OTFS Orthogonal Time Frequency Space A novel modulation scheme addressing the challenges of 5G Anton Monk IEEE CTW 2016
Cohere Technologies FOUNDED IN 2009 Headquartered in Completed A, B and C Industry Leading Santa Clara, CA Rounds of Financing Investors OTFS TM – An innovative form of modulation. OTFS simultaneously extracts time, frequency & spatial channel behavior resulting in greater coverage , higher capacity , and cost savings . Cohere Technologies ~ Proprietary & Confidential 2
OTFS Air Interface Overview • 2D (Delay-Doppler) Modulation scheme • Utilizes a Delay-Doppler channel model that explicitly represents a stable and deterministic geometry of the channel • Novel 2D Basis functions spread information symbols over both time and frequency • Channel estimation is efficient, accurate and compact – High density pilots can be used with both OFDM and OTFS • Enables linear scaling of performance with MIMO order in all mobility scenarios – Performance is robust against Doppler Cohere Technologies ~ Proprietary & Confidential 3
3GPP ETU-300 Channel: 𝑰(𝒈, 𝒖) vs 𝒊(𝝊, 𝝃) 𝐼(𝑔,𝑢) 𝐼 𝑔, 𝑢 = 𝑇𝑧𝑛𝑞𝑚𝑓𝑑𝑢𝑗𝑑 𝐺𝑝𝑣𝑠𝑗𝑓𝑠 𝑈𝑠𝑏𝑜𝑡𝑔𝑝𝑠𝑛 ℎ(𝜐, 𝜉) 300 Hz Doppler 5 usec Delay Spread ℎ(𝜐, 𝜉) Cohere Technologies ~ Proprietary & Confidential 4
OTFS Channel Model • Transmitted signal is a superposition of QAM symbols, 𝑦 C,D with their component basis functions 𝜚 C,D 𝑢 − 𝜐 P = 𝜚 CQC R ,D 𝑢 𝑇 𝑢 = F 𝑦 C,D 𝜚 C,D 𝑢 𝑒𝜐𝑒𝜉 𝑓 GHID R J 𝜚 C,D 𝑢 = 𝜚 C,DQD R 𝑢 Delay-Doppler Covariance Condition • Received signal 𝑆 𝑢 = F ℎ(𝜐, 𝜉)𝑓 GHIDJ 𝑇 𝑢 − 𝜐 𝑒𝜐𝑒𝜉 OOO OOO = F 𝜚 C,D 𝑢 ℎ 𝜐, 𝜉 ∗ 𝑦 C,D 𝑒𝜐𝑒𝜉 𝑧 C,D = Matched filter output Cohere Technologies ~ Proprietary & Confidential 5
OTFS – The 2D Approach For 5G Orthogonal Time Frequency Space Transmit Receive 𝑧 C,D = ℎ(𝜐,𝜉) ∗ 𝑦 C,D Delay-Doppler (QAM) Domain 𝑦 C,D 𝑧 C,D 2D OTFS 2D OTFS Transform Transform -1 Time-Frequency Domain 𝑌 T,J 𝑍 𝑍 T,J = 𝐼(𝑔, 𝑢) O 𝑌 T,J T,J Multicarrier Multicarrier Filter Bank Filter Bank 𝑢 𝑢 Cohere Technologies ~ Proprietary & Confidential 6 Channel
OTFS Channel Model 𝑦 C,D ∗ ℎ 𝜐,𝜉 = 𝑧 C,D ∗ = 𝜐 𝜐 𝜐 𝜉 𝜉 𝜉 Transmitted OTFS Delay-Doppler Received OTFS QAM Symbols Impulse Response Symbols • A novel, unique and time-independent relationship • Received OTFS symbols in the D-D domain are just the transmitted QAM symbols convolved with the Delay-Doppler impulse response! Cohere Technologies ~ Proprietary & Confidential 7
Delay-Doppler (Information) to Time-Frequency (Signal) 𝑂 J 𝑂 T 𝑂 T Time-Frequency (Signal) 𝑂 J Delay-Doppler (Information) Cohere Technologies ~ Proprietary & Confidential 8
Reference Signals Cohere Technologies ~ Proprietary & Confidential 9
