Resilient Large-Scale Cognitive Radio Ad Hoc Networking Using Path-Time Codes

Transcription

1 IEEE ICC 2017 Cognitive Radio and Network Sympoium Reilient Large-Scale Cognitive Radio Ad Hoc Networking Uing Path-Time Code Yi-Chi Chen 1, I-Wei Lai 2 and Kwang-Cheng Chen 3 Graduate Intitute of Communication Engineering, National Taiwan Univerity, Taiwan 1 Department of Electrical Engineering, National Taiwan Normal Univerity, Taiwan 2 Department of Electrical Engineering, Univerity of South Florida, USA 3 d @ntuedutw, iweilai0924@gmailcom, and kwangcheng@ufedu Abtract Cognitive radio ad hoc network CRAHN emerge a a pectrum efficient networking technology to enable autonomou machine-to-machine communication among maive number of IoT device However, pectrum haring reult in opportunitic link and CRAHN become a kind of opportunitic network To reduce latency in CRAHN and to achieve overall pectrum efficiency by avoiding tremou feedback ignaling, CRAHN of open-loop phyical layer tranmiion open a new avenue under maive operation The new technology challenge aociated with uch new CRAHN lie in error control with only local networking information without relying on feedback control over each opportunitic link Path-time code virtually realizing multi-input-multi-output over network layer have been innovated to reolve uch a dilemma However, effective multipath routing conidering interference remain unclear In thi paper, be taking network topological factor and interference into account, we analytically derive SINR approximation to deign power control and multi-path greedy routing By tochatic geometry analyi, we alo how that the reilient operation for large-cale CRAHN can be facilitated with the aid of path-time code Index Term Internet of thing IoT, machine-to-machine communication, cognitive radio ad hoc network CRAHN, virtual multiple-input multiple-output MIMO, pace-time code, path-time code PTC, tochatic geometry, Poion point proce PPP I INTRODUCTION In cognitive radio ad hoc network CRAHN, econdary uer SU are conidered a unlicened uer with lower priority for channel acce, while primary uer PU have highet priority for their licened band By utilizing dynamic pectrum ening to acce pectrum hole, a large amount of SU device are allowed to be co-exited with PU, which greatly enhance the pectrum efficiency Through many technological iue for CRAHN, eg, elf-organization in reilient heterogeneou network [1], efficient CRAHN can eaily upport many application cenario for Internet of Thing IoT A the link in CRAHN are opportunitic due to pectrum opportunitie, the relay path of -to tranmiion can be vulnerable and unidirectional [2] Furthermore, ince only local information among SU in the cloe vicinity i available, the centralized control require tremou control ignaling that conume good bandwidth Intead of the conventional ad hoc networking of cloedloop communication that require tremou overhead for the -to- information exchange and network control, the open-loop communication attract attention to reduce latency and ignaling bandwidth conumption [3], [4] However, the reilient operation of CRAHN can be a great challenge To reolve thi technology dilemma, virtually utilizing multiple-input multiple-output MIMO and exploiting multiple tranmiion path ha been innovated to facilitate the error control of CRAHN of open-loop communication [5], [6] Novelly applied the well-invetigated pace-time code STC of phyical-layer MIMO ytem, path-time code PTC enhance the -to- tranmiion reliability by encoding the data along the time and path coordinate, on top of network layer While previou virtual effort [5], [6] focu on the code deign given multipath routing, in thi paper, we invetigate the multipath routing for the PTC, particularly incorporating interference by concurrent tranmiion in CRAHN Following the tochatic geometry to analyze interference, the PU and SU are randomly ditributed according to the homogeneou Poion point proce PPP [7], [8] The routing for multihop ingle-path ha been well deigned in the PPP network topology [9], [10] and further theoretical effort, uch a outage probability, tranport