IEEE TRANSACTIONS ON COMMUNICATIONS 1 Efficiet Access Cotrol for Broadbad Power Lie Commuicatios i Home Area Networks Yijia Huo, Studet Member, IEEE, Gautham Prasad, Studet Member, IEEE, Lutz Lampe, Seior Member, IEEE, ad Victor C. M. Leug, Fellow, IEEE Abstract I this paper, we address the problem of improvig the medium access cotrol (MAC) layer efficiecy i idoor broadbad power lie commuicatio (BB-PLC) etworks. Several overheads i the MAC layer, like radom back-offs ad collisio recovery, degrade the MAC efficiecy. To reduce these overheads, we apply i-bad full-duplexig (IBFD), which eables medium-aware trasmissio at all the etwork odes. Specifically, we propose two ew schemes called cotetio-free pre-sesig ad mutual preamble detectio to miimize the time spet durig cotetios ad collisios. Cosiderig the oidealities of IBFD, we aalytically show the feasibility of our solutios. We further desig a comprehesive simulatio model with multiple priority data frames ad Poisso etwork traffic arrival to emulate a real i-home etwork traffic. We the preset umerical results for both the classical saturated etwork model ad the comprehesive traffic model, to show through OMNeT++ simulatios that our preseted solutios achieve over 95% of the optimum MAC efficiecy that ca oly be attaied i the idealized case of o cotetios or collisios. Idex Terms Power lie commuicatios, home area etwork, MAC efficiecy, cotetio-free pre-sesig, mutual preamble detectio. I. INTRODUCTION BROADBAND Power Lie Commuicatio (BB-PLC) provides a attractive alterative for a backboe ad/or stad-aloe commuicatio medium for home area etworks (HANs) as it uses the existig i-home wirig ifrastructure for high-speed ad reliable data commuicatios [], [3]. Sice the itroductio of the 10-Mbps class BB-PLC products of HomePlug 1.0 [4], data rates provided by BB-PLC have icreased multi-fold. Curret HomePlug AV compliat devices use multiple wires available i most i-home wirig istallatios to achieve multiple-iput multiple-output operatio, ad offer data rates of up to Gbps [5]. The gigabit rage of throughput ad the widespread availability of access poits (i.e., power outlets) reder power lies as a favorable commuicatio medium for HANs [6]. A. Backgroud ad State-of-the-art i BB-PLC Despite the high data rate obtaied i the physical (PHY) layer, it remais a challege for the Medium Access Cotrol The authors are with the Departmet of Electrical ad Computer Egieerig, The Uiversity of British Columbia, Vacouver, BC, Caada. Email: yortka@ece.ubc.ca, gauthamp@ece.ubc.ca. A part of this work has bee preseted at the IEEE Global Commuicatios Coferece (GLOBECOM), Washigto D.C., USA, December, 016 [1]. This work was supported by fudig from the Natioal Natural Sciece Foudatio of Chia (Grat No. 61671088) ad the Natural Scieces ad Egieerig Research Coucil of Caada (NSERC). (MAC) layer to traslate this PHY data rate efficietly ito MAC throughput. The cause for this ca be uderstood by examiig the chael access procedure followed i typical BB-PLC protocols. Carrier sese multiple access (CSMA) with collisio avoidace (CA) is implemeted as the primary medium access scheme i popular BB-PLC stadards like HomePlug AV (HPAV) ad IEEE 1901 [5], [7]. CSMA/CA uses a radom back-off strategy to prevet collisios. Whe a collisio evertheless occurs, a relatively log time is spet o collisio recovery [8]. These cotetios ad collisio overheads lead to a iefficiet MAC protocol, sice o payload data is trasferred over the medium durig the radom back-offs or the collisio recovery phase. A possible solutio to avoid the legthy collisio recovery is to implemet CSMA with collisio detectio (CD). Applyig CSMA/CD o power lies has bee cosidered ifeasible as it requires etwork odes to support a full-duplex operatio [9, Ch. 5]. The recet itroductio of i-bad full-duplexig (IBFD) for BB-PLC eables etwork odes to sese the medium while simultaeously trasmittig data [10]. This ispires us to propose ot oly a practical CD scheme, similar to CSMA/CD i full-duplex wireless etworks [11], [1], but also devise a IBFD-based method to elimiate the redudat backoff stages. Although CSMA/CD is also implemeted i early Etheret etworks [13, Ch. 6], we face uique challeges i BB-PLC scearios as explaied i Sectio III ad Sectio IV. B. Related Works o CSMA/CD usig IBFD CSMA/CD was also cosidered ifeasible i wireless etworks whe the etwork odes were uable to trasmit ad receive sigals simultaeously i the same bad [14]. Pseudo- CSMA/CD procedures, like CSMA with collisio otificatio (CN), were istead proposed as a middle-groud solutio betwee CSMA/CA ad CSMA/CD [14]. However, the itroductio of IBFD has propelled feasible CSMA/CD methods to be proposed for wireless etworks. The authors i [15], [16] used IBFD to eable the receiver ode to cotiuously trasmit ackowledgmets as collisio-free idicators while receivig the data payload. Such a scheme ot oly deprives a IBFD system of the bidirectioal data payload trasmissio, but also potetially causes multiple false alarms i coditios of packet errors. Furthermore, it itroduces additioal power cosumptio at the destiatio ode for the cotiuous ackowledgmet trasmissio [17]. Alterative CSMA/CD techiques were proposed for wireless etworks i [11], [1] to detect a collisio at the trasmitter by sesig the medium
IEEE TRANSACTIONS ON COMMUNICATIONS durig trasmissio without relyig o the feedback from the destiatio ode. However, [11], [1] provided aalysis of CSMA/CD uder the assumptio of Rayleigh chael ad a fixed self-iterferece cacellatio performace. I cotrast, we specify a complete detectio ad reactio procedure to realize CSMA/CD i BB-PLC etworks through the IBFD detectio of preamble symbols, ad prove the feasibility of our solutio by aalytically derivig the detectio error ad false alarm rates uder a worst-case power lie atteuatio coditio. For our calculatios, we use the self-iterferece cacellatio performace reported i the literature [10], [18], which is show to be depedet o the power lie chael atteuatio. C. Cotributios I this paper, we exploit the medium-aware trasmissio eabled by IBFD to propose two ovel techiques. First, we propose a cotetio free pre-sesig (CFP) scheme to elimiate the redudat back-off stages. I this scheme, we use the IBFD operatio to eable etwork odes to simultaeously trasmit ad sese for priority resolutio symbols (PRSs) durig the priority resolutio procedure (PRP). This lets a etwork ode idetify a cotetio-free coditio (CFC) where o other odes trasmit a MAC frame of the same or a higher priority. Uder such a coditio, we allow the ode to skip the radom back-off stage, ad gai access to the power lie medium immediately after the PRP. As a result, the redudat back-off stages ca be elimiated, ad the MAC efficiecy ca be improved. Next, with the same uderlyig priciple, we propose a secod access cotrol scheme, called mutual preamble detectio (MPD), which, whe