2D OTFS Transform • The 2D Discrete Symplectic Fourier Transform Y _ [\ Y Z [\ 𝑌 𝑙,𝑚 = X X 𝑦 𝑛,𝑜 𝑐 `,] 𝑙, 𝑚 `^P ]^P [GHI(b` Y _ [ c] Y Z ) 𝑐 `,] 𝑙,𝑚 = 𝑓 • The 2D Discrete Inverse Symplectic Fourier Transform Y _ [\ Y Z [\ ∗ 𝑦 𝑛, 𝑜 = X X 𝑌 𝑙, 𝑚 b `,] 𝑙,𝑚 b^P c^P GHI(b` Y _ [ c] Y Z ) ∗ b `,] 𝑙, 𝑚 = 𝑓 Cohere Technologies ~ Proprietary & Confidential 10
OTFS Basis Functions Span Time and Frequency Delay-Doppler Time-Frequency Domain Domain Cohere Technologies ~ Proprietary & Confidential 11
OTFS Architecture & Compatibility QAM Symbols OTFS OTFS Post- OFDM/UFMC OFDM/UFMC Pre-processing processing and Modulator Demodulator Block Equalization Transmitter Receiver • OTFS is a 2D extension of proposed multicarrier modulations (OFDM, FBMC, UFMC, etc.) • OTFS is a 2D extension of CDMA techniques • OTFS is an evolutionary augmentation of OFDM – A pre-processing / post-processing block • Architecturally compatible with LTE Cohere Technologies ~ Proprietary & Confidential 12
OTFS PILOT ARCHITECTURE Cohere Technologies ~ Proprietary & Confidential 13
Data & Pilot Lattices – Time-Frequency Domain • Data Lattice (green): • Pilot Lattice (red): Example – M=1, N=14 – 𝑁Δ𝑔 =pilot frequency spacing; 𝑂Δ𝑢 =pilot time spacing Cohere Technologies ~ Proprietary & Confidential 14
24 Antenna Ports (Ref Signals) - Delay Doppler Grid Cohere Technologies ~ Proprietary & Confidential 15
OTFS Antenna Port Multiplexing • Cohere claims OTFS can multiplex a large number of antenna port reference signals in the Delay-Doppler domain – Depends on maximum delay and Doppler spread Parameter LTE OTFS Type of Reference Signal CRS 𝑂 = 14, 𝑁 = 1 𝑂 = 14, 𝑁 = 1 # of antenna ports (AP) 4 20 88 Total Overhead 14.3% 7.1% 7.1% (Overhead per AP) (3.6% per AP) (0.36% per AP) (0.08% per AP) Supported Channel with ETU-200 ETU-200 ETU-50 no CSI Degradation Cohere Technologies ~ Proprietary & Confidential 16
Pilot Packing Summary • OTFS Delay-Doppler pilot architecture significantly reduces pilot overhead – Supports high Doppler • Flexible pilot tiling for different channel conditions • Ideal for massive MIMO which requires large number of pilots • Enables efficient channel prediction for precoding Cohere Technologies ~ Proprietary & Confidential 17
OTFS PERFORMANCE Cohere Technologies ~ Proprietary & Confidential 18
Spectral Efficiency – TTI = 1ms MIMO Scalability • OTFS maintains Consistent Higher Capacity per Stream Parameter Value SC spacing 15 KHz Number of 600 subcarriers 300 Hz Max Doppler Bandwidth 10 MHz Multipath EVA, ETU model Max Doppler 300 Hz Transmission Time Interval 1 msec length Transmission 2x2, 4x4 scheme MIMO-TM3 FEC Coding Turbo (LTE) TM3 for Precoding OFDM; identity for OTFS Channel Ideal estimation Genie aided Equalization MMSE-SIC & DFE Cohere Technologies ~ Proprietary & Confidential 19
