Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks

Transcription

1 Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks Philippe Ciblat Joint work with N. Ksairi, A. Le Duc, C. Le Martret, S. Marcille Télécom ParisTech, France

2 Part 1 : Introduction to HARQ Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 2 / 29

3 Standard communication scheme bits d info CODAGE DE CANAL bits codés MODULATION CANAL. No feedback about no-error or error at RX side Adaptive Modulation and Coding if performance model available for considered channel model parameters known at TX side Drawbacks Lack of robustness to channel mis-knowledge Limited number of Modulation and Coding Scheme (MCS) in practice More important, weak adaptability to the real propagation states (noise, etc) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 2 / 29

4 MCS design Example : QAM size (according to target Symbol Error Rate). BPSK 4QAM 16QAM 64QAM 10 1 Symnol Error Rate SER Cible 10 4 ZONE INTERDITE BPSK 4QAM 16QAM 64QAM SNR (db). AMC done on average performance, not on instantaneous one Idea : try/error principle Send one (symbol) packet if OK (ACK), ր if KO (NACK), ց send it again Need for one-bit feedback way (providing information on the instantaneous channel) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 3 / 29

5 From ARQ (Automatic ReQuest)... Let S = [s 0,, s N 1 ] be a packet composed by N uncoded symbols. TX RX S 1 T S 1 NACK NON OUI S 2 ACK. Management for T : Stop-and-Wait Parallel Stop-and-Wait Selective Repeat Assumption : perfect feedback (neither error, nor delay T = 0) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 4 / 29

6 ... Towards Hybrid ARQ (HARQ) : Type-I HARQ Remark Retransmission does not contradict forward error coding (FEC) Type-I HARQ : packet S is composed by coded symboles s n first packet is more protected there is less retransmission transmission delay is reduced Efficiency is upper-bounded by the code rate Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 5 / 29

7 Type-II HARQ Comments on Type-I HARQ Each received packet is treated independently Mis-decoded packet is thrown in the trash Memory at RX side is considered Type-II HARQ. TX RX S 1 (1) S 1 (2) NACK NON S 2 (1) ACK OUI. Main examples : Chase Combining (CC) Incremental Redundancy (IR) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 6 / 29

8 Examples : CC-HARQ and IR-HARQ CC Y 1 = S 1 + N 1 Y 2 = S 1 + N 2 then detection on Y = (Y 1 + Y 2 )/2 SNR-Gain equal to 3dB IR Y 1 = S 1 (1)+N 1 Y 2 = S 1 (2)+N 2 then detection on Coding gain Y = [Y 1, Y 2 ]. TX RX. TX RX S 1 S 1(1) S 1 NACK + S 1(2) NACK S 2 ACK = OUI. S 2(1) ACK = OUI. Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 7 / 29

9 Performance metrics Packet Error Rate (PER) : PER = Prob(information packet is not decoded) Efficiency (Throughput/Goodput/etc) : η = (Mean) delay : information bits received without error transmitted bits d = # transmitted packets when information packet is received Jitter : σ d = delay standard deviation Quality of Service (QoS) Data : PER and efficiency Voice on IP : delay Vidéo Streaming : efficiency and jitter Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 8 / 29

10 Closed-form expressions for metrics PER L = 1 p(k) k=1 η d = σ d = L k=1 p(k) L(1 L k=1 p(k))+ L k=1 kp(k) L k=1 kp(k) L k=1 p(k) L k=1 k 2 p(k) L k=1 p(k) d 2 with p(k) probability to receive information pacjket in exactly k transmissions L maximum number of transmissions per information packet Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 9 / 29

11 Example : Type-I HARQ Let π 0 be the probability the information packet is mis-decoded (in one transmission). Then p(k) = (1 π 0 )π k 1 0 Let an information packet composed by N BPSK uncoded symbols. Then ( ( )) N π 0 = 1 1 Q 2SNR Results PER Efficacite Delai Gigue PER = π L 0 η 1 π 0 d = L+ 1 1 π 0 L 1 π L SNR (db) - (avec N=100 et L=3) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 10 / 29

12 Part 2 : HARQ based resource allocation 2.1 Trade-off Retransmission-Physical Layer performance 2.2 Waterfilling-like algorithm 2.3 Application to Mobile Ad Hoc Networks (MANETs) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 11 / 29

13 Trade-off Retransmission-Physical Layer performance When only PHY layer is considered : Power minimization with target SNR Rate maximization with power constraint ( #bits/pcu = log 2 1+ SNR ) Γ with Γ SNR-gap wrt. Shannon capacity for one FEC and target SER Target PHY layer is required When retransmission (HARQ) is considered : Rate is replaced with Efficiency Rate maximization leads to the optimal PHY layer performance through p(k) PHY layer performance is not fixed in advance Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 11 / 29

