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Limited Feedback Beamforming with Delay: Theory and Practice

This presentation provides an in-depth exploration of limited feedback beamforming techniques in MIMO systems, emphasizing both theoretical foundations and practical implementations. The talk discusses channel coding, feedback compression, and measures the impact of feedback delay on throughput. It reviews past research while introducing novel approaches, including the use of Markov models to better handle temporally correlated channels. Applications in industry, such as WiMax and LTE, illustrate the relevance of these concepts in real-world wireless communications.

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Limited Feedback Beamforming with Delay: Theory and Practice

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  1. Limited Feedback Beamforming with Delay: Theory and Practice Huang Kaibin Collaborators: Robert Daniels Prof. Robert W. Heath Jr. Prof. Jeffrey G. Andrews Wireless Networking and Communications Group (WNCG) Dept. of Electrical and Computer Engineering The University of Texas at Austin 08/15/2007 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  2. A new area: MIMO with Limited Feedback • Single-user 2) Multi-user 3) Wireless network talk scope MIMO: a Personal View 1996 Channel capacity (Telatar, Foschini) 1998 Gaussian broadcast Caire & Shamai Vish., Jindal & Goldsmith Viswanath & Tse Yu & Cioffi Space-time codes (Tarokh, Alamouti, Jafarkani) 2000 2002 Multi-user Diversity Knopp & Humblet Viswanath & Tse Sharif & Hassibi Diversity-multiplexing tradeoff (Zheng & Tse, Heath & Paulraj) 2004 IEEE 802.16e (WiMax) 2006 IEEE 802.11n (WiFi) 3GPP-LTE 2008 1

  3. Feedback Enhances Communication In the darkness… ? Here! listener speaker listener speaker no feedback feedback 2

  4. feedback feedback Beamforming Increases Throughput beamforming weights no feedback 3

  5. Wireless Channel Limited Feedback Concept • Adaptive Transmission • Precoder • Beamformer • AMC, etc Receiver Transmiter CSI Finite-Rate Feedback Channel Codebook based quantizer

  6. Limited Feedback Beamforming Increases Throughput quantizer partition index feedback quantizer surface of unit hyper-sphere 4

  7. Prior Work on Limited Feedback Beamforming • Narrow-band block fadingchannels • Research focuses on the codebook design. • Grassmannian line packing [Love & Heath 03] [Mukkavilli et al 03] • Lloyd algorithm [Roh & Rao 06][Xia et al 05] • Broadband channels (MIMO-OFDM) • Sub-channel grouping [Mondal & Heath 05] • Beamformer interpolation [Choi & Heath 04] • Spatially correlated channels • Codebook switching based channel correlation [Mondal & Heath 06] • Temporally correlated channels (considered in this talk) • Delta modulated feedback [Roh & Rao 04] • Drawback: multiple feedback streams • 1-bit feedback based on subspace perturbation [Banister 03] • Drawback: periodic broadcast of matrices

  8. Limited Feedback Beamforming in Industry • Local Area Networks (IEEE 802.11n) • Optional feature for 600 Mbps • IEEE 802.16e (WiMax) • Codebook based precoding/beamforming • 3GPP Long Term Evolution (LTE) • Single- and multi-user limited feedback beamforming • 4G • Lots of discussion

  9. Channel State S1 S2 S3 S4 S1, S2, … are independently distributed. Channel Coherence Time Motivation • Conventional: Block fading channels • (Narula et al 98, Love et al 03, Mukkavilli et al 03, Xia et al 04) • (Pro): Focus on quantizer codebook designs • (Con): Omits temporal correlation in wireless channels • (Con): Analysis of feedback delay and rate is difficult • New: Temporally-correlatedchannels • Feedback rate (vs. channel coherence time) • Feedback compression in time • Effect of feedback delay on throughput Important for designing practical limited feedback systems 6

  10. Outline • Part I: Theory • Channel Markov model • Feedback compression and rate • Feedback delay • Part II: Practice • Experiment setup • Measurement results

  11. System Model CSI {H1, H2, … } is a correlated sequence 7

  12. Proposed Approach: Assumption and Overview • The CSI index Jnvaries as a discrete-time finite-state Markov chain • Accurate for slowly time-varying SISO channel (Wang & Moayeri 95) Temporally Correlated MIMO Channel Markov Chain Feedback rate, compression, delay 8