capacity, and delay characterization in ingle-path multihop network [11], [12], have been invetigated On top of thee fruitful reult, we can compreh the reilient network operation and the performance of CRAHN uing PTC with multipath routing and power control, under local networking information and without replying on feedback control ignaling to improve latency In thi paper, while error control to enure reilient network operation, we optimize the mean number of hop that repreent latency of networking The near optimal routing policy i deigned with repect to the network environment, eg, node denity, interference level, and number of path Baed on the progre rule [10] that maximize the effective hop ditance o a to minimize the number of hop for the path earch, we propoe a multipath-earch algorithm for multipath routing and coding-aided cheme with PTC for error-reilient control and efficient -to- tranmiion in CRAHN With network topological factor and tochatic geometry analyi, we how that the reilient operation for large-cale CRAHN can be facilitated with the aid of PTC Thi paper i organized a follow: In Section II, we introduce the virtual MIMO PTC -to- tranmiion In Section III, we reviit tochatic geometry for PPP network and ext progre rule to propoe a multipath-earch algo /17/$ IEEE

2 IEEE ICC 2017 Cognitive Radio and Network Sympoium 2 rithm for electing relay a PTC tranmiion In Section IV, baed on the per-hop and -to- outage probability, the theoretical reult focuing on per-hop tranmit SNR on multiple path are analyzed Numerical imulation are preented in Section V, addreing the relation among reliability, power control, maximum allowance for waiting period, and number of hop under different interference level Finally, Section VI preent our main concluion II SYSTEM MODEL Let the term link or hop denote the connection between two node, and path the -to- route between a pair of ource S and detination D node Thi work focue on the cae of ditributed networking without centralized control We conider multihop networking with K link-dijoint path compriing N k 1 relay node, k {1,,K} Such multihop/multipath routing can be etablihed uing the algorithm propoed in [13] [15] In thi paper, we focu on developing a practical way for the multipath contruction and invetigate the influence caued from imperfect route in PPP network Fig 1 how the K = 3 cae without failed path in Fig 1 a and with one-failed path due to interferer PU tranmitter in Fig 1 b For the PTC tranmiion, defining χ a the contellation et, the ource node encode a data packet x χ M by a coding matrix C C K M and tranmit the reulting coded packet at time intant m Then, the equivalent received coded packet can be expreed a y m =h m v m Cm x + K k=1 η m,k =h m v m Cm x + η m, 1 where denote tranpoition, η m,k i the noie aggregated from all link in the kth path, i the Schur product, h m = [h m,1,,h m,k ] C K i the path fading gain, and v m = [v m,1,,v m,k ] {0, 1} K to indicate if the coded packet i uccefully propagated to the detination in the mth time intant through the kth path The value of h m,k and v m,k are determined by the location of the elected relay, following a procedure decribed in Section III The received PTC-coded packet y =[y 1,,y M ] C M from m =1to m = M can be repreented a y = + h 1 v h M v M η 1 η M } {{ } η C 1 C M } {{ } C h 1 v 1 C1 = x + η } h M v M CM {{ } H eq V,C x = H eq V, Cx + η, 2 where the coding matrix C = [ C 1, C M ] C KM M repreented cacaded C m, and eraure indicator matrix V = a Example of perfect route, fully upported from elected relay, in the SU network without interference b Example of imperfect route with one failed path caued from a PU tranmitter a an interferer coexited in the SU network Fig 1 Example topology of -to- tranmiion in a cognitive radio ad hoc network with multipath K =3 [v 1,,v M ] {1, 0} K M With the equivalent channel H eq V, C, the formulation in 2 can be interpreted a virtual MIMO ytem where multiple node are coordinated to form the multihop/multipath route between the ource and detination pair The PTC exploit path and time diverity to increae