Abstract—This work presents a blind synchronizer for ortho-gonal frequency-division multiplexing (OFDM) systems based on signal-to-interference-and-noise-ratio (SINR) maximization. Due to the incurred losses from inter-symbol interference (ISI) and inter-carrier interference (ICI) introduced by synchronization errors, the SINR of the received data drops drastically. By taking advantage of this characteristic, both the symbol time and carrier frequency offsets are intuitively estimated by maximizing the SINR metric. For the SINR metric, we propose a blind SINR estimation, which does not need prior knowledge of the channel profiles and transmitted data. As such, the proposed maxi-mum-SINR (MSINR) synchronization algorithm is non-data-aided (NDA) so that the transmission efficiency can be improved. Moreover, to reduce the computational complexity, the early-late gate (ELG) technique is proposed for the implementa-tion of the synchronizer. Simulaimplementa-tion results exhibit better per-formance for the MSINR algorithm than conventional techniques in multipath fading channels.
I. INTRODUCTION
Orthogonal frequency-division multiplexing (OFDM) is a promising technology for broadband transmission due to its high spectrum efficiency, and its robustness to the effects of multipath fading channels. However, it is sensitive to syn-chronization errors. First, uncertain OFDM symbol arrival time introduces a symbol time offset (STO). Second, the mismatch of the oscillators in carrier frequencies (CF) between the transmitter and the receiver produces a carrier frequency offset (CFO).
The symbol time (ST) estimation is usually the first step in an entire OFDM synchronization process, because it provides an estimated symbol boundary for the remaining synchroniza-tion steps. When the ST is not located in the ter-symbol-interference-free region, the ter-symbol-interference (ISI) will be inevitable. The CFO in-troduces additional inter-carrier interference (ICI).
In [1], the STO and CFO are jointly estimated by a de-layed-correlation algorithm. It is a maximum-likelihood (ML) estimation and only good for the additive white Gaussian noise (AWGN) channel. Some techniques [2]-[3] have good ST performances. However, extra time-domain training symbols are needed. In [3] and [4], the channel frequency response (CFR) must be estimated first. The inverse fast Fourier trans-form (IFFT) is then applied to obtain the channel impulse re-sponse (CIR), which is then used to adjust the symbol boundary. Some works locate the symbol boundary at the sampling point that has the minimum-interference [5]-[6].
The proposed scheme is to effectively reduce the synchro-nization errors, including the STO and the CFO, so that the
signal-to-interference-and-noise-ratio (SINR) is maximized. In other words, not only the interference power is considered but also the signal power. A blind SINR estimation is proposed for the maximum-SINR (MSINR) synchronization algorithm. As such, the proposed MSINR algorithm is non-data-aided (NDA) such that the bandwidth efficiency can be improved. In addition, to reduce the computational complexity, the early-late gate (ELG) technique is also proposed for the implementation of the new MSINR algorithm.
The rest of this paper is organized as follows. The OFDM system and signal models are introduced in Section II. The blind SINR estimation, MSINR synchronization algorithm, and the ELG technique are then detailed and analyzed in Section III. The performance is analyzed in Section IV. Simulation results are provided in Section V. Finally, we conclude our work in Section VI.
