Self-interference Handling in OFDM Based Wireless Communication Systems Tevfik Yücek yucek@eng.usf.edu University of South Florida Department of Electrical Engineering Tampa, FL, USA (813) 974 759 Tevfik Yücek Page 1 of 26
Agenda Introduction System description Frequency selectivity and delay spread estimation ICI Handling Summary Tevfik Yücek Page 2 of 26
Application areas Military HF radio (195 s-196 s) ADSL DAB, DVB-T Wireless LAN: IEEE 82.11a/g, HyperLAN/2, HiSWANa Strong candidate for IEEE 82.15.3 and 4G cellular Tevfik Yücek Page 3 of 26
Why OFDM? Why OFDM? Resistant to multipath (especially important for high data rate transmission) Offers a natural resistance to narrowband interference Problems Transmitter and receiver (timing) synchronization Frequency synchronization Large peak-to-average power ratio Tevfik Yücek Page 4 of 26
How it works? Data is transmitted in parallel over different sub-carriers Each sub-carrier will observe flat fading More sensitive to frequency errors Tevfik Yücek Page 5 of 26
OFDM system model Processing in the frequency domain Processing in the time domain S P Transmitter Receiver Data IN Data Out MOD DEMOD P P FFT IFFT S S ADD Cyclic Ext Remove Cyclic Ext D/A Lowpass Sampling A/D RF Up Conv. RF Down Conv CHANNEL S P Baseband Signal HF Signal Tevfik Yücek Page 6 of 26
Cyclic prefix extension Cyclicly Extended OFDM Symbol Original OFDM Symbol T g Multipath Componet C Multipath Componet A Multipath Componet B T τ max More than one transmission path between transmitter and receiver Received signal is the sum of many versions of the transmitted signal with varying delay and attenuation A copy of the last part of the OFDM symbol of length equal to or greater than the maximum delay spread of the channel. Tevfik Yücek Page 7 of 26
Agenda Introduction System description Frequency selectivity and delay spread estimation Averaged parameter estimation Instantaneous parameter estimation ICI Handling Summary Tevfik Yücek Page 8 of 26
Motivation & Prior work Applications Adaptation of the length of the cyclic prefix Adaptation of subcarrier bandwidth Adaptation of bandwidth of the channel estimation filters Prior work Using CIR Time domain channel estimation is required Taking IDFT of channel frequency response Using CFR Frequency Domain Level Crossing Rate (LCR) Tevfik Yücek Page 9 of 26
Freq. selectivity & Chan. Freq. Cor. (CFC) 1.9.8 τ rms =τ Ideal Estimated The correlation values obtained over each OFDM symbol Normalized frequency correlation.7.6.5.4.3.2 τ rms =3τ τ rms =2τ These estimates averaged over many OFDM symbols Note that CFC is Fourier transform of PDP.1 5 1 15 2 25 Frequency ( x 1/T OFDM Hz) In coherent OFDM systems often channel frequency response is available CFC estimate is obtained using channel frequency response estimates PDP can be obtained by IDFT, then related parameters can be calculated from PDP (but, computationally complex) Direct relation between time-domain channel parameters and CFC is desired Tevfik Yücek Page 1 of 26
Delay spread estimation K Channel frequency correlation 1.9.8.7.6.5.4 τ rms =2τ τ rms =τ τ rms =.6τ Coherence bandwidth is obtained by using CFC (see figure) Exact relation between coherence bandwidth and RMS delay spread is derived for exponential power delay profile.3 5 1 15 2 25 3 Discrete frequency ( ) 1 2 3 Coherence bandwidth: Range of frequencies over which two frequency components have correlation above K. RMS delay spread is calculated using this relation Algorithm is tested for other power delay profiles as well Tevfik Yücek Page 11 of 26
Delay spread estimation For given K and the corresponding value, RMS delay spread is derived as τ RMS = ln 2 2K2 cos 2π N τ + (2K 2 cos 2π N 2)2 4(1 K 2 ) 2 2(1 K 2 ) Rms delay spread (τ rms ) x τ 4 35 3 25 2 15 1 5 K=.9 K=.5 K=.5 True K=.5 Approximation K=.9 True K=.9 Approximation.2.4.6.8.1.12.14.16 Coherence bandwidth (B c ) x 1/τ Hz. An approximation to above found in the form τ RMS C τ, and gives accurate and less complex results. A bound relationship between B c and τ RMS is given by Fleury (96) as B c cos 1 K 2πτ RMS Tevfik Yücek Page 12 of 26
