Analytical Models of the Performance of C-V2X Mode 4 Vehicular Communications

Transcription

1 1 Analytcal Models of the Pefomance of C-VX Mode 4 Vehcula Communcatons Manuel Gonzalez-Matín Mguel Sepulce Rafael Molna-Masegosa Jave Gozalvez Abstact The C-VX o LTE-V standad has been desgned to suppot VX (Vehcle to Eveythng) communcatons. The standad s an evoluton of LTE and t has been publshed by the 3GPP n Release 14. Ths new standad ntoduces the C-VX o LTE-V Mode 4 that s specfcally desgned fo VV communcatons usng the PC5 sdelnk nteface wthout any cellula nfastuctue suppot. In Mode 4 vehcles autonomously select and manage the ado esouces. Mode 4 s hghly elevant snce VV safety applcatons cannot depend on the avalablty of nfastuctue-based cellula coveage. Ths pape pesents the fst analytcal models of the communcaton pefomance of C-VX o LTE-V Mode 4. In patcula the pape pesents analytcal models fo the aveage PDR (Packet Delvey Rato) as a functon of the dstance between tansmtte and eceve and fo the fou dffeent types of tansmsson eos that can be encounteed n C-VX Mode 4. The models ae valdated fo a wde ange of tansmsson paametes and taffc denstes. To ths am ths study compaes the esults obtaned wth the analytcal models to those obtaned wth a C-VX Mode 4 smulato mplemented ove Vens. Index Tems C-VX LTE-V Mode 4 cellula VX LTE- VX VV PC5 sdelnk communcaton analytcal model. I. INTRODUCTION Vehcula netwoks ae essental to suppot actve taffc safety and advanced management applcatons [1]. The Thd Geneaton Patneshp Poject (3GPP) publshed n Release 14 an evoluton of the LTE standad to suppot VX (Vehcle to Eveythng) communcatons. Ths evoluton s commonly efeed to as C-VX Cellula VX LTE-V LTE-VX o LTE-VV. C-VX s consdeed an altenatve to IEEE 80.11p snce t suppots dect communcaton between vehcles usng the PC5 nteface (also known as VX sdelnk communcatons). Release 14 ntoduces two new communcaton modes (Mode 3 and Mode 4) specfcally desgned fo VV (Vehcle to Vehcle) communcatons and that sgnfcantly dffe fom Modes 1 and defned n Copyght (c) 018 IEEE. Pesonal use of ths mateal s pemtted. Howeve pemsson to use ths mateal fo any othe puposes must be obtaned fom the IEEE by sendng a equest to pubs-pemssons@eee.og. Ths wok was suppoted n pat by the Consellea de Educacón Investgacón Cultua y Depote of Genealtat Valencana though the poject AICO/018/A/095 the Spansh Mnsty of Economy and Compettveness and FEDER funds unde the pojects TEC R and TEC R and eseach gant PEJ-014-A336. Manuel Gonzalez- Matn Mguel Sepulce Rafael Molna-Masegosa and Jave Gozalvez ae wth the UWICORE Laboatoy Unvesdad Mguel Henandez de Elche (UMH) Span. E-mal: magmatn10@gmal.com msepulce@umh.es afael.molnam@umh.es j.gozalvez@umh.es. Release 1 fo DD (Devce-to-Devce) communcatons. In Mode 3 the cellula netwok selects and manages the ado esouces used by vehcles fo the dect VV communcatons. In Mode 4 vehcles autonomously select and manage the ado esouces wthout any cellula nfastuctue suppot. To ths am Mode 4 defnes a sensngbased Sem-Pesstent Schedulng (SPS) scheme that vehcles must mplement to autonomously select the ado esouces wthout the assstance of the cellula nfastuctue. Mode 4 s hghly elevant snce VV safety applcatons cannot depend on the avalablty of nfastuctue-based cellula coveage. Recent studes have analyzed the pefomance of C-VX Mode 4 and compaed t to that acheved wth IEEE 80.11p standads such as DSRC o ITS-G5 [4]. These studes ae based on netwok smulatons and to the authos knowledge thee ae no analytcal models of the C-VX Mode 4 communcaton pefomance n the lteatue. Exstng and ecent C-VX analytcal models focus on C-VX Mode 3 whee the ado esouces ae managed and assgned by the nfastuctue. Fo example [5] poposes analytcal models usng combned Makov chans to evaluate the pefomance of dffeent schedulng schemes n C-VX. [6] analytcally models C-VX Mode 3 and compaes ts scalablty to that of IEEE 80.11p. The authos utlze the model poposed n [7] to analyze the beaconng esouce occupaton. Po to [5] and [6] othe studes have epoted analytcal models fo VI (Vehcle to Infastuctue) communcatons usng LTE. Fo example [8] poposes a M/M/m queung model to evaluate the pobablty that a vehcle fnds all channels busy and to deve the expected watng tmes. An analytcal famewok s poposed n [9] to compae IEEE 80.11p and LTE n tems of the pobablty to delve a packet befoe a deadlne. Ths study consdes that vehcles tansmt the packets n an uplnk channel to the LTE base staton and the base staton etansmts the elevant packets to each vehcle ove a downlnk channel. Analytcal models ae an mpotant evaluaton tool to povde nfomaton about the pefomance unde a wde ange of paametes and condtons. Analytcal studes can then be complemented by moe compehensve but also moe computatonally expensve netwok smulatons. In ths contex ths pape pesents and valdates the fst analytcal models of the communcaton pefomance of C-VX Mode 4. The models povde the aveage PDR (Packet Delvey Rato) as a functon of the dstance between tansmtte and eceve. In addton the models quantfy the fou dffeent types of