14 Example : Type-I HARQ Rayleigh channel : Each packet is encoded with coding rate R π 0 = Prob h (log 2 (1+ h 2 SNR) < R) R π0 = log 2 1+ SNR Best PHY layer is given by [Jin09] π 0 = arg max π 0 R π0 (1 π 0 ) }{{} η π0 : efficiency ( 1 ) 1 log 1 π ε * 0.4 Best required PER Reliable PHY layer is not required at all (thanks to retransmission)! SNR (db) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 12 / 29

15 Waterfilling-like algorithm : data rate optimization TX P(1) H(1) 2 σ 2 RX Power constraint : P(n) P(N)... H(n) 2... H(N) 2 σ 2 σ 2 N P(n) = P max n=1 with maximum power P max. Perfect CSIT Problem : which data rate criterion to be used? (Shannon) sum-capacity : [P(1),, P(N) ] = ( ) arg max N P(1),,P(N) n=1 log 2 1+ H(n) 2 P(n) σ 2 (HARQ) sum-efficiency : [P(1),, P(N) ] = arg max P(1),,P(N) N n=1 m(n) (1 P e(n)) with 2 m(n) -QAM and P e (n) SER (packet=symb, here). Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 13 / 29

16 Practical algorithms Convex optimization problem ( KKT conditions) Capacity : Waterfilling [Sha48] P(n) = (ν σ2 H(n) 2 with ν chosen s.t. N n=1 P(n) = P max. ( ) + = max(0, ). Efficiency : [unpublished] ( P(n) 2σ 2 ( )) m(n)γ(n) H(n) 2 + = γ(n) H(n) 2 log µσ 2 with µ chosen s.t. N n=1 P(n) = P max. γ(n) modulation gain at channel #n ) + Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 14 / 29

17 Numerical illustrations N = 16, SNR = 0dB (left), SNR = 20dB (right) Power optimization abs(h) Power optimization abs(h) subcarrier index subcarrier index Remark The best subcarriers do not have necessary the highest powers (at high SNR) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 15 / 29

18 Mobile Ad Hoc Networks (MANETs) Infrastructure-free Highly flexible Fast and short-lived communications deployment Rx1 Rx2 G1 Cluster Head and Rx3 G2 G3 T x1 Tx3 Tx2 Clusterization Centralized coordination of the pairwise communications at CH Feedback latency Channel statistics known at CH Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 16 / 29

19 Communication scheme OFDMA PHY layer : cancel ISI due to multipath spread Multiple access : cancel multiuser interference inside a cluster HARQ manage fast channel variations Statistical channel model : let us consider the k-th link Let h k (m) be the m-th filter tap. Ind. (but not i.d.) CN(0,ς 2 k,m) H k (n) non-ind. wrt n but i.d. CN(0,ς 2 k) with ς 2 k = m ς2 k,m Rayleigh fading channel Channel statistics (for H k (n)) ind. of subcarrier n Subcarriers are statistically equivalent Consequence for the k-th link Bandwidth proportion and identical energy per subcarrier Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 17 / 29

20 Resource allocation issue Q k : Energy of link k in OFDM symbol γ k : Bandwidth proportion assigned to link k E k : Energy of link k in entire bandwidth Q k = γ k E k Modulation (order 2 m k ) and coding scheme (rate R k ) Goal [Mar13] min K k=1 Q k min K (γ,e) k=1 γ k E k s.t. QoS k (γ k, E k ) QoS (0) k, k K γ k 1 k=1 γ k 0, E k 0, k for various Quality of Service (QoS) : eff., eff.+per, eff.+delay Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 18 / 29

21 Type-I HARQ case PER expression 1 P k (SNR) SNR d min Valid for fast-fading channel model (BICM + FH) Efficiency expression η k (γ k, E k ) = γ k m k R k (1 P k (G k E k )) Delay expression d k (γ k, E k ) = 1 ( 1 γ k 1 P k (G k E k ) L P k(g k E k ) L ) 1 P k (G k E k ) L Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 19 / 29

22 Optimization problem 1 : rate constrained Write the problem in (γ, Q) instead of (γ, E) min K (γ,q) k=1 Q k s.t. η k (γ k, Q k ) η (0) k, k K γ k 1 k=1 γ k 0, Q k 0, k Results Solution exists iff K k=1 η(0) k /(m kr k ) < 1 Problem is convex in (γ, Q) Optimal solutions exhibited in closed-form (from KKT) given mcs k = (m k, R k ) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 20 / 29

23 Numerical results K = 4 links Free-space path loss Random distances in [50, 1000] m L = 3 45 Total transmit power (dbm) MCSc3 MCSc2 MCSc1 MCSc5 MCSc4 MCSc6 Exhaustive MCS selection Greedy MCS selection Fixed same MCS for all links Total spectral efficiency (bit/s/hz) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 21 / 29

