Cross-layer Wireless Networking:

Transcription

1 Cross-layer Wireless Networking: Complexity, Approximation, and Opportunities for SP Research Nikos Sidiropoulos Dept. ECE, TU Crete IEEE SPAWC, 23/6/21 Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 1 / 4

2 ACKs Students Evaggelia Matskani Ioannis Mitliagkas Dimitris Evaggelinakis Colleagues Zhi-Quan Luo Ananthram Swami Leandros Tassiulas Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 2 / 4

3 Outline 1 Power control 2 Joint power and admission control 3 Multi-hop routing 4 Opportunities for SP research Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 3 / 4

4 Power control Where PHY and NET first met Co-channel users/links Frequency reuse or CDMA (PCS) Cellular voice SINR constraints Power control Various contexts: PCS, UMTS-LTE ad-hoc peer-to-peer cognitive underlay User Transmission Interference Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 4 / 4

5 Power control Properties & some history Linear Programming (LP) But wait, there s more: Feasibility - spectral radius (Perron-Frobenius) Simple distributed algorithm (Foschini) Well-developed theory Foschini, Zander, Yates, Bambos,... Many flavors Power Control K l=1, l k min K {p k R +} K k=1 k=1 p k p k Pk MAX, k G kk p k G lk p l + σ 2 k c k, k Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 5 / 4

6 Joint power and admission control Real problem is much tougher Often infeasible admission control Admission and power tightly coupled Jointly pick users and powers to Max # of users admitted Under SINR, power constraints Min total power Combinatorial? Andersin, Rosberg, Zander 96: contained in NP-hard... vs. contains NP-hard Gradual removals (Zander et al) Active link protection (Bambos et al) Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 6 / 4

7 Joint power and admission control Joint power and admission control Stage 1: Admission Control Maximal subset S, p(s ) Satisfying Max power Min SINR Stage 2: Power Control Minimize total power in S Satisfying Max power Min SINR Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 7 / 4

8 Joint power and admission control Joint power and admission control Stage 1: Admission Control S = s.t. k S arg max S {1,...,K },{p k R +} K k=1 p k P MAX k S Stage 2: Power Control min p k {p k R +} k S k S s.t. k S p k P MAX k l S, l k G kk p k G lk p l + σ 2 k c k l S, l k G kk p k G lk p l + σ 2 k c k Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 8 / 4

9 Complexity Joint power and admission control Start from any graph Special instance of AC S = arg max S S {1,...,K },{p k [,1]} K k=1 Construct instance of AC baptise `link 1' set G13=G31= `link 3' set G12=G21=1 s.t. l S, l k p k G lk p l 1, k S + 1 Maximal independent set indep (cyan) feas feas 1 +1 indep `link 2' Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 9 / 4

10 Joint power and admission control A ruler analogy Introduce binary scheduling variables Formulate as single stage problem Cost of dropped users Cost of power 1 P MAX = 2 3 ǫp MAX Total Cost Fully prioritizes user admission over power minimization [MatSidLuoTas:7]; [MitSidSwa:8] Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 1 / 4

11 Joint power and admission control Single stage reformulation Binary scheduling variables s k = {, 1} ( for admitted) Auxiliary constants ǫ and δ k min {p k R +,s k {,1}} K k=1 K K ǫ p k + (1 ǫ) k=1 k=1 s.t. p k P MAX k, k {1,...,K} G kk p k + δ 1 k s k K l=1, l k G c lkp l + σk 2 k, k {1,..., K } Proven equivalent to two-stage optimization for suitable ǫ, δ k s k Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 11 / 4

12 Joint power and admission control Convex relaxation Problem is non-convex (binary scheduling variables) Convex relaxation? - Lagrange bi-dual Lagrange bi-dual binary s k continuous s k s 1 1 s s 2 1 s 2 Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 12 / 4

13 Convex relaxation Joint power and admission control Convex (bi-dual) relaxation min {p k R +,s k R} K k=1 K K ǫ p k + (1 ǫ) k=1 k=1 s.t. p k P MAX k, k {1,...,K} G kk p k + δ 1 k s k K l=1, l k G c lkp l + σk 2 k, s k k {1,...,K} s k 1, k {1,...,K} Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 13 / 4