combied with CFP, further icreases the MAC efficiecy. Usig the IBFD operatio, we eable etwork odes to preempt ad thus avoid possible future frame collisios by sesig the medium while trasmittig preambles. I this way, we elimiate the legthy recovery time associated with a frame collisio. This is especially beeficial for future i-home PLC etworks that are expected to ofte operate uder a heavily loaded etwork coditio with a icreased frame collisio rate. To determie the applicability of our schemes i BB-PLC etworks, we aalytically derive closed-form expressios for the pertiet detectio error ad false alarm rates. We the use the self-iterferece cacellatio gai values reported for IBFD BB-PLC systems uder realistic i-home chael ad oise scearios [18], to prove that the worst-case probabilities of false alarms ad detectio errors for a wide-rage of PLC chael coditios are ear-zero. Fially, we build a comprehesive i-home power lie etwork simulatio model with multiple priority data frames ad Poisso etwork traffic arrival to emulate a real HAN traffic. Usig both this model ad the classical simplistic model with a sigle priority saturated etwork traffic, we perform etwork simulatios usig OMNeT++, ad demostrate that the MAC layer overheads caused by cotetios ad collisios are sigificatly reduced by applyig our ew schemes. D. Outlie The rest of the paper is orgaized as follows. I Sectio II, we describe the fuctioig of the curret HPAV MAC protocol, focusig o the aspects relevat to the schemes we propose. I Sectio III ad Sectio IV, we improve the MAC efficiecy by proposig our ew CFP ad MPD schemes. We provide umerical results i Sectio V, where we describe the adopted simulatio models ad preset the OMNeT++ simulatio results. I Sectio VI, we discuss the implemetatio costs associated with our proposed solutios, ad their iteroperability with legacy devices. Fially, we coclude this paper i Sectio VII. Throughout this work, we cosider the chael access procedure specified i the HPAV protocol [8]. However, due to the iheret upward ad dowward compatibility that HPAV provides, as well as the icorporatio of a HPAV-like MAC protocol i the IEEE 1901 stadard [19, Ch. 8] ad the ITU- T G.h stadard [0, Ch. 1], all solutios that we propose i this paper ca also be easily exteded to these BB-PLC stadards [1], []. II. FUNCTIONING OF THE HPAV MAC LAYER I this sectio, we briefly describe some aspects of HPAV MAC protocol [8] that we modify i Sectios III ad IV, ad also defie the MAC efficiecy, which we ited to improve with our proposed access cotrol schemes. A. MAC Operatio i CSMA/CA Mode Fig. 1 shows the time lie of a MAC frame trasmissio uder a stadard CSMA/CA operatio. I the followig, we itroduce compoets of its operatio, which are relevat to the schemes we propose. 1) Priority Resolutio Procedure: A MAC frame trasmissio is iitiated with a PRP. The HPAV protocol specifies four priority levels from 0 (lowest) to 3 (highest) that the etwork odes ca choose from usig two priority bits. The priorities are resolved bit-by-bit startig with the slot for PRS 0, ad followed by PRS 1, with PRS 0 idicatig the most sigificat bit i the biary represetatio of the priority level. Nodes with the highest priority level i the etwork wi the PRP, which esures messages of higher priority levels always get trasmitted before those of lower priority levels [8, Ch. 3]. ) Collisio Avoidace: Collisio avoidace i CSMA/CA is realized through the radom back-off mechaism. Nodes wiig the PRP, or recoverig from a collisio, participate i the back-off stage, which cosists of a variable umber of back-off time slots of equal time itervals. At each back-off time slot, the back-off couter (BC) of a participatig ode is decreased by oe. Upo arrivig at BC = 0, a preamble is trasmitted by this ode i the subsequet back-off time slot. The odes trasmittig a preamble gai access to the chael ad the trasmit a frame cotrol (FC) message of type startof-frame (SOF), followed by the data payload [3]. 3) Collisio i the Network: Despite the precautios take to avoid collisios, CSMA/CA does ot guaratee collisiofree trasmissio, especially with icreased umber of cotedig odes [4]. A collisio i the etwork ode occurs
IEEE TRANSACTIONS ON COMMUNICATIONS 3 Source Node PRS0 PRS1 Back-Off Stage PB FC of type SOF Data Payload CIFS Destiatio Node RIFS PB FC of type SACK CIFS Fig. 1. Time lie of a HPAV MAC frame trasmissio i CSMA/CA mode. (PB = Preamble) Coflictig Node1 PRS0 PRS1 Back-Off Stage PB FC of type SOF Data Payload Back-Off Stage Coflictig Node No- Trasmittig Node PRS0 PRS1 Back-Off Stage PB FC of type SOF Data Payload EIFS Back-Off Stage Back-Off Stage Fig.. Time lie of a MAC frame trasmissio i case of a collisio. Source Node PRS0 PRS1 PB FC of type SOF Data Payload CIFS Destiatio Node RIFS PB FC of type SACK CIFS Fig. 3. Time lie of a MAC frame trasmissio with CFP whe a CFC successfully detected. Coflictig Node1 PRS0 PRS1 Back-Off Stage PB PB Back-Off Stage Coflictig Node PRS0 PRS1 Back-Off Stage PB PB Back-Off Stage No- Trasmittig Node CIFS Back-Off Stage Fig. 4. Time lie of a MAC frame trasmissio i case of a collisio with the deploymet of MPD. whe multiple odes simultaeously trasmit the preamble sigal i a back-off time slot to gai access to the chael. A collisio is determied at a etwork ode if the ode does ot receive a selective ackowledgmet (SACK) frame before the exteded iter-frame space (EIFS) timer expires, as show i Fig.. 4) Collisio Recovery: Nodes recover from a collisio immediately after the EIFS timer expires, ad starts to backoff regardless of the priority level of the trasmittig MAC frames. This operatio is illustrated i Fig.. The EIFS has a duratio of t EIFS = t p + t FC + MaxFL + t RIFS + t CIFS, (1) where t p, t FC, MaxFL, t RIFS, ad t CIFS are the time itervals of the preamble, the FC, the maximum time iterval of the data payload, the respose iter-frame space (RIFS), ad the cotetio iter-frame space (CIFS), respectively. EIFS is therefore legthy, ad reders a collisio very costly to recover from. B. MAC Efficiecy As show i Fig. 1, a data payload is oly trasmitted i the time iterval followig the SOF trasmissio. All other time itervals are overheads that impede the ability of the MAC layer to efficietly traslate PHY data rate ito the MAC throughput. To quatify this cross-layer throughput trasfer, we defie the MAC efficiecy as the portio of time utilized by the MAC layer to trasmit the data payloads, which is also referred to i the literature as the ormalized throughput to evaluate the performace of a MAC protocol [5], [6]. For N collisio-free frame trasmissios over a time duratio T, we defie the MAC efficiecy as η 1 T N t i, () i=1 where t i idicates the data payload iterval of the ith frame, which is depedet o the traffic demads of the trasmissio statio as well as the data payload PHY trasmissio rate, ad is limited by MaxFL.
