DSL Spectrum Management

Transcription

1 DSL Spectrum Management Dr. Jianwei Huang Department of Electrical Engineering Princeton University Guest Lecture of ELE539A March 2007 Jianwei Huang (Princeton) DSL Spectrum Management March / 26

2 Acknowledgements Collaborations: Raphael Cendrillon, Mung Chiang, Marc Moonen Sponsorships: Alcatel, NSF Jianwei Huang (Princeton) DSL Spectrum Management March / 26

3 Digitial Subscriber Line (DSL) Networks Wireline communications networks based telephone copper lines Cost-effective broadband access network More than 160 million users world-wide CO TX (Central Office) RT (Remote Terminal) TX RX Customer crosstalk RX Customer Jianwei Huang (Princeton) DSL Spectrum Management March / 26

4 Digitial Subscriber Line (DSL) Networks Wireline communications networks based telephone copper lines Cost-effective broadband access network More than 160 million users world-wide Speed is the bottleneck CO TX (Central Office) RT (Remote Terminal) TX RX Customer crosstalk RX Customer Jianwei Huang (Princeton) DSL Spectrum Management March / 26

5 How DSL Works? Copper line can support signal transmissions over a large bandwidth Voice transmission: up to 3.4 KHz DSL transmissions: up to 30 MHz Multi-carrier transmissions: Discrete Multitone Modulation Voice DSL Frequency (KHz) Jianwei Huang (Princeton) DSL Spectrum Management March / 26

6 Network and Channel Model CO TX (Central Office) RT (Remote Terminal) TX RX Customer crosstalk RX Customer Mathematical model: multi-user multi-carrier interference channel Each telephone line is a user (transmitter-receiver pair) Generate mutual crosstalks over multiple frequency tones Jianwei Huang (Princeton) DSL Spectrum Management March / 26

7 Network and Channel Model CO TX (Central Office) RT (Remote Terminal) TX RX Customer crosstalk RX Customer Physical model: mixed CO/RT case Channel attenuates with distance Central Office (CO) connect customers who are reasonably close Remote Terminal (RT) connect customers who are farther away Jianwei Huang (Princeton) DSL Spectrum Management March / 26

8 Network and Channel Model CO TX (Central Office) RT (Remote Terminal) TX RX Customer crosstalk RX Customer Frequency-Dependent Channel Direct channel gain decreases with frequency Crosstalk channel gain increases with frequency Jianwei Huang (Princeton) DSL Spectrum Management March / 26

9 Network and Channel Model CO TX (Central Office) RT (Remote Terminal) TX RX Customer crosstalk RX Customer Frequency-Dependent Channel Direct channel gain decreases with frequency Crosstalk channel gain increases with frequency Lead to near-far problem RT generates strong crosstalk to CO line, especially in high tones CO generates little crosstalk to RT in all tones Jianwei Huang (Princeton) DSL Spectrum Management March / 26

10 Crosstalk System Model N users (lines) and K tones (frequency bands) User n s achievable rate on tone k is ( ) bn k = log 1 + SINR k n where SINR k n = Total data rate of user n p k n m n αk n,mp k m + σ k n R n = k b k n Jianwei Huang (Princeton) DSL Spectrum Management March / 26

11 Network Objective: Maximize Rate Region Rate Region: set of all achievable rate vectors R 1 Rate Region R 2 Jianwei Huang (Princeton) DSL Spectrum Management March / 26

12 Network Objective: Maximize Rate Region Rate Region: set of all achievable rate vectors R 1 Rate Region Problem A: (Find One Point On the Rate Region Boundary) maximize {p n P n} n n w n R n User n chooses a power vector p n P n = { k pk n P max n, p k n 0 }. R 2 Jianwei Huang (Princeton) DSL Spectrum Management March / 26

13 Network Objective: Maximize Rate Region Rate Region: set of all achievable rate vectors R 1 Rate Region Problem A: (Find One Point On the Rate Region Boundary) maximize {p n P n} n n w n R n User n chooses a power vector p n P n = { k pk n P max n, p k n 0 }. Changing different weights trace the entire rate region boundary R 2 Jianwei Huang (Princeton) DSL Spectrum Management March / 26

14 Network Objective: Maximize Rate Region Rate Region: set of all achievable rate vectors R 1 Rate Region Problem A: (Find One Point On the Rate Region Boundary) maximize {p n P n} n n w n R n User n chooses a power vector p n P n = { k pk n P max n, p k n 0 }. Changing different weights trace the entire rate region boundary A suboptimal algorithm leads to a reduced rate region R 2 Jianwei Huang (Princeton) DSL Spectrum Management March / 26