II. OFDMSYSTEM AND SIGNAL MODELS
In the following discussion, all the quantities indexed with l belong to the l-th symbol. A simplified OFDM system model is shown in Fig. 1. In this figure, Xl,k Xl,k
~
/ is the transmit-ted/received frequency-domain data at the k-th subcarrier; xl n,
is the transmitted time-domain data after the IFFT; xl n, ′ is the received time-domain data, where −NG ≤ n′<N , N is the
number of subcarriers, and NG is the cyclic prefix (CP) length;
1/T is the sampling frequency; S
ε
f is the CFO divided by f , cwhere fc is the carrier frequency; nΔ
is the estimated STO; and
f
ε is the estimated CFO divided by f . On the transmitter side, c N complex data symbols are modulated onto N subcarriers by
A Blind Maximum-SINR Synchronization Technique for OFDM Systems
Wen-Long Chin and Sau-Gee Chen
Department of Electronics Engineering and Institute of Electronics National Chiao Tung University
1001 Ta Hsueh Rd, Hsinchu, 30050, Taiwan, ROC e-mail: johnsonchin@pchome.com.tw MSINR Synchronizer nΔ Data Sink Signal Demap-per E qua liz er N-point FFT CP Removal ADC channel DAC CP Insertion N-point IFFT Signal Mapper Data Source k l X, xl,n 2 c j f t e π S T / 1 1/TS AWGN k l X, ~ 2 (1 f)c j f t e− π ε− f ε ,ln x ′ P/S S/P MSINR Synchronizer nΔ Data Sink Signal Demap-per E qua liz er N-point FFT CP Removal ADC channel DAC CP Insertion N-point IFFT Signal Mapper Data Source k l X, xl,n 2 c j f t e π S T / 1 1/TS AWGN k l X, ~ 2 (1 f)c j f t e− π ε− f ε ,ln x ′ P/S S/P
Fig. 1. A simplified OFDM system model. The MSINR synchronizer oper-ates in frequency domain by utilizing the FFT operations. Detailed block diagram of the synchronizer can be found in Fig. 3.
using the IFFT. The last NG IFFT output samples are copied to
form the CP that is inserted at the beginning of each OFDM symbol. By inserting the CP, a guard interval is created so that ISI can be avoided and the orthogonality among subcarriers can be sustained. The receiver uses the fast Fourier transform (FFT) to demodulate received data.
The estimated ST generally falls into one of the three regions of an OFDM symbol: the Bad-ST1 region, the Good-ST region (also known as the ISI-free region), and the Bad-ST2 region in which the STO n , is confined within the ranges of Δ
1
G G d
N nΔ N τ
− ≤ ≤ − + − , 0−NG+ ≤τd nΔ≤ , and 1≤nΔ≤ − , respectively, where N 1 τd is the maximum delay
spread of the channel. Detailed analysis of the received fquency-domain data (at the k-th subcarrier) in these three re-gions can be found in [7], and rewritten below (for only the Bad-ST2 region) , , d l k l k k X = X +N (1) where ( ) , , s f lN kn d l k k l k N N n X H X W N Δ − − Δ − ε (2)
is the desired data, Hk is the CFR at the k-th subcarrier, WN is 2 /
j N
e− π , and
S G
N = +N N is the OFDM symbol length in-cluding the CP; and
( ) ( ) 1 ' , ' 0 , , 1 N n m k f lNs f kn k N m l m N k m k n ici isi l k l k N W H X W v N X X Δ − − − + − − ≠ = + − +
∑ ∑
ε ε (3)is the combined interference and the AWGN vk, where
( ) ( ) 1 ' , , ' 1 f s f N n m k lN kn ici l k N m l m N m k n N n X W H X W N ε ε Δ Δ − − − + − − ≠ = − =
∑ ∑
(4)is the ICI term, and
( ) ( ( )) 1 ' , 1, ' 1 f s f G N n m k lN k n N isi l k N m l m N m n N n X W H X W N ε ε Δ Δ − − − + − − + + = − =
∑ ∑
(5)is the ISI term. It can be easily shown that the theoretical SINR is , 2 2 ( , ) d l k k th f X N k k n η Δ ε =
∑
σ∑
σ (6) where 2 , 2 2 2 d l k k X X N n m H N σ = ⎜⎛ − Δ⎞ ⎟ ⎝ ⎠ (7)is the desired signal power,
( )( ) ( ) ( )( ) 1 2 1 2 1 2 1 2 1 2 1 2 2 1 1 2 2 2 0 0 1 1 2 1 1 2 2 2 + f k f f k N N n n m k X N m N m k n n N N n n N k n N n n N n N N n n m k N m v m k n N n n N n W H N W H W H ε ε ε σ σ σ Δ Δ Δ Δ − − − − − + ≠ = = − − − − = − = − − − − − − + ≠ = − = − ⎧⎪ = ⎨ ⎪⎩ + ⎫⎪ + ⎬ ⎪⎭
∑ ∑ ∑
∑ ∑
∑ ∑ ∑
(8)is the combined interference-and-the-AWGN power, 2 X
σ is the transmitted data power, and 2
k
v
σ is the AWGN power.