2 packet eos that affect C-VX Mode 4 [10]: eos due to half-duplex tansmssons eos due to a eceved sgnal powe below the sensng powe theshold eos due to popagaton effects and eos due to packet collsons. The accuacy of the poposed models s valdated by compang the esults to those obtaned usng a compehensve C-VX Mode 4 netwok smulato developed ove Vens and pesented n [10]. The model s valdated fo a wde ange of tansmsson paametes and taffc denstes. In patcula the model has been valdated fo seveal tansmsson powe levels Modulaton and Codng Schemes (MCS) and subchannelzatons and packet tansmsson fequences. II. C-VX MODE 4 A. Physcal laye C-VX utlzes SC-FDMA and suppots 10 and 0MHz channels. Each channel s dvded nto sub-fames Resouce Blocks (RBs) and sub-channels. Sub-fames ae 1ms long (lke the Tansmsson Tme Inteval). A RB s the smallest unt of fequency esouces that can be allocated to a LTE use. It s 180kHz wde n fequency (1 sub-caes of 15kHz). C-VX defnes sub-channels as a goup of RBs n the same sub-fame. The numbe of RBs pe sub-channel can vay. Sub-channels ae used to tansmt data and contol nfomaton. The data s tansmtted n Tanspot Blocks (TBs). A TB contans a full packet to be tansmtted e.g. a beacon o a CAM (Coopeatve Awaeness Message)/BSM (Basc Safety Message). TBs can be tansmtted usng QPSK o 16-QAM and tubo codng. Each TB s tansmtted wth a Sdelnk Contol Infomaton (SCI) that occupes RBs n the same sub-fame and epesents the sgnalng ovehead n C- VX Mode 4. The SCI ncludes nfomaton such as the modulaton and codng scheme used to tansmt the TB and the RBs used to tansmt the TB. Its coect ecepton s necessay fo othe vehcles to be able to eceve and decode the tansmtted TB. The maxmum tansmt powe s 3dBm and the standad eques a senstvty powe level at the eceve of -90.4dBm [11]. Fg. 1 (left pat) llustates the C- VX sub-channelzaton when the avalable bandwdth s dvded n 4 sub-channels and the contol nfomaton s adjacent to the data. Fequency Sub channel Contol (SCI) Data (TB) 1ms sub fames T 1000 ms Packet geneaton Aveage RSSI fo esouce R Selecton Wndow (100ms) T 100 ms T ms Resouce R (not excluded n Step ) Fg. 1. C-VX sub-channelzaton and aveage RSSI of a esouce fo λ=10hz B. Sensng-based Sem-Pesstent Schedulng In C-VX Mode 4 vehcles autonomously select the esouces wthout the assstance of the cellula nfastuctue. Tme To ths am they use the sensng-based SPS schedulng scheme specfed n Release 14 [1][13]. A vehcle eseves the selected esouce(s) fo a andom numbe of consecutve packets. Ths numbe depends on the numbe of packets tansmtted pe second (λ) o nvesely the packet tansmsson nteval. Fo λ=10hz 0Hz and 50Hz ths andom numbe s selected between 5 and 15 between 10 and 30 and between 5 and 75 espectvely. When a vehcle needs to eseve new esouces t andomly selects a Reselecton Counte. Afte each tansmsson the Reselecton Counte s decemented by one. When t s equal to zeo new esouces must be selected and eseved wth pobablty (1- p es ) whee p es ϵ [00.8] 1. Each vehcle ncludes ts packet tansmsson nteval and the value of ts Reselecton Counte n ts SCI. Vehcles use ths nfomaton to estmate whch esouces ae fee when makng the own esevaton to educe packet collsons. The pocess to eseve esouces s oganzed n the followng 3 steps. Step 1. When a vehcle v t needs to tansmt a new packet and the Reselecton Counte s zeo v t has to eseve new esouces wthn a Selecton Wndow. The Selecton Wndow s the tme wndow between the tme the packet has been geneated (t b) and the defned maxmum latency (Fg. 1 ght pat). The maxmum latency s 100ms fo λ=10hz 50ms fo λ=0hz and 0ms fo λ=50hz [1]. Wthn the Selecton Wndow the vehcle dentfes the esouces t could eseve. A esouce s a goup of adjacent sub-channels wthn the same sub-fame whee the packet (SCI+TB) to be tansmtted fts. Step. Vehcle v t then ceates a lst L A of avalable esouces t could eseve. Ths lst ncludes all the esouces pevously dentfed n Step 1 except those that meet the followng two condtons: 1) v t has eceved n the last 1000 sub-fames an SCI fom anothe vehcle ndcatng that t wll utlze ths esouce n the Selecton Wndow o any of ts next Reselecton Counte packets. ) v t measues an aveage Refeence Sgnal Receved Powe (RSRP) ove the esouce hghe than a gven theshold. Vehcle v t also excludes all the esouces of sub-fame f n the Selecton Wndow f v t was tansmttng dung any pevous sub-fame f j whee j=-100k and k ϵ N 1 k 10 fo λ=10hz. Afte Step s executed L A must contan at least 0% of all the esouces ntally dentfed n the Selecton Wndow dung Step 1. If no Step s teatvely executed untl the 0% taget s met. In each teaton the RSRP theshold s nceased by 3dB. Step 3. v t ceates a lst of canddate esouces L C that ncludes the esouces n L A that expeenced the lowest aveage RSSI (Receved Sgnal Stength Indcato). The sze of L C must be equal to the 0% of all the esouces n the Selecton Wndow dentfed dung Step 1. The RSSI value s aveaged ove all the pevous t R -100j sub-fames (j ϵ N 1 j 1 pes s usually set equal to 0 [14]. Ths value s assumed n ths study. Fo λ=0hz j=-50k and k ϵ N 1 k 0. Fo λ=50hz j=-0k and k ϵ N 1 k 50.

3 3 10) fo λ=10hz 3 (Fg. 1). Vehcle v t then andomly chooses one of the canddate esouces n L C and eseves t fo the next Reselecton Counte tansmssons. III. TRANSMISSION ERRORS IN C-VX MODE 4 C-VX Mode 4 tansmssons can encounte the followng fou mutually exclusve eos that ae analytcally quantfed n the next secton: 1) Eos due to half-duplex tansmssons (HD). The C-VX ado s half-duplex. Ths eo s then poduced when a packet cannot be eceved by a vehcle because the vehcle s tansmttng ts own packet n the same sub-fame. Ths type of eo does not depend on the dstance between tansmtte and eceve but just on the pobablty that two vehcles select the same sub-fame to tansmt the packets. The pobablty of not coectly ecevng a packet due to ths effect s hee efeed to as δ HD: HD P e HD (1) ) Eo due to a eceved sgnal powe below the sensng powe theshold (). Ths eo s poduced when a packet s eceved wth a sgnal powe below the sensng powe theshold P and hence t cannot be decoded. Ths eo manly depends on the tansmsson powe the sensng powe theshold the popagaton and the dstance between tansmtte and eceve. Ths type of eo excludes those quantfed n 1). The pobablty of not coectly ecevng a packet due to ths effect s hee efeed to as δ : P e e HD () 3) Eo due to popagaton effects. In ths case a packet s eceved wth a sgnal powe hghe than P but the eceved SNR (Sgnal to Nose Rato) s not suffcent to guaantee the coect ecepton of the packet. Ths type of eo does not consde ntefeences and collsons (.e. t s only due to popagaton) and hence depends on the