Leveraging Quantum Annealing for Large MIMO Processing in - PowerPoint PPT Presentation

Leveraging Quantum Annealing for Large MIMO Processing in Centralized Radio Access Networks Minsung Kim, Davide Venturelli, Kyle Jamieson Presented by Minsung Kim 1

NEW SERVICES ! • Global mobile data traffic is increasing exponentially. • User demand for high data rate outpaces supply. Wireless Capacity has to increase ! 2

Users Multi-User Multiple Input Multiple Output (MU-MIMO) Centralized Data Center Centralized Radio Access Networks (C-RAN) 3

MIMO Detection Users Base Station Demultiplex Mutually Interfering Streams 4

Maximum Likelihood (ML) MIMO Detection : Non-Approximate but High Complexity 𝒘 𝟐 𝒊 𝟐𝟐 … 𝒊 𝟐𝑶 … Channel: H = 𝒊 𝑶𝟐 … 𝒊 𝑶𝑶 𝒘 𝑶 𝒐 𝟐 𝟑 𝑶 log 2 𝑁 𝐪𝐩𝐭𝐭𝐣𝐜𝐣𝐦𝐣𝐮𝐣𝐟𝐭 𝐠𝐩𝐬 … Noise: n = N x N MIMO with M modulation 𝒐 𝑶 𝒘 𝟐 Received Signal: y ( = Hv + n ) … Symbol Vector: v = 𝒘 𝑶 Wireless Channel: H Time available for processing is at most 3-10 ms. 5

Sphere Decoder (SD) : Non-Approximate but High Complexity Maximum Likelihood (ML) Detection Tree Search with Constraints Reduce search operations but fall short for the same reason Parallelization of SD [Flexcore, NSDI 17], [Geosphere, SIGCOMM 14], … Approximate SD [K-best SD, JSAC 06], [Fixed Complexity SD, TWC 08], …. 6

Linear Detection : Low Complexity but Approximate & Suboptimal 𝒘 𝟐 [BigStation, SIGCOMM 13], Zero-Forcing [Argos, MOBICOM 12], 𝑰 𝟐𝟐 … 𝑰 𝟐𝑶 … … Channel: H = 𝑰 𝑶𝟐 … 𝑰 𝑶𝑶 Nullifying Channel Effect: 𝒘 𝑶 𝒐 𝟐 𝐈 −𝟐 𝒛 = 𝐈 −𝟐 𝐈𝐰 + 𝐈 −𝟐 𝐨 … Noise: n = 𝒐 𝑶 𝒘 𝟐 Received Signal: y ( = Hv + n ) … Symbol Vector: v = 𝒘 𝑶 Wireless Channel: H Performance Degradation due to Noise Amplification 7

Ideal Performance ML Detection high throughput low bit error rate Linear Detection Computational Time Ideal: High Performance & Low Computational Time

Opportunity: Quantum Computation ! 9

QuAMax: Main Idea MIMO Detection Quantum Computation Quantum Annealing Maximum Likelihood (ML) Detection Better Performance ? Motivation: Optimal + Fast Detection = Higher Capacity 10

QuAMax Architecture Quantum Processing Unit Maximum Likelihood Detection Maximum Likelihood Detection Centralized Data Center Centralized Radio Access Networks (C-RAN) 11

Maximum Likelihood Detection Quadratic Unconstrainted Binary Optimization Quantum Processing Unit D-Wave 2000Q (Quantum Annealer) 12

Contents 1. PRIMER: QUBO FORM 2. QUAMAX: SYSTEM DESIGN 3. QUANTUM ANNEALING & EVALUATION 13

Quadratic Unconstrainted Binary Optimization (QUBO) Variables (0 or 1) Coefficients (real) ▪ Example (two variables) State QUBO Energy Q upper triangle matrix : = (0,0) -> 0 = (0,1) -> 0.5 = (1,0) -> 2 = (1,1) -> -2 QUBO objective : 2 𝑟 1 + 0 .5𝑟 2 − 4 .5 𝑟 1 𝑟 2 14

Contents 1. PRIMER: QUBO FORM 2. QUAMAX: SYSTEM DESIGN 3. QUANTUM ANNEALING & EVALUATION 15

Key Idea of ML-to-QUBO Problem Reduction ▪ Maximum Likelihood MIMO detection: ▪ QUBO Form: QUBO Form! The key idea is to represent possibly-transmitted symbol v with 0,1 variables. If this is linear , the expansion of the norm results in linear & quadratic terms. Linear variable-to-symbol transform T 16

Revisit ML Detection Example: 2x2 MIMO with Binary Modulation -1 +1 Received Signal: y -1 +1 Wireless Channel: H Symbol Vector: 17