14 Joint power and admission control Approximation algorithm Algorithm Linear Programming Deflation 1 U {1,..., K } 2 Solve the relaxed problem 3 If all links attain target SINR terminate Else use heuristic to choose a link remove it from U go to Step 2. Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 14 / 4

15 Joint power and admission control Approximation algorithm Algorithm Linear Programming Deflation 1 U {1,..., K } 2 Solve the relaxed problem 3 If all links attain target SINR terminate Else use heuristic to choose a link remove it from U go to Step 2. Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 14 / 4

16 Joint power and admission control Approximation algorithm Algorithm Linear Programming Deflation 1 U {1,..., K } 2 Solve the relaxed problem 3 If all links attain target SINR terminate Else use heuristic to choose a link remove it from U go to Step 2. Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 14 / 4

17 Joint power and admission control Options Practical implementation Distributed Dual decomposition (slow) Consensus-on-max (deflation) Robust imperfect CSI G lk Polynomial complexity, overhead Optimal solution? LPD lower & upper bounds on opt cost Branch & Bound w/ LPD Implicit search - pruning Complexity ENUM Still exp in w-c Sphere decoding Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 15 / 4

18 Joint power and admission control Simulations - admission performance mean # of users served Enumeration Branch & Bound using LPD Branch & Bound using SLP Gradual Admissions LPD GRN DCPC # of users that request service Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 16 / 4

19 Joint power and admission control Simulations - average complexity mean execution time (in secs) Enumeration Branch & Bound using LPD Branch & Bound using SLP Gradual Admissions LPD GRN DCPC # of users that request service Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 17 / 4

20 Joint power and admission control Simulations - worst-case complexity worst case execution time (in secs) Enumeration Branch & Bound using LPD Branch & Bound using SLP Gradual Admissions LPD GRN DCPC # of users that request service Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 18 / 4

21 Multi-hop routing Multi-hop routing: shortest path Connectivity Shortest paths 1.5 network connectivity weights load, delay, cost for all weights equal Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 19 / 4

22 Multi-hop routing Shortest path vs. dynamic back-pressure SP DP: BF, FW,... Distributed Must know arrival rate Quasi-static, very slow to adapt to changing arrivals/load availability/failure fading/interference patterns Claim: Low delay (shortest path)... but only at low system loads BP [Tassiulas 92] One-hop differential backlog Distributed Lightweight Auto-adapts Highly dynamic, agile Claim: maximal stable throughput (all paths)... but delay can be large - U(load), rand walk! Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 2 / 4

23 Back-pressure routing Multi-hop routing source W1=7... D(2,1)=7 D(2,3)=14 D(2,4)=2 W3= D(2,5)= W2=14 W4=12 W5=3... dest Favors links with low back-pressure (hence name) Backtracking / looping possible! Local communication, trivial computation Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 21 / 4

24 Multi-hop routing Back-pressure routing Multiple destinations, commodities? multiple queues per node (max diff backlog) winner-takes-all per link Wireline: local communication, trivial computation Wireless? Broadcast medium: interference Link rates depend on transmission scheduling, power of other links Globalization - but also opportunity to shape-up playing field through appropriate scheduling, power control Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 22 / 4

25 Multi-hop routing Back-pressure power control SINR G ll p l γ l = k L,k l G klp k + V l Link capacity c l = log(1 + γ l ) Diff backlog link l = (i time t D l (t) := max {, W i (t) W j (t) } BPPC max D l (t)c l {p l } l L l L s.t. p l P i, i N l:tx(l)=i p l P (l),l L Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 23 / 4

26 Multi-hop routing Back-pressure power control BPPC max D l (t)c l {p l } l L s.t. l L l:tx(l)=i p l P (l),l L p l P i, i N Link activation / scheduling: { p l, P (l)},l L [Tassiulas et al, 92 ] Max stable throughput Backbone behind modern NUM Core problem in wireless networking Countable control actions: random, adopt if > current Still throughput-opt! [Tass 98] - but D Continuous opt vars? Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 24 / 4

27 Multi-hop routing Back-pressure power control Non-convex due to c l log(1+γ l ) - diff of concave At high SINR γ l, 1 + γ l = γl c l log(γ l ) always Tempting... Giannoulis, Tsoukatos, Tassiulas, ICC 6 Gradient projection, best response Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 25 / 4