  13. S2 S1 p13 p33 p63 S3 S6 p64 p43 S4 S5 Proposed Approach: CSI Index Markov Chain • Definition ofMarkov state space • Partition channel space using existing codebook-design techniques • (Love et al 03, Xia et al 05, Rho & Rao 05) • Computation of stationary and transition probabilities • Monte Carlo simulation (next slide) Unit Hyper-Sphere Markov Channel Model 9

  14. S2 S1 p13 p33 p63 S3 S6 p64 p43 S4 S5 Proposed Approach: CSI Index Markov Chain • Computation of stationary and transition probabilities • Generate a long channel sequence • Compute CSI index sequence • Compute stationary probability {pn} • Compute transition probability {pnm} 9

  15. Outline • Part I: Theory • Channel Markov model • Feedback compression and rate • Feedback delay • Part II: Practice • Experiment setup • Measurement results

  16. Overview of Feedback Compression CSI Quantization • Extensively studied • [Love et al 04] [Mukkavilli et al 03] Compression (frequency) Compression (time) Compression (space) • Adaptive Codebooks • [Mondal and Heath 05] • Incremental Feedback • [Roh 04][Banister 03] • Subspace Interpolation • [Choi et al 04] Finite-Rate Feedback

  17. Time Variation of Quantized Channel Feedback? Yes No No Yes No No Temporally Correlated Static (Feedback is unnecessary) Fast fading (Compression is ineffective) Aperiodic Feedback • Motivation:Infrequent channel state changes due to temporal correlation • Proposed: aperiodic feedback triggered by channel state changes • Conventional: periodic feedback per block

  18. Feedback Compression = 2 ! 1 bit Truncation Threshold:  = 0.02 -neighborhood of Channel State 1 Truncation of Channel State Transitions Motivation: Given a current state, the next state belongs to a subset of the state space with high probability

  19. Result 1: Average Feedback Rate Proposition 1: The time-average feedback rate converges with time as where Aperiodic Feedback Transition Truncation

  20. ·  >  Truncation of state transitions Quantization Regions Instantaneous Capacity Result 2: Ergodic Capacity Proposition 2: The average capacity converges as where

  21. Case Study: Beamforming for 2£1 Channel • i.i.d CN(0,1) vector • Clark’s correlation function Partial CSI: Beamformer Partial CSI Codebook lookup • Finite rate • Free of error Grassmanian codebook [Love & Heath 03] [Xia & Giannakis 05]

  22. Compression (colors,  = 1e-6) Reference (black,  = 0) Nt = 2 Compression Ratio > 3 Compression Ratio = 2 Case Study: Beamforming for 2£1 Channel Significant reduction on average feedback rates

  23. Case Study: Beamforming for 2£1 Channel Feedback compression causes no loss on ergodic capacity  = 1e-6

  24. Outline • Part I: Theory • Channel Markov model • Feedback compression and rate • Feedback delay • Part II: Practice • Experiment setup • Measurement results

  25. Recap: System Model • Feedback delay exists due to • Propagation • Signal processing • Protocol 7

  26. S2 S1 t S3 S6 t+1 t+2 S4 S5 How to Model Delay ? CSI Variation at Receiver Feedback Delay Model

  27. Convergence of CSI Index Markov Chain Transition probability matrix Stationary Distribution

  28. Result 1: Ergodic Capacity with Feedback Delay Theorem 1: The ergodic capacity with a feedback delay of D symbols is where Quantization Regions Instantaneous Capacity

  29. Result 2: Feedback Capacity Gain Def: Feedback Capacity Gain Theorem 2: The feedback capacity gain C decreases at least exponentially with the feedback delay D as 2 is the 2nd largest eigenvalue of P

  30. Result 2: Feedback Capacity Gain Remarks: D: Feedback Delay  depends on • Type of System • precoding, beamforming etc. • CSI Quantization Codebook  increases inversely with • Channel Coherence Time

  31. Case Study: Beamforming for 2£1 Channel • i.i.d CN(0,1) vector • Clark’s correlation function Partial CSI: Beamformer Partial CSI Codebook lookup • Feedback delay D • Finite rate • Free of error Grassmanian codebook [Love & Heath 03] [Xia & Giannakis 05]