QuAMax’s ML-to-QUBO Problem Reduction Example: 2x2 MIMO with Binary Modulation 1. Find linear variable-to-symboltransform T: 2. Replace symbol vector v with transform T in : -1 +1 3. Expand the norm -1 +1 Symbol Vector: QUBO Form! 18

ML-to-QUBO Problem Reduction QuAMax’s linear variable-to-symbol Transform T BPSK (2 symbols) : QPSK (4 symbols) : 16-QAM (16 symbols) : ▪ Coefficient functions f(H, y) and g(H) are generalized for different modulations. ▪ Computation required for ML-to-QUBO reduction is insignificant. 19

Maximum Likelihood Detection Quadratic Unconstrainted Binary Optimization Quantum Processing Unit D-Wave 2000Q (Quantum Annealer) 20

Contents 1. PRIMER: QUBO FORM 2. QUAMAX: SYSTEM DESIGN 3. QUANTUM ANNEALING & EVALUATION 21

Quantum Annealing ▪ Quantum Annealing (QA) is analog computation (unit: qubit) based on quantum effects, superposition, entanglement, and quantum tunneling. N qubits can hold information on 2 N states simultaneously. At the end of QA the output is one classic state (probabilistic). superconducting circuit qubit D-Wave chip 22

QUBO on Quantum Annealer : - 𝑟 1 + 2 𝑟 2 + 2𝑟 3 − 2𝑟 4 + 2𝑟 1 𝑟 2 + 4𝑟 1 𝑟 3 −𝑟 2 𝑟 4 −𝑟 3 𝑟 4 Example QUBO with 4 variables Linear (diagonal) Coefficients : Energy of a single qubit Quadratic (non-diagonal) Coefficients : Energy of couples of qubits Quantum Annealing coupler qubit 23 From D-Wave Tutorial

QuAMax’s Metric Principles ▪ One run on QuAMax includes multiple QA cycles. Number of anneals ( 𝑂 𝑏 ) is another input. ▪ Solution (state) that has the lowest energy is selected as a final answer. Evaluation Metric: How Many Anneals Are Required? Target Solution’s Probability Bit Error Rate (BER) Empirical QA Results 24

QuAMax’s Empirical QA results ▪ Run enough number of anneals 𝑂 𝑏 for statistical significance. ▪ Sort the L ( ≤ 𝑂 𝑏 ) results in order of QUBO energy. ▪ Obtain the corresponding probabilities and numbers of bit errors. Example. L-th Solution 25

QuAMax’s Expected Bit Error Rate (BER) QuAMax’s BER = BER of the lowest energy state after 𝑂 𝑏 Anneals Probability of k -th solution Corresponding BER being selected after 𝑂 𝑏 anneals of k -th solution = never finding a solution better than k-th solution Probability of finding k-th solution at least once This probability depends on number of anneals 𝑂 𝑏 Expected Bit Error Rate (BER) as a Function of Number of Anneals ( 𝑶 𝒃 ) 26

QuAMax’s Comparison Schemes QA parameters: embedding, anneal time, pause duration, pause location, … ▪ Opt: run with optimized QA parameters per instance (oracle) ▪ Fix: run with fixed QA parameters per classification (QuAMax)

QuAMax’s Evaluation Methodology ▪ Opt: run with optimized QA parameters per instance (oracle) ▪ Fix: run with fixed QA parameters per classification (QuAMax) Expected Bit Error Rate (BER) as a Function of Number of Anneals ( 𝑶 𝒃 ) Time-to-BER (TTB) 28

Time-to-BER for Various Modulations Lines: Median Dash Lines: Average x symbols: Each Instance 29

QuAMax’s Time -to-BER ( 𝟐𝟏 −𝟕 ) Performance Practicality of Sphere Decoding Well Beyond the Borderline of Conventional Computer 30

QuAMax’s Time-to-BER Performance with Noise ▪ When user number is fixed, higher TTB is required for lower SNRs. Comparison against Zero-Forcing ▪ Better BER performance than zero-forcing can be achieved. Same User Number Different SNR 31

Practical Considerations ▪ Significant Operation Cost: About USD $17,000 per year ▪ Processing Overheads (as of 2019): Preprocessing, Read-out Time, Programming Time = hundreds of ms D-Wave 2000Q (hosted at NASA Ames) Future Trend of QA Technology More Qubits (x2), More Flexibility (x2), Low Noise (x25), Advanced Annealing Schedule, … 32

CONTRIBUTIONS ▪ First application of QA to MIMO detection ▪ New metrics: BER across anneals & Time-to-BER (TTB) ▪ New techniques of QA: Anneal Pause & Improved Range ▪ Comprehensive baseline performance for various scenarios 33

CONCLUSION ▪ QA could hold the potential to overcome the computational limits in wireless networks, but technology is still not mature. ▪ Our work paves the way for quantum hardware and software to contribute to improved performance envelope of MIMO.. 34

Supported by 35

Thank you! 36