IEEE TRANSACTIONS ON COMMUNICATIONS 4 To determie the extet to which η ca be improved, the ideal maximum MAC efficiecy uder CSMA operatio ca be computed uder the coditio that a etwork ode cotiuously trasmits frames of maximum legth without icurrig a collisio, or back-off 1. Uder such coditios, each data payload is of the maximum time iterval MaxFL, ad each MAC frame show i Fig. 1 is of a idetical duratio of t SLOT + t p + t FC + MaxFL + t RIFS + t p + t FC + t CIFS = t SLOT + t EIFS, where t SLOT is the time iterval for two PRSs. Thus, the maximum MAC efficiecy ca be expressed as MaxFL η max =. (3) t SLOT + t EIFS With the objective of ehacig practical values of η as close as possible to η max, we attempt to reduce the MAC overheads caused by cotetios ad collisios, by proposig two ew access cotrol schemes i the followig two sectios. III. CONTENTION FREE PRE-SENSING I this sectio, we propose our first scheme called CFP to detect a CFC durig the PRP. A. Network Operatio with CFP Recall that a CFC at a ode is a coditio where o other etwork ode trasmits a MAC frame of the same or a higher priority. To detect a CFC, we eable etwork odes with the IBFD operatio, ad allow them to detect the PRS trasmitted by other odes while trasmittig a PRS themselves. If a ode does ot detect ay other PRS sigals durig its trasmissio, it idetifies the chael to be cotetio-free, i.e., detects the presece of a CFC. I case a CFC is detected, as show i Fig. 3, we skip the radom back-off stage that traditioally follows the PRP, ad let the source ode trasmit a preamble sigal to gai access to the power lie medium immediately after the PRP. Due to this, we observe from Figs. 1 ad 3 that we save a time duratio of up to CW max t SLOT, which is otherwise wasted for a redudat back-off. CW max idicates the maximum cotetio widow size. B. Detectig CFC usig IBFD CFP Cosider a etwork of K odes, where N of those odes coted to trasmit a frame, with priority level p associated with each of the = 1,,..., N odes. A CFC occurs whe oly oe of the N odes trasmits a message of the maximum priority level of all trasmittig odes, max(p ), with 0 < max(p ) p std, where p std = m 1 (m Z + ) is the highest supported priority level of a message i the operatig stadard. For example, i the IEEE 1901 ad HPAV stadards, m =. I order to provide upward compatibility for future stadards that may decide to support a greater umber of priority levels to effectively serve traffic of varied ature, we preset a aalysis of our proposed CFP procedure for geeral m. 1 For the sake of simplicity, we igore the burstig ad iverse burstig procedure specified i the HPAV protocol for this computatio, without ay adverse effects o our proposed solutio. Results obtaied i this paper ca be easily exteded to cases with burstig. We defie that a p x -CFC occurs whe oly oe etwork ode trasmits a message with max(p ) = p x. Our CFP scheme is aimed to successfully detect such p x -CFCs, for all 0 < p x p std. Every priority level p ca be expressed as p = m 1 i=0 m 1 i χ i, (4) where χ i {0, 1} is the biary value of the ith PRS, PRS i, i.e., χ i = 1 whe a PRS i is trasmitted by the ode ad χ i = 0 otherwise. The priority levels are resolved bit-by-bit through the m priority bits from PRS 0 to PRS m 1, with the most sigificat bit, χ 0, trasmitted first as PRS 0. Durig the PRP, a ode of priority p trasmits the PRS sigal i PRS i (0 i m 1) if ad oly if χ i = 1. Every p (p 0) is associated with a slot positio j, for which χj = 1 while χ j = 0, j > j. That is, χj is the least sigificat bit 1 i the biary otatio of p. With a itetio to preserve the legacy PRP ad itroduce CFP as a add-o feature, we compel the th etwork ode with priority p to perform CFP oly at PRSj, whe it has wo all previous PRSs. If the ode loses the PRP before PRSj, it resigs from the PRP cotetio as per the legacy PRP, ad therefore does ot proceed to perform CFP. Whe the ode has wo i all the previous priority resolutio slots, it trasmits a PRS at PRSj, ad so will ay other ode with the same or a higher priority level. Therefore, if the th ode detects aother PRS trasmitted at PRSj, it deduces the presece of other ode(s) of either the same or a higher priority level. I either case, the th ode deduces a o-cfc. However, if it does ot detect ay PRS i PRSj, it deduces a absece of ay other ode with the same or a higher priority level. I such a CFC, the ode skips the followig back-off stage as described i Sectio III-A. This way, we esure that the CFP procedure does ot iterfere with the covetioal PRP, ad is oly a supplemetary feature itroduced to elimiate the redudat back-off stage uder CFC. The successful detectio of a CFC is depedet o the extet of self-iterferece cacellatio achieved by the IBFD solutio. A o-ideal self-iterferece cacellatio i IBFD could subject CFP to detectio failure or false alarms. I the followig, we aalytically compute the probabilities of detectio errors ad false alarms usig realistic self-iterferece cacellatio gai values reported i [18]. C. Detectio Error ad False Alarm Rates We deote the false alarm ad detectio error rates of the CFP at a etwork ode as P FA ad P DE, respectively. To aid our derivatios, we defie the followig three evets at a give etwork ode. E 0 : The ode trasmits a PRS. E 1 : The ode detects the presece of at least oe PRS sigal trasmitted by aother ode i the etwork. E : At least oe ode other tha the cosidered ode actually trasmits a PRS. A false alarm occurs at a PRS trasmittig ode whe it detects the presece of a PRS while o etwork odes have
