A Multistage Channel Estimation And Ici Reduction Method For

TU3A.4

A Multistage Channel Estimation and ICI Reduction Method for OFDM Systems in Doubly Dispersive Channels Ali Ramadan Ali, Ali Aassie Ali, and Abbas S. Omar Chair of Microwave and Communication Engineering, University of Magdeburg, P.O. BOX 4120, Magdeburg D-39106, Germany {ramadan|ali}@iesk.et.uni-magdeburg.de, [email protected]

Abstract — Rapidly time-varying channels degrade the performance of the orthogonal frequency division multiplexing OFDM due to loosing the orthogonality between the sub-carriers resulting in Inter-CarrierInterference ICI and necessitate estimating the complete elements of the channel matrix. In this paper a low complexity multistage pilot-based channel estimator is introduced, in which, the time delays and number of paths are first estimated using a super resolution technique. The main diagonal of the channel matrix is estimated via Wiener filtering. The whole channel matrix which is used for ICI cancellation is built by applying a linear interpolation to approximate the channel time variation between three successive symbols.

In an OFDM system, the input bit stream is first modulated using a common modulation scheme like QAM or PSK before applying the IFFT operation as shown in Fig. 1. P/S

Coding & Interleaving

IFFT

Bit stream

+GI

D/A

RF front end Channel

Pilots AWGN

S/P

FFT

Decoding & Deinterleaving

Channel estimation& Equalization

Bit stream

P/S &QAM Demap.

The entire channel of OFDM system is divided into many mathematically orthogonal sub-carriers which are transmitted simultaneously using the inverse fast Fourier transform (IFFT). Transmitting many subcarriers simultaneously increases the symbol duration and makes OFDM being the most practical technique for combating inter-symbol-interference (ISI) caused by fading channels. ISI can be completely eliminated by adding a guard interval between symbols longer than the channel impulse response. The guard interval can be performed by extracting a portion of an OFDM symbol at the end and append it to the beginning, this keeps the orthogonality and enables circular convolution with the channel. This robustness against frequency fading could not be found in case of time-variation environment, so that OFDM is often considered sensitive to frequency offset and phase noise and may experiences significant inter-carrier-interference (ICI) because of loosing the orthogonality between the sub-carriers caused by Doppler effect. The performance degradation due to ICI becomes significant as the number of carriers, carrier frequency, and vehicle velocity increase [1]. One way of canceling ICI is based on estimating the whole channel matrix using Wiener filtering [2]. Such an estimator requires a Wiener filter and a multiplication operation for each element of the channel matrix and also matrix inversion, which increases the complexity of the receiver for large number of sub-carriers. To reduce the complexity, only the main diagonal of the channel matrix is first estimated using Wiener filtering. In order to cancel the effect of ICI, a linear approximation approach is applied as described in [3-5].

II. SYSTEM MODEL

QAM Map.& S/P

I. INTRODUCTION

Moreover, in [2], the knowledge of the channel parameters e.g. (number of paths, and time delays) had been assumed in order to optimize the Wiener filter. Such parameters will be estimated in this contribution using a super resolution technique.

-GI

A/D

RF front end

Fig. 1. Baseband block diagram for an OFDM system

The transmitted OFDM symbol can be written as N −1

xn = ∑ S m e

j

2πnm N

0 ≤ n ≤ N − 1,

(1)

m =0

where S m is the QAM word at the m th sub-carrier and N is the number of sub-carriers. If we assume the guard interval to be longer than the channel impulse response, the transmitted symbols will convolve circularly with the channel impulse response [3]. The received symbol can be expressed as L

y n = ∑ hn(l ) x n −τ l + θ n ,

(2)

l =1

where hn and τ l are the complex random variable and the corresponding tap delay, respectively that characterize the l th path of the multipath channel , and θ n describes the additive white Gaussian noise at sample n . The frequency domain signal at the receiver becomes then (l )

1 Yk = N

N −1

L

∑ (∑ h x n−τ l + θ n )e n= 0

(l ) n

−j

2πnk N

3 shows the estimated impulse response of a 4-path (3) channel. The third and fourth paths are overlapped in case of using the conventional FFT method. With the same bandwidth, they are clearly separated using the Root-MUSIC method.

.

l =1

Equation (3) can be simplified [1] to N −1

Yk = S k H k , k + ∑ S m H m , k + Θ k .

