Parameterized Cancellation of Partial-Band Partial-Block-Duration Interference for Underwater Acoustic OFDM Zhaohui Wang † , Shengli Zhou † , Josko Catipovic ‡ , and Peter Willett † † Department of Electrical and Computer Engineering University of Connecticut ‡ Naval Undersea Warfare Center WUWNet’11 Seattle December 1-2, 2011 Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 1 / 22
Outline Motivation with a story 1 Interference parameterization 2 The proposed OFDM receiver for interference cancellation 3 Simulation results 4 Experimental results 5 Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 2 / 22
An Interesting Story Behind This Work Dr. Catipovic to Dr. Zhou: I’ve collected some OFDM data in the AUTEC. Can you decode it? Dr. Zhou to Zhaohui: Can you have a try? Zhaohui to Dr. Zhou: Sure. Zhaohui to Dr. Zhou: Most files can be decoded, but several others cannot. Dr. Zhou to Zhaohui: What’s the reason? Zhaohui to Dr. Zhou: Here it is, the unknown waveform of 45 ms, 2 kHz • the time-frequency spectrum • the time domain waveform 0.03 Interference Interference 0.02 Passband signal 0.01 0 −0.01 −0.02 HFM Preamble ZP−OFDM Blocks −0.03 0 2 4 6 8 10 Time [s] Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 3 / 22
An Interesting Story Behind This Work (Cont.) Dr. Catipovic: These could be the interference from sonar users. Dr. Zhou to Zhaohui: Can you do an investigation on the existing interference cancellation methods? Zhaohui to Dr. Zhou: Sure. ◮ Limited research on interference cancellation in UWA communications ◮ External interference cancellation in radio communications ⋆ Narrowband interference with large time -duration ⋆ Impulsive interference with large bandwidth Zhaohui to Dr. Zhou: These methods do not apply to this kind of partial-band (e.g., 2 kHz vs 5 kHz) partial-block-duration (e.g., 45 ms vs 150 ms) interference Dr. Zhou to Zhaohui: Hmm..., let’s develop our own method. After a couple of weeks’ thinking and discussions, on a sunny morning, ⇒ A parameterized interference cancellation approach! ¨ ⌣ ¨ ⌣ ¨ ⌣ Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 4 / 22
Generality of the Proposed Method During the development of this work, we realized that... The method applies as long as the interference can be parameterized. External interference, e.g., ◮ Unintentional interference, e.g. interference from sonar operations ◮ Interference from marine mammals ◮ Dumb malicious jamming, as you’ll see later Internal interference, e.g., ◮ Interblock interference ◮ Multi -access interference ⇒ How does it work? Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 5 / 22
Interference Parameterization Assume the prior of the interference time -duration T I and frequency band B I = [ f Ic − B I / 2 , f Ic + B I / 2 ] , and define N I = ⌈ B I T I ⌉ The baseband representation of the interference by N I unknowns: { c l } N I / 2 − 1 ∞ c l e j 2 π l T I t ≈ c l e j 2 π l T I t , t ∈ [ 0 , T I ] , I ( t ) = � � l = −∞ l = − N I / 2 The passband representation of the interference, ¯ f l := f Ic + l / T I N I / 2 − 1 c l e j 2 π ¯ I ( t ) = 2Re f l t t ∈ [ 0 , T I ] ˜ � , l = − N I / 2 Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 6 / 22
Impact of Interference on OFDM Illustration of interference in OFDM in time domain ~ t y ( ) t 0 T T T T I I g τ I : relative delay of the interference to the start of the OFDM block Illustration of interference in OFDM in frequency domain B I ( M I subcarriers) f f f f f K / 2 1 K / 2 m Ic c N I samples f f f N / 2 l / N 2 1 I I Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 7 / 22
Modeling Interference for Block -by-Block OFDM Receiver For interference ˜ I ( t − τ I ) , frequency component at the m th subcarrier N I / 2 − 1 � T + T g ν [ m ] = 1 I ( t − τ I ) e − j 2 π f m t dt = e − j 2 π f m τ I ˜ � u l ρ m , l T 0 l = − N I / 2 ρ m , l = sin ( π ( f m − ¯ f l ) T I ) with e − j π ( f m − ¯ f l ) T I u l = T I / Tc l , π ( f m − ¯ f l ) T I � ν [ − K / 2 ] , · · · , ν [ K / 2 − 1 ] � T A compact representation: ν = ν = Λ ( τ I ) Γ I u where, Λ ( τ I ) : a K × K diagonal matrix, Γ I : a matrix of size K × N I , and u : a column vector of length N I , with � T [ Λ ( τ I )] m , m = e − j 2 π f m τ I , [ Γ I ] m , l = ρ m , l , u = u − N I / 2 , · · · , u N I / 2 − 1 � Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 8 / 22