IEEE TRANSACTIONS ON COMMUNICATIONS 5 actually trasmitted a sigal. Similarly, a PRS trasmittig ode is subject to detectio errors whe it fails to detect a PRS sigal whe at least oe other etwork ode has trasmitted the sigal. Therefore, we formulate the error probabilities as P FA = P (E 0 (E 1 Ē)), (5) P DE = P (E 0 (Ē1 E )), (6) where E represets the o-occurrece of the evet E. I order to calculate P FA ad P DE, cosider a etwork with two odes A ad B, with ode A cotiuously trasmittig PRSs, while ode B either trasmits a PRS or remais silet. To determie the detectio error ad the false alarm rate at ode A, we view this sceario as a o-off keyig (OOK) trasmissio, with ode B trasmittig bit 1 whe it trasmits a PRS, ad bit 0 whe it does ot. Here, bit 1 correspods to the PRS sigal s 1, whose samples are give by [8] s 1 [l] = 103/0 L c C ( ) π c l cos ψ(c), L l = 0, 1,..., L 1, (7) where L is the total umber of time samples trasmitted i the PRS sigal, C is the set of orthogoal frequecy divisio multiplexed (OFDM) sub-carriers used for PRS trasmissio, ad ψ(c) is a sub-carrier specific phase agle [8]. Thus, P FA represets the probability of ode A detectig a 1 whe a 0 is trasmitted by ode B, ad P DE represets the probability of detectig a 0 whe a 1 is trasmitted. Cosiderig that the sigal is subject to possible phase distortios alog the lie, we apply o-coheret detectio at ode A. Uder such a coditio, P FA ad P DE are the bit error probabilities of o-coheret OOK detectio, ad ca be expressed as [7, Ch. 7] ( ) P FA = exp b 0, (8) ( ) P DE = 1 Q γ, b0, (9) where Q(, ) is the first-order Marcum-Q fuctio, b 0 is the decisio threshold of o-coheret OOK ormalized to the root-mea-square oise value, ad γ is the sigal-to-oise ratio (SNR). The latter is give as γ = E b N 0 + Ψ RSI, (10) where E b represets the received eergy per-bit, N 0 is the average power spectral desity (PSD) of the cumulative oise at the receiver of ode A, ad Ψ RSI is the average residual self-iterferece (RSI) PSD after o-ideal self-iterferece cacellatio. For brevity, we defie N 0,FD = N 0 + Ψ RSI as the ew effective oise floor uder IBFD operatio. To determie realistic values of P DE ad P FA i a HAN, we derive a expressio for γ i terms of kow trasmissio parameters ad chael coditios. The received bit-eergy ca be writte as E b = Φ R t pd, where t pd is the time iterval The term bit here refers to the PRS sigal i oe PRS slot used for sigal detectio. for PRS detectio, which is related to the PRS time t SLOT as t pd = t SLOT t RI, where t RI is the roll-off time iterval at the begiig ad the ed of a PRS ad is ot used for sigal detectio. O the other had, Φ R is the power of the received sigal, which ca i tur be writte as Φ R = f f 1 Ψ R (f)df, (11) with Ψ R (f) beig the PSD of the received sigal at a frequecy f, ad f 1 ad f are the lower ad upper frequecy limits of the trasmissio bad, respectively. We further express Ψ R (f) i terms of the kow trasmit PSD, Ψ T (f), as Ψ R (f) = Ψ T (f) H(f), where H(f) is the power lie chael frequecy respose at frequecy f from ode B to ode A. The maximum trasmit PSD is typically regulated to limit the electromagetic iterferece caused by BB-PLC [1]. For our aalysis, we cosider the devices to always trasmit sigals with maximum PSD Ψ T,max, although ewer devices support variable trasmit PSDs [8]. Further, it is safe to assume the chael gai to be flat withi each sub-carrier, sice the HPAV PRS sub-carrier spacig is smaller tha the observed chael coherece badwidth i typical i-home BB- PLC etworks [8], [9]. We ca therefore re-write (11) as Φ R = Ψ T,max H(f c ) f, (1) c C where f c is the ceter frequecy of the cth OFDM subcarrier, ad f is the sub-carrier spacig. Sice N 0,FD = N 0,FD (f c ), where N 0,FD (f c ) is the effective oise 1 C c C floor of the cth OFDM sub-carrier uder IBFD operatio, we express (10) as H(f c ) c C γ = Ψ T,max t pd f C N 0,FD (f c ). (13) c C We ow determie the optimal value of the threshold b 0 to be used i (8) ad (9). Deotig the overall etwork ode error rate as P e = P (E E 0 )P DE + P (Ē E 0 )P FA, (14) we defie the optimal threshold as b opt arg mi P e. (15) b 0 I the appedix, we derive a closed-form approximatio of the optimal threshold solutio as b opt b (γ + l τ) opt = + 4(γ + l τ), (16) γ where τ = P (Ē E0) P (E E 0). The value of τ at a give ode depeds o the trasmittig priorities ad the cogestio coditios of other etwork odes. Whe a ode trasmits a PRS, i.e., whe the evet E 0 occurs, the other etwork odes have a coditioal probability of P (Ē E 0 ) to ot trasmit ay PRS, ad P (E E 0 ) to
