst term may not be predictable with sufficient accuracy because frequency may be several orders of magnitude larger than the inverse of the path delay,the second term can be predicted using the estimates of the Doppler scaling factors.With this fact in mind,we proceed to develop a channel prediction method that focuses on two general terms:a complex-valued coefficient and a mo-tion-induced phase.In other words, we model the baseband channel as(9) where we treat each as an unknown complex-valued channel coefficient,which is assumed to be stable over a prolonged period of time(tens of seconds),and as an unknown motion-induced phase,which is modeled as a second-order polynomial based on expressions(7)and(8).We 2Here we should make a distinction between making the prediction for one travel time ahead,and for the round-trip time(two travel times ahead),since the two cases correspond to different feedback implementation strategies,i.e., different functions performed by the two ends of a link.360IEEE JOURNAL OF OCEANIC ENGINEERING,VOL.39,NO.2,APRIL2014Fig.2.Channel estimates obtained by the RLS and the MP algorithm. emphasize that this model is valid for some interval of time,but its parameters may change from one such interval to another. Our goal is to develop a two-step procedure in which wefirst estimate the channel coefficients at the receiver from a probe signal,and then use the so-obtained estimates to form predic-tions,which arefinally fed back to the transmitter.This CSI will be used at the receiver(or the transmitter)to perform adaptive allocation of the modulation levels and power for each subcar-rier in the current OFDM block transmission.C.Channel EstimationChannel estimation consists of two steps.In thefirst step, initial phase compensation is performed to produce a stable reference signal.This step includes resampling by a nominal (average)Doppler factor and removal of the phase offset. Here,we should emphasize that the process relies on the esti-mates of the Doppler scaling factors,which are assumed to be available with a certain precision(e.g.,from a dedicated synchronization preamble).In the second step,the so-obtained signal is used to estimate the path coefficients.The Doppler factors are not needed thereafter,as we conjecture that the channel coefficients after motion compensation exhibit sufficient stability to allow prediction several seconds into the future.Fig.2illustrates the channel estimates obtained from real data collected during the KAM08experiment.Specifically, in this section,we will focus on channel estimates obtained from a short probe signal described in[29].After the initial phase compensation where a phase-locked loop(PLL)was used,we perform channel estimation from the received signal using the matching pursuit(MP)algorithm[30].Note from Fig.2that the MP algorithm produces eight coefficients,where neighboring coefficients belong to the same propagation path due to the path dispersion[1].For further analysis,we weigh the adjacent coefficients based on the channel tap power and merge them,so as to represent the channel via four propagation paths,,,and.Therefore,the MP algorithm provides estimates of the channel coefficients,assuming that channel coefficients are sufficient for the description of the sparse multipath structure.These estimates are denotedby Fig.3.(a)Magnitudes and(b)phases of the channel path coefficients.,and computed at time instances separated by155ms.For comparison purposes,we also provide the channel estimate obtained using the RLS algorithm.Different peaks in the channel estimates can be associated with multiple surface and bottom reflections calculated from the geometry of the experiment.As can be seen from thefigure,the MP algorithm successfully estimates the significant channel coefficients,and reduces the estimation error with respect to that incurred by the RLS algorithm.We emphasize that positions of the significant paths may drift on a larger time scale(tens of seconds),and,therefore,have to be updated accordingly.In Fig.3,we show the magnitudes and phases of the significant paths over a time period of8s.As we initially conjectured,the phases of remain relatively stable for more than a few seconds(a propagation delay over several kilometers).III.C HANNEL P REDICTIONAs we previously reported in[27],the future values of are predicted from the estimates.In particular, if the OFDM blocks are periodically transmitted at time instances,we use observations made at timesto predict the channel at time.To account for possible correlation between the path coefficients, we allow for their joint prediction.In other words,we use all channel coefficients to predict each new coefficient.The prediction is thus made as(10) where(11)(12) Matrix contains prediction coefficients that are to be determined.RADOSEVIC et al.:ADAPTIVE OFDM MODULATION FOR UNDERWATER ACOUSTIC COMMUNICATIONS 361Table IP REDICTION RLS ALGORITHMBecause the second-order statistics are not available for the random process ,we compute adaptively,by ap-plying the RLS algorithm as speci fied in Table I.In (14),is an matrix,which represents an estimate of the in-verse joint autocorrelation matrix and is a small constant,typically a fraction of the minimum among vari-ances of the channel coef ficients jointly predicted by the RLS algorithm.As discussed earlier,UWA systems suffer from inherently long propagation delays,which pose additional challenges in the design of a predictor.To counteract this problem,channel prediction one travel time ahead is achieved by using an RLS predictor of a low-order (e.g.,or )and a small forgetting factor [e.g.,,which corresponds toan effective window of length].Note that the forgetting factor is uniquely speci fied for all channel coef ficients.With a small order and only a few sig-ni ficant paths,i.e.,a small ,computational complexity of joint channel prediction is suf ficiently low to allow for a practical im-plementation.The structure of matrix is primarily driven by the ge-ometry of the propagation