ytem reliability In thi paper, we adopt the dicrete Fourier tranform DFT-baed PTC [6] where the l, mth entry of the coding matrix C take the form of C l,m = 1 e j2πlm KM, l =1,,KM, m=1,,m K 3 Thi choice of the DFT-baed PTC matrix C dipere x m through all the K path and M time intant A long a v m 0, all entrie of the kth row vector of H eq V, C are nonzero Thu, x i uccefully received at time intant m, which reult in increaed diverity [6] III RANDOM NETWORK TOPOLOGY VIA STOCHASTIC GEOMETRY In Section II, the ytem model of PTC -to- tranmiion 2 i baed on the aumption of perfect routing In thi paper, we propoe a routing algorithm in the random network with local information In random network, the failed path poibly occur when no relay node are in the cloe vicinity, or ignal are contaminated by evere interference

3 IEEE ICC 2017 Cognitive Radio and Network Sympoium 3 of potential relay and detination Fig 2 provide an example for the multipath-earch procedure The propoed multipathearch algorithm how a follow: Fig 2 Example to the multipath-earch among SU in 5 for no interference cae: The red-dah-dotted curve boundary indicate the relay node are poibly elected for the maximum progre from S toward detination With the elected relay {Z k,n } correponding to the nth hop in the kth path, d k,n and θ k,n imply denoted for the effective hop ditance d Z k,n and angle θ Z k,n Notice that the 1t path-earch red-line node can not upport the 2nd path relaying Thu, the 2nd path-earch green-line elect another relay node with maximum progre value except occupied node and o on for the 3rd path blue-line We leverage homogeneou Poion point proce PPP from tochatic geometry to imulate network topology Since all S D pair are tochatically equivalent, we invetigate the performance at a typical S D pair [11] and conider SU network with randomly cattered relay node for PTC -to tranmiion We aume the S D pair i predetermined in a fixed ditance, ie, d S D i fixed Let the location of SU be Φ SU that follow homogeneou PPP with denity λ SU For SU co-exited with PU, we conider SU network with interference caued from PU tranmitter Φ PT which alo follow homogeneou PPP with denity λ PT Thu, by the tationary of homogeneou PPP, the ignal-to-interference-plunoie ratio SINR requirement of a ucceful tranmiion for the nth link in the kth relay path can be repreented a P SU G SU dz k,n β, 4 N 0 + I PT where I PT = I j Φ PT G PT P PT d E I j, Z k,n i the interference from PU tranmitter {I j } to the elected node located in the {Z k,n }, d E, i the Euclidean ditance, and dz k,n i the nth hop ditance in the kth relay path, ie, dz k,n =d E Z k,n 1, Z k,n, Z k,0 = S for all k, i the path lo exponent, G SU, G PT are exponential ditributed power with unit mean, and β denote the SINR requirement for ucceful tranmiion per-hop The progre rule indicate that maximizing the effective hop ditance equal the minimization of the number of hop in a line [10] We ext thi path-earch procedure from inglepath to multipath The elected relay the nth hop in the kth path could be generally expreed a Z k,n = argmax dz k,n D,Z k,n Φ SU P SU G SU dz k,n t co θ{dz k,n } +, N 0 + I PT β, from 4, 5 where Φ SU denote Φ SU excluding elected relay node, and θ{ } i the operator for finding the angle between direction Algorithm: Multipath-earch algorithm Initialize: Coded packet i tranmitted from ource node {S} = {Z k,n k =1,,K; n =0} with Φ SU =Φ SU for k =1,,K a the kth path do Reet n =0for coded packet tarting at {S}; for n = n +1 a the nth hop do Calculate 5 and elect {Zk,n }; if {Zk,n } = {D} reaching detination then Hop to {Zk,n } for contructed path; ele if {Zk,n } Φ SU then Hop to {Zk,n }; Update Φ SU Φ SU \{Z k,n }; ele For failed path; Set n = N k hop in the kth path; Find out all elected relay {Zk,n }, k =1,,K, n =1,,N k, upporting PTC-aided multipath routing For oberving reception timing of the mth PTC coded packet at the detination, the per-hop fading gain g m,k,n [t] hould atify SINR requirement in 4 with ubtitution G SU = g m,k,n [t] 2 for forwarding coded packet The ynchronized timing t = T m,k,n N can be viewed a tranmiion