IEEE TRANSACTIONS ON COMMUNICATIONS 6 trasmit at least oe. Thus, τ ca be estimated locally at ay give ode by coutig the umber of priority resolutio slots where at least oe other ode also trasmits a PRS, while the cosidered ode trasmits a PRS itself. This ca easily be achieved due to the IBFD operatio applied at each etwork ode. Such a estimatio of τ relies o a local historical record of PRS detectio. Whe this record is uavailable, such as durig the bootstrappig of the etwork, the ode sets τ = 1 as i [1] to miimize P FA +P DE. This serves as a upper boud for both P FA ad P DE idividually ad yields ear-zero error rates as show later i this sectio. The ode the dyamically updates τ to miimize P e. Sice P e is a mootoically decreasig fuctio with respect to γ for the optimum detectio threshold b opt (which is closely approximated by b opt ) [7, Ch. 7], ad sice H(fc) N 0,FD(f c) decreases with H(f c ) [10], we use the worst-case miimum chael gai, H mi, across all sub-carriers to obtai a upper boud for the total error, P tot, as P tot = P DE + τp FA (17) ( ) ( ) b opt 1 Q γmi, b opt +τ exp, (18) where γ mi = Ψ T,max C H mi ft pd N 0,FD. The oly remaiig ukow is N 0,FD, which we determie by referrig to [10, Table II] that reports the sigal-tocaceled-iterferece-plus-oise-ratio (SCINR) after the selfiterferece cacellatio uder differet chael coditios. We compute N 0,FD as N 0,FD (f) = Ψ R(f) SCINR(f). (19) It has also bee show i [10] that SCINR(f) varies with chagig H(f). Sice we cosider a worst-case performace with H mi, we calculate N 0,FD as N 0,FD = Ψ T,max H mi, (0) SCINR where SCINR is the associated self-iterferece cacellatio performace for H mi. We ow calculate the values of γ mi that we obtai for differet H mi. I accordace with the HPAV specificatios, we set Ψ T,max = 50 dbm/hz, f = 195 khz, C = 153, ad t pd = 5.9 µs [8]. The resultig γ mi values are listed i Table I. Next, we compute the associated b opt. Fially, we use (18) to determie the practical upper-boud values of P tot that we expect to ecouter whe CFP is deployed i i-home etworks. As a example, we cosider the case where τ = 1 to evaluate P tot. With the values computed i Table I ad usig (16), we calculate P tot to be ear-zero (< 10 100 ) uder various miimum chael gai coditios dow to H mi = 60 db. For other values of τ ragig betwee 0.01 ad 100, we fid P tot, P FA, ad P DE to all be early zero as well. This assures us that the deploymet of CFP i practical i-home BB-PLC etwork eviromets results i virtually o detectio errors or false alarms. TABLE I PRS SNR UNDER VARYING MINIMUM CHANNEL GAINS D. Impact of PLC Noise H mi SCINR N 0,FD γ mi (db) (db) (dbm/hz) (db) -5 3-87 60-10 30-90 58-0 7-97 56-30 7-107 56-40 1-111 50-50 1-11 40-60 -11 30 The performace of our proposed solutio is etirely depedet o the self-iterferece cacellatio ability of the IBFD solutio used, ad our solutio is equally applicable uder all PLC oise coditios. Uder moderate to low oise scearios, where Ψ RSI is the more domiat compoet of N 0,FD, the values preseted i Table I remai uchaged as it is equivalet to the coditio that we have reported our values for, i.e., with N 0 = 10 dbm/hz ad N 0,FD 11 dbm/hz. O the other had, whe power lie oise is the limitig factor of SCINR, i.e., whe N 0 is the more domiat compoet of N 0,FD, the values of γ mi are lower tha those reported i Table I. However, ote that such a coditio is similar to a half-duplex (HD) sigal detectio ad is ot a result of IBFD detectio. The PRS sigals are desiged i the HPAV stadard with multiple repetitios i order to be resiliet to harsh power lie oise coditios. For example, with τ = 1, ad a power lie oise as high as N 0 = 103 dbm/hz o all sub-carriers, we still achieve a total error rate of P tot = 10 0. The multiple PRS repetitios also eable a impulse oise resiliet PRS sigal detectio. I additio, the impulse oise evets occur with a low probability [30], [31]. Despite this, if a ode is uable to detect a PRS sigal set by aother etwork ode, the adverse effects associated (such as, the two odes beig hidde from each other durig the PRS trasmissio phase) are exactly the same as those i a HD case. Such coditios could potetially result i data payload collisios, just as it would i a HD operatio. However, we do ot address such collisios i this work. We focus o the more commo cause of frame collisios resultig from two or more etwork odes havig the same value of BC. I the followig sectio, we use the uderlyig techique built i Sectio III to desig a MPD scheme to elimiate such collisios. IV. MUTUAL PREAMBLE DETECTION I this sectio, we itroduce our secod access cotrol scheme called MPD, where we use the medium-aware trasmissio ability provided by the IBFD operatio to avoid the legthy collisio recovery by predictig a future frame collisio. Through MPD, we essetially propose a practical scheme to realize CSMA/CD i BB-PLC etworks by detectig the overlappig preamble sigals.
