IEEE Trans. Wireless Commun.大修审稿意见回复信

Authors’ResponsesDearDr.MehdiBennisandreviewers,Thankyouforyourtimeandeffortputinreviewingourmanuscript.Wealsothankyouforyourdetailedcommentsthathelpedusimprovethequalityofthispaper.Inthefollowing,weaddressyourconcernsintheorderthattheywerementioned.Sincerely,LingQiu.ResponsestoReviewer1’sComments:GeneralRemarks:Thepaperanalyzestheareaspectralefficiencyandenergyefficiencyformulti-useMIMOcellularnetworks.Thepapertopicistimelyandtheresultsarenovelandinteresting.However,thereareseveraldrawbacksthatshouldbeaddressedbeforethepaperisrecommendedforpublication.Response:Wethankyouforyourappreciationofourcontributions.Weaddressyourconcernsintherevisedversionofthispaper.Wearegratefultoyouforyourcomments,whichmakeourpapermoreprecise.Comment1:Thesystemmodelandassumptionsarenotwellexplainedinthepaper.Theauthorsjustusetheresultsof[18]withoutexplainingforwhichprecodingschemeandunderwhatconditionstheseresultshold.Response:Thankyouverymuchforyourcomment.Indeed,asthereviewermentioned,weadoptthesystemmodelin[18]([17]intherevisedpaper).WefocusonZFprecodingandassumeperfectCSIateachBS.Wealsoassumeequalpowerallocationfortheusersineachcell.Therefore,thechannelpowerofthedesiredlink00gcanbedemonstratedtobeGammadistributed.Fortheinterferingchannelpowergains0ig,wefollowtheapproximationin[18],i.e.,ignorethespatialcorrelation.Thus,wetreat0igasGammarandomvariableinthispaper.Toexplaintheprecodingschemeandrelatedassumptions,weaddedthedescriptionsofsystemmodelinSectionII-A(Page7)asfollows:“Denotethe1Mvector~(0,)ikhIasthesmallscalefadingbetweenthei-thBSanditsk-thactiveuser.LetikwdenotetheprecodingvectoratBSiforthek-thuser.ConsideringZFprecoding,theunit-normprecodingvectorikwequalsthek-thnormalizedcolumnof†1iiiHHH,where01(1),,...,iiiiKHhhh.Therefore,thetransmittedsignalofthei-thBSis10Kiikikkszw,whereiksisthedatasymboldestinedforthek-thactiveuser.……”Comment2:Theauthorsclaimthattheyobtainaclosed-formexactexpressionforE[R]intheorem1.However,theobtainedexpressionisneitherexactnorinaclosedform.Atfirst,theexpressionisnotinaclosedformasitcontainsintegrals.Iwouldrathercallitatractableexpression.Secondly,theexpressionisnotexactastheanalysisinthepaperisbasedontheresultsof[18]whichcontainapproximationsfortractability.Infacttheresultsin[18]requirethattheprecodingmatricesforeachinterferingBStohaveunit-normorthogonalcolumns,whichisnottrueduetotheemployedprecodingtechnique.Thisisstatedin[18]bythefollowingquote“Forthedistributionoftheinterferinglinks,weassumethattheprecodingmatriceshaveunit-normorthogonalcolumnsandthatW_jiscalculatedindependentlyofu_{jy}.”Response:Thankyouverymuchforyourcomment.Indeed,theexpression[]ERisobtainedbasedtheassumptionofGammadistributionfortheinterferinglinks.Therefore,theexpressionfor[]ERisanapproximation.Astheexpressionfor[]ERcontainstwointegrals,theexpressioninnotincloseform.Tomakethispapermoreprecise,wemadethefollowingmodifications:1)Insteadof“exactexpression”and“closed-form”,weuse“originalexpression”and“tractable”todescribetheexpressionfor[]ER.2)WehaveclarifiedtheassumptionfortheinterferinglinksinSectionII-A(Page7)asfollows:“Fortheinterferingremarks,asikwisaunit-normvectorandindependentof†0iv,2†0iikvwisthesquared-normofcomplexGaussian,whichisexponentialdistributed.Wefollowtheapproximationin[18],i.e.,neglectthecorrelationbetween2†0iikvwfordifferentk.Therefore,theequivalentchannelgain0igisthesumofKindependentexponentialdistributedrandomvariables,whichfollows,1,0GammaKi.Theaccuracyofthisapproximationwillbedemonstratedinournumericalresults.”Comment3:Theauthorsshouldclearlystatethesystemmodelandusedapproximationtoavoidanymisleadingresults.Response:Thankyouverymuchforyourcomment.Accordingtothecomment,wehaveclarifiedtheassumptionintherevisedversionofthispaper.DetailsarethesametotheresponsestoComment1andComment2.Comment4:Sincetheauthorsbuilttheirresultsonanapproximation,theyshouldvalidatetheirresults.Ididseesomevalidationsagainstsimulation,however,thesimulationmodelisnotexplainedinthepaper.Notethattheauthorscannotuseasimulationmodelthatincludestheaforementionedapproximation.ThismeansthataSISOnetworkwithGammachannelgainscannotbeusedtovalidatetheresults.Instead,theauthorsshouldsimulateaMU-MIMOcellularnetworkwheretheprecodingmatricesareconstructedaccordingtothetechniqueusedin[8]andwithoutenforcingorthogonallybetweenthecolumnsofeachprecodingmatrix.Response:Thankyouverymuchforyourcomment.Tovalidatetheassumptionforthechannelpoweroftheinterferinglinks,wehavere-implementedthesimulations.Theequivalentchannelgains0igofinterferinglinksarecalculatedbasedontheprecodingmatrices.Actually,asshowninthefiguresbelow,wefind0igisnotGammadistributed.Especially,whenKislarge,themismatchcannotbeignored.However,fortheaveragedaterateofthetypicaluser,wefindthemismatchbetweenthesimulationsandTheorem1isnegligible,whichisdepictedinthefollowingfigure(Fig.2intherevisedpaper).Thatistosay,Gammadistributionisanaccurateapproximationfortheanalysisofaveragedatarateofthetypicaluser.Tohighlightthevalidationoftheapproximation,weaddedsomesentencesinSectionIII-