28 Beware! Multi-hop routing Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 26 / 4

29 Multi-hop routing Reminiscent of... DSL: sum-rate maximization BPPC Rx 1 Tx Rx 2 Rx 3 Single-hop DSL Listen-while-talk Dedicated (Tx,Rx) Free choice of G k,l s NP-hard [Luo, Zhang] Multi-hop network No listen-while-talk X Shared Tx, Rx Restricted G k,l s NP-hard? Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 27 / 4

30 Peel off Multi-hop routing Generic backlogs Choosing backlogs Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 28 / 4

31 Multi-hop routing DSL Multi-hop network optimization Backlog reduction BPPC contains DSL also NP-hard Can reuse tools from DSL In particular, lower approximation algorithms: High SINR Geometric Programming Successive approximation from below: SCALE [Papandriopoulos and Evans, 26] Uses α log(z) + β log(1 + z) for { α = z o 1+z o β = log(1 + z o ) zo 1+z o log(z o ) tight at z o ; log(z) log(1 + z) as z o Start from high SINR, tighten bound at interim solution Majorization (actually, minorization) Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 29 / 4

32 Multi-hop routing Key difference with DSL BPPC problem must be solved repeatedly for every slot Batch algorithms: prohibitive complexity Need adaptive, lightweight solutions (to the extent possible) Built custom interior point algorithms Normally, one would init using solution of previous slot; take refinement step Doesn t work... Why? Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 3 / 4

33 Multi-hop routing Proper warm-start No listen-while-talk, shared Tx/Rx Push-pull wave propagation Solution from previous slot very different from one for present slot Even going back a few slots Quasi-periodic behavior emerges Idea: hold record of solutions for W previous slots. W > upper bound on period W evaluations of present objective function (cheap!) Pick the best to warm-start present slot Needs few IP steps to converge Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 31 / 4

34 Multi-hop routing Quality of approximation? Max lower bound link rates attainable Sims indicate solutions far outperform prior art in networking in terms of key network metrics: throughput, delay, stability margin OK, but upper bound? Normally, dual problem Here computing dual function is also NP-hard :-( [Tx: Tom Luo] Resort to Yu and Lui 6, originally for spectrum balancing in DSL Yields approximate solution of dual problem - approximate upper bound When properly tuned... can be very slow... Sanity check / gauge Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 32 / 4

35 Simulation setup Multi-hop routing 1 Network topology graph meters meters N = 6 nodes, low-left = s, top-right = d, L = 21 links G l,k 1/d 4, G = 128, no-listen-while-talk 1/eps V l = 1 12, P (l) = 5, l Deterministic (periodic) arrivals Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 33 / 4

36 High SINR Multi-hop routing Scenario1, Batch high SINR algorithm; 8 16 arrival rate per slot = 9.7 relay backlogs source backlog power throughput Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 34 / 4

37 High SINR Multi-hop routing Scenario1, Batch high SINR algorithm; 15 3 arrival rate per slot = 9.8 relay backlogs 1 5 source backlog power throughput Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 35 / 4

38 Multi-hop routing Successive Approximation Scenario1, Batch S.A. algorithm; 8 18 arrival rate per slot = 1.4 relay backlogs source backlog power throughput Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 36 / 4

39 Multi-hop routing Successive Approximation Scenario1, Batch S.A. algorithm; 1 25 arrival rate per slot = 1.8 relay backlogs source backlog 2 15 power throughput Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 37 / 4

40 Best Response Multi-hop routing Scenario1: Back Pressure Best Response algorithm; relay backlogs source backlog arrival rate per slot = power throughput arrival rate 5 1 Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 38 / 4

41 Multi-hop routing Gap to optimal: ISB approximation objective value Differential backlog weighted sum of link capacities; arrival rate = 8 ISB BSA objective value arrival rate = ISB 4 BSA Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 39 / 4

42 Opportunities for SP research Opportunities for SP research Looking ahead Distributed BPPC Robustness (imperfect / outdated CSI) LMS-like? - Ribeiro, Gatsis+Giannakis MIMO nodes - beamforming? precoding? spatial MUX? Other modalities - multicasting? All NP-hard, need effective approximation Paradigm shift Network coding? Cooperation among nodes? Nikos Sidiropoulos (Dept. ECE, TU Crete) Cross-layer Wireless Networking IEEE SPAWC, 23/6/21 4 / 4