(4)

0.7

m=0 k≠m

FFT method Root-MUSIC

0.6

 

0.5

Equation (4) in matrix form can be written as:

y = Hs + θ ,

(5)

Amplitude

ICI

0.4

0.3

0.2

where H is the channel matrix and θ is the frequency domain noise vector. In equation (4), the main diagonal of H represents the average of the time varying channel weights for each sub-carrier, which will be estimated using Wiener filtering, while other elements represent the ICI effect, which will be estimated using a linear approximation method. Fig. 2 shows the proposed estimation and equalization stages that will be discussed in the subsequent sections.

y Super resolution Estimating the paths

Wiener Filtering

sˆ

ˆ -1 y H Save 3 symbols

Equalization

Estimating chanel matrix

Channel tracking

Fig. 2. Estimation and equalization stages

0.1

0

0

0.2

0.4

0.6 0.8 Delay (sec)

1

1.2

1.4 -3

x 10

Fig. 3. Estimated channel impulse response

IV. CHANNEL TRACKING We will model the channel using a wide-sense stationary uncorrelated scattering WSSUS model [7], and the path gains that need to be tracked will be assumed WSS stochastic process. The pilots are distributed among the transmitted data in order to track the random amplitude of the channel gains. Wiener filter can be designed according to linear minimum squared error (MMSE) criteria [2]. The main diagonal of the channel matrix H is estimated by filtering the received symbols.

Hˆ k , k = w Hk ,k y ,

III. TIME DELAY ESTIMATION

(7)

In order to properly estimate the time delays and the where w k , k is the Wiener filter vector corresponding number of paths, pure training symbols (pilots) s p are to the element ( k, k ) of the channel matrix. Wiener filter first transmitted as a starting phase. The channel is optimized using MMSE criterion frequency response on pilots can be calculated as 2 follows MSE = E H − w H y = min . (8)

{

ˆ = diag (s ) −1 y , H p p p

(6)

( ) is a diagonal matrix whose diagonal

where diag s p

k ,k

k ,k

}

N w k ,k

The solution of (8) gives −1 w Opt k ,k = R v k ,k ,

(9)

elements are that of a vector s p . From the calculated

where R is the autocorrelation matrix of the channel frequency response and using the root-multiple observation vector y and v k , k is the cross-correlation signal classification (Root-MUSIC) method [6], which vector between y and the desired filter response H k ,k . is one of the super resolution techniques, the time delays can be estimated efficiently using the available R = E yy H , v k ,k = E yH k*, k . limited bandwidth. The conventional FFT method on the other hand requires a much wider bandwidth, as to H in the previous formulas is the conjugate transpose distinguish between two time delays τ 1 and τ 2 , a operator. Utilizing the distributed pilots that are known for the transmitter and the receiver, R and v k , k can be 1 determined as described in [2]. is required. As an example Fig. bandwidth of

{ }

τ 2 −τ1

{

}

ˆ H (H ˆH ˆ H + σ 2 I ) −1 y , sˆ = H θ

V. ICI REDUCTION

(14) order to cancel the effect of ICI, all 2 N × N elements of the channel matrix have to be where σ θ is the noise variance and I is the identity estimated. Here, a linear approximation method which matrix. makes use of the adjacent symbols of the symbol of interest and utilizes a Taylor expansion is introduced. VI. SIMULATION RESULTS The channel matrix can be written as To test the effect of the multipath channel, a two-path 2π N −1 fading channel with different Doppler spreads is −j n(k −m) 1 H k ,m = U m (n)e N , (10) considered in this simulation. The ISI is assumed to be N n =0 completely removed by choosing the guard interval longer than the channel impulse response. Perfect where U m (n) are the time varying channel weights for synchronization between the transmitter and the each sub-carrier m and time sample n . We assume receiver is assumed. The considered OFDM system has that, the channel impulse response varies in linear parameters summarized in Table I. In this simulation fashion during one OFDM symbol. Let U k represent Uncoded symbols are considered. The Doppler power spectrum model is assumed to have a Gaussian shape the U k (n) at the middle of the symbol as having been according to the digital radio mondiale (DRM) channel estimated early using Wiener filter [9]. In

∑

U k = H k ,k

1 = N

N −1

∑U

k

( n) .