15 Difficulties of Solving Problem A Non-convexity: total weighted rate not concave in power. Physically distributed: local channel information Performance coupling: across users (interferences) and tones (power constraint) Jianwei Huang (Princeton) DSL Spectrum Management March / 26

16 Dynamic Spectrum Management (DSM) State-of-art DSM algorithms: IW: Iterative Water-filling [Yu, Ginis, Cioffi 02] R 1 IW Algorithm Operation Complexity Performance IW Autonomous O (KN) Suboptimal R 2 Jianwei Huang (Princeton) DSL Spectrum Management March / 26

17 Dynamic Spectrum Management (DSM) State-of-art DSM algorithms: IW: Iterative Water-filling [Yu, Ginis, Cioffi 02] OSB: Optimal Spectrum Balancing [Cendrillon et al. 04] ISB: Iterative Spectrum Balancing [Liu, Yu 05] [Cendrillon, Moonen 05] R 1 OSB/ISB IW Algorithm Operation Complexity Performance IW Autonomous O (KN) Suboptimal OSB Centralized O ( Ke N) Optimal ISB Centralized O ( KN 2) Near Optimal R 2 Jianwei Huang (Princeton) DSL Spectrum Management March / 26

18 Dynamic Spectrum Management (DSM) State-of-art DSM algorithms: IW: Iterative Water-filling [Yu, Ginis, Cioffi 02] OSB: Optimal Spectrum Balancing [Cendrillon et al. 04] ISB: Iterative Spectrum Balancing [Liu, Yu 05] [Cendrillon, Moonen 05] ASB: Autonomous Spectrum Balancing [Huang et al. 06] R 1 OSB/ISB/ASB IW Algorithm Operation Complexity Performance IW Autonomous O (KN) Suboptimal OSB Centralized O ( Ke N) Optimal ISB Centralized O ( KN 2) Near Optimal ASB Autonomous O (KN) Near Optimal R 2 Jianwei Huang (Princeton) DSL Spectrum Management March / 26

19 Optimal Spectrum Balancing Global optimization based on dual decomposition Key: the duality gap is asymptotically zero under frequency-sharing property R target 1 R 1 w = 0 C A w = γ ɛ D B w = γ + ɛ R 2 L l E l X Y X Y w = 1 Fig. 2. Operating points in X Y can be found through a weighted rate-sum optimization c Cendrillon et. al., ICC, 2004 Theorem 2: For any rate region X, define X as the boundary of X, Y as the convex hull of X, and Y as the boundary of Y. Consider any operating point C (R1, c R2) c which is achievable C X and on the boundary of the convex hull finely enough then neighbouring tones same channels (both direct and crosstal Imagine that the tone spacing is fi h n,m k h n,m k+l, 0 l L 1. Co the rate region, A = (R1, a R2) a and B corresponding PSDs (s 1,a k, s2,a k ) and (s1 k to operate at a point E = ( l L Ra 1 + L l L R any 0 l L 1 as depicted in Fig. 2. the PSDs to (s 1,a k, s2,a k ) on tones k {p all integer values of p, and to (s 1,b k, s2,b k For example, to operate at a point B (on the side closer to A), it is and L = 3. Thus the PSDs are set to k {1, 2, 4, 5, 7, 8,..., K 1} and to k {3, 6, 9,..., K}. For this to work be small enough such that the channel over L = 3 neighbouring tones. That i h n,m k h n,m k+1 hn,m k+2, k {1, 4,..., For large L (small tone spacing), pra point between A and B can be achiev points in the rate region, any point betwe the rate region. This is the definition of Jianwei Huang (Princeton) DSL Spectrum Management the rate region Marchis2007 approximately 10 / convex 26

20 Optimal Spectrum Balancing Partial Lagrangian: L (p 1,..., p N ) = n w n k ( ) log 1 + SINR k n n λ n ( k p k n P max n ) Decompose K nonconvex subproblems, one for each tone k: ( w n log 1 + SINR k n λ n pn k maximize {p k n} n 0 n ) n Joint exhaustive search of optimal transmission power of all users Optimal values of λ 1,..., λ N can be found using bisection or subgradient search Jianwei Huang (Princeton) DSL Spectrum Management March / 26

21 Optimal Spectrum Balancing Pros Solve a long-standing open problem Find the global optimal solution (asymptotically) Linear complexity in K Cons Centralized algorithm Exponential complexity in N Jianwei Huang (Princeton) DSL Spectrum Management March / 26