High Mobility & Codeword Length Invariance • OTFS performance unaffected by codeword length • Performance gap increases with high Doppler • Performance improves with increased observation time • Performance gap increases with lower BLER 16-QAM, SISO EVA-200 , 1x1, LTE CQI 9 (16-QAM) EVA-600 , 1x1, LTE CQI 9 (16-QAM) 10 0 10 0 OTFS L=500, 1ms TTI OTFS L=500, 1ms TTI OTFS L=1000 1ms TTI OTFS L=1000 1ms TTI OTFS L=2000 1ms TTI OTFS L=2000 1ms TTI OFDM L=500 1ms TTI OFDM L=500 1ms TTI OFDM L=1000 1ms TTI OFDM L=1000 1ms TTI OFDM L=2000 1ms TTI OFDM L=2000 1ms TTI OTFS L=500 5ms TTI OTFS L=500 5ms TTI OTFS L=1000 5ms TTI OTFS L=1000 5ms TTI OTFS L=2000 5ms TTI OTFS L=2000 5ms TTI 10% OFDM L=500 5ms TTI OFDM L=500 5ms TTI 10 -1 10 -1 OFDM L=1000 5ms TTI OFDM L=1000 5ms TTI OTFS OFDM L=2000 5ms TTI OFDM L=2000 5ms TTI 5 msec BLER BLER OFDM 1% 10 -2 10 -2 200 Hz Doppler 600 Hz Doppler OTFS Spread Spread 1 msec 10 -3 10 -3 5 10 15 20 25 30 5 10 15 20 25 30 SNR (dB) SNR (dB) Cohere Technologies ~ Proprietary & Confidential 20
High Mobility & Codeword Length Invariance • High ICI accentuates performance gap 64-QAM, SISO EVA-600 , 1x1, LTE CQI 13 (64-QAM) EVA-200 , 1x1, LTE CQI 13 (64-QAM) 10 0 10 0 OTFS L=500, 1ms TTI OTFS L=500, 1ms TTI OTFS L=1000 1ms TTI OTFS L=1000 1ms TTI OTFS L=2000 1ms TTI OTFS L=2000 1ms TTI OFDM L=500 1ms TTI OFDM L=500 1ms TTI OFDM L=1000 1ms TTI OFDM L=1000 1ms TTI OFDM L=2000 1ms TTI OFDM L=2000 1ms TTI OTFS L=500 5ms TTI OTFS L=500 5ms TTI OTFS L=1000 5ms TTI OTFS L=1000 5ms TTI OTFS L=2000 5ms TTI OTFS L=2000 5ms TTI 10% OFDM L=500 5ms TTI OFDM L=500 5ms TTI 10 -1 10 -1 OFDM L=1000 5ms TTI OFDM L=1000 5ms TTI OFDM L=2000 5ms TTI OFDM L=2000 5ms TTI BLER BLER 1% 10 -2 10 -2 10 -3 10 -3 15 20 25 30 35 15 20 25 30 35 SNR (dB) SNR (dB) Cohere Technologies ~ Proprietary & Confidential 21
Low vs Medium Spatial correlation – 16QAM • Performance gap increases with medium correlated channels 2.6 dB 1.2 dB Cohere Technologies ~ Proprietary & Confidential 22
Low vs Medium Spatial correlation – 64QAM • Performance gap increases with medium correlated channels 2.8 dB 4.5 dB Cohere Technologies ~ Proprietary & Confidential 23
Ultra High Mobility – OTFS-Turbo vs OFDM-LMMSE • 16-QAM, R=2/3 • Doppler = 444 Hz and 1820 Hz (ICI dominated regime) EVA-444, 1 # 1 10 0 OTFS-Turbo16-QAM, R=2/3 OFDM-LMMSE16-QAM, R=2/3 1.4 dB 10 -1 5.9 dB BLER 10 -2 10 -3 10 -4 10 12 14 16 18 20 22 SNR (dB) Cohere Technologies ~ Proprietary & Confidential 24
Ultra High Mobility – OTFS-Turbo vs OFDM-LMMSE • 16-QAM, R=3/4 • Doppler = 444 Hz and 1820 Hz EVA-444, 1 # 1 10 0 OTFS-Turbo16-QAM, R=3/4 OFDM-LMMSE16-QAM, R=3/4 BLER 2.2 dB 10 -1 10 -2 10 12 14 16 18 20 22 24 26 28 30 SNR (dB) Cohere Technologies ~ Proprietary & Confidential 25
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