Efficient Joint Carrier Offset and Channel Estimator for T ... - IEEE Xplore

The First International Conference of Electrical, Communication, Computer, Power and Control Engineering ICECCPCE'13/December17-18, 2013

Efficient Joint Carrier Offset and Channel Estimator for T-OFDM System Mohammed Sh. Ahmed College of Petroleum and Minerals Engineering, Tikrit University, Iraq Emails:[email protected]

Abstract-The high sensitivity of multicarriers systems to the channel estimation errors, transceiver oscillators mismatch and/or Doppler effect has received a considerable attention in the recent studies. In this work, a new two semi-blind and data­ aided techniques are proposed to achieve an accurate carrier frequency offset (CFO) and flat fading channel estimation in the orthogonal frequency division multiplexing (OFDM) based T­ transform (T-OFDM) system. The semi-blind is utilised only two trial values to achieve joint CFO and channel estimation. Also, a new data-aided CFO estimator over the additive white Gaussian noise is proposed. The two proposed techniques are based on a low computational complexity T-transform, which was developed formally to combine the Walsh-Hadamard transform and inverse discrete Fourier transform into a single unitary transform. The unique butterfly structure of the T-transform can be exploited in the semi-blind joint CFO and channel estimator by utilizing only two trial samples from the T-OFDM symbol. This technique is able to estimate the CFO mismatch and the flat fading channel varying in every transmitted frame. The main advantages of the proposed techniques over the existing schemes are lower computational complexity, lower data rate losses, and an accurate estimation for the fine CFO and the coefficients of the flat fading channels.

I.

INTRODUCTION

The principal advantages of orthogonal frequency division multiplexing (OFDM) are the spectral efficiency and robust­ ness against frequency-selective mUltipath fading propagation that are a consequence of splitting a high-rate data stream into a number of lower rate streams to transmit simultaneously over a number of orthogonal subcarriers and transforming a wideband frequency-selective channel to a set of parallel nonselective (flat) fading narrowband channels, which sub­ stantially simplifies the channel equalization problem. In a sequel, its employed in various high data rate standards communication systems, such as IEEE208.11a/n, IEEE802.16, and IEEE802.20 [1]. However, the mismatched oscillators at the OFDM transceiver and/or Doppler frequency shifts due to mobility lead to intercarrier interference (lCI) among the adjacent subcarriers, which destroy the orthogonality among the overlap subcarriers and cause degradation in the bit error rate (BER) performance. Therefore, carrier frequency offset (CFO) estimation and compensation has been received a considerable attention in the recent studies. In general CFO estimation techniques may be classified as time-domain (pre-fast Fourier transform (FFT» or frequency­ domain (post-FFT) techniques. The later are usually used to

Salah A. Al-iesawi Computer College, AI Anbar University, Iraq Email:[email protected]

estimate the integer part of the CFO after the fractional part has been identified and corrected. Time-domain methods are used to estimate the fractional part of the CFO, albeit some of these techniques can also estimate the integer part of the CFO. In literature, various algorithms such as data-aided (or pilotbased) [2]-[5], blind [6]-[9], and semiblind [10]-[12] can be utilized to estimate and compensate the CFO values. In pilot-based methods, known pilot symbols are transmitted to estimate channel parameters and CFO; in blind techniques, the input is not known, but some statistical properties, such as independent and identically distributed (iid) inputs, may be known. The semiblind algorithms refer to both those use both pilots and statistical properties of data and to those exploit additional features, such as finite alphabet, of the unknown symbol stream. In this work, two schemes based on the low computational complexity T-transform, which was developed in [13] and utilized in [14] and [15] to achieve a substantial bit error performance over multipath fading channel as a consequence of diversity increasing are proposed to achieve a joint CFO and flat channel estimation. The first two trial samples are employed in the semi-blind technique to estimate the CFO and the Rayleigh flat fading channel coefficients. Moreover, the second proposed technique is the low complexity data­ aided technique to estimate the CFO over the additive white Gaussian noise (AWGN). The mean square error (MSE) of the two proposed estimators linearly decreased with the bit energy-to-noise ratio (Eb/No) increasing. The main merits of the proposed schemes are the accurate estimation, low computational overhead, and low data rate losses. The rest of this paper is organized as follows. Section II describes the orthogonal frequency division multiplexing (OFDM) based T-transform (T-OFDM) system under the CFO mismatch. The proposed two schemes of CFO and channel es­ timation are presented in Section III. Section IV demonstrates the numerical results, along with their discussion. Lastly, Section V concludes the paper. II. T-OFDM

SY STEM UNDER

CFO

On the transmitter side of the T-OFDM system which was constructed in [14] and [15], the incomin� modulated data vector during the i-th block, x(i) = [X'6 ) , X'l ) . . . ) xlY_IlT is fed to N-points inverse T-transform. Thus, the time-domain