  32. Nt = 2, Nr = 1, N = 16 Feedback Capacity Gain • Feedback capacity gain decreases exponentially with feedback delay; • Decreasing rate is determined by Doppler • Parameters (WiMax): • Carrier = 2.3 GHz • Symbol rate = 1.5 MHz

  33. Nt = 2, Nr = 1, N = 16 Design Example • Requirement A: • Delay ·0.4 ms • Capacity gain ¸1 bps/Hz • Requirement B: • Speed = 140 km/h • Delay = 0.27 ms Vehicular speed ·43 km/h • Parameters (WiMax): • Carrier = 2.3 GHz • Symbol rate = 1.5 MHz Capacity gain = 0.6 bps/Hz

  34. Summary of Theory • We proposed an analytical framework for designing practical limited feedback beamforming system • Feedback rate • Feedback compression • Feedback delay • Observations • Feedback rate increases (e.g. linearly) with Doppler. • Feedback compression significantly reduces feedback rate. • Feedback capacity gain diminishes at least exponentially with feedback delay.

  35. Motivation for Measurement Results • Validate the analytical model • Channel Markov chain assumption • Shannon capacity gain vs. throughput (QAM, adaptive MCS) • Verify theoretical results • Evaluate the impact of practical factors • Synchronization errors • Channel estimation errors • Frequency offset • Phase noise

  36. Outline • Part I: Theory • Channel Markov model • Feedback compression and rate • Feedback delay • Part II: Practice • Experiment setup • Measurement results

  37. Measurement Setup: Hydra Prototype

  38. IEEE 802.11n Transmitter Extended Training: Non-beamformed training symbols to measure true channel Frame Format Bit Parsing: Unnecessary for our experiment with only 1 spatial stream Transmission Process

  39. IEEE 802.11n Receiver Header Decoding: Any problems with header decoding result in dropped measurements Receiver Header Processing Receiver Data Processsing Equalization: Maximal ratio combining for experiments

  40. Feedback Channel Construction • Wired Feedback Advantages (for measurements): • Low latency (compared to Hydra over-the-air feedback) • High reliability (no dropped feedback packets due to frame synchronization errors) • “Perfect” CSI returned to transmitter (floating point samples)

  41. Measurement Topology Wireless Path: 10 m wireless path between transmitter and receiver obstructed by cubicles and office equipment Usage Scenario: Typical wireless local area network (WLAN) environment

  42. Channel Temporal Statistics (Mobility) Antennas: Mounted on oscillating table fans Oscillation Period: TX Period = 13.75 seconds RX Period = 11.25 seconds

  43. Outline • Part I: Theory • Channel Markov model • Feedback compression and rate • Feedback delay • Part II: Practice • Experiment setup • Measurement results

  44. Measurement Procedure Collecting CSI CDD Sounding LF-BF TX RX • Send a packet with cyclic delay diversity from the uninformed transmitter (baseline case). • Send a sounding packet from the transmitter. • Estimate the MIMO channel using the sounding packet. • Select a beamformer from a codebook and return the index over the wired feedback channel. • Send data packets using beamforming with a desired feedback delay. • Repeat steps 1-5 for 1000 iterations and measure the bit error of each packet.

  45. Measure Throughput Gain IEEE 802.11n Modulation and Coding Schemes (Single Stream) Translation to Throughput: Optimal Adaptation: Measurements taken for each MCS over all SNR

  46. Sample Measurement: • MCS 4 (16-QAM w/ 3/4 coding rate) • 5-bit Grassmannian codebook Results - BER Scatter Plot Throughput Curve Fitting: SNR binning with cubic spline interpolation

  47. Results - Throughput Gain Using adaptive MCS

  48. Results - Transition Probability Matrix

  49. Results - Feedback Delay Best Fit: Least squares mapping of measured data to an exponential decay function Theoretical Upper Bound: Analytically derived (earlier) upper bound using transition probability matrix calculation

  50. Conclusions • We proposed an analytical framework for designing limited feedback beamforming systems • Allocate feedback bandwidth • Compress CSI feedback • Compute allowable mobility range, and signal processing and protocol delay. • Theoretical result on feedback delay is validated using measurement data. • More experiments are being carried for verifying other theoretical results. • The proposed framework can be extended to other types of limited feedback systems e.g. precoding.

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