www.DLR.de • Chart 1 > Multiuser Positioning > Ronald Raulefs • 4 th COST Workshop > 09.10.2013 Multiuser Positioning Ronald Raulefs, Siwei Zhang, Wei Wang DLR: www.dlr.de/kn WHERE2 Project: www.ict-where2.eu
www.DLR.de • Chart 2 > Multiuser Positioning > Ronald Raulefs • 4 th COST Workshop > 09.10.2013 Motivation: Indoor Navigation Base station Base station
www.DLR.de • Chart 3 > Multiuser Positioning > Ronald Raulefs • 4 th COST Workshop > 09.10.2013 Motivation: Indoor Navigation Base station Base station
www.DLR.de • Chart 4 > Multiuser Positioning > Ronald Raulefs • 4 th COST Workshop > 09.10.2013 Motivation: Indoor Navigation Base station Base station
www.DLR.de • Chart 5 Motivation: Indoor Navigation GNSS may be unavailable or insufficient, but devices are seldom alone Questions: • How to improve positioning? • How to range simultaneously? Base station Base station
www.DLR.de • Chart 6 Outline - Motivation - Cooperative positioning and related work - Multicarrier Ranging and Positioning Cramer-Rao Lower Bound - Multiuser positioning concept - Measurement evaluation - Conclusions & Outlook
www.DLR.de • Chart 7 Cooperative Positioning: Deep Indoors BS BS 1 2 29m Office wall with 3dB penetration loss Core building wall with 22m 10dB penetration loss Ranging variance: 1m BS 3 0 2 4 6 8 10 Position Error in m
www.DLR.de • Chart 8 Related Work Multicarrier Ranging Coop. Pos. with link (Luise et al. [2009]) selection in WSN (Wymeersch et al. [2012]) Communication Standards – • Resource Allocation in Device-2-Device: Coop. Pos. • WiFi-direct (Android [today]) • Multiuser D2D Ranging • LTE-direct (R12 discussion)
www.DLR.de • Chart 9 Ranging � Measuring the Wireless Channel • Received Signal Strength (RSS) – Corrupted by the propagation effects Time of Arrival (TOA) • – Requires synchronization between transmitter and receiver - -80dBm - t a =3.4µs - 0dBm
www.DLR.de • Chart 10 Cramér-Rao Lower Bound (CRLB) for Ranging and Positioning with Multicarrier Signals
www.DLR.de • Chart 11 System Model - Distance between cooperating node and node of interest 1: 𝒚|| = √ (𝑦↓ 1 − 𝑦)↑ 2 + (𝑧↓ 1 − 𝑧)↑ 2 𝑒 = ||𝒚↓ 𝒚↓ 1 − 𝒚| s(t)= 1 /√ 𝑂 ∑𝑜 =− ¡ 𝑂/ 2 ↑𝑂/ 2 ▒𝑇↓𝑜 𝑓↑𝑘 2 𝜌 nf ↓𝑡𝑑 𝑢 - OFDM Signal: - Received signal under line-of-sight conditions (single slope path loss model): r (𝑢) = 𝑏↓ 0 (𝑒/𝑒↓ 0 )↑ − 𝛿/ 2 𝑡(𝑢 − 𝑒/𝑑↓ 0 ) + 𝑨(𝑢) - 𝑇↓𝑜 is the n ’th signal sample of the transmitted multicarrier signal -‑ ¡ 𝑜 ¡ subcarrier index -‑ ¡ 𝑔↓𝑇𝐷 ¡ subcarrier spacing - 𝑂 number of subcarriers - 𝛿 attenuation / path loss exponent ( 𝛿 ¡ = 2 for free space) - 𝑏↓ 0 path loss at the reference distance 𝑒↓ 0 - z Gaussian thermal noise - 𝑑↓ 0 speed of light
www.DLR.de • Chart 12 Joint CRLB TOA and Received Signal Strength - Subcarrier index - CRLB(TOA) = 𝜏↑ 2 /𝑔↓𝑇𝐷↑ 2 / 2 ¡ 𝑔↓𝑑↑ 2 𝑒↑ 2 ∑𝑜 =− 𝑂/ 2 ↑𝑂/ 2 ▒𝑜↑ 2 | 𝑇(𝑜) | ↑ 2 - Signal power - CRLB(RSS) = 𝜏↑ 2 /𝑑↓ 0 ↑ 2 / 8 ¡ 𝜌↑ 2 𝑔↓𝑑↑ 2 𝑒↑ 4 ∑𝑜 =− 𝑂/ 2 ↑𝑂/ 2 ▒ | 𝑇(𝑜) | ↑ 2 - Bandwidth ( 𝑔↓𝑇𝐷 ( 𝑂 +1) ) - 𝑔↓𝐷 ¡: Carrier frequency - CRLB(RSS,TOA) = 𝜏↑ 2 /𝑑↓ 0 ↑ 2 / 8 ¡ 𝜌↑ 2 𝑔↓𝑑↑ 2 𝑒↑ 4 ∑𝑜 =− 𝑂/ 2 ↑𝑂/ 2 ▒ | 𝑇(𝑜) | ↑ 2 + ¡ 𝑔↓𝑇𝐷↑ 2 / 2 ¡ 𝑔↓𝑑↑ 2 𝑒↑ 2 ∑𝑜 =− 𝑂/ 2 ↑𝑂/ 2 ▒𝑜↑ 2 | 𝑇(𝑜) | ↑ 2 - Signal power -‑ 𝑔↓𝐷 ¡: Carrier frequency used to include free space path loss
www.DLR.de • Chart 13 Ranging Bounds for TOA and RSS – Path Loss Integrated 𝐾↓𝑈𝑃𝐵 = 2 𝑏↑ 2 /𝜏↑ 2 (𝑒/𝑒↓ 0 )↑ − 𝛿 4 ¡ 𝜌↑ 2 𝑔↓𝑇𝐷↑ 2 /𝑑↑ 2 ∑𝑜 =−{ 𝑂 −1 / 2 } ↑{𝑂 −1 / 2 }▒𝑜↑ Fisher Information Matrix 𝐾↓𝑆𝑇𝑇 = 2 𝑏↑ 2 /𝜏↑ 2 (𝑒/𝑒↓ 0 )↑ − 𝛿 𝛿↑ 2 / 4 𝑒↑ 2 ∑𝑜 =−{ 𝑂 −1 / 2 } ↑{𝑂 −1 / 2 }▒𝑇[𝑜]↑ 2 ¡ ¡ 𝐾↓𝐾𝑝𝑗𝑜𝑢 = 𝐾↓𝑈𝑃𝐵 + 𝐾↓𝑆𝑇𝑇 Cramer-Rao Lower Bound CRLB ↓ Joint = ¡ 1 /𝐾↓𝐾𝑝𝑗𝑜𝑢
www.DLR.de • Chart 14 Bandwidth affects Ranging CRLB Different bandwidths: • More bandwidth reduces CRLB • Parameters: • 𝑄↓ 0 =−30 ¡ 𝑒𝐶𝑛 / 𝑡𝑣𝑐𝑑𝑏𝑠𝑠𝑗𝑓𝑠 • 𝑔↓𝑇𝐷 =15 ¡ 𝑙𝐼𝑨 AWGN channel •
