Channel Estimation 黃偉傑

Small Scale Fading -- 1 Problem 1: multi-path induces delay spread.

Impulse Response Model of a Multipath Channel A mobile radio channel may be modeled as a linear filter with a time varying impulse response, where the time variation is due to receiver motion in space. The filtering nature of the channel is caused by the summation of amplitudes and delays of the multiple arriving waves at any instant of time.

Channel Impulse Response Due to the different multipath waves which have propagation delays which vary over different spatial locations of the receiver, the impulse response of the linear time invariant channel should be a function of the position of the receiver.

Received Signal

Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems

Reference Sinem Coleri, Mustafa Ergen, Anuj Puri, and Ahmad Bahai, “Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems,” IEEE Trans. On Broadcasting., Vol. 48, No. 3, pp. 223-229, Sep., 2002.

Outline OFDM Overview Pilot Arrangement Channel Estimation @ Block-Type Channel Estimation @ Comb-Type Pilot Interpolation @ Comb-Type

Introduction The channel estimation can be performed by either inserting pilot tones into all of the subcarriers of OFDM symbols with a specific period (block type) or inserting pilot tones into each OFDM symbol (comb type). The block type estimation can be based on Least Square (LS) or Minimum Mean-Square (MMSE). The comb type estimation can be based on LS or MMSE or Least Mean-Square (LMS) then interpolate the channel.

OFDM Overview Divides high-speed serial information signal into multiple lower-speed sub-signals. Transmits simultaneously at different frequencies in parallel. Modulation ( BPSK,QPSK,16QAM, 64QAM). Pilot subcarriers used to prevent frequency and phase shift errors.

Benefits of OFDM Higher data rates Overlap of subcarriers Lower bandwidth than spread spectrum. High spectral efficiency Lower multi-path distortion Usage of cyclic prefix

System Architecture

System Architecture 1 Input to Time Domain 2 Guard Interval 3 Channel 4 Guard Removal 5 Output to Frequency Domain 6 Output Channel ICI AWGN 7 Channel Estimation Estimated Channel

Pilot Arrangement Comb Type Block Type Some sub-carriers are reserved for pilots for each symbol Block Type All sub-carriers reserved for pilots with a specific period

Channel Estimation @Block-Type If ISI is eliminated by the guard interval, we can write where

Channel Estimation @Block-Type If the time domain channel vector h is Gaussian and uncorrelated with the channel noise W, the frequency domain MMSE estimate of h is given by: where [1]

Channel Estimation @Block-Type The LS estimate is represented by : where [1]

Channel Estimation @Block-Type When the channel is slow fading, the channel estimation inside the block can be updated using the decision feedback equalizer at each sub-carrier. For fast fading, the comb-type estimation performs much better. Decision Feedback Equalizer

Channel Estimation @Block-Type

Channel Estimation @ Comb-Type The Np pilot signals uniformly inserted in X(k) according to the following equation: where L= # of Carriers / Np and xp(m) is the mth pilot carrier value. We define {Hp(k) k=0,1,…,Np} as the frequency response of the channel at pilot sub-carriers Yp(k) and Xp(k) are output and input at the kth pilot sub-carrier respectively.

Channel Estimation @ Comb-Type The estimate of the channel at pilot sub-carriers based on LS estimation is given by: Yp(k) and Xp(k) are output and input at the kth pilot sub-carrier respectively. Since LS estimate is susceptible to noise and ICI, MMSE is proposed while compromising complexity.

Channel Estimation @ Comb-Type d0 d4 P-21 d5 d17 P-7 d18 d23 DC d24 d29 P7 d30 d42 P21 d43 d47 -26 -21 -7 7 21 26

Interpolation @ Comb-Type Linear Interpolation Second Order Interpolation Low pass Interpolation Spline Cubic Interpolation Time Domain Interpolation

Interpolation @ Comb-Type Linear Interpolation

Interpolation @ Comb-Type Second Order Interpolation

Interpolation @ Comb-Type Low Pass Interpolation (interp in MATLAB) Insert zeros into the original sequence Low-pass FIR filter while passing original data unchanged Interpolation such that mean-square error between ideal and interpolated values min.

Interpolation @ Comb-Type Spline Cubic Interpolation (spline in MATLAB) [2]

Interpolation @ Comb-Type Spline Cubic Interpolation-cont.

Interpolation @ Comb-Type Time Domain Interpolation The time domain interpolation is a high-resolution interpolation based on zero-padding and DFT/IDFT. We first convert it to time domain by IDFT: The signal is interpolated by transforming the points into N points with the following method: [3]

Interpolation @ Comb-Type Time Domain Interpolation The estimation of the channel at all frequencies is obtained by:

Conclusion OFDM System Block Type Comb Type Modulation Direct or Decision Feedback Comb Type LS or LMS estimation at pilot frequencies Interpolation Techniques Linear Second Order Low Pass Spline Time Domain Modulation BPSK,QPSK,16QAM,64QAM

References [1] Steven M. Kay, “Fundamentals of Statistical Signal Processing Estimation Theory,” Prentice Hall, 1993. [2] Erwin Kreyszig, “Advanced Engineering Mathematics,”John wiley & Sons, 1983. [3] Yuping Zhao, Aiping Huang, “A novel channel estimation method for OFDM mobile communication systems based on pilot signals and transform-domain processing ,” IEEE VTC , Vol. 3, May 1997. [4] Sinem Coleri, Mustafa Ergen, Anuj Puri, and Ahmad Bahai, “Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems,” IEEE transactions on Broadcasting, Vol. 48, No. 3, September 2002.