Simulation results 1 1 Exponential Rectangular Triangular Smulders normalized mean squared error 1 1 1 1 2 1 5 5 1 15 Channel SNR (db) Tevfik Yücek Page 13 of 26
Instantaneous parameters estimation 3 Channel Frequency Responce (CFR) 6 Channel Impulse Responce (CIR) CIR estimate is used for this purpose Magnitude 2 1 Magnitude 4 2 CIR obtained from CFR Magnitude 3 2 1 1 2 3 4 5 6 Subcarrier index Magnitude 2 4 6 Taps 6 4 2 CFR can be sampled to reduce computational complexity 3 1 2 3 4 5 6 Subcarrier index 2 4 6 Taps 6 Nyquist rate for sampling Magnitude 2 1 Magnitude 4 2 τ max fs f 1 1 2 3 4 5 6 Subcarrier index 2 4 6 Taps Useful for estimating for short term parameters τ max : maximum excess delay f : subcarrier spacing S f : sampling interval Tevfik Yücek Page 14 of 26
Results 1.4 1.2 1 S f =1, Sim S f =1, Theo S f =2, Sim S f =2, Theo S f =4, Sim S f =4, Theo S f =5, Sim Mean squared error.8.6.4.2 5 1 15 2 25 Channel SNR (db) Mean squared error is increasing as sampling frequency is decreasing. However, computational complexity is reducing. Tevfik Yücek Page 15 of 26
Agenda Introduction System description Frequency selectivity and delay spread estimation ICI Handling ICI Cancellation ICI Cancellation based channel estimation Summary Tevfik Yücek Page 16 of 26
Motivation Loss of orthogonality among subcarriers causes inter-carrier interference (ICI). Frequency offset, Doppler shift, or phase noise. ICI affects both channel estimation and detection. Previous channel estimation algorithms treat ICI as part of the additive noise. Tevfik Yücek Page 17 of 26
ICI cancellation using AR modeling ICI is colored in nature ICI is whitened by fitting an AR process and filtering 1 15 ICI signal AR 1 AR 2 AR 15 Received = Desired + ICI + Noise 2 Desired signal is estimated PSD (db) 25 3 ICI+Noise is modeled as AR process and whitened 35 4 1.8.6.4.2.2.4.6.8 1 Frequency (Hz) x 1 7 Tevfik Yücek Page 18 of 26
ICI cancellation based channel estimation Prior work Channel estimation Least-squares (LS) Minimum mean-square error (MMSE) Maximum-Likelihood (ML) Channel estimation & ICI Linear minimum mean-square error (LMMSE) Time domain filtering to suppress ICI Tevfik Yücek Page 19 of 26
Basic idea y = S ɛp Xh + n (S ɛh X) 1 y = (S ɛh X) 1 S ɛp Xh + (S ɛh X) 1 n h ɛh = X 1 S 1 ɛh S ɛp }{{} S ɛ p ɛ h =S ɛ r Xh + n ɛh 1 Norm. Freq. Offset =.1 1 Norm. Freq. Offset =.3 Amplitude of coefficients.8.6.4.2 Amplitude of coefficients.8.6.4.2 1 2 3 4 5 6 1 2 3 4 5 6 Carrier index Carrier index Tevfik Yücek Page 2 of 26
Basic idea Properties of S ɛp S H S = I ( Unitary matrix). S 1 = S H. S ɛ1 S ɛ2 = S ɛ1 +ɛ 2 S ɛ = S H ɛ Circulant matrix (rows and columns) Selection method for best hypothesis Channel frequency correlation decreases as frequency offset increases. R hɛh (τ) = R h () + σ2 n σ 2 s τ = R h (τ) S ɛr () 2 τ S ɛr () = sin (πɛ r ) N sin (πɛ r /N) Only first correlation value, R hɛh (1), is used. Tevfik Yücek Page 21 of 26
Searching algorithm Binary search is used to decrease the computational complexity. Choose the max and min frequency offset hypothesis. Find corresponding channel correlation values. Move point with smaller correlation to the middle point between previous points. Repeat for a pre-defined number of times. We only need the interference matrices only for ɛ max, ɛ max /2, ɛ max /4, ɛ max /8,... ɛ max can be chosen adaptively. Tevfik Yücek Page 22 of 26
Reducing complexity In S, most of the energy is concentrated around the diagonal, i.e. interference is mostly due to neighboring subcarriers. 1 Norm. Freq. Offset =.1 1 Norm. Freq. Offset =.3 Amplitude of coefficients.8.6.4.2 Amplitude of coefficients.8.6.4.2 1 2 3 4 5 6 Carrier index 1 2 3 4 5 6 Carrier index 1 1 Amplitude of coefficients.8.6.4.2 Amplitude of coefficients.8.6.4.2 1 2 3 4 5 6 Carrier index 1 2 3 4 5 6 Carrier index Tevfik Yücek Page 23 of 26