The First International Conference of Electrical, Communication, Computer, Power and Control Engineering ICECCPCE'13/December17-18, 2013

samples can be represented as

vi( ) = TH Xi( ) , V�i ) = [vi6 ) , vii ) , . . . , VW_l ]T, T = -hF

where

N

x

(1) W is the

e(e,i)

N forward T-transform, which combine the normalized

re-arranged with rows reverse order discrete Fourier transform (DFT) matrix, F, and Walsh-Hadamard transform ( W HT) matrix, W, and (. ) H is the hermitian operator. The flowchart structure of T-transform can be constructed as illustrated in [14]. This means that the inverse T-transform, TH can be expressed as, 1 TH =-WFH ' (2)

N

where FH is the normalized re-arranged with column reverse order inverse discrete Fourier transform (IDFT) matrix. The elements of Wand FH can be expressed as

AWGN

Fig. 1. T-OFDM block diagram with joint CFO and flat fading channel estimation

and to avoid the inter-carrier interference (ICI), the value of 8E,i should be estimated and compensated for. This means, the output of forward T-transform can be expressed as

(3) (9)

H = ej21rkn/N , Fkn

where mn kr are the bits representation of the integer values m and k, respectively. Consequently, the elements of the inverse T-transform can be expressed as

N (N)-l m kor+ kn/N H = 1 "" r 2 j1r =6 (Lr ), e Tmn N � k=O The n-the sample of vi( ) can be written as, N-l H ( ) Tmn° Vin( ) = "" � Xim m=O -1

log

_

(5)

III.

0

0

.N- 1

(7)

l

T . g ([e;2", E,1 =dza 8(.) N (O+C ) , e;2u N (HC ) , ..., e;2u N ((N-l ) +C )

I

( ( ) l ]T denotes the i( ) = [gio( ) , gli( ) , · · · , giNC = z (N+Ng ) , gn additive white Gaussian noise with zero mean and variance

a; = E[lgnI2].

Before fed the received sequence

r� )

PROPOSED TECHNIQUES

Estimator

(6)

where (>9 stands for the circular convolution, c represents i the normalized fractional CFO {c E (-0.5, 0.5)}, and 8;,: represents the effect of the accumulated phase shift caused by the CFO on the time-domain samples

.

,

A. Proposed Semi-Blind Joint CFO and Flat Fading Channel

In multiplicative channel, a guard interval with Ng samples of the back-end should be appended into the front-end of the time-domain samples in order to mitigate the intersym­ bol interference (lSI) phenomenon. The length of these Ng samples is chosen based on the constraint greater or equal to the maximum path delay of multipath channel. At the receiver, with assumption of perfect time synchro­ nization, the received time-domain sequence after dropping the the first Ng can be expressed as

,(in ) = 8n(E,i ) (h(in ) (>9 vin( ) )+gin' ( ) for n = 0

. ( ) l ] T and c" IS the estImate ) X" d where , Xin( ) = [,Xio( ' li( ) " 'XiNCFO. Subsequently, the channel equalization of the amended signal xi( ) can be achieved either in Walsh-domain by using Dyadic convolution [15], or utilizing frequency equalization that employed in the traditional OFDM system, i.e computing DFT of r, equalization, then the WHT of the equalized sequence is computed. ,

(4)

to forward T-transform

The first proposed scheme is based on only two trial values from entire transmitted frame, therefore its called semi-blind joint CFO and flat channel estimator. As shown in Fig.I, over the AWGN noise, the semi-blind approach is achieved by transmitting known (at the transmitter and receiver sides) trial value, I on the second subcarrier X2, which equivalent to V / N in time-domain of T-transform. If the data symbols are selected from a constant modulus (CM) constellation, i.e. IXnl 2 = 1, the trial value has been chosen as I = vE[lxI2], where E[.] denotes the expectation operator, in order to keep the average power of the transmitted signal unchanged. It is important to mention that the WHT do not has any deleterious effect on the average power due to the unitary feature of this transform. Also, the amplified I can be used in order to increase the accuracy of CFO estimation, but with the expense of average power increasing. Over Gaussian noise channel, the distorted trial value at the receiver side will be calculated as

2

(10)

where vectors r and x are the received signal in time-domain and Walsh-domain, respectively. Consequently, the estimated

The First International Conference of Electrical, Communication, Computer, Power and Control Engineering ICECCPCE'13/December17-18, 2013

CFO can be computed as,

L( i(i) )

t

_.