same factos as ) plus also on the MCS. In ths study ths type of eo excludes those quantfed n 1) and ). The pobablty of not coectly ecevng a packet due to ths effect s hee efeed to as δ PRO : PRO P e PRO e HD e (3) 4) Eo due to packet collsons (). Ths eo s poduced when a vehcle tansmts on the same esouce (.e. the same sub-channel and sub-fame) than anothe vehcle and the ntefeence geneated pevents the coect ecepton of the packet by the eceve due to nsuffcent SINR (Sgnal to Intefeence and Nose Rato). It depends on the confguaton and opeaton of the SPS scheme of C-VX Mode 4 as well as on the tansmsson paametes the popagaton dstance between tansmtte and eceve and taffc densty. In study ths type of eo excludes those quantfed n 1) ) and 3). The pobablty of not 3 Fo λ=0hz tr-50j sub-fames (j ϵ N 1 j 0). Fo λ=50hz tr-0j sub-fames (j ϵ N 1 j 50). coectly ecevng a packet due to ths effect s efeed to as δ : P e e HD e e PRO (4) IV. ANALYTICAL MODELS Ths secton analytcally quantfes the fou possble tansmsson eos n C-VX Mode 4 and deves an analytcal model of the PDR as a functon of the dstance between tansmtte and eceve. To ths am we consde a hghway scenao wth multple lanes whee vehcles ae sepaated by 1/β metes (.e. a taffc densty of β vehcles pe mete). All vehcles peodcally tansmt λ packets pe second on the same 10MHz channel wth tansmsson powe P t. We consde that all packets have the same sze (B bytes) and ae tansmtted usng the same MCS. To deve the analytcal expessons we consde that vehcle v t wll act as tansmtte and vehcle v as eceve. Both vehcles ae sepaated by a dstance d. The analytcal models poposed consde that a packet s coectly eceved f none of the dentfed types of eo occu. Snce these eos ae exclusve the PDR can be calculated as: PDR d 1 HD1 d 1 PRO d 1 d We can nomalze the pobablty of each type of eo and expess the PDR as: PDR ˆ ˆ ˆ ˆ (6) whee 1 HD PRO HD HD (5) ˆ (6.1) d d ˆ 1 (6.) t HD t d d d ˆ 1 1 PRO t HD t PRO t (6.3) d d d d ˆ t HD t PRO t t (6.4) 0 1 (6.5) HD PRO 0 ˆ ˆ ˆ ˆ 1 (6.6) HD PRO Appendx A shows how to deve eq. (5) fom eq. (6) usng eq. (6.1)-(6.4). Table I dentfes the sub-sectons and equatons used to descbe each of the fou types of eo. Ths table can be used as a efeence by the eade to follow the descpton of the analytcal models. Table II also lsts the vaables and paametes used to deve and descbe the models. TABLE I. EQUATIONS AND SECTIONS DESCRIBING EACH TYPE OF ERROR Type of eo Vaable Equaton(s) Sub-secton Half duplex H D (7) IV.A Sensng (8) to (10) IV.B Popagaton PRO (1) to (13.1) IV.C Collson (14) to (34) IV.D

4 4 TABLE II. VARIABLES Vaable Descpton α Weghtng facto that epesents the mpact of Step and Step 3 n the selecton of the NC canddate esouces β Taffc densty (vehcles/mete) CBR Channel Busy Rato Δ Incement of the sensng theshold (db) Pobablty of packet loss due to collson fom any vehcle Pobablty of packet loss due to collson fom vehcle v Pobablty of packet loss due to half-duplex effect H D Pobablty of packet loss due to popagaton effects PRO Pobablty of packet loss due to eceved sgnal below sensng theshold λ Numbe of packets tansmtted pe second pe vehcle (Hz) N Total numbe of esouces contaned n the Selecton Wndow NA Numbe of assgnable esouces (not excluded by Step ) NC Numbe of canddate esouces afte Steps and 3 NE Numbe of esouces excluded n Step CA(d) Numbe of common avalable esouces between vt and v CC(d) Numbe of common canddate esouces between vt and v CE(d) Numbe of common excluded esouces between vt and v PDR Packet Delvey Rato P Receved ntefeence powe fom vehcle v (dbm) P Receved sgnal powe fom vehcle vt (dbm) P Sensng theshold (dbm) Pt Tansmsson powe (dbm) p ) Pobablty that ntefeence fom v s hghe than theshold INT p ) Pobablty of packet loss due to low SINR SINR psim ) Pobablty that vt and v smultaneously tansmt usng the same esouce psim ) Pobablty that vt and v smultaneously tansmt usng the same esouce when only Step s executed psim ) Pobablty that vt and v smultaneously tansmt usng the same esouce when only Step 3 s executed S Numbe of esouces pe sub-fame SINR Sgnal-to-Intefeence-and-Nose Rato (db) SNR Sgnal-to-Nose Rato (db) SPSR Aveage numbe of vehcles that a vehcle could sense n the Selecton Wndow f thee wee no packet collsons A. Half-duplex eos The pobablty that two vehcles cannot eceve the packets because of the half-duplex effect does not depend on the dstance the C-VX Mode 4 SPS scheme o the channel occupancy. Two vehcles have cetan pobablty of selectng the same sub-fame fo tansmttng the packets. Ths pobablty depends on the numbe of packets tansmtted pe vehcle pe second λ and the numbe of sub-fames wthn a second. Consdeng 1ms sub-fames the pobablty of not ecevng a packet due to the half-duplex effect can be appoxmated by the followng equaton: HD (7) 1000 Ths effect s local and only affects those vehcles tansmttng n the same sub-fame.e. vehcles tansmttng n othe sub-fames can stll eceve the packets. B. Eos due to a eceved sgnal powe below the sensng powe theshold To calculate the pobablty of ecevng a packet wth a sgnal powe below the sensng powe theshold we take nto account the pathloss (PL) and shadowng (SH). The pathloss epesents the aveage sgnal attenuaton wth the dstance between tansmtte and eceve (d ) and s typcally modeled wth a log-dstance functon. The shadowng epesents the effect of obstacles on the sgnal attenuaton and s modeled wth a log-nomal andom dstbuton wth zeo mean and vaance σ. The eceved sgnal powe P at the eceve s hence a andom vaable that can be expessed as: P ) Pt PL ) SH (8) whee P t s the tansmsson powe PL(d ) s the pathloss at the dstance d and all vaables ae n db. The pobablty that the eceved sgnal powe s lowe than the sensng powe theshold P s: whee f P d t P d P d f p dp (9) p epesents the PDF of the eceved sgnal powe at a dstance d. The shadowng follows a log-nomal andom dstbuton so the PDF of the eceved sgnal powe can be expessed as: f P d p 1 Pt PL ) p exp (9.1) The combnaton of eq. (9) and (9.1) esults n that the pobablty that the eceved sgnal powe at d s lowe than the sensng powe theshold s equal to: 1 P PL ) P ) 1 ef t (10) whee ef s the well-known eo functon. 