environment,i.e.,not all of the prop-agation paths are mutually correlated.In the present data set,the strongest arrival often exhibits more stability,and the con-tribution from the other,weaker paths in its prediction appears to be negligible.Therefore,the strongest path can be predicted independently,without loss in performance.In other words,if channel coef ficient corresponds to the strongest path,(18)can be modi fied as follows:the th column of is recursively updated only for those elements that correspond to the prior ob-servations of the th coef ficient.In addition,exploiting the correlation among the re-maining paths may lead to a performance improvement,whose exact amount is determined by the environmental pro file,and accuracy of the channel and Doppler estimates.After performing channel prediction at the receiver,the so-obtained CSI is used to initialize adaptive allocation of the modulation levels and power across the OFDM subcarriers.As we will discuss later,depending on which end of the com-munication link performs adaptive allocation,different types of information are fed back over a low-rate feedback channel.In the following,we describe the design framework,initiallyproposed in [26],under which we developed two practical adaptive modulation schemes,and we also discuss the design of bandlimited feedback.IV .A DAPTIVE M ODULATION AND P OWER A LLOCATION The system model assumes that residual Doppler effects are negligible after proper initial motion compensation [resampling by a nominal Doppler factor and removal of the phase offset].After this initial step,it is also assumed that the channel is constant at least over the transmission interval of one OFDM block.Therefore,the received signal can be expressed as(20)where(21)and ,,and are,respectively,the received signal after fast Fourier transform (FFT)demodulation,the transmitted power,and zero-mean circularly symmetric complex AWGNwith varianceper dimension.The noise term includes the effects of ambient noise and residual ICI on the th subcarrier and the th OFDM block,which is approximated as a Gaussian random variable.For the transmission of each OFDM block,we adaptivelycompute the size of the modulation alphabetand the transmission power .The objective of our adaptive OFDM system is to maximize the throughput by maintaining a target average BER.To maintain the BER at a fixed value,we propose the following optimization criterion:maximize subject to(22)where is the overall average power allocated to the th OFDM block,is the average BER for the th subcarrier,and is the target average BER.The average power can beexpressed aswhere is a constant and is the residual power from the previous block which was not allocated (i.e.,is less than the minimum power increment required by the algorithm for a one-bit increase of the overall throughput).Here,we should emphasize the difference be-tween total power allocation and distribution of this total power among the subcarriers.In the former case,one can designan adaptive scheme where the total poweris adaptively allocated (and uniformly distributed among the subcarriers)to achieve the prespeci fied performance [e.g.,the target average BER or signal-to-noise (SNR)at the receiver]for the fixed system throughput,whereas in the latter case,the fixed total362IEEE JOURNAL OF OCEANIC ENGINEERING,VOL.39,NO.2,APRIL2014power is nonuniformly distributed among the subcarriers to achieve the prespecified performance,and to maximize the system throughput.For the purpose of experimental sea trials, the total power allocation is initially set to a value which is able to support the target error rate,and avoid the outage scenario(no data transmission).To reduce the computational complexity of the adaptive algo-rithm,the subcarriers of the th OFDM block can be grouped into clusters.If we assume,we group consecutive sub-carriers into clusters,where is the size of each cluster.We denote by and,respectively,the allocated power and the level to the th cluster,.The optimal power level for each cluster depends on the transfer function of the channel.If the channel does not change much within a cluster,computation of and is performed based on the average channel gain cluster that if a cluster is affected by a deep fade, it will be dominated by the subcarrier with the lowest channel gain.Clustering reduces the computational load(see[26]for more details),but implies possible error penalization and/or a decrease in throughput as compared to the full computation of modulation levels and powers for all subcarriers.A.Thresholds for Modulation LevelsDue to the large propagation delays,the proposed adaptive OFDM transmission relies on channel prediction.We obtain predictions of the channel gains one travel time ahead based on the time-domain predictions of the most significant channel coefficients(10).We model the prediction error on the th channel path as a complex zero-mean circularly symmetric Gaussian random variable with variance per dimension. Furthermore,based on the a priori obtained from the channel prediction,we model as a complex Gaussian random variable with mean(23) and variance,where is the number of sig-nificant time-domain channel coefficients.Assuming that the current channel gain is perfectly known,we apply max-imum likelihood symbol detection for the AWGN channel at the output of the matchedfilter.Thus,the probability of bit error for the th subcarrier for M-ary phase-shift keying(MPSK)/mul-tiple quadrature amplitude modulation(MQAM)is well approx-imated by[18](24) where coefficients are determined numerically for each modulation alphabet,as accurately as desired for the BER approximation and take values for,respectively.For transmission of the th OFDM block,the adaptive system has knowledge of the predicted values,but not of the full channel.Therefore,from(24),the average BER on the th subcarrier is obtained as[18](25) For a given target,we now compute the thresholds for the available modulation levels.The solution for is given by(26) where is