trial a random variable For the mth coded packet tranmitted in the kth path with N k hop reaching detination, the total number of attempt can be expreed a T m,k = N k n=1 T m,k,n, where T m,k N for the mth coded packet tranmiion delay in the kth relay path For the finite time-out at the detination, the maximum allowance A m i adopted for receiving mth coded packet from all K path, ie, T m,k A m for the mth coded packet reception in 1 We generalize our algorithm to routing with imperfect cenario in 2 Since {Z k,n } i elected for multiple K path, it i reaonable to aume that the entire PTC codeword uing the M time intant follow the ame route and avoid unneceary re-routing The imperfect route ha failed path occurred when coded packet have no potential relay forwarding and doe not reach detination, imply denoted a {Z k,n=nk } {D} for the kth failed path Thu, the imperfect route can be conidered a eraure channel For expreing relation between relay location and number of attempt, we define a function f :{Z k,n }, a mth coded packet propagation T m,k N, 6 and then interpret the generalized eraure indicator a { 1, Tm,k A v m,k = m, 7 0, T m,k >A m

4 IEEE ICC 2017 Cognitive Radio and Network Sympoium 4 Thu, given A m, the -to- outage probability can be repreented a P out = PrV = 0 K M A m PrV = 0 K M A m a = Prv m = 0 K 1 A m = Pr{Z k,n=nk } = {D}, k =1,,K, 8 where A m denote the ufficiently large allowance, and thu a how the all-path-failed probability lead to the minimum value when all K-path failed a a lower bound For the generalized path gain h m,k correponding to {Z k,n } in 2, one can interpret the path gain a the product of link gain Thi allow u to how that h m,k = N k n=1 [ PSU g m,k,n [t] dz k,n /2], t P SU g m,k,n [t] 2 dz k,n N 0 + I PT β, from 4, 9 With the determined hop ditance dz k,n, the mth coded data i tored in the buffer and then forwarded to the next hop a 4 atified The generalized path gain in 9 i exted from product of Gauian link gain [6] and i ubjected to condition with repect to per-hop SINR requirement We reinterpret virtual MIMO PTC -to- tranmiion in 2 connected to tochatic geometry By ubtitution v m,k and h m,k with the above generalized eraure characteritic and path gain derived in 7 and 9, the bit error rate BER could be obtained from decoding 2 given A m With A m in 8, one can find that BER = P e 1 P out P out 1 2 P out, 10 where P e denote the error probability of received packet, and 1/2 indicate the error probability of blindly gueing the binary bit value {1, 0} when the -to- outage occur IV THEORETICAL ANALYSIS In thi ection, we tudy the -to- outage probability and invetigate the relation between per-hop tranmit SNR and mean number of hop under different interference level In multihop networking, the aumption of relay with equally paced egment between S D, ie, d = d S D / N with N hop, can implify the analyi and provide a lower bound on the delivery delay [9] Further followed multiple K path with the ame number of hop N = N i for i =1,,K in [16], the theoretical -to- outage with K-path i denoted a P out and could be repreented a P out 1 p N K, 11 followed on the aumption of indepent K-fold of the ingle-path -to- outage 1 p N with the iid per-hop ucce probability p From 4, p can be expreed a { PSU G SU d } p = Pr β N 0 + I { PT } β = Pr G SU P SU d N 0 + I PT =exp βn [ ] 0 β P SU d E exp P SU d I PT a =exp βn 2 0 P SU d exp λ PT d 2 βppt ξ, P SU b =exp βn 0 N P SU d S D }{{} p,noi 2 2 ds D βppt exp λ PT ξ N P SU } {{ } p,int = p,noi p,int 12 where a come from the moment generating function of I PT [8], [10], ξ = 2π2 in 2π, and b i ued with d = d S D / N For the cae of no interference, we combine 11 with p = p,noi which come from λ PT =0in 12, and expre the per-hop tranmit SNR i bounded by P SU N 1 βd S D 13 N 0 ln 1 P 1 K out Under the interference-limited cenario and for the eae of expoition, we ignore the noie-effect and thu have p = p,int in 12 Replacing p in 11 with p = p,int,wecan how the per-hop tranmit SNR i bounded by P SU N 0 λ PTd 2 S D ξ 2 βppt N ln 1 P 1 K N 0 out 14 Thee theoretical approximation of tranmit SNR