(11)

n =0

TABLE I System Parameters

Taking the first two terms of a Taylor series

Parameter Input modulation scheme Number of carriers Number of pilots Guard interval length FFT length Bandwidth

N −1 U k ( n) ≈ U k + U k ( n − ), (12) 2 ′ where U k is the derivative of U k which can be ′

calculated using the adjacent symbols as ( next sym.)

− U k( prev. sym.) , 2N s

′ U Uk = k

(13)

where N s is the symbol duration including the guard interval. Using the approximation in (12) and making ˆ can be calculated [3]. Fig. 4. use of (10) and (4), H shows the estimated channel matrix . From the figure, one can notice that the sub-carrier of interest is significantly affected by the adjacent sub-carriers.

value 4-QAM 52 8 16 samples (330 µs ) 64 4.5 KHz

In Fig. 5 we plot the normalized MSE between the actual and the estimated channel for different Doppler spreads. Fig. 6. Illustrates the system performance (BER) for two different Doppler spreads and compares between the case of estimating the main diagonal of the channel matrix only and the case of compensating the effect of ICI by estimating the whole matrix. -1

10 20

18Hz 2 Hz ICI free

Magnitude

10 0

-2

10

-10 -20

NMSE

-30 -40 60 6

40 40 20 Carrier index

-3

10

0

-4

10

20 0

Carrier index

Fig. 4. The absolute values of the normalized channel matrix coefficients

-5

10

15

After estimating the channel matrix, an MMSE equalization method [8] is applied on the received symbols to get the transmitted data back, this results in

20

25

30

35

40

45

SNR

Fig. 5. NMSE vs. SNR for different Doppler spreads

50

-1

[8] P. Schniter and S. D' Silva, “Low-Complexity Detection of OFDM in Doubly-Dispersive Channels,” Proc. Asilomar Conf. on Signals, Systems, and Computers, (Pacific Grove, CA), 2002. [9] ETSI: “Digital Radio Mondiale (DRM)-System Specification”, ETSI TS 101 980, V1.1.1, Sep. 2001.

10

main diag.4Hz complete.4Hz main diag.18Hz complete.18Hz

-2

BER

10

-3

10

-4

10

-5

10

15

20

25

30

35

40

45

50

SNR

Fig. 6. BER vs. SNR for different Doppler spreads

VII. CONCLUSION The conventional one-tap equalizer considers ICI as another source of noise which degrades the performance of OFDM systems especially in high mobility environments. In this paper we outperformed methods proposed earlier and combined them together to design a multistage estimator used for combating ICI with less complexity. The utilized super resolution technique works well also for very small delays between the paths and solves the problem of the model mismatching. The linear approximation method is applicable when the Doppler spread is less than the frequency spacing between the sub-carriers which is usually the case. The system performance has shown good improvement in the error floor. REFERENCES [1] W. Jeon, K. H. Chang, and Y. S. Cho,“An Equalization Technique for Orthogonal Frequency Division Multiplexing Systems in Time Variant Multipath Channels”. IEEE Trans. on commun. Vol. 47. p. 29-32. Jan 1999. [2] C. Sgraja and J. Linder, “Estimation of Rapid TimeVariant Channels for OFDM using Wiener Filtering” Proc. IEEE International Conference on Communications (ICC), vol. 4, pp.2390-2395, Anchorage (AK), US, May 2003. [3] V. Fischer, A. Kurpiers and D. Karsunkc, “ICI Reduction Method for OFDM Systems”, 8th International OFDMWorkshop 2003, Hamburg, Germany, 24th/25th Sep. 2003 [4] J.P.M.G. Linartz and A. Grokhov : “New equalization approach for OFDM over dispersive and rapidly time varying channel. Proc. PIMRC’00, London, Sept. 2000. [5] Y. Mostofi and C. Cox, “ICI Mitigation for Pilot-Aided OFDM Mobile Systems”, IEEE Trans. on Wireless Communication, vol. 4, No. 2 ,pp 765-774, Mar. 2005 [6] Bhaskar D. Rao and K. V. S. Hari, “Performance Analysis of Root-Music”, IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. 43, pp. 1939-1949, 1989. [7] P. A. Bello, “Characterization of randomly time-variant linear channels”, IEEE Trans. on Commun. Systems, vol. 11, no. 4,pp. 360-393, Dec. 1963.