1-δ s the PSR (Packet Sensng Rato) and eq. (10) can be genealzed to compute the PSR at any dstance d: 1 Pt PL) P PSR) 1 ef (11) C. Eo due to popagaton The pobablty that a packet s lost due to popagaton effects depends on the PHY laye pefomance of the eceve. Ths pefomance s modeled n ths study usng the lnk level pefomance epoted n [15] and epesented by means of Look-Up Tables (LUTs). These LUTs povde the Block Eo Rate (BLER) as a functon of the SNR fo a gven packet sze MCS scenao (hghway o uban) and elatve speed between tansmtte and eceve. To model tansmsson eos due to popagaton effects we consde that the SNR at a eceve s a andom vaable expessed n db as: t t t t SNR d P d N P PL d SH N (1) 0 0 whee N 0 s the nose powe. At a gven dstance between tansmtte and eceve PL s constan and theefoe SNR follows the same andom dstbuton as SH but wth a mean value equal to P t - PL - N 0. The pobablty that a packet s lost due to popagaton effects can hence be expessed as: whee P d BL( s) f ( s) (13) PRO t SNR P d s

5 5 f fsnr d ( s) ( s) 1 0 SNR P P d f P P f P P (13.1) In eq. (13) the tem BL(s) epesents the BLER fo an SNR equal to s followng the LUTs n [15]. Ths tem s multpled by fsnr P ( ) P d s whch s the PDF of the SNR expeenced at a dstance d fo those SNR values fo whch the P s hghe than P. The objectve s to omt those packets wth a eceved sgnal powe lowe than the sensng powe theshold P ; these packets have aleady been taken nto account n δ (eq. (9)). The PDF of the SNR.e. fsnr d t () s needs to be nomalzed by 1- δ n eq. (13.1) so that the ntegal of ths equaton between - and + s 1 and the pobablty δ PRO of not ecevng a packet due to popagaton effects s a value between 0 and 1. D. Eos due to packet collsons Ths eo s poduced when a gven ntefeng vehcle (v ) tansmts on the same sub-fame and sub-channel than the tansmttng vehcle (v t ) and the ntefeence geneated pevents the coect ecepton of the packet by the eceve (v ). Both condtons must happen to lose a packet due to packet collson. Ths eo depends on the lnk level pefomance the sensng-based SPS schedulng scheme defned n C-VX Mode 4 the scenao and the dstances between vehcles v t v and v. Fg. summazes the steps followed to compute the pobablty of packet loss due to collsons (δ ). Ths pobablty can be computed as a functon of the pobablty that a vehcle v povokes a packet loss due to collson ( ) wth the followng equaton: d 1 1 d d d (14) t t t v can povoke a packet loss due to collson f v t and v smultaneously tansmt usng the same esouce and the ntefeence geneated by v s such that t wll povoke the packet loss. The pobablty of packet loss due to a collson povoked by vehcle v can then be expessed as: d d d p d p d d (15) t t SIM t INT t p SIM(d ) s the pobablty that v t and v smultaneously tansmt usng the same esouce. p INT (d d ) epesents the pobablty that the ntefeence geneated by v on the eceve v s hghe than a theshold that would povoke that f v t and v smultaneously tansmt usng the same esouce then the packet cannot be coectly eceved at v. p INT (d d ) depends on the scenao the lnk level pefomance and the dstances between the tansmtte and eceve (d ) and between the ntefee and the eceve (d ). On the othe hand p SIM(d ) depends on the MAC opeaton and confguaton (.e. on the sensng-based SPS schedulng scheme) as well as on the popagaton condtons and the dstance between v t and v. Fg.. Man steps to calculate the pobablty of packet loss due to collson. D1. Pobablty p INT(d d ) that ntefeence s hghe than theshold To calculate p INT(d d ) we assume that the negatve effect of the ntefeence eceved fom vehcle v ove the eceved sgnal at v s equvalent to addtonal nose. The SINR expeenced by the eceve v can be then expessed as: t t SINR d d P d P d N0 (16) whee all vaables ae n db o dbm and P s the sgnal powe eceved by v fom v. SINR s theefoe a andom vaable that esults fom the addton of two andom vaables (P and P ). The PDF of the SINR can hence be obtaned fom the coss coelaton of the PDF of P and P [16]. As a esul the pobablty that the eceve eceves a packet wth eo due to low SINR (.e. low P and/o hgh P ) s: P p SINR dt d BL s fsinr P d d ( s) (17) s Ths equaton ncludes the packets that could not be eceved due to popagaton effects.e. those packets that would have been lost even wthout the ntefeence eceved fom v. Snce these packets wee aleady consdeed n δ PRO we need to pefom the followng nomalzaton to only consde those packets that ae lost due to collsons n p INT: p d d INT 1 PRO d p d d d SINR t PRO t (18) whee δ PRO s obtaned fom eq. (13). The same LUTs used to calculate δ PRO n eq. (13) (and obtaned fom [15]) can be used n eq. (17) to estmate the BLER n BL(s) assumng that the negatve effect of the ntefeence ove the eceved sgnal s equvalent to addtonal nose. D. Pobablty p SIM (d ) that v t and v smultaneously tansmt usng the same esouce also depends on p SIM (d ) as shown n eq. (15). p SIM (d ) C VX Mode 4 paametes and dstances between v t v and v Pobablty that ntefeence fom v s hghe than theshold: p INT (d d ) n eq. (18) Pobablty of packet loss due to collson by v : n eq. (15) Pobablty of packet loss due to collson by any vehcle: n eq. (14) Pobablty that v t and v tansmt usng the same esouce: p SIM (d ) n eq. (1) epesents the pobablty that the tansmttng vehcle v t and an ntefeng vehcle v tansmt smultaneously n the same esouce.e. n the same sub-channel and the same sub-fame. Fg. 3 shows the man steps needed to calculate the pobablty p SIM (d ) and that ae explaned next. Fg. 3 seves as a gude fo the eade to follow the pocess.