under the cenario with interference 14 and without 13 a upper bound compare to the imulation reult in Section V V SIMULATION In thi ection, we perform a multipath-earch algorithm propoed in Section III for multipath routing in PPP network topology, and then apply the coding-aided cheme of PTC and repetition code REP [17] verifying their validity for error control Notice that our multipath cae with M data tream coding-aided cheme either REP or PTC follow the code rate 1/M for the ame throughput comparion The ytem parameter, partly referred from [8], [16], are hown a follow: λ SU1 = or λ SU2 = 10 3, d S D = 200, P SU for tranmit power control, noie level N 0 =10 9 eg, P SU =01 for P SU /N 0 =80dB, λ PT from 10 5 to , P PT =03, =4, and β =1 With QPSK modulation and DFT-baed PTC, BER performance i obtained from decoding in 2 uing maximum a poteriori MAP criterion [6], [18] and with elected relay location

5 IEEE ICC 2017 Cognitive Radio and Network Sympoium 5 BER path uncoded 2 2 PTC 4 4 PTC 2 2 REP 4 4 REP 1 2 P out, K =4 BER path uncoded, Int 1-path uncoded, No int 2 2 PTC, Int 2 2 PTC, No int 4 4 PTC, Int 4 4 PTC, No int P SU /N 0 [db] a No interference cenario: BER veru power control The parameter are et a λ SU1 =5 10 4, d S D = 200, =4, and β =1 BER path uncoded 2 2 PTC 4 4 PTC 2 2 REP 4 4 REP 1 2 P out, K = P SU /N 0 [db] b With interference cenario: BER veru power control The parameter are et a λ SU2 =10 3, P PT =03, λ PT =10 5, d S D = 200, =4, and β =1 Fig 3 BER veru power control comparing different coding cheme followed with the propoed path-earch algorithm In the cae a of no interference cenario and b with interference cenario Single-path cae are uncoded denoted a uncoded while multipath cae K =2, 4 are applied with the repetition code REP and the DFT-baed PTC briefly denoted a M K REP and PTC on the figure The 4 4 PTC outperform REP in both cenario a and b and almot reache optimal value hown with 1 2 P out obtained in 10 It demontrate that PTC-aided multipath routing reache decent error performance even under interference {Z k,n } followed our propoed multipath-earch algorithm And thu coded packet reception 2 with generalized eraure indicator v m,k in 7 and path gain h m,k in 9 are alo obtained and inherited from the elected relay {Z k,n } The following three cae are dicued: CASE I: Reliability and power control in A m In Fig 3 a b, we focu on error rate performance veru tranmit SNR power control in the no interference cae in Fig 3 a and with the interference cae in Fig 3 b Here we conider the maximum allowance i ufficiently large, and compare uncoded, repetition coded, and path-time coded cheme 1 1 For implicity, we only focu on the interference impact from PU to SU More interference interaction, eg, inter-interference from SU to PU, are invetigated in [8] A m Fig 4 BER veru allowance A m comparion from ingle path uncoded to multipath coded under cenario with interference and without In the cae of no interference cae denoted no int on the figure, the parameter are et a P SU =01, N 0 =10 9, λ SU2 =10 3, d S D = 200, =4, β =1 0 db In the cae with interference denoted int on the figure, the ame parameter are followed and with interferer P PT =03, λ PT =10 5 While ingle-path cae are uncoded with K =1, multipath cae K =2, 4 are applied with DFT-baed PTC briefly denoted a M K REP and PTC on the figure A m how ufficiently large extreme value for comparion finite allowance Followed our propoed multipath-earch algorithm and 10, one-half of numerical -to- outage 1 2 P out erve a the bench mark lower bounded curve for BER with coding-aided cheme PTC with multipath outperform uncoded and REP cenario It even validate that the 4 4 PTC reache near optimal BER approaching 1 2 P out in 10 with P e 0 Thu, PTC-aided multipath routing uing more path, eg K =4 here, provide robutne with error control under the cenario with interference and without CASE II: Reliability and allowance in finite A m Ditinct to Fig 3 a b with the ufficiently large allowance A m, Fig 4 depict BER veru finite-range allowance A m for the practical decoding cheme of receiving PTC packet y