OFDM System Model for Interference Cancellation The input -output relationship in the frequency domain z = Hs + Λ ( τ I ) Γ I u + w Unknowns to estimate: ◮ Channel matrix: H ◮ Information symbols in s ◮ Interference vector: u ◮ Interference relative delay: τ I in Λ ( τ I ) What we have: ◮ Frequency measurements: z ◮ Pilot symbols in s Receiver structure ◮ Joint estimation of all the unknowns using the Bayesian method: high computational complexity ◮ Iterative receiver structure: to estimate the unknowns iteratively Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 9 / 22
An OFDM Receiver for Interference Cancellation z = Hs + Λ ( τ I ) Γ I u + w Preprocessing, i = 0 Initialization: with interference Initialization prewhitening, to get an initial i = i + 1 estimate of H and s GLRT Interference Detection GLRT detector: to estimate the interference parameter Yes Interference and detect the presence of Present? No the interference Interference Channel Estimation Noise Subtraction Conventional OFDM receiver: Variance Update channel estimation, ICI Noise Variance Update equalization and nonbinary ICI Equalization LDPC decoding Nonbinary LDPC Stopping criteria: once the Decoding parity check condition of the No nonbinary LDPC decoder is Success or i = i max ? satisfied, or i reaches i max , the Yes Decisions iteration stops. Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 10 / 22
Interference Detection and Estimation H and ˆ s from the initialization or the last iteration With ˆ Define Θ as a selector matrix of size M I × K , with M I = ⌈ B I / ∆ f ⌉ The interference frequency components within the frequency band z = Θ ( z − ˆ H ˆ s ) = B ( τ I ) u + ¯ w , ¯ where B ( τ I ) = ΘΛ ( τ I ) Γ , w = Θ w + Θ (ˆ H ˆ s − Hs ) ¯ w ∼ CN ( 0 , σ 2 B I I M I ) Assume ¯ H 0 : absence of interference H 1 : presence of interference Generalized log -likelihood ratio test (GLRT) statistic z | τ I , u , H 1 ) { τ I , u } ln f (¯ z ) = max L (¯ z |H 0 ) f (¯ 1 z H B ( τ I ) u + u H B H ( τ I )¯ z − u H B H ( τ I ) B ( τ I ) u = max � ¯ � ≷ Γ th σ 2 { τ I , u } B I Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 11 / 22
Interference Detection and Estimation Define an objective function z H B ( τ I ) u + u H B H ( τ I )¯ z − u H B H ( τ I ) B ( τ I ) u J = ¯ Setting the derivative ∇ J u to zero yields � − 1 B H ( τ I )¯ u = B H ( τ I ) B ( τ I ) z , � ˆ The estimate of τ I : obtained using 1 -D grid search � − 1 B H ( τ I )¯ τ I = arg max z H B ( τ I ) B H ( τ I ) B ( τ I ) z , � ˆ ¯ τ I GLRT statistic 1 u H B H (ˆ z ) = τ I ) B (ˆ u ≷ Γ th L (¯ ˆ τ I )ˆ σ 2 B I Γ th : determined based on the probability of detection or the probability of false alarm Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 12 / 22
Conventional OFDM Receiver Processing If the presence of the interference is declared, the desired OFDM components z = z − Λ (ˆ u = Hs + ˇ w , ˇ τ I ) Γ I ˆ Sparse channel estimator: to estimate H LMMSE equalizer: to estimate information symbols in s Nonbinary LDPC decoder: to recover information bits Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 13 / 22
Simulation Setup OFDM Parameters: Channel profile: Center frequency: f c = 13 kHz The sparse channel: Bandwidth: B = 9 . 77 kHz 10 discrete paths Number of subcarriers: Inter-arrival time of paths: exponentially K = 1024 , including 672 data distributed with the mean 1 ms subcarriers, 256 pilot Amplitudes of paths: decay exponentially, subcarriers, and 96 null with the difference at the beginning and subcarriers end of the guard interval 20 dB Symbol duration: T = 104 . 86 ms The Doppler rate of each path: Guard interval: T g = 24 . 6 ms a zero mean uniform distribution with the A rate -1/2 nonbinary LDPC code std σ v f c / c , with σ v : std of platform speed; and a 16-QAM constellation are c : sound speed in water 1500 m/s. adopted. Z. Wang, S. Zhou, J. Catipovic, and P . Willett () Interference Cancellation for OFDM WUWNet’11 14 / 22
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