6 6 Estmate excluded and common excluded esouces: N E (d ) n eq. (9) C E (d ) n eq. (30) Calculate common avalable esouces: C A (d ) n eq. (7) Compute common canddate esouces: C C (d ) n eq. (6) Pobablty that v t and v select the same esouce wth Step : p ) n eq. (3) SIM C VX Mode 4 paametes and dstances between v t v and v Step Step 3 Impact of Step and Step 3 Pobablty that v t and v do not hea each othe s tx: p s (d ) n eq. (4) Estmate excluded and common excluded esouces: N E (d ) n eq. (33) C E (d ) n eq. (30) Calculate common avalable esouces: C A (d ) n eq. (7) Compute common canddate esouces: C C (d ) n eq. (6) Pobablty that v t and v select the same esouce wth Step 3: p ) n eq. (31) Pobablty that v t and v tansmt usng the same esouce: psim ) n eq. (1) Estmate excluded and common excluded esouces: N E (d ) n eq. (9) C E (d ) n eq. (30) Calculate channel busy ato: CBR n eq. (34) Weghtng facto between Step and Step 3: α n eq. () Fg. 3. Man steps followed to calculate the pobablty that vt and v tansmt usng the same esouce. The fgue ncludes all the steps caed out whle executng Steps and 3 of the sensng-based SPS scheme and the steps needed to calculate the weghtng facto that epesents the mpact of Step and Step 3 n the selecton of the canddate esouces. To calculate p SIM(d ) we need the followng defntons (see Fg. 4). N s the total numbe of esouces n all subfames contaned n the Selecton Wndow. N E s the numbe of esouces excluded n Step of the sensng-based SPS scheme of C-VX Mode 4. N A s the numbe of assgnable esouces.e. those esouces that wee not excluded by Step (.e. N A s equal to the sze of lst L A and N A=N-N E). N C s the numbe of canddate esouces that could be used by the tansmttng vehcle afte Steps and 3 and s theefoe equal to the sze of lst L C. N C s equal to the 0% of N. Snce we assume a constant taffc densty vehcles ae unfomly dstbuted n the scenao and have the same tansmsson paametes all vehcles have the same N N E N A and N C. N E Excluded esouces SIM N A Assgnable esouces (L A geneated by Step ) Selecton Wndow (N esouces) N C Canddate esouces (L C geneated by Step 3) Fg. 4. Classfcaton of esouces followng the sensng-based SPS scheme. To educe the complexty of the analytcal model we sepaate the devaton of p SIM(d ) unde Steps and 3 of the sensng-based SPS scheme. Ths appoach s motvated by the fact that t s not always necessay to take nto account both Steps as t s next explaned: Step 3 has lmted effect on the esouce selecton pocess when the channel load s hgh. Ths s the case because when the channel load s hgh Step excludes most of the esouces and the sze of the lst of avalable esouces L A s equal to the 0% of all esouces n the Selecton Wndow. Step 3 bulds the lst of canddate esouces L C fom lst L A. The sze of L C must be equal to the 0% of all esouces n the Selecton Wndow. Thus when the channel load s hgh Step 3 wll not modfy the esouces selected by Step (Fg. 5a). As a esul when the channel load s hgh we can compute p SIM (d ) as the pobablty that vehcles v t and v tansmt smultaneously n the same esouce when only Step s executed: p ) p ) (19) SIM SIM Step has lmted effect on the esouce selecton pocess when the channel load s low. When the channel load s low Step would exclude only a few esouces to buld the lst of avalable esouces L A. Step 3 would buld the lst of canddate esouces L C by selectng fom L A those esouces wth the lowest aveage RSSI ove the last 1000 sub-fames. Step 3 s able to exclude the esouces that Step would exclude and the same L C could be obtaned even f Step was not executed (Fg. 5b). The utlty of Step s hence lmted when the channel load s low. In ths case p SIM (d ) can be computed as the pobablty that v t and v tansmt smultaneously n the same esouce when only Step 3 s executed: (a) Hgh load (b) Low load Excluded Assgnable Canddate p ) p ) (0) SIM SIM Step nceases RSRP theshold (whte aow) untl 0% of N esouces ae assgnable Step selects a hgh amount of esouces Step 3 would select the same esouces even f Step was not executed Step 3 does not modfy the selecton Fg. 5. Impact of Step and Step 3 on LC fo low and hgh channel loads. Step and Step 3 need to be consdeed fo ntemedate channel load levels. Unde ntemedate channel load levels we model the pobablty of packet collson p SIM (d ) as: p ) p ) (1 ) p ) (1) SIM SIM SIM whee α є [01] s a weghtng facto that epesents the mpact of Step and Step 3 n the selecton of the N C canddate esouces. As pevously dscussed f the channel load s hgh α=1 because only Step has an nfluence on the esouces selected and Step 3 s not needed. If the channel load s low α=0 because only Step 3 s needed. The specfc value of α depends on the channel load whch s measued n ths study usng the CBR (Channel Busy Rato) that epesents the aveage numbe of esouces sensed as busy. The C-VX Mode 4 smulato descbed n Secton V has been utlzed to deve α though smulaton. To ths am psim ) psim t )

7 7 and SIM p ) have been obtaned though smulaton and the values have been used to calculate α as a functon of the CBR (depcted n Fg. 6 as dots). The value of α has been deved consdeng a wde ange of tansmsson paametes and taffc denstes. Fg. 6 also epesents the lnea appoxmaton of α that s used n ou analytcal model and that s expessed as: 0 f CBR 0. CBR 0.4 f 0. CBR 0.7 () 1 f CBR 0.7 Fg. 6. Weghtng facto α n eq. (1). To deve p SIM(d ) we deve fst psim ) and psim ) whch epesent the pobablty that vehcles v t and v tansmt usng the same esouce when only Step o Step 3 ae executed espectvely. If only Step was executed each vehcle would ceate ts set of canddate esouces L C by andomly selectng them fom ts set of assgnable esouces L A (.e. thee s no Step 3 to select the esouces wth lowest RSSI). Each vehcle then andomly selects the esouce that wll be used to tansmt a packet fom the set of N C canddate esouces. As a esul the pobablty that two vehcles select the same esouce fo tansmsson depends on the numbe of canddate esouces that they have n common. Ths numbe s hee efeed to as the numbe of common canddate esouces C C. Fg. 7 llustates the concept of C C. Snce the N C canddate esouces ae selected fom the N A assgnable esouces C C depends on the numbe of common assgnable esouces C A (Fg. 7).e. on how many esouces the L A lsts of vehcles v t and v have n common. In tun C A depends on the numbe of common excluded esouces C E (Fg. 7). C E epesents the esouces excluded by both vehcles v t and v. We need to compute the numbe of common excluded assgnable and canddate esouces (C E C A and C C) fo vehcles v t and v n ode to calculate the pobablty that v t and v tansmt usng the same esouce. Vehcle v t Vehcle v Fg. 7. Illustaton of common excluded (CE) assgnable (CA) and canddate (CC) esouces fo two vehcles. p ) depends on the numbe of common canddate SIM Excluded Selecton Wndow (N esouces) O E Assgnable esouces between vehcles v t and v whch depends on the dstance between the two vehcles C C(d ). It also depends on O C Canddate O A the pobablty p s(d ) that v t and v do not take nto account the espectve tansmssons befoe selectng a new esouce. Ths can occu f the two vehcles cannot sense each othe. It can also occu when v t and v select the esouces nealy at the same tme and hence they cannot take nto account each othe s selecton as they have not been able yet to sense any packet tansmtted usng the newly selected esouce. The pobablty that vehcles v t and v tansmt usng the same esouce when only Step of the sensng-based SPS scheme s executed can then be expessed as: C SIM s NC C d p d p d (3) If the two vehcles ae not able to take nto account the espectve tansmssons the pobablty that they smultaneously select a gven esouce that belongs to the set of canddate esouces s 1/ N. Eq. (3) s obtaned by C multplyng ths pobablty by the numbe of common canddate esouces and the pobablty that they do not take nto account the espectve tansmssons. p s (d ) depends on the pobablty that the tansmttng and ntefeng vehcles (v t and v sepaated by a dstance d ) ae able to sense the espectve tansmssons whch s epesented by the Packet Sensng Rato PSR(d ) (see eq. (11)). It also depends on the aveage numbe of consecutve packet tansmssons τ fo whch each vehcle has to use the same esouce 4. We model the elatonshp between p s (d ) PSR(d ) and τ as follows: 1 1 1/ p d PSR d (4) s t t If the tansmttng and ntefeng vehcles (v t and v ) ae out of each othe s sensng ange (.e. PSR(d )=0) they wll not detect the espectve tansmssons and hence p s (d )=1. When both vehcles ae close to each othe and PSR(d )=1 they wll detect each othe and can consde the pevous tansmssons n the esouce selecton pocess. Ths s howeve not possble f one of the two vehcles has to select a esouce and the othe vehcle has just selected ts esouce but has not yet made any tansmsson usng the newly selected esouce. Ths effect occus wth pobablty 1/τ and theefoe deceases as τ nceases. To compute psim ) we also need to calculate C C (d ) that s a functon of the numbe of common assgnable esouces C A(d ). When Step 3 s not executed C A(d ) s equal to the numbe of assgnable esouces that both the tansmttng vehcle v t and the ntefeng vehcle v dd not exclude n Step of the sensng-based SPS scheme. Snce vehcles andomly select the esouce fom the set of assgnable esouces when Step 3 s not modeled the elatonshp between C C (d ) C A (d ) the numbe of canddate esouces N C and the numbe of assgnable esouces N A s: CC d t CA d t N A N N C N A C (5) 4 Fo example τ=(15+5)/ n the C-VX Mode 4 when λ=10hz snce the Reselecton Counte s andomly selected between 5 and 15.