IEEE TRANSACTIONS ON COMMUNICATIONS 7 A. Network Operatio with MPD We eable all odes i the etwork with the ability to trasmit a preamble ad simultaeously sese the power lie medium for other possible preamble sigal trasmissios. I this way, whe two or more etwork odes trasmit a preamble sigal at the same back-off time slot ad gai access to the power lie chael simultaeously, they each predict a future data payload collisio by detectig a preamble other tha their ow. Uder such circumstaces, we compel these coflictig odes to trasmit aother preamble sigal subsequetly. This acts as a jammig sigal to esure that all etwork odes are made aware of a potetial collisio. We the let the odes follow the stadard HPAV collisio recovery procedure withi a iterval of t CIFS. This operatio is illustrated i Fig. 4. We otice that the time iterval betwee the two back-off stages (the back-off stage of the collidig MAC frame ad the back-off stage after the collisio recovery) is reduced to t p + t CIFS with our MPD scheme, while it is of duratio t EIFS i the origial HPAV MAC protocol, as show i Fig.. B. IBFD Preamble Detectio To determie the success of IBFD preamble detectio, cosider a BB-PLC etwork with two odes, A ad B, with ode A cotiuously trasmittig preambles slot-by-slot, while i each time slot, ode B either trasmits a preamble or ot. Similar to Sectio III-C, we view the behavior of ode B as a source cotiuously trasmittig iformatio bits usig ooff keyig, with the preamble sigal beig the trasmissio pulse. I every preamble time slot, ode B trasmits a bit 1 to sed a preamble to ode A, ad a 0 whe it has othig to trasmit. A IBFD eabled ode A is able to cotiuously detect the iformatio bit set by ode B i each time slot. This sceario is similar to the oe cosidered i Sectio III-C, albeit, the trasmissio pulse is ow a preamble sigal, s, where s [l] = 103/0 L c C ( ) π c l cos + ψ(c), L l = 0, 1,..., L 1, (1) with the value of L beig the same as that for the PRS sigal. The preambles also use the same set of OFDM sub-carriers as the PRSs, with the phase shift of each correspodig subcarrier beig the same i magitude but opposite i sig. Therefore, the P FA ad P DE formulatios i Sectio III-C also apply to the above sceario. This also implies that all the computatios i (8) (0), as well as the data reported i Table I, are valid for detectig preambles as well. Thus, the detectio error rate ad the false alarm rate for MPD are also practically zero. V. NUMERICAL EVALUATIONS I this sectio, we first describe the comprehesive simulatio model we build to emulate a real HAN traffic. I particular, we eable multiple priority levels that are idicative of the heterogeeous ature of the HAN traffic. Further, we itroduce the Poisso traffic shapig (PTS) to emulate a real HAN traffic arrival, ad apply a etwork resource allocatio scheme to esure that each priority level acquires a appropriate share of the etwork resource. We the use both the classical simplistic model ad the comprehesive model we built to preset OMNeT++ simulatio results of the CFP ad MPD performaces, to verify the effectiveess of our proposed schemes. A. Network Traffic The performace of a distributed coordiated etwork is ofte evaluated with the assumptios of a sigle-priority saturated etwork traffic [5], [6], [3]. However, such assumptios are ot oly ot idicative of realistic i-home PLC etworks, but they also limit our ability to test the effectiveess of our proposed schemes. For example, recall that a CFC is a coditio where a sigle ode wis the PRP amog all cotedig odes. With a sigle-priority saturated etwork traffic arrival, all the etwork odes coted with the same priority level i each PRP, which ever creates a CFC. O the other had, etwork traffic i a typical HAN is heterogeeous i ature, which is well accommodated by the multiple priority levels of HPAV. Furthermore, a typical HAN cosists of etwork traffic from both high-speed multimedia ad smart home applicatios. While etwork traffic arrivals of the smart home applicatios are foud to be well emulated by the Poisso process [33], [34], those of the multimedia applicatios are foud to be self-similar i ature [35], ad well emulated by a Markov-Modulated Poisso Process (MMPP) [36]. Thus, we build a comprehesive simulatio model with multiple priority levels ad PTS to geerate a realistic etwork traffic coditio. Sice the performace with a sigle-priority saturated etwork traffic is also a importat evaluatio metric of MAC protocols, we use both the classical simplistic model ad our comprehesive model for our etwork simulatios. B. Poisso Traffic Shapig For simplicity, we emulate the etwork traffic arrivals of the multimedia applicatios with the 1-state MMPP, so that we ca emulate the HAN traffic arrivals with the Poisso process as i [3]. The PTS adopted i our comprehesive model pushes the MAC frames accordig to the Poisso process [37], with a mea arrival rate of λ,i at the th etwork ode for the ith priority MAC frame (i {1,, 3}). Note that we do ot shape data packets with priority 0. Whe all the higher priority messages are successfully trasmitted by the ode, it attempts to trasmit a best-effort data frame of priority 0. C. Network Resource Allocatio Recall from Sectio II-A that the PRP esures messages of higher priority levels always get trasmitted before those of lower priority levels. However, this has bee show, i [38], to result i lower priority starvatio whe the etwork traffic of higher priority levels gets saturated. Therefore, to eable a heterogeeous etwork traffic with multiple priority levels, ad to esure a miimum badwidth guaratee for the lower
IEEE TRANSACTIONS ON COMMUNICATIONS 8 TABLE II SIMULATION PARAMETERS Parameter Value Power Lie Fig. 5. I-home BB-PLC etwork simulatio topology. priority frames, our comprehesive model allocates a appropriate share of the etwork resource to each priority level, beyod the covetioal PRP of the HPAV protocol. We deote the average MAC frame itervals at the th etwork ode as µ,i for the ith priority MAC frame (i {1,, 3}). This ca be see i Fig. 1 as the duratio from the begiig of the PRS 0 to the ed of the CIFS. For a etwork with N active etwork odes, we esure that N (µ,3 λ,3 + µ, λ, + µ,1 λ,1 ) = κ, () =1 where κ < 1. We choose κ by accoutig for a fair portio of the etwork resource to be reserved for collisios ad retrasmissios. The remaiig etwork resource is utilized for best effort message trasmissio. This guaratees that every ith (i 0) priority level gets a appropriate share of the etwork resource, κ i = N µ,i λ,i. =1 D. Simulatio Cofiguratio We use a discrete evet simulator, OMNeT++, to simulate the i-home PLC etwork [39]. A set of N odes are itercoected to each other through the power lie medium to form a fully meshed etwork, as show i Fig. 5. I our simulatios, we assume a idetical time iterval of the data payload, t FL, regardless of its priority level. Further, we do ot cosider the MAC frame retrasmissios associated with trasmissio errors i data payloads as they do ot affect η as defied i (). We elist all simulatio parameters i Table II, which are based o the HPAV specificatios [8]. The statistical sigificace of the simulatio results is guarateed by the sufficiet duratio of each simulatio ru, T S, where the resultat MAC efficiecy is the average performace of several thousads of MAC frame trasmissios. By deotig the total umber of collisio-free MAC frames trasmitted as T, we compute η at the ed of each simulatio ru as η = Tt FL T S. (3) E. Performace of CFP with Sigle Node Floodig For our first result, we use the followig etwork settig to test the effectiveess of the CFP scheme. We set N = 1 η 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 Simulatio time, T S 30 s t CIFS 100 µs PRS ad Back-off slot time, t SLOT 35.84 µs t p 35.84 µs t FC 133.9 µs MaxFL 341.1 µs t RIFS 140 µs t EIFS 90.64 µs without CFP with CFP 0 0 0 40 60 80 100 t FL (% of MaxFL) Fig. 6. MAC efficiecy as a fuctio of t FL with sigle ode floodig. by lettig a sigle ode be the oly active etwork ode that cotiuously trasmits priority-3 MAC frames to all the other etwork odes without chael idlig. Uder such a sceario, our proposed MPD scheme has o effect as o cotetios or collisios occur with this settig. The impact of varyig t FL o the achieved MAC efficiecy with ad without CFP is show i Fig. 6. Sice the etwork experieces o collisio or idle time itervals, the power lie medium is kept busy by cotiuously trasmittig MAC frames show i Fig. 1. Uder such coditios we refer to (1) ad express the MAC efficiecy as η = t FL (t EIFS MaxFL) + t FL + ( + E[ BF ])t SLOT, (4) where E[ BF ] is the expected umber of back-off time slots. The absece of cotetios ad collisios cotais the cotetio at the base stage, which provides E[ BF ] = CWmi for the origial HPAV protocol, where CW mi is the miimum cotetio widow. However, with our CFP deployed, the trasmittig ode detects a CFC at every frame trasmissio, which results i E[ BF ] = 0, thereby icreasig η. We ca also observe i Fig. 6 that the maximum MAC efficiecy show i (3) is achieved whe t FL = MaxFL.