"1

=

7r

__

---e--

--e-- Channel

(11)

On the other hand, the same technique can be utilised over unknown flat fading channel. In this case, the first two direct paths of T-transform will be employed to transmit two known trial values, 10 and 11, which have been chosen based on the same criterion mentioned formerly and transmitted indepen­ dently over Xo and Xl paths, respectively. 10 will be utilised to estimate the channel coefficient and 11 will be used in the CFO estimation, as mentioned before. Intuitively, 10 transmitted under CFO environment affected by 80 = eJ2'rr €O/N = 1, and its value on the receiver side can expressed as

10

=

fIolo+go ·

=

10 10

Trial values=1

o

5

10

(13)

Fig.

2.

t

1

"1

=

7r

c::=

where r

=

E[ri( )] and v r

=

=

�

(15)

1. Upon substituting (8) into (15),

N-l

'"

� N n=O

ej27rin/N ,

(16)

To avoid the exponential term in (16), the logarithm of both side is computed . Thus,

log (fN) Let S

S

=

=

log

(� ej27rin/N ) .

'L::lO ej27rin/N , thus {I +ej27ri/N +ej47ri/N +...+ej27ri(N-l ) /N }

=

where sin(x)

=

- ej27ri 1 - ej27ri/N ej7ri [e- j7ri - ej7ri] ej7ri/N [e- j7ri/N - ej7ri/N ] sin(7rt) 7r eJ €� ' 1

.

X for Ixl

(17)

=

(18)

,

E =

,N-l

«

1. Upon substituting (19) into

'S{log (f N)} N-l 7r---w-

where the logarithm of complex number z calculated as log (z) = log (Izl)+je, where e

=

(19)

7rt/N

(17),

With the assumption that the value of E is slowly changed over consecutive OFDM symbols, and the channel is AWGN, the proposed data-aided estimation is introduced by transmit­ ting a trial symbol with unitary values. This symbol can be produced by feeding a sequence of ones into the T-transform. Then, the statistical average of the received distorted signal r is computed in order to eliminate (nearly completely) the zero mean AWGN noise, i.e. E[gi( )] = O. This means,

E[vi( ) e(ii, )]+E[gi( )] vi( ) E[e(ii, )]

35

= ----,-:,-= ---;:-,

(14)

B. Proposed Data-Aided CFO Estimation Technique

=

30

For simplicity purpose, the geometric series in (18) can be reformulated as,

S

Future work will focus on investigating an efficient joint frequency selective channel and CFO estimation that matches with the T-transform. This investigation will consider some other types of modulation further to QPSK.

r

25

20 (dB)

MSE versus Eb/NO(dB) for CFO and /late fading channels.

Also, the normalized CFO can estimated as

LCi1(i)/H)

15 Eb/NO

(12)

This means, the estimated coefficient of flat fading channel can be computed as

fI

CFO over flat fading

(20) =

X+jy

can be (21)

tan-l(�). IV.

NUMERIC AL RESULTS

The T-OFDM system considered in this paper has N = 128 subcarriers modulated using QPSK, and cyclic prefix (CP) with length of Ng = 32. Estimated values are evaluated by computing the mean square error (MSE) of such values. As reported in [15], the T-OFDM is achieved a significant BER improvement over the multipath transmission and a noticeable computational complexity reduction compared with the traditional OFDM system. The proposed semi-blind joint CFO and flat fading channel estimator is assessed over addi­ tive white Gaussian noise (AWGN) and Rayleigh flat (non­ selective) fading channel. The MSE of this technique with In = vE[lvI2] = 1 and amplified In = 3.16 over AWGN channels is depicted in Fig. 2. Obviously, the MSE of the proposed technique is linearly decreased with high Eb/No. Also, the proposed technique with high power In is achieved lower MSE, i.e. better estimation, albeit with expense of

The First International Conference of Electrical, Communication, Computer, Power and Control Engineering ICECCPCE'13/December17-18, 2013

two trial samples through the T-transform has been proposed to estimate the joint CFO and flat fading channel coefficient. -a-- T-OFDM Estimation Also, more accurate data-aided CFO estimator over the AWGN channel has been introduced. The two proposed techniques are based on a low computational complexity unitary T-transform. The unique butterfly structure of the T-transform has been exploited in the semi-blind joint CFO and channel estimator by utilizing the first two direct path of T-transform. This technique is able to estimate the CFO mismatch and the flat fading channel in every transmitted frame. Moreover, an accurate data-aided CFO estimator is employed with the low computational complexity T-transform by transmitting a trial frame with unitary amplitudes over the AWGN channel. The -4 10 L---���--L�--����--��� main advantages of the proposed techniques over the existing 20 5 25 o 10 30 35 15 schemes are lower computational complexity, lower data rate Eb/NO (dB) losses, outstanding BER performance, and an accurate esti­ mation for the fine CFO and the coefficient of the flat fading Fig. 3. BER versus Eb/NO(dB) over AWGN and flat fading channels. channel. ----+-- T -OFDM Perfect

