Mult lticarrie ier Underw rwater Acoustic Communication Gilad - PowerPoint PPT Presentation

Andrew and Erna Viterbi Faculty of Electrical Engineering Tim ime Vary rying Carrie ier Frequency Offset Estimation in in Mult lticarrie ier Underw rwater Acoustic Communication Gilad Avrashi Supervised by Prof. Israel Cohen and Dr. Alon Amar

Contents • Introduction • Signal Space Estimation • Pilot Design Optimization • Time-Varying CFO Estimation • Conclusions 2/

Introduction

Why underwater communications? Pipeline Inspection Mine Detection Submarines Divers Autonomous Underwater Vehicles Manned Vehicles

Challenges of f Underw rwater Communications • EM signals are attenuated quickly in the UW medium → pressure waves (sound) have been chosen for long range communications • Sound waves characteristics: • Propagation speed: 1500 m/s (times 200,000 slower than EM waves!) • Frequency dependent losses • Frequency related ambient noise

Orthogonal Frequency Div ivision Mult ltiplexing • The comm. bandwidth is divided into sub-carriers • Each subcarrier is modulated to carry a digital communication symbol • Pros: • Easy to implement using FFT operations 𝐿Δ𝑔 = 𝑋 No Doppler scaling 1.5 • Robustness to frequency selective channels 1 • Simple channel equalizer Magnitude 0.5 • Cons: 0 • Very sensitive to frequency shifts -0.5 2.095 2.1 2.105 2.11 • High peak-to-average power ratio (PAPR) frequency [Hz] 4 x 10 Orthogonality is achieved by Δ𝑔 = 1 𝑈

OFDM modulation The baseband OFDM signal: 𝐿−1 𝐿−1 𝐿−1 = 𝑕[𝑜] 𝑡 𝑙 𝑓 𝑘2𝜌 𝑜 𝑡 𝑙 𝑓 𝑘2𝜌 𝑜 𝑘2𝜌𝑜𝑙 𝑋 𝑙Δ𝑔 = 𝑕[𝑜] ෍ 𝑋 𝑔 𝑙 = 𝑕[𝑜] ෍ 𝑦 𝑜 = 𝑕[𝑜] ෍ 𝑡 𝑙 𝑓 IDFT{𝑡 𝑙 } 𝐿 𝐿 𝑙=0 𝑙=0 𝑙=0 𝐭 ∈ ℂ 𝐿×1 𝐼 𝐭 ∈ ℂ 𝐿×1 𝐼 𝐭 ∈ ℂ 𝐿+𝑀×1 𝐆 𝐿 𝐲 = 𝐔 𝑎𝑄 𝐆 𝐿 Information bits QPSK IFFT Zero Padding Mapping 𝐜 ∈ {0,1} 2𝐿×1 quadrature In-phase Upsampling & Modulation

Sea Tria ial l OFDM Sig ignal ℎ 𝑜, 𝜐 𝑦[𝑜] + 𝑧[𝑜] Recording from sea trial in the Mediterranean, December 2016 𝑤[𝑜] 𝑀 -tap CIR

Research Goal Develop a carrier frequency offset estimator for underwater acoustic OFDM modems. The solution is required to be computationally efficient and practical for the underwater acoustic channel. 9/

Mult lticarrier UAC Effects Transmitted block zero padding frequency time

Mult lticarrier UAC Effects Transmitted block Received block zero padding frequency Doppler scaling OFDM blocks time

Mult lticarrier UAC Effects Transmitted block Received block zero padding frequency Doppler scaling 𝜗Δ𝑔 OFDM blocks time

Received Sig ignal Model Li et al. ‘ 08 𝑘2𝜌𝜗0𝑜 𝑧 𝑜 = 𝑓 ℎ 𝑜 ∗ 𝑦 𝑜 + 𝑤[𝑜] or in matrix form 𝐳 = 𝚫 𝐿 𝜗 0 ด 𝐈𝐲 + 𝐰 𝐿 𝐴 packet block by block Doppler Channel Sync. CFO est. Demod. rescaling equalizer

Radio Frequency Approaches Training blocks with periodic Block to block pilot signal cross- characteristics correlation (Classen & Meyer ‘ 94) (Schmidl & Cox ‘ 97) Estimate CFO Estimate CFO Apply Estimation In UAC – CFO varies between adjacent blocks

Ƹ UAC Approaches Null Carriers Pilot aided Minimum variance Maximum power (Li et al. ‘ 08) (Li et al. ‘ 06) Hypothesized 𝜗 𝑗 Δ𝑔 extract frequency max 𝐷(𝜗 𝑗 ) 𝜗 single block pilots\ shift 𝜗 nulls Requires exhaustive grid search