IEEE TRANSACTIONS ON COMMUNICATIONS 9 F. Performace Evaluatios with Multiple Active Nodes For our ext set of results, we ru our simulatios with multiple active odes uder both, the classical simplistic etwork traffic model ad the comprehesive model described i Sectio V-A. We form two sub-settigs where we fix N = 10 ad vary t FL i the first case, while we fix t FL = MaxFL ad vary N i the secod. Network Resource Allocatio i our Comprehesive Model: We estimate the average MAC frame iterval at the th etwork ode i our simulatios as µ,i µ = (t EIFS MaxFL) + t FL + t SLOT. (5) We ca the rewrite () as N µ =1 (λ,3 + λ, + λ,1 ) = κ. (6) To accout for the back-off time slots we igored i our approximatio of (5), we choose a smaller κ = 0.65. By N settig λ,i = κi µ, the comprehesive model allocates a =1 certai portio of etwork resource to the ith priority etwork traffic, which for simplicity, is further allotted equally to all N etwork odes. Thus, we have λ,i = 1 κ i N µ, N ad i {1,, 3}. I our simulatios, we set κ 3 = 0.5, ad κ = κ 1 = 0.. 1) Varyig t FL : We first simulate the etwork with varyig t FL ad fix N = 10. The variatio of the MAC efficiecy with varyig t FL uder the two etwork traffic models is show i Fig. 7. The curves essetially resemble those i sigle ode floodig, but with reduced η i both traffic scearios, because of cotetios ad collisios. More specifically, we observe i the results for the saturated etwork traffic that the MAC efficiecy is sigificatly degraded due to the large umber of cotetios ad collisios caused by the costat frame trasmissios of all etwork odes. However, our MPD scheme successfully improves the MAC efficiecy such that the obtaied η with N = 10 essetially matches that of the sigle-ode floodig case. We further otice that while the performace ehacemets provided by MPD ca be observed i both etwork traffic models, the itroductio of CFP shows o improvemets with the simplistic model as saturated siglepriority data arrival produces o CFCs. We observe that uder a realistic HAN traffic sceario, simultaeous deploymet of CFP ad MPD with t FL = MaxFL yields a η = 76.80%, which achieves 98.16% of the optimal MAC efficiecy, max(η) = 78.4%. Uder the same coditios, a covetioal HPAV protocol oly maages to provide η = 69.43%, which is further reduced to η = 54.37% uder a saturated etwork sceario. ) Varyig Active Nodes: For our fial result, we simulate the etwork with varyig N ad a fixed t FL = MaxFL. The simulatio results of this sub-settig uder the two etwork traffic models are show i Fig. 8. We observe that without our MPD scheme, η decreases as the umber of active etwork odes icreases i both the etwork traffic models, due to the icreased collisio rate as well as the legthy collisio η 0.8 0.7 0.6 0.5 0.4 0.3 HPAV 0. CFP MPD 0.1 CFP+MPD 1 Node Floodig 0 0 50 100 t FL (% MaxFL) η 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 0 0 50 100 t FL (% MaxFL) HPAV CFP MPD CFP+MPD Fig. 7. MAC efficiecy as a fuctio of t FL for the classical simplistic traffic model (left) ad the comprehesive multiple priority PTS model (right). η 0.85 0.8 0.75 0.7 0.65 0.6 0.55 HPAV CFP MPD CFP+MPD η 0.78 0.76 0.74 0.7 0.5 0.68 4 6 8 10 4 6 8 10 Number of active etwork odes 0.8 0.7 HPAV CFP MPD CFP+MPD Fig. 8. MAC efficiecy as a fuctio of the umber of active odes for the classical simplistic traffic model (left) ad the comprehesive multiple priority PTS model (right). recovery time. However, we achieve a stable η across differet umber of odes usig our MPD scheme, which is attributed to the reduced collisio recovery time. Similar to the results see i Fig. 7, we see o improvemets due to CFP with the saturated etwork traffic model while the improvemets are clearly visible uder the comprehesive simulatio model. We observe that we obtai the greatest η, both i terms of absolute value ad stability across icreasig odes, usig both our proposed schemes of CFP ad MPD uder a realistic etwork traffic sceario. VI. DEPLOYMENT OF CFP AND MPD ON A BB-PLC DEVICE A. Hardware Implemetatio Costs The elemetary requiremet for implemetig CFP ad MPD i power lie etworks is to eable BB-PLC modems with the IBFD operatio. Recet works have show that a IBFD implemetatio o legacy BB-PLC devices requires miimal chages to the modem chip-sets, with oly a addi-