m in 1 Fig 4 provide an eential perpective for the practical ytem deign criterion, ie, tradeoff relation between reliability BER and the maximum allowance A the number of path multipath K increae, the error rate decreae under the cenario with interference and without Thi phenomenon manifet that multipath cheme propel low latency in -to- tranmiion epecially greatly improved in no interference cenario, eg, the lowet curve in Fig 4 CASE III: Relation among tranmit power control, interference level, and the number of hop in A m Fig 5 a depict SU power control in λ SU2 =10 3 veru different PU tranmitter denity λ PT Both numerical and theoretical reult are adopted with 4 4 PTC-aided multipath routing achieving BER = {5 10 2, }, where lower BER can be viewed a higher quality of ervice QoS requirement With adaptation of tranmit power for fixed BER in Fig 5 a, the correpondent average number of hop can be oberved in Fig 5 b For the theoretical tranmit power approximation, given the average number of hop, Fig 5 a alo how the analytical reult in 13 for the no interference

6 IEEE ICC 2017 Cognitive Radio and Network Sympoium 6 PSU/N0 [db] Average number of hop Theo reult at BER = Theo reult at BER = Num reult at BER = Num reult at BER = λ PT a Power control veru PU tranmitter denity λ PT λ PT at BER = at BER = b Average number of hop veru PU tranmitter denity Fig 5 The relation among power control, PU tranmitter denity λ PT for interference level, and average number of hop The parameter are et a varying P SU, N 0 = 10 9 eg, P SU = 01 for P SU /N 0 = 80 db, λ SU2 =10 3, P PT =03, d S D = 200, =4, and β =1 In a, numerical Num and theoretical Theo power control for fixed BER = {5 10 2, } achieved by 4 4 PTC Theoretic reult of power control are obtained from 13 and 14 In b, numerical average number of hop dep on tranmit power control correponding to numerical reult in a With cloely fitted reult between theoretical and numerical in a, the PTC-aided multipath routing demontrate reilient operation with power control for the hop number and error control under interference cenario λ PT = 0 and 14 for the interference-limited cenario λ PT from to , where theoretical reult are followed with BER 1 2 P out achieved by 4 4 PTC in 10 From obervation in Fig 5 a, the theoretical and numerical reult cloely fit, epecially in higher QoS requirement Thee theoretical approximation of per-hop tranmit power requirement in 13 and 14 provide inight to deign power control under different interference level for reliable and efficient PTC tranmiion VI CONCLUSION In thi paper, we propoe a multipath-earch algorithm for multipath routing and coding-aided cheme with PTC for error-reilient control and efficient -to- tranmiion in CRAHN With only local information available, the propoed multipath-earch algorithm provide near optimal routing policy to minimize the number of hop By tochatic geometry analyi, we demontrate that the reilient operation can be facilitated with the aid of path-time code The relation between reliability, power control, maximum allowance, and the number of hop are addreed The analytical reult for theoretical power control are alo derived and cloely fit the imulation reult Thee reult provide inight to deign power control under different interference level for reilient operation in PTC tranmiion A many application cenario in Internet of Thing inevitably require pectrum haring multi-hop networking, thi reearch verifie a new avenue to facilitate reilient IoT networking deign ACKNOWLEDGEMENT Thi tudy i conducted under the Advanced communication technology reearch and laboratory development project of the Intitute for Information Indutry which i ubidized by the Minitry of Economic Affair of the Republic of China REFERENCES [1] H Zhang, C Jiang, R Q Hu, and Y Qian, Self-organization in diaterreilient heterogeneou mall cell network, IEEE Network, vol 30, no 2, pp , 2016 [2] K-C Chen and S-Y Lien, Machine-to-machine communication: Technologie and challenge, Ad Hoc Network, vol 18, pp 3 23, 2014 [3] S-C Hung, D Liau, S-Y Lien, and 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