Pil ilot Based Estim imation G carriers 𝐿−1 𝑦 𝑜 = 1 𝑘2𝜌𝑜𝑙 ෍ 𝑡 𝑙 𝑓 𝐿 𝐿 𝑙=0

Pil ilot Based Estim imation 𝐿−𝑅 data signal ~𝒪 0, 𝑅 1 𝑘2𝜌𝑜𝑙 G carriers ෍ 𝑡 𝑙 𝑓 𝐿 𝐿 𝑙∈𝑇 𝐸 𝐿−1 𝑦 𝑜 = 1 𝑘2𝜌𝑜𝑙 ෍ 𝑡 𝑙 𝑓 = 𝐿 𝐿 𝑙=0

Pil ilot Based Estim imation 𝐿−𝑅 data signal ~𝒪 0, 𝑅 1 𝑘2𝜌𝑜𝑙 G carriers ෍ 𝑡 𝑙 𝑓 𝐿 𝐿 𝑙∈𝑇 𝐸 𝐿−1 𝑦 𝑜 = 1 𝑘2𝜌𝑜𝑙 + ෍ 𝑡 𝑙 𝑓 = 𝐿 𝑅−1 𝐿 𝑘2𝜌𝑜𝑟 1 𝑙=0 ෍ 𝑡 𝑟𝐻 𝑓 𝑅 𝐿 𝑟=0 pilot signal 𝑅 -periodic Idea : Use correlation between periods of the pilot signal Problem : Low “ SNR ” – Pilot to Data Ratio (PDR) Solution : Design pilot signal with “ Good ” auto-correlation

ǁ Best auto correla latio ion: id identic ical pil ilots Amar, Avrashi, Stojanovic ‘ 16 𝑅−1 𝑘2𝜌𝑜𝑟 𝑡 𝑜 = 1 + 1 𝑘2𝜌𝑜𝑙 𝑅 ෍ 𝑣𝑓 ෍ 𝑡 𝑙 𝑓 𝐿 𝐿 𝐿 𝑟=0 𝑙∈𝑇 𝐸 Q samples

Exploiting In Inter-Segment Correlations 𝑘2𝜌𝜗 0 𝑜 𝑧 𝑜 = 𝑓 ℎ 𝑜 ∗ 𝑦 𝑜 𝐿 𝑨[𝑜] 𝑕 ′ 𝑕 𝐒 𝑕 ′ −𝑕 𝐼 𝐳 𝑕 ′ = 𝑓 −𝑘2𝜌 𝐻 𝜗 0 𝐼 𝐴 𝑕 ′ 𝐳 𝑕 𝐴 𝑕 𝛽(𝜗 0 )

Eig igen Valu lue Decomposition The cost function in matrix formulation 𝜗 that minimizes (maximizes) We look for Ƹ 𝑚 = 𝛃(𝜗) 𝐼 𝐒𝛃(𝜗) 𝐒 Under two constraints: 1 1 • 𝛽 1 𝛃 = 1 𝛽 −1 𝛽 −(𝐻−1) 𝐻 1 ⋯ ⋮ • arg(𝛃) ∝ 𝜗 𝛽 𝐻−1

Ƹ EVD estim imator 𝛃 ෝ 𝐳 𝜗 Min. Var. LS 𝛃] ≈ − 2𝜌 arg[ෝ 𝛃 𝛃 𝐼 𝐒𝛃 s. t. 𝛃 𝐼 𝛃 = 1 𝐻 𝐡𝜗 min 𝐻−1 𝑕 arg ෝ σ 𝑕=0 𝛃 𝜗 = − 𝐻 𝑕 ➔ ෝ ➔ Ƹ 𝛃 = 𝐖 min (𝐒) 𝐻−1 𝑕 2 2𝜌 σ 𝑕=0 Decompose 𝐒 → find the eigenvector of the smallest EV → extract ො 𝝑

Research objectives • The EVD-based estimator has two drawbacks: • High PAPR • Requires constant CFO during the block • Our goal : Propose a CFO estimator for UAC with the following characteristics: • Low complexity • Negligible PAPR • Adjustable for time-varying channels

Signal Space Estimation

Two sid ides of f the same coin in 𝐼 𝐴 𝑕 ′ 𝐴 𝑕 Uncorrelated Correlated array processing interpretation Steering 𝜗 in the noise \ signal space to achieve lowest \ highest SNR