8 8 and hence: N C CC d CAd (6) N A Usng Fg. 7 t s possble to elate C A (d ) and C E (d ) as: C ) N N C ) (7) A E E N s the total numbe of esouces n the Selecton Wndow and can be computed as follows consdeng that thee ae 1000 sub-fames pe second: S N 1000 (8) whee S s the numbe of sub-channels pe sub-fame and λ s numbe of packets tansmtted pe vehcle pe second. To compute C A (d ) we need to calculate C E (d ) and N E. N E depends on the taffc densty the total numbe of esouces n the Selecton Wndow the tansmsson powe and the scenao and s hee estmated 5 as: S / S PSR PSR k N E max1 0 (9) k 1 N SPSR / whee S PSR epesents the aveage numbe of vehcles that a vehcle could sense n the Selecton Wndow f thee wee no packet collsons. S PSR can be estmated consdeng that a packet tansmtted by a vehcle located at a gven dstance d s sensed f ts eceved sgnal powe s hghe than the sensng powe theshold. A vehcle located at a shot dstance would be sensed wth pobablty PSR(d)=1 but a vehcle at a lage dstance wll be sensed wth pobablty PSR(d)=0. Vehcles at ntemedate dstances wll be sensed wth pobablty 0<PSR(d)<1. S PSR can be then estmated as functon of the packet sensng ato wth the followng equaton: SPSR PSR d PSR PSR (9.1) whee β s the taffc densty n vehcles/m. Ths equaton consdes the theoy of the Remann sum to take out the taffc densty fom the PSR summaton. To calculate C E(d ) let s consde that a vehcle v k s tansmttng n a gven esouce. The pobablty that two vehcles (v t and v ) exclude the esouce used by vehcle v k depends on the dstance to v k (d k and d k espectvely) and s equal to PSR(d k)psr(d k). In the consdeed taffc scenao ths pobablty can also be expessed as PSR(d +d k)psr(d k). If v t and v ae at the same locaton they would exclude appoxmately the same esouces because they would sense the tansmssons of appoxmately the same vehcles. Howeve f vehcles v and v t ae sepaated by long dstances the esouces excluded by each one of them can be consdeed ndependent. In ths case the popoton of common excluded esouces between both vehcles tends to N E/N and theefoe the numbe of common excluded esouces C E tends to N E /N. We can then compute C E fo vehcles v t and v sepaated by a dstance d as: 5 Ths appoxmaton has been valdated though smulatons usng the C- VX Mode 4 smulato pesented n Secton V. C E d R d N R N N R0 SPSR N N PSR E 0 E E (30) whee R0 R PSR 0 (30.1) and R PSR(d ) s the autocoelaton of the PSR functon at d : j j RPSR d PSR d PSR (30.) j In eq. (30.) please note that the dstance between two consecutve vehcles s 1/β when the taffc densty s β and ths s why the tem j/β s ntoduced. Combnng eq. (3)-(30.) we can compute psim ) that epesents the pobablty that the tansmttng vehcle v t and an ntefeng vehcle v smultaneously tansmt usng the same esouce when only Step of the sensng-based SPS scheme s consdeed. To compute p SIM ) we follow a smla appoach than fo p ) and can be computed as: SIM C SIM s NC C d p d p d (31) The elatonshp between C C C A and C E s mantaned whethe we consde Step o Step 3 of the sensng-based SPS scheme. As a esul eq. (4) to (8) and (9.1) to (30.) obtaned fo Step ae also vald to compute psim ). Ths s not the case fo the expesson of N E that needs though to be computed when only Step 3 s executed. In ths case L C s bult fom the assgnable esouces and Step 3 excludes the esouces wth the hghest aveage RSSI expeenced dung the last 1000 sub-fames. When the channel load s hgh t s possble that Step 3 excludes moe than 80% of the esouces. Snce the sze of L C must be equal to 0.N f moe than 0.8N esouces ae excluded Step 3 must consde as assgnable cetan esouces that t had pevously excluded untl fllng L C. Step 3 ncludes n L C the esouces wth the lowest aveage RSSI that t had pevously excluded untl L C s flled. Ths pocess s equvalent to nceasng the sensng powe theshold fom P to cetan P +nδ whee n s a postve ntege and Δ s cetan small ncement n db. We need to fnd the mnmum value of n that educes the numbe of excluded esouces to less than 0.8N. Ths s equvalent to fndng the mnmum value of n that satsfes the followng elaton: whee S max N (3) ( n ( n ) S ) PSR / PSR k ( n ) k 1 N SPSR / ( n ) SPSR PSRn PSRn (3.1) 1 PT PL) ( P n) PSRn ) 1 ef (3.) Eq. (3.1) consdes a β facto nstead of β as n eq. (9.1). Ths s the case because Step 3 needs to take nto account the numbe of dffeent esouces occuped n the last 1000 sub-

9 9 fames. In 1000 sub-fames each vehcle tansmts n dffeent esouces on aveage (.e. t wll pefom one esouce e-selecton pe second on aveage). Fo example fo λ=10hz each vehcle pefoms a esouce selecton evey (5+15)/=10 packet tansmssons on aveage.e. evey 1000 sub-fames o 1000ms. To take ths effect nto account n Step 3 we have estmated S PSR (.e. the aveage numbe of vehcles that could be sensed f thee wee no packet collsons) consdeng that the taffc densty β s doubled. Gven that the PSR n functon monotoncally deceases as n nceases we can solve the poblem by evaluatng nceasng values of n statng at n = 0. Once the mnmum value of n that satsfes eq. (3) s found the numbe of excluded esouces that wll not be pat of L C can be appoxmated as: ( n ( n ) S ) / S PSR PSR k N E max1 0 ( n ) k 1 N SPSR / (33) psim ) s then computed followng eq. (31) and usng eq. eq. (4) to (8) and (9.1) to (30.) and the numbe of excluded esouces N E n eq. (33). The pobablty that the tansmttng vehcle v t and an ntefeng vehcle v smultaneously tansmt usng the same esouce p SIM(d ) s then computed followng eq. (1) that elates psim ) and psim ). The value of α s calculated usng eq. () consdeng that the CBR can be analytcally estmated as: N E CBR (34) N whee the numbe of excluded esouces N E s calculated wth eq. (9) fo Step snce t consdes only those esouces that ae occuped n the last Selecton Wndow. We can then compute the pobablty of packet loss due to a collson povoked by vehcle v ( ) usng eq. (15) and eq. (18) and (1) to epesent p INT (d d ) and p SIM (d ). The pobablty of packet loss due to collsons (δ ) s then computed followng eq. (14). Fnally the PDR s computed usng eq. (5) whee δ HD δ δ PRO and δ ae obtaned fom eq. (7) (10) (13) and (14) espectvely. V. MODEL VALIDATION A. Famewok and Smulaton Envonment The poposed C-VX Mode 4 analytcal models have been mplemented n Matlab 6. The models ae valdated n ths secton by compang the outcome wth that obtaned wth a C-VX Mode 4 smulato developed ove Vens and pesented n [10]. The esults obtaned wth ths smulato ae used as benchmak snce no othe open-souce C-VX Mode 4 mplementaton s cuently avalable and to the authos knowledge no analytcal models of the C-VX Mode 4 communcaton pefomance have been epoted n the lteatue. Vens ntegates OMNET++ fo weless netwokng smulaton wth the open-souce taffc smulaton platfom SUMO. The smulatons conducted utlze ealstc moblty of vehcles usng the open souce taffc smulato 6 The mplementaton s eleased at: SUMO. SUMO models the moblty of vehcles usng the Kauss ca followng model that mantans a safe dstance between a vehcle and ts vehcle n fon and selects the speed of vehcles so that vehcles can stop safely and avod ea-end collsons. The moblty of vehcles has been geneated fo the hghway scenao consdeed n ths study and followng the paametes specfed n Table III. The smulato mplements the complete MAC of C-VX Mode 4 ncludng the sensng-based SPS scheme and the Wnne+ B1 popagaton model ecommended by the Euopean poject METIS fo DD/VV [17]. The physcal laye pefomance s modelled though the lnk level LUTs pesented n [15]. The compason between the analytcal models and the smulatons s conducted consdeng that vehcles tansmt packets at λ=10hz wth a tansmsson powe P t=0dbm and an MCS usng QPSK and a codng ate of 0.7. Ths settng esults n that each packet occupes 10 RBs and thee ae hence 4 sub-channels pe sub-fame. Howeve the models have been valdated fo othe tansmsson powe levels dffeent packet tansmsson fequences and an MCS usng QPSK and a codng ate of 0.5 ( sub-channels pe subfame). Table III summazes the man paametes consdeed fo the valdaton and that follow the 3GPP gudelnes fo the evaluaton of C-VX Mode 4 [18]. The smulatons consde a hghway of 5km wth 4 lanes ( lanes pe dvng decton) and vehcles movng at 70km/h. To avod bounday effects statstcs ae only taken fom the vehcles located n the km aound the cente of the smulaton scenao. The accuacy of the poposed analytcal models s estmated usng the Mean Absolute Devaton (MAD) metc that quantfes the absolute dffeence between two vectos of M elements m s and m a : M 100 MAD[%] ms ma (35) M 1 The MAD metc s hee used to compae the PDR and the fou possble tansmsson eos obtaned though smulatons and usng the analytcal model poposed. The compason eques epesentng the esults as vectos. The MAD metc epesents then as a pecentage the aveage dffeence between the esults obtaned analytcally and though smulatons. Fo example a MAD equal to 1% means that on aveage the esults obtaned analytcally and though smulatons dffe by 1%. The MAD metc numecally complements the vsual compason of the analytcal and smulaton esults. TABLE III. PARAMETERS Paamete Values analyzed Taffc densty (β) veh/m Avg. numbe of vehcles Max. speed of vehcles 70 km/h Hghway length 5km Numbe of lanes 4 ( pe decton) Channel bandwdth 10MHz Tansmsson powe (Pt) 0 3 Packet tx fequency (λ) 10 0 Hz Packet sze (B) 190 bytes Sub-channels pe sub-fame (S) 4 RBs pe sub-channel 17 ( sub-channels) 1 (4 sub-channels) Modulaton and codng scheme MCS 7 (QPSK 0.5 fo sub-channels) MCS 9 (QPSK 0.7 fo 4 sub-channels)

10 10 B. Valdaton Fg. 8a compaes the PDR cuves obtaned wth the poposed analytcal model (dashed lnes) and wth the C-VX Mode 4 smulato (sold lnes) fo P t =0dBm λ=10hz 4 subchannels pe sub-fame an MCS of QSPK wth codng ate of 0.7 and dffeent taffc denstes. The fgue clealy shows that the PDRs obtaned wth the poposed analytcal model closely match those obtaned by smulaton. Ths tend s mantaned espectve of the taffc densty and the esultng CBR. Fo example a taffc densty β of 0.1veh/m esulted n an estmated CBR of appoxmately 0.3 whle a taffc densty of β=0.3veh/m esulted n a CBR 7 of 0.6. Fg. 8a shows that the analytcal model s capable to povde an accuate PDR fo low and hgh taffc denstes and hence channel load levels. The poposed analytcal models have also been evaluated fo dffeent tansmsson powe levels. Fg. 8a depcted the PDR fo P t=0dbm and Fg. 8b depcts t fo P t=3dbm. Fo the late the analytcal CBR anged fom 0.7 (β=0.1veh/m) to 0.69 (β=0.3 veh/m). Fg. 8b shows agan that the PDRs obtaned wth the poposed analytcal model closely match the ones obtaned by smulaton. Anothe mpotant paamete that nfluences the opeaton and pefomance of C-VX Mode 4 s the numbe of packets tansmtted pe second pe vehcle λ. Ths paamete nfluences the numbe of sub-fames wthn the Selecton Wndow and the channel load and ntefeence expeenced by all vehcles. Fg. 8c shows the PDR obtaned fo P t =0dBm and λ=0hz fo 3 taffc denstes. The fgue shows once moe the close match between the PDRs obtaned by smulaton and usng the poposed analytcal models. Fo β=0.3 veh/m the channel load was so hgh (analytcal CBR of 0.85) that the poposed model slghtly devates fom the smulaton esults (6.5% mean absolute devaton). Howeve t s mpotant to consde that such hgh CBR levels would compomse the system s stablty and scalablty and should hence be avoded usng congeston contol mechansms. In fac elevant studes ecommend that the taget CBR fo VX systems usng IEEE 80.11p should be n the ange of [19] and ETSI ecommends a default maxmum CBR of 0.5 [0]. The 3GPP has not defned yet a taget CBR fo C-VX. The MCS nfluences the lnk level pefomance of C-VX the numbe of RBs that each packet occupes and hence the numbe of sub-channels pe sub-fame. The pevous esults wee obtaned wth a MCS usng QPSK and a codng ate of 0.7 (4 sub-channels pe sub-fame). Fg. 8d shows the PDRs obtaned wth a MCS usng QPSK and a codng ate of 0.5 ( sub-channels pe sub-fame). Fg. 8d demonstates the valdty of the pesented