Results OFDM system with 64 subcarriers 6-tap symbol-spaced CIR with exponential PDP 8 iterations used in search alg. (8 + 1 = 9 hypotheses). Reduced matrix considers only 32 neighboring subcarriers 1 3 Full Matrix Reduced Matrix CR Bound 1 Least Squares Method Proposed Method 1 4 1 1 Mean squared error 1 5 Mean squared error 1 2 1 6 1 7 5 1 15 2 25 3 35 SNR (db) 1 3 5 1 15 2 25 3 35 SNR (db) Tevfik Yücek Page 24 of 26
Summary Average RMS delay spread of the channel is calculated from the channel frequency correlation estimate. Exact relation between coherence bandwidth and RMS delay spread is derived Time domain CIR is obtained by taking IFFT of the sampled CFR. The optimal sampling rate for sampling the channel response is investigated and simulation results for different sampling rates are given. An ICI cancellation method based on AR modeling is explained. A novel frequency-domain channel estimator which mitigates the effects of ICI by jointly finding the frequency offset and CFR is described. Tevfik Yücek Page 25 of 26
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System model An OFDM based system is considered x m (n) = y m (n) = L 1 l= N 1 k= S m (k)e j2πnk/n x m (n l)h m (l)+z m (n) Y m (k) = S m (k)h m (k) + Z m (k) Ĥ m (k) = Y m(k) S m (k) = H m(k)+w m (k) S m : Symbols to be transmitted x m : Transmitted signal h m : Channel impulse response y m : Received signal (time) z m : Noise (time) Y m : Received signal (Frequency) H m : Channel frequency response Z m : Noise in frequency domain Ĥ m : Channel frequency response estimate Tevfik Yücek Page 28 of 26
Effect of impairments (Long Term Est.) Additive noise: effect of noise on the CFC appears as a DC term whose magnitude depends on noise variance (this can be removed by noise variance estimator) φ H ( ) = φ H ( ) if φ H () + σ 2 w if =. Constant Phase Shift in Channel: constant phase shift does not effect proposed algorithm as it does not change the correlation H m = H m e jφ. φ H ( ) = E m,k { H m(k) H m (k + )} = φ H ( ), Tevfik Yücek Page 29 of 26
Effect of impairments (Long Term Est.) Carrier-dependent Phase Shift in Channel: It causes a constant phase shift in the CFC. However, this is not a problem since we are using the magnitude of CFC. 2πkθ j H m (k) = H m (k)e N, φ H ( ) = E m,k { H m(k) H m (k + )} 2π θ j = φ H ( )e N. Tevfik Yücek Page 3 of 26
Tested PDPs.35 a) Exponential power delay profile.2 b) Smulders power delay profile Normalized power.3.25.2.15.1.5 5 1 15 2 Taps (x τ sec) Normalized power.15.1.5 5 1 15 2 Taps (x τ sec).14 d) Triangular power delay profile.7 c) Rectangular power delay profile.12.6.1.8.6.4.2 5 1 15 2 Taps (x τ sec) Normalized power.5.4.3.2.1 5 1 15 2 Taps (x τ sec) Tevfik Yücek Page 31 of 26
Effect of impairments (Short Term Est.) Additive Noise : When IDFT is taken the power of noise decreases within a desired window since signals energy is concentrated on CIR while noise energy is spread. Constant Phase Shift in Channel : Not a problem since the time domain statistics depends on the magnitude of CIR which is not changing. h m (l) = h m (l)e jφ Carrier-dependent Phase Shift in Channel : Biases time domain parameter estimates, by causing additional ISI which is not due to medium. Requires accurate timing and synchronization to reduce this effect. Tevfik Yücek Page 32 of 26
System model y : vector of received symbols y = S ɛp Xh + n X : diagonal matrix with the transmitted symbols on its diagonal h : vector representing the CFR to be estimated n : AWGN vector with mean zero and variance of σ 2 n S ɛp : interference (crosstalk) matrix that represents the leakage between subcarriers, i.e. ICI. Elements of S ɛp can be found using S ɛp (m, n) = sin π(m n + ɛ p) N 1 N sin π N (m n + ɛ p) ejπ N (m n+ɛ p) Tevfik Yücek Page 33 of 26