IEEE TRANSACTIONS ON COMMUNICATIONS 10 tioal power cosumptio of about 0.1 W for the active hybrid circuit that is used at the power lie-modem iterface [18]. B. Iteroperability Our proposed CFP ad MPD schemes are completely iteroperable with HD devices. With the CFP scheme, a IBFDeabled ode ca detect a CFC whe it is the oly ode trasmittig the highest priority message regardless of whether the other odes are IBFD-eabled. However, such a HD ode is uable to detect a CFC. O the other had, the MPD techique still offers improvemets i η whe oly a part of the etwork odes are IBFD-eabled, but with reduced effect compared to the case whe all the etwork odes are IBFDeabled. As log as the coflictig odes are IBFD-eabled, a data payload collisio ca be successfully predicted ad avoided usig MPD. However, whe a HD ode is ivolved as a coflictig ode, the esuig data payload collisio is ievitable, ad it takes the etwork a time iterval of EIFS to recover from it. VII. CONCLUSION I this paper, we have leveraged the medium-aware trasmissio eabled by IBFD to propose two ovel schemes called CFP ad MPD to improve the MAC efficiecy of a stadard HPAV protocol. Specifically, we proposed CFP to elimiate the redudat back-off stages by IBFD detectio of the PRSs, ad MPD to avoid the legthy collisio recovery by IBFD detectio of the preamble sigals. By adoptig realistic selfiterferece cacellatio performace reported i IBFD BB- PLC systems, our aalytical results suggest that both CFP ad MPD work with virtually o detectio errors or false alarms. Further, we have developed a comprehesive simulatio model to evaluate the performace of our proposed schemes as a supplemet to the classical simplistic etwork traffic sceario. Our simulatio results have show that both our proposed schemes provide cosiderable improvemet i MAC efficiecy whe applied idepedetly, ad further improve the efficiecy sigificatly whe used together. APPENDIX OPTIMAL DETECTION THRESHOLD AND ITS CLOSED-FORM APPROXIMATION I this appedix, we derive a aalytical expressio ad a closed-form approximatio for the optimum detectio threshold, b opt, by solvig (15). A. Optimal Detectio Threshold We start with (14), ad divide both sides by P (E E 0 ) to get P e P τ = P (E E 0 ) = P DE + τp FA, (7) where τ = P (Ē E0) P (E E 0). Sice P (E E 0 ) is a costat for a give etwork operatio, miimizig (7) also solves (15). To derive the optimum detectio threshold that miimizes (7), we study the derivative of P τ with respect to the ormalized decisio threshold b 0, which ca be expressed as D(b 0 ) = P DE b 0 + τ P FA b 0. (8) We first idividually fid the partial derivatives of both the compoets of P τ usig (8) ad (9) to get ( ) P FA = b 0 exp b 0, (9) b 0 P DE = ( ) 1 x exp x + γ ( I 0 x ) γ dx b 0 b 0 b ( 0 = exp γ + ) b ) 0 I 0 (b 0 γ b 0, (30) where I ( ) is the th-order modified Bessel fuctio of the first kid. Therefore, ( ) ( D(b 0 ) = b 0 exp b )) 0 τ + exp( γ)i 0 (b 0 γ = f(b 0 )D N (b 0 ), (31) where f(b 0 ) = b 0 exp( b 0 ), ad D N (b 0 ) = τ + exp( γ)i 0 (b 0 γ). (3) Sice b 0 is the ormalized threshold of the sigal eergy for o-coheret OOK detectio, it ca oly take o-egative values. Thus, we oly study sg (D(b 0 )) for b 0 0, where sg( ) is the sigum fuctio [40, Ch. 6]. For b 0 = 0, it is easily observable that sg (D(b 0 )) = 0. For the cases of b 0 > 0, we ote that sg (D(b 0 )) = sg (D N (b 0 )), (33) as f(b 0 ) > 0. Sice I 0 ( ) is a mootoically icreasig fuctio, we coclude from (3) that D N (b 0 ) also mootoically icreases with b 0 for a give γ. Thus, the values of lim D N(b 0 ) ad b 0 0 + sg (D N (b 0 )) for b 0 > 0. We first obtai the limit lim D N(b 0 ) reveal the exact ature of b 0 + lim D N (b 0 ) = τ + exp( γ) lim I 0(b 0 γ) b 0 0 + b 0 0 + = τ + exp( γ). (34) By referrig to Table I, we fid that for various miimum power lie chael gai coditios, γ is large eough to esure that τ exp(γ) > 1 for practically operable values of τ. Therefore, lim D N(b 0 ) < 0. (35) b 0 0 + Next, we have lim D N(b 0 ) = τ + exp( γ) lim I 0(b 0 γ) b 0 + b 0 + = τ + exp( γ)i 0 ( γ lim b 0 + b 0) = +. (36)
IEEE TRANSACTIONS ON COMMUNICATIONS 11 With (35), (36) ad the mootoicity of D N (b 0 ), we ca deduce that there exists a uique positive zero-poit b zp > 0, such that 1, 0 < b 0 < b zp sg(d N (b 0 )) = 0, b 0 = b zp (37) +1, b 0 > b zp. Therefore, from (33) ad (37), we coclude b opt = b zp. (38) Sice b zp is the solutio to the differetial equatio D(b 0 ) = 0, we get ( ) exp( γ)i 0 b opt γ = τ. (39) = b opt = I 0 (τ exp(γ)), (40) γ where I ( ) is the iverse of th-order modified Bessel fuctio of the first kid. B. Closed-form Approximatio Fially, we derive a closed-form approximatio of (40) for the purposes of practical implemetatio. To this ed, we use the prove result that b = + γ provides a excellet ( ) aalytic approximatio to the solutio of exp( γ)i 0 b γ = 1 [7, Eqs. 7-4-13, 7-4-14, Fig. 7-4-3]. Thus, we have ( ) exp(γ) I 0 γ(γ + 4) = I 0 ( b opt γ ) exp ( ) b optγ + 4. 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