analytcal models fo dffeent MCS and numbe of sub-channels pe sub-fame. The PDR s shown fo taffc denstes of and 0.3 veh/m that coespond to analytcal CBR levels of and The accuacy of the poposed analytcal models to calculate the pobablty of packet loss due to the dffeent eos dentfed has also been evaluated. Fg. 9 depcts the pobablty of packet loss due to collsons as a functon of the dstance between tansmtte and eceve fo P t =0dBm λ=10hz 4 sub-channels pe sub-fame and dffeent taffc denstes. Fg. 9 shows that the poposed analytcal model s also capable to accuately quantfy ths type of packet eos as ts pefomance closely matches that obtaned though smulatons. The same accuacy s obseved fo dffeent taffc denstes. Fg. 9 shows that the pobablty of losng a packet due to collsons has a maxmum aound m. Ths s the dstance at whch the hdden-node poblem causes hghe degadaton n ths scenao. Fg. 10 shows the pobablty of losng a packet due to the half-duplex effec due to a eceved sgnal powe below the sensng powe theshold and due to the popagaton. The pobabltes ae shown as a functon of the dstance between tansmtte and eceve fo P t =0dBm λ=10hz and 4 subchannels pe sub-fame. These pobabltes ae ndependent of Dstance [m] (a) Pt=0dBm λ=10hz 4 sub-channels/sub-fame (QPSK 0.7). PDR (b) Pt=3dBm λ=10hz 4 sub-channels/sub-fame (QPSK 0.7). PDR Smulaton Analytcal = 0.3 = 0. = 0.1 (c) Pt=0dBm λ=0hz 4 sub-channels/sub-fame (QPSK 0.7). PDR (d) Pt=0dBm λ=10hz sub-channels/sub-fame (QPSK 0.5) Fg. 8. PDR as a functon of the dstance between tansmtte and eceve fo dffeent taffc denstes. 7 CBR levels analytcally estmated usng eq. (34).

11 11 the taffc densty. Fg. 10 shows agan a good match between the values obtaned by smulaton and usng the analytcal models. The pobablty of losng a packet due to the halfduplex effect (Fg. 10a) depends on the duaton of C-VX sub-fames and the numbe of packets tansmtted pe second. Howeve t does not depend on the dstance between tansmtte and eceve o the taffc densty. The pobablty of losng a packet due to popagaton (Fg. 10a) s almost null at shot dstances and has a maxmum at aound 450m to the tansmtte. At hghe dstances ths pobablty deceases because most of the packets cannot even be detected due to a eceved sgnal powe below the sensng powe theshold. In fac the pobablty of losng a packet because ts eceved sgnal powe s below the sensng powe theshold nceases as the dstance to the tansmtte nceases (see Fg. 10b). The accuacy of the poposed analytcal models s analyzed n Tables IV V and VI. The tables epot the MAD metc fo the PDR and the fou possble tansmsson eos n C-VX mode 4 unde dffeent condtons. The MAD metc s utlzed to compae the esults obtaned analytcally and though smulatons. The MAD metc s shown fo dffeent tansmsson powe levels taffc denstes packet tansmsson fequences and numbe of sub-channels pe sub-fame (o MCS). The tables also show n the last column the CBR level (analytcally estmated) fo each combnaton of paametes epoted n the tables. The esults obtaned show that the PDR estmated analytcally (usng the models pesented n ths pape) dffes on aveage by less than.5% compaed to the PDR obtaned though smulatons n all scenaos whee the CBR s below 0.8. In many cases the devaton s smalle than 1% whch demonstates the hgh accuacy that can be acheved wth the poposed analytcal Fg. 9. Pobablty ˆ of packet loss due to collsons as a functon of the dstance between tansmtte and eceve fo Pt=0dBm λ=10hz 4 subchannels/sub-fame (QPSK 0.7) and dffeent taffc denstes. Pobablty Pobablty (a) Eos due to HD and (b) Eos due to sgnal powe popagaton below sensng powe theshold Fg. 10. Pobablty of losng a packet due to (a) HD and popagaton effects and due to a eceved sgnal powe below sensng powe theshold (b). Pt=0dBm λ=10hz and 4 sub-channels/sub-fame (QPSK 0.7). Pobablty models. The tables show that the type of eo that has a hghe contbuton to the MAD of the PDF s actually the eo due to packet collsons; ths type of eo was the most dffcult to model due to the opeaton of C-VX Mode 4 and ts sensngbased SPS scheme. TABLE IV. MAD FOR THE PDR AND THE DIFFERENT TYPES OF ERRORS. λ=10hz AND 4 SUB-CHANNELS PER SUB-FRAME (QPSK 0.7) Pt β PDR ˆHD ˆ ˆPRO ˆ CBR TABLE V. MAD FOR THE PDR AND THE DIFFERENT TYPES OF ERRORS. λ=0hz AND 4 SUB-CHANNELS PER SUB-FRAME (QPSK 0.7) Pt β PDR ˆHD ˆ ˆPRO ˆ CBR TABLE VI. MAD FOR THE PDR AND THE DIFFERENT TYPES OF ERRORS. λ=10hz AND SUB-CHANNELS PER SUB-FRAME (QPSK 0.5) Pt β PDR ˆHD ˆ ˆPRO ˆ CBR VI. CONCLUSIONS Ths pape has pesented the fst analytcal models of the communcaton pefomance of C-VX o LTE-V Mode 4. In patcula the pape has pesented models of the aveage PDR as a functon of the dstance between tansmtte and eceve and of the fou types of tansmsson eos that can be encounteed n C-VX Mode 4 communcatons. The models ae valdated n ths pape fo a wde ange of tansmsson paametes (tansmsson powe packet tansmsson fequency and MCS) and taffc denstes. To do so the pape compaes the esults obtaned wth the analytcal models to those obtaned wth a C-VX Mode 4 smulato mplemented ove the Vens platfom. The conducted analyss has shown that the analytcal models ae capable to accuately model the C-VX Mode 4 communcatons pefomance. In fac the mean absolute devaton of the esults obtaned wth the analytcal models s geneally below.5% compaed wth the esults obtaned by smulaton. The analytcal models hence epesent a valuable tool fo the communty to evaluate and povde nsghts nto the communcatons pefomance of C- VX Mode 4 unde a wde ange of paametes. Ths wok paves the way fo futhe studes and evolutons of C-VX Mode 4. Fo example the 3GPP standad does not specfy concete values fo some of the paametes that defne the opeaton and confguaton of C-VX Mode 4. In fac ETSI s cuently defnng the default confguaton of C-VX Mode 4 paametes and a detaled analyss of the optmum confguaton of C-VX Mode 4 s needed fo the futue deployment of C-VX technologes. Also dffeent studes have hghlghted possble neffcences of C-VX Mode 4 to