24 Optimization problem 2 : rate + PER constrained PER Rate only (MAC,L=3) PER 10-2 (MAC,L=3) Total spectral efficiency (bit/s/hz) min K (γ,q) k=1 Q k s.t. η k (γ k, Q k ) η (0) k, k P k (Q k /γ k ) P (0) k, k K γ k 1 k=1 γ k 0, Q k 0, k Results P k is a quasi-convex function of (γ k, Q k ) KKT are optimal [Las10] but it is O ( 2 K 1)......Suboptimal KKT resolution (SKA)...Suboptimal alternate directional descent wrt. (γ k, E k ) (SLA) Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 22 / 29

25 Numerical Results Rate constraint only PER constraint (10-2 ) Total transmit power (dbm) 0-5 Optimal (10-2 ) SKA (10-2 ) SLA (10-2 ) Total transmit power (dbm) Optimal (10-4 ) -15 SKA (10-4 ) SLA (10-4 ) Total spectral efficiency (bit/s/hz) Total spectral efficiency (bit/s/hz) Remarks SLA offers almost the same performance as KKT Constraining the PER to 10 2 adds an energy cost of about 2 db Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 23 / 29

26 Optimization problem 3 : rate + delay constrained min K (γ,e) k=1 γ k E k s.t. η k (γ k, E k ) η (0) k, k d k (γ k, E k ) d (0) k, k K γ k 1 k=1 γ k 0, E k 0, k Results Solution exists iff ( ) K k=1 max η (0) k /(m k R k ), 1/d (0) k < 1 d k quasi-convex in E k, convex in γ k, no information in joint directions KKT-based algo. (KBA) : KKT solved, but no optimality theorem Ping-Pong algo. (PPA) : optimization alternately in both directions Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 24 / 29

27 Numerical Results 4 Total transmit power (dbm) (0) KBA (d τ = 1 ms) k (0) PPA (d τ = 1 ms) k (0) KBA (d τ = 2.5 ms) k (0) PPA (d τ = 2.5 ms) k Total spectral efficiency (bit/s/hz) Remark KBA is optimal when the delay constraint is strictly satisfied Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 25 / 29

28 Type-II HARQ case Much more complicated : see efficiency expression in Slide 9 Actually, the efficiency for any Type-II HARQ writes as follows η k (γ k, E k ) = m k R k γ k 1 q k,l (G k E k ) 1+ L 1 l=1 q k,l(g k E k ) where q k,l (SNR k ) is the probability that the first l transmissions of a HARQ round are all received in error. Let π k,l be the probability for not decoding the information packet based on the first l transmissions. π k,l g k,l(m k, R k ) SNR d k,l(r k ) k where d k,l represents a minimal Hamming distance. Remark q k,l can be upper-bounded by π k,l [Duc10] Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 26 / 29

29 Optimization problem : rate min γ,e K k=1 1 π k,l (G k E k ) γ k E k s.t. γ k 1+ L 1 l=1 π k,l(g k E k ) η (0) k, k m k R k K γ k 1 k=1 γ k > 0, E k > 0, k Results It is a geometric program [Ksa13] Transformation into a convex optimization problem by γ k = e x k and E k = e y k KKT solved Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 27 / 29

30 Numerical results K = 10 links, Bandwidth W = 5 MHz, QPSK Feasability condition satisfies for sum rates up to 5 Mbps. 28 Transmit sum-power (dbm) CC-HARQ R 1 =1/2 Type-I HARQ R 1 =1/2 IR-HARQ R 1 =8/10 IR-HARQ R 1 =1/ Target sum-rate (kbps) Remarks Nested-codes IR-HARQ outperforms RCP-codes IR-HARQ 4/5-rate IR-HARQ outperforms 1/2-rate Type-I and CC-HARQ up to 3.3 Mbps. For higher target rates, its worse pre-harq performance (π k,1 ) plays a role. Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 28 / 29

31 Conclusion Extension done to per-link power constraint Applications : HSPA, Wimax, LTE New metrics for resource allocation References : [Jin09] P. Wu and N. Jindal, Coding Versus ARQ in Fading Channels : How reliable should the PHY be?, IEEE Globecom Conference, Nov [Las10] J. B. Lasserre, On representations of the feasible set in convex optimization, Optim. Lett., [Duc10] A. Le Duc, Derivations and analysis of HARQ schemes in a cross-layer context, Telecom ParisTech PhD thesis, [Mar13], S. Marcille, Resource allocation for HARQ based mobile ad hoc network, Telecom ParisTech PhD thesis, [Ksa13], N. Ksairi, P. Ciblat, and C. Le Martret, Optimal Resource Allocation for Type-II HARQ-based OFDMA Ad Hoc Networks, submitted to IEEE GlobaSIP Conference, Dec Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 29 / 29