Exploiting In Inter-Segment Correlations 𝑘2𝜌𝜗 0 𝑜 𝑧 𝑜 = 𝑓 ℎ 𝑜 ∗ 𝑦 𝑜 𝐿 𝑨[𝑜] 𝑕 ′ 𝑕 𝐒 𝑕 ′ −𝑕 𝐼 𝐳 𝑕 ′ = 𝑓 −𝑘2𝜌 𝐻 𝜗 0 𝐼 𝐴 𝑕 ′ 𝐳 𝑕 𝐴 𝑕 𝛽(𝜗 0 )

Ƹ EVD in in Sig ignal Space 𝛃 s ෝ 𝐳 s 𝜗 s Max. Var. LS 𝛃] ≈ − 2𝜌 arg[ෝ 𝛃 𝐼 𝐒 s 𝛃 s. t. 𝛃 𝐼 𝛃 = 1 𝐻 𝐡𝜗 max 𝛃 𝐻−1 𝑕 arg ෝ σ 𝑕=0 𝛃 𝜗 = − 𝐻 𝑕 ➔ ෝ ➔ Ƹ 𝛃 s = 𝐖 max (𝐒 s ) 𝐻−1 𝑕 2 2𝜌 σ 𝑕=0 Decompose 𝐒 s → find the eigenvector of the largest EV → extract ො 𝝑

Ƹ Ƹ Ƹ Combined LS estim imate 𝛃 s ෝ Max. 𝐳 s Var. DR 𝜗 c LS ෝ 𝛃 n Min. Var. 𝐳 n DR 𝜗 c = 𝛾 Ƹ 𝜗 n + 1 − 𝛾 𝜗 s , 0 ≤ 𝛾 ≤ 1

Ƹ Generali lized EVD 𝐳 s 𝛃 g (𝜗) ෝ 𝜗 g GEVD LS 𝐳 n 𝛃 𝐼 𝐒 s 𝛃 s. t. 𝛃 𝐼 𝛃 = 1 max 𝛃 𝐼 𝐒 n 𝛃 𝛃 ➔ ෝ −1 𝐒 s 𝛃 g = 𝐖 max 𝐒 n −1 𝐒 s → find the eigenvector of the largest EV → extract ො Decompose 𝐒 n 𝝑

Computational Complexity Method Complexity Grid Search 𝒫(𝐿 𝐿) 𝒫(𝐻 2 (𝑅 − 𝑀)) = 𝒫 𝐿𝐻 Noise Space EVD 𝒫(𝐻 2 𝑀) Signal Space EVD 𝒫(𝐻 2 max{𝑅 − 𝑀, 𝑀}) Combined LS 𝒫(𝐻 2 max{𝑅 − 𝑀, 𝑀}) Generalized EVD

RMSE vs SNR Long Delay Spread Short Delay Spread CFO = 0.2Δ𝑔 G=8 K=2048 L=100 L=50

Effect of f Dela lay Spread Q L

Pool Tria ial

Pilot Design Optimization

PDR and PAPR tradeoff Low PDR High PDR Random Pilots Identical Pilots max |𝑦[𝑜]| 2 Low PAPR High PAPR PAPR = 1 𝐿 |𝑦[𝑜]| 2 𝐿 σ 𝑜=1 pilot level pilot level data level data level data level pilot level

Proposed pil ilot design formulation 1 𝜔[𝑜] = 𝑅 IDFT{𝜚[𝑙] } Pilot signal (one period): 𝜚 𝑙 = 𝑡 𝑟𝐻 = 𝑓 𝑘𝜚 𝑙 Pilot tones: Unit amplitude Known envelope 1 , 𝑜 < 𝑀 𝑞 Find the phases 𝜚 𝑙 𝑀 𝑞 𝑥 𝑀 𝑞 𝑜 = ൞ 0, 𝑜 ≥ 𝑀 𝑞 2 𝐼 𝛠 Phase retrieval problem: min 𝐗 𝑀 𝑞 𝛚 − 𝐆 𝑅 𝛚,𝛠

Pil ilot design – generalized GSA algorithm Initialize Initialize 𝛠 0 = rand 𝑅, 1 , 𝐾 = ∞ while while 𝐾 > 𝜃 do do 𝛚 𝑗 = 𝑓 𝑘∢ IFFT{𝛠 𝑗−1 } time domain pilot signal 𝛠 𝑗 = 𝑓 𝑘∢ FFT{𝐗𝛚 𝑗 } pilot tones |IFFT 𝛠 𝑗 | − 𝐱 2 𝜁 = envelope error norm max |IFFT 𝛠 𝑗 | 2 𝑞 = PAPR 1 𝑅 |IFFT 𝛠 𝑗 | 2 𝑅 σ 𝑜=1 𝐾 = 𝛽𝜁 + 𝛾𝑞 end while end while return return 𝛠 𝑗

Sim imula lation results

Time-Varying CFO Estimation