the principal branch of the Lambert -function,the inverse function of.Note that if,the threshold goes to zero,i.e.,.This case corresponds either to high SNR regimes with reliable CSI,or to very high target BERs of the system.Reasonably accurate approximations for,which can be computed efficiently,are provided in[31].We should emphasize that different thresholds correspond to different av-erage values of,since all of the subcarriers are affected by the prediction error of the same variance.The optimization problem(22)is hard to solve from the standpoint of a practical implementation,because it is com-putationally too intensive to be run at the receiver(or the transmitter)for every OFDM block.Therefore,we pursue suboptimal solutions which are obtained by relaxing one of the problem constraints.Specifically,we focus on two adaptive schemes in the rest of this section.B.Adaptive Scheme1The optimal solution for(22)includes a nonuniform power allocation for a maximum attainable throughput,such that the target average BER is.This causes that each subcarrier con-tributes to the average BER differently,due to the frequency se-lectivity of the channel.However,the problem can be simplified if we consider adaptive allocation of the modulation levels while distributing the power uniformly among the subcarriers.Since we adaptively allocate only the modulation levels,the so-ob-tained solution for(22)will be suboptimal.Specifically,we apply a greedy algorithm that computes the modulation levels in a given block using the allocations from the previous block for initialization.The proposed algorithm is given inRADOSEVIC et al.:ADAPTIVE OFDM MODULATION FOR UNDERWATER ACOUSTIC COMMUNICATIONS 363Table IIM ODULATION L EVEL ALLOCATIONTable II.Similar greedy algorithms have already been consid-ered in [32]and [33].After initialization of the algorithm for each subcarrier,as given by (27)–(30),we successively increase the modulation levels for those subcarriers that require the smallest power in-crement (31)–(43),while maintaining the average BER below the target .If the set of modulation levels from the previous transmission interval is not a greedy-based solution for the cur-rently available CSI ,the algorithm greedily searches for the closest solution which is used as a new initialization point of the algorithm.Also,if the algorithm does not support the throughput from the previous transmission interval (i.e.,it fails during the initialization step),it searches for the subcarrier with the largest power decrement that is required to decrease the modulation level .The algorithm is terminated when theprespeci fiedis achieved.C.Adaptive Scheme 2In the second scheme,we consider adaptive allocation of themodulation levels and the subcarrier powers such that for each subcarrier.Once the thresholds are computed from (26),we apply the adaptive algorithm of Table III to generate the signal of the thOFDM block.The algorithm is terminated when the available power is exhausted,or when all subcarriers achieve the max-imum modulation level (16QAM).Here,we emphasize that for those subcarriers that are in a deep fade no data are transmitted (zero power is allocated).In other words,the subcarrier with index is in deep fade if threshold is high enough to violate the power constraint in (22).Because of the additional freedom to adjust the power,this scheme will achieve a higher overall throughput as compared to scheme 1.D.Limited Feedback for Adaptive UWA SystemsWe assume that a limited-feedback channel is available for conveying information from the receiver back to the transmitter.The receiver has knowledge of the channel frequency response at subcarrier frequencies and the corresponding channel im-pulse response.The transmitter needs to know the modulation levels and the power levels at the frequencies.To accomplish this,there are different feedback options.Here we consider three different alternatives.A first option is to feed back the frequency response at the subcarriers,where is typically of the order of 1000.If the channel frequency response changes slowly across frequencies,neighboring subcarriers would be allocated the same modula-tion and power levels.In such a case,it is not necessary to feed back the channel frequency response in amplitude and phase for each subcarrier.Hence,the total number of bits fed back can be reduced from a factor of to some factor,say ,where is the number of subcarriers contained in the coher-ence bandwidth of the channel.A second option is to transmit the actual modulation levels and the power levels directly to the transmitter at the subcar-rier frequencies.bits may be used to represent the available modulation levels.For example,in our case,we usedbits.The power levels can be uniformly quantized,such that bits are used to represent each quantization level.A third option is to feed back the values of the quantized channel impulse response.Since the impulse response is sparse,the total number of bits required to convey this information to the transmitter is ,where is the number of sig-ni ficant coef ficients in the channel impulse response (typically,or less for the shallow-water channels considered),is the number of bits required to represent the quantized com-plex-valued channel coef ficients,and is the number of bits required to represent the time delay of each dominant channel coef ficient.To further reduce the number of bits fed back to the trans-mitter,we applied a lossless data compression technique.In par-ticular,we employed run length encoding (RLE)[34],which is a simple coding scheme that provides good compression of data that contains many runs of zeros or ones,together with the well-known Lempel–Ziv–Welch (LZW)algorithm (used as an inner code)[35],to ef ficiently compress the feedback informa-tion.As we will see in the following section,assuming perfect CSI at the receiver,feeding back the sparse channel impulse re-sponse and computing the modulation levels and power levels at the transmitter requires signi ficantly fewer bits.。