-4 10

REFERENCES --e-- CFO

-5 10 10 U-l (/J

::E

10

,"

-6

-7

-8 10

Average Power= 10

-9 10 -10 10

[ 1] Y Li and G. Stuber, "Orthogonal Frequency Division Multiplexing for Wireless Communications New York:Springer-Verlag, 2006. [2] A. Laourine, A. Stphenne and S. Affes, "A new OFDM synchronization symbol for carrier frequency offset estimation," IEEE Signal Process. Lett., vol. 14, no. 5,pp. 32 1-324, May 2007. [3] I. M. Schmidl and D. C. Fox, "Robust frequency and timing syn­ chronization for OFDM," IEEE Trans. Commun., vol. 45, no. 12, pp. 16 13 162 1, Dec. 1997. [4] M. Morelli and U. Mengali,"Carrier-frequency estimation for transmis­ sions over selective channels," IEEE Trans. Commun., vol. 48, no. 9,pp. 15801589, Sept. 2000. [5] D. Huang and K. B. Letaief, "Enhanced carrier frequency offset estima­ tion for OFDM systems using channel side information," IEEE Trans. Wireless Commun., vol. 5, no. 10, pp. 27842792, Oct. 2006. [6] A. AI-Dweik, A. Hazmi, S. Younis, B. Sharif and C. Tsimenidis, "Carrier frequency offset estimation for OFDM systems over mobile radio channels," IEEE Trans. Veh. Techno/., vol. 59, no. 2,pp. 974-979, Feb. 2010. [7] L. Wu, X.-D. Zhang, P.-S. Li and Y-I. Su, " A closed-form blind CFO estimator based on frequency analysis for OFDM systems," IEEE Trans. Commun., vol. 57, no. 6,pp. 1634-1637, June 2009. [8] A. M. Karim and M. Othman, "Improved fine CFO synchronization for MB-OFDM UWB," IEEE Commun. Lett., vol. 14, no. 4, pp. 35 1-353, April 2010. [9] I. Fusco and M. Tanda, " Blind synchronization for OFDM systems in multipath channels," IEEE Trans. Wireless Commun., vol. 8, no. 3, pp. 1340-1348, March 2009. [ 10] L. He, S. Ma, Y-C. Wu and I.-S. Ng, " Semi-blind CFO, channel estimation and data detection for OFDM systems over doubly selective channels," in Proc. ISCAS 2010, pp. 1887- 1890. [ 1 1] M. Ghogho, A. Swami, "Semi-blind frequency offset synchronization for OFDM," in Proc. ICASSP 2002, pp. 2333-2336. [ 12] I. Fusco, F. Marrone and M. Tanda, "Semiblind Carrier Frequency Offset Estimation for OFDM Systems ," in Proc. ICC 2007, pp. 773778. [ 13] S. Boussakta and A. G. J. Holt,"Fast Algorithm for calculation of both Walsh-Hadamard and Fourier Transforms (FWFTs)," lEE Electron. Lett., vol. 25, no. 20, pp. 1352-1354, Sep. 1989. [ 14] M. Sh. Ahmed, S. Boussakta, B. Sharif, and C. C. Tsimenidis, "OFDM based on low complexity transform to increase multipath resilience and reduce PAPR " IEEE Trans. Signal Process., vol. 59 no. 12, pp. 59946007, Dec. 20 1 1. [ 15] M. Sh. Ahmed, S. Boussakta, B. Sharif, and C. C. Tsimenidis, "OFDM Based New Transform with BER Performance Improvement Across Multipath Transmission," Proc. IEEE ICCIO, South Africa, 2010, pp. 1-5.

0

5

10

15

20

25

30

35

Eb/NO (dB) Fig. 4.

MSE versus

Eb/NO(dB)

for CFO over AWGN channels.

higher average transmitted power. The BER performance of the proposed technique over the AWGN and Rayleigh static (fix for entire transmitted frame period) flat fading channel versus the Eb/NO is presented in Fig. 3. As clear in this figure, the proposed technique achieve nearly closed performance to the same system with perfect knowledge of CFO and channel coefficient. On the other hand, the proposed data-aided CFO estimator is assessed with the assumption that the value of E slowly changes over consecutive OFDM symbols, and the channel is AWGN. Fig. 4 illustrates the MSE of this scheme over the AWGN channel. As clear in this figure, the proposed technique is achieved an accurate estimation for the CFO values. V.

CONCLUSION

This work has proposed two attractive simple overhead schemes to estimate the CFO and flat fading channel in the T-OFDM system. The semi-blind technique, which based on