www.DLR.de • Chart 15 Different Zones of the CRLB Shorter distances favor RSS estimator à cooperative links! Triangular zone: Jointly RSS plus TOA – here for 20MHz
www.DLR.de • Chart 16 CRLB Positioning Bound Important aspects: • Ranging performance • Geometric constellation - Mobility and limited ranging increases uncertainty - Simultaneous ranging possible? DOI10.1002/ett.2572 - Raulefs, Zhang, Mensing: “Bound-based spectrum allocation for cooperative positioning”
www.DLR.de • Chart 17 LTE Frame Structure - Todays multicarrier based cellular Control signals Data communication systems, such as LTE, use for 5 ms synchronization and positioning: - Primary and Secondary synchronization Cell specific Primary reference signal synchronization signal signal à Chunk of signals (low bandwidth) - Positioning Reference Signals (PRS) are scattered over the available bandwidth Secondary à Grid of reference signals (scale with Positioning synchronization reference 1MHz communication load) signal signal - Can we apply such a scheme to range simultaneously multiple users? - What is the impact on the CRLB bound in case LTE frame structure (10 subframes) only limited subcarriers are used?
www.DLR.de • Chart 18 Multiuser Ranging - Sharing: Spectrum Allocation 1. Chunks Nodes (spatial) Chunk : Like Primary/ Secondary synchronization Signals in LTE Full band Subcarrier(f)
www.DLR.de • Chart 19 Multiuser Ranging - Sharing: Spectrum Allocation 2. Grid Nodes (spatial) Grid : Like Positioning Reference Signals (PRS) in LTE Full band Subcarrier(f)
www.DLR.de • Chart 20 RSS CRLB with Block Fading Channel 1 10 • Block Fading Channel 0 10 • Grid and Chunk scheme perform similar -1 10 • Full band uses more signal power CRLB[m] RSS CRLB Full RSS CRLB Grid 1 • Channel is known! RSS CRLB Grid 2 -2 10 RSS CRLB Grid 3 RSS CRLB Chunk 1 • 1540 subcarriers (grid: every 77 th RSS CRLB Chunk 2 RSS CRLB Chunk 3 -3 or chunk: 77 subcarriers) 10 -4 10 0 20 40 60 80 100 Distance[m]
www.DLR.de • Chart 21 Received Signal Strength Ranging - Using distance dependent path loss model to determine distance 𝑄(𝑒) = 𝑏↓ 0 ¡ (𝑒↓ 0 /𝑒 )↑ − 𝛿 - If link budget (TX power, antenna gains, path loss, etc.) is known à distance estimation possible Indoors: - LoS condition between devices is reasonable - Short ranges à RSS-CRLB outperforms TOA-CRLB 𝑄↓ 0 : Averaged received power at distance 𝑒↓ 0 𝑒 : ¡ Distance in m 𝛿 =1.13 Environmental path-loss exponent (determined by measurement campaign)
www.DLR.de • Chart 22 Received Signal Strength Ranging: Channel Snapshot Full-band: 120MHz bandwidth Distance estimation using the chunk scheme : • high variance for medium distances • lower variance for short distances Distance estimation for grid and full band overlap à Coherence bandwidth ~20MHz à Grid = Sampled channel fits path loss model
www.DLR.de • Chart 23 Received Signal Strength Ranging with Real Data 2.5 Path loss for single slope model: P (𝑒) = 𝑏↓ 0 (𝑒↓ 0 /𝑒 )↑ − 𝛿 , ¡ 𝛿 =1.13 2 120MHz channel bandwidth (1 track) 1.5 RMSE[m] Chunk : Mismatch compared to the 1 derived path loss model Grid and full band approach fits fairly 0.5 well (same performance as full band) 0 0 5 10 15 20 Selected Chunk or Grid Scheme
www.DLR.de • Chart 24 Conclusions - Cooperative positioning improves performance significantly (esp. indoors) - Received signal strength ( RSS ) is a simple non-synchronous scheme ranging scheme - Multiuser positioning concept: - Frequency division multiple access - Benefits for grid vs. chunk scheme to represent the broadband path loss model
www.DLR.de • Chart 25 www.DLR.de • Chart 25 > Multiuser Positioning > Ronald Raulefs • 4 th COST Workshop > 09.10.2013
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