22 Iterative Water-Filling Game-theoretic model based on selfish optimizations Each user wants to maximize payoff: total achievable rate S n ( pn, p n ) = Rn ( pn, p n ) Jianwei Huang (Princeton) DSL Spectrum Management March / 26

23 Iterative Water-Filling Game-theoretic model based on selfish optimizations Each user wants to maximize payoff: total achievable rate S n ( pn, p n ) = Rn ( pn, p n ) Best Response: the power vector that maximizes payoff ( ) B n (p n ) arg max S n pn, p n p n P n Convex optimization Coupled across tones by total power constraint Can be solved by dual decomposition Jianwei Huang (Princeton) DSL Spectrum Management March / 26

24 Iterative Water-Filling Game-theoretic model based on selfish optimizations Each user wants to maximize payoff: total achievable rate S n ( pn, p n ) = Rn ( pn, p n ) Best Response: the power vector that maximizes payoff ( ) B n (p n ) arg max S n pn, p that no interference subtraction is performed n p regardless n P n of Convex optimization (7) Coupled across Comparing tones the above by expression total with (2), power it is easy to identify constraint Can be solved by dual decomposition (8) Solution: water-filling (9) TROL FOR DIGITAL SUBSCRIBER LINES 1109 YU et al.: DISTRIBUTED MULTIUSER POWER CONTROL FOR DIGITAL SUBSCRIBER LINES 1109 interference strength, the data rates are rformed regardless of and similarly for and. Thus, the simplified model incurs no loss of generality. The interference channel game considered here is not a zero-sum game, i.e., one player s loss is not (6) equal to the other player s gain. The main objective here is to characterize all pure-strategy Nash equilibria in an interference channel game. At a Nash equilibrium, each user s strategy is the optimal response to the other (7) player s strategy. So fixing, the optimal must be ), it is easy to identify the solution to the following optimization problem: (8) (6) (9) s.t. Fig. 4. Simultaneous water-filling. c Yu, Ginnis and Cioffi, JSAC, 2002 s, the simplified model (10) nce channel game Jianwei con- Huang (Princeton) DSL Spectrum ManagementNash equilibrium can be reached by an iterative March water-filling / 26

25 Iterative Water-filling Pros Autonomous: no explicit communication among users (interference plus noise can be locally measured) Low computational complexity of O(KN): separable across users and tones Achieve better performance than the current practice Cons Selfish optimization No consideration for damages to other users Highly suboptimal in the mixed CO/RT case Jianwei Huang (Princeton) DSL Spectrum Management March / 26

26 Autonomous Spectrum Balancing Key idea: reference line - static pricing for static channel A virtual line representative of the typical victim in the network Good choice: the longest CO line Parameters (power, noise, crosstalk) are publicly known Each user will choose its transmit power to protect the reference line Jianwei Huang (Princeton) DSL Spectrum Management March / 26

27 Reference Line CO CP RT CP RT CP RT CP Jianwei Huang (Princeton) DSL Spectrum Management March / 26

28 Reference Line CO CP CO Reference Line CP RT Actual Line CP RT CP RT CP Jianwei Huang (Princeton) DSL Spectrum Management March / 26

29 Reference Line s Rate User n s obtains the reference line parameters locally Reference Line Length & Location Operator Database Reference Power: Reference Noise: Reference Crosstalk: p k,ref σ k,ref α k,ref n Jianwei Huang (Princeton) DSL Spectrum Management March / 26

30 Reference Line s Rate User n s obtains the reference line parameters locally Reference Line Length & Location Operator Database Reference Power: Reference Noise: Reference Crosstalk: p k,ref σ k,ref α k,ref n The reference line rate R ref n = k log ( 1 + p k,ref αn k,ref pn k + σ k,ref ) Interference only depends on user n s transmit power p k n Locally computable without explicit message passing Jianwei Huang (Princeton) DSL Spectrum Management March / 26

31 Frequency Selective Water-filling Under high SNR approximation of the reference line B k n ( p n ) = w n λ n + α k,ref n /σ k,ref 1 {p k,ref >0} αn,mp k m k σ k n m n + Reference line is not active in high frequency tones Special case: traditional water-filling (ignore α k,ref n /σ k,ref ) Jianwei Huang (Princeton) DSL Spectrum Management March / 26

32 Frequency Selective Water-filling Under high SNR approximation of the reference line B k n ( p n ) = w n λ n + α k,ref n /σ k,ref 1 {p k,ref >0} αn,mp k m k σ k n m n + Reference line is not active in high frequency tones Special case: traditional water-filling (ignore α k,ref n /σ k,ref ) Power Interference & Noise Traditional Water Filling Frequency Jianwei Huang (Princeton) DSL Spectrum Management March / 26

33 Frequency Selective Water-filling Under high SNR approximation of the reference line B k n ( p n ) = w n λ n + α k,ref n /σ k,ref 1 {p k,ref >0} αn,mp k m k σ k n m n + Reference line is not active in high frequency tones Special case: traditional water-filling (ignore α k,ref n /σ k,ref ) Power Interference & Noise Active Reference Line Frequency Frequency Selective Water Filling Jianwei Huang (Princeton) DSL Spectrum Management March / 26

34 Convergence of ASB Algorithm ASB Algorithm: users update their individual power allocation according to best responses either sequentially or in parallel Theorem ASB algorithm globally and geometrically converges to the unique N.E. if the crosstalk channel is small, i.e., max n,m,k αk n,m < 1 N 1. Independent of the reference line parameters. Recover the convergence of iterative water-filling as a special case. Proof: contraction mapping Jianwei Huang (Princeton) DSL Spectrum Management March / 26

35 Proof Outline 1 Key Lemma: min-max of an increasing function and an decreasing function is achieved at the intersection. 2 Construct two such functions based on the ASB algorithm. 3 Show the maximum difference between the PSD during adjacent iterations is decreasing. { } [ ] + [ ] max max p k,t+1 n n pn k,t, pn k,t+1 pn k,t max max n k { k [ p k,t n p k,t 1 n k ] +, k [ p k,t n } ] pn k,t 1 Sequential updates: bound the maximum eigenvalue of the mapping matrix. Parallel updates: more realistic with cleaner proof. Jianwei Huang (Princeton) DSL Spectrum Management March / 26

36 ASB Performance 4 ADSL lines. Mixed CO/RT deployment. Practical channel and background noise models. User 1 CO 5Km CP User 2 2Km RT 4Km CP User 3 3Km RT 3.5Km CP User 4 4Km RT 3Km CP Jianwei Huang (Princeton) DSL Spectrum Management March / 26

37 ASB Performance 4 ADSL lines. Mixed CO/RT deployment. Practical channel and background noise models. Both users 2 and 3 acheive fixed rates 2Mbps. Examine the rate region in terms of users 1 and 4 s rates. User 1 CO 5Km CP User 2 2Km RT 4Km CP User 3 3Km RT 3.5Km CP User 4 4Km RT 3Km CP Jianwei Huang (Princeton) DSL Spectrum Management March / 26

38 Achievable Rate Regions of Different Algorithms 1.8 User 1 s Rate (Mbps) Best Available Today (IW) ASB Optimal (OSB) User 4 s Rate (Mbps) Jianwei Huang (Princeton) DSL Spectrum Management March / 26

39 Power Allocation Power Allocation under ASB Power Allocation under Iterative Waterfilling R 1 = 1 Mbps, R 2 = 2 Mbps, R 3 = 2 Mbps R 4 = 7.3 Mbps under ASB, and 3 Mbps under Iterative Waterfilling. Around 150% rate increase for user 4 Jianwei Huang (Princeton) DSL Spectrum Management March / 26

40 Robustness of Reference Line Choice 2 5km 1.5 CO 4km RT crosstalk 3km CO Rate (Mbps) m 4020 m 4050 m 4100 m 5000 m 6000 m downstream transmissions RT Rate (Mbps) Two-line Topology Rate Region w/ various Reference Line Choice Performance is robust to reference line choices. Jianwei Huang (Princeton) DSL Spectrum Management March / 26

41 Summary Topic: spectrum management in DSL multiuser interference channels Key idea: static pricing using reference line Algorithm: ASB: autonomous, low complexity, and robust Performance: close to optimal, provable convergence Practice: achieve significantly larger rate region compared with the state-of-the-art distributed algorithm Main contribution: static pricing for static coupling Jianwei Huang (Princeton) DSL Spectrum Management March / 26

42 Background Reading IW: W. Yu, G. Ginis, and J. Cioffi, Distributed multiuser power control for digital subscriber lines, IEEE Journal on Selected Areas in Communication, June 2002 OSB: R. Cendrillon, W. Yu, M. Moonen, J. Verlinden, and T. Bostoen, Optimal multi-user spectrum balancing for digital subscriber lines, IEEE Transactions on Communications, May 2006 ASB: R. Cendrillon, J. Huang, M. Chiang, and M. Moonen, Autonomous spectrum balancing for digital subscriber lines, to appear in IEEE Transactions on Signal Processing, 2007 Jianwei Huang (Princeton) DSL Spectrum Management March / 26