III. PROPOSED MSINRSYNCHRONIZATION TECHNIQUE
The signal power decreases while the interference power increases when the STO and/or the CFO increase [8]-[9], as also suggested in (7) and (8), respectively. Consequently, it is evident that the SINR is a good metric to indicate the syn-chronization offsets. In comparison, those mini-mum-interference synchronizers [5]-[6] considering only the interference power may have performance losses.
A. Blind SINR Estimation for MSINR Algorithm
Before introducing the MSINR synchronization technique, the SINR estimation for (6) is investigated first.
1) SINR Estimation Based on Coherence Function: The coherence function [10]-[11] is often used to determine the degree to which one observed signal is related to another ob-served signal. If we have uncorrelated noise and the coherent signal, the amount of the powers due to noise and coherent signal can be determined. The concept of coherence function can be applied to the OFDM systems, so that the SINR, at the k-th subcarrier of the l-th symbol, can be written as
2 , , 2 , ( , ) 1 l k l k f l k n γ η ε γ Δ = − (9) where 2 * 2 , 1, 2 , 2 2 , , 1, , , 0 1 l k l k l k l k l k l k E X X k P E X E X γ + γ + ⎡ ⎤ ⎣ ⎦ ∈ ≤ ≤ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ (10)
is the magnitude-squared coherence (MSC) at the k-th subcar-rier of the l-th symbol, and P is the pilot set. The MSC is the cross-power spectrum of two consecutive symbols normalized by their auto-power spectra, which can be viewed as the correlation between like frequency components of the received frequency-domain data.
Originally, the MSC in [10] was realized by the commonly used technique of time sample average, which is based on the assumption of signal ergodicity. Besides, it is only applicable for data-aided (DA) systems. In OFDM systems, since there is only one data sample at each subcarrier within an OFDM symbol, and the channels are possibly time-selective fading, it is inadequate to realize the cross-correlation in (10) by aver-aging over data segments (or symbols). Therefore, to blindly
estimate the MSC without known data (or pilots) and derive the SINR profile in reasonable amounts of symbols, we propose to average the MSC over all N subcarriers within an OFDM symbol as follows 2 * , 1, 2 2 2 , 1, 1 1 1 l k l k k l l k l k k k X X N X X N N γ + + ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ = ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠
∑
∑
∑
(11)where the bar on top of γl
denotes the sample average over N
subcarriers. Finally, the SINR can be obtained by (9) as
2 2 ( , ) . 1 l l f l n γ η ε γ Δ = − (12)
Note that the SINR estimation (12) can be averaged over symbols to improve the accuracy.
2) Estimated SINR Profiles: We assume an OFDM system
with the following specifications: N = 256, NG = 32, fc = 2.4
GHz, Ts = 115.2 sμ , and the signal bandwidth is 2.5 MHz. The
SINR estimates (12) against the STO and CFO (normalized by the subcarrier spacing) in a multipath fading channel are demonstrated in Figs. 2(a) and 2(b), respectively. The channel
is assumed to have NG paths. The channel taps are randomly
generated by independent zero-mean, complex Gaussian variables. As can be seen, the SINR estimates in Figs. 2(a) and 2(b) have the prominent peak values in the Good-ST region (at
the 0th sample) and at CFO = 0, respectively. This figure also
shows that how drastically the ISI/ICI is affected by the STO/CFO.
B. MSINR Synchronization Algorithm
1) MSINR Global Search Algorithm (MSINR-GSA): As
ob-served and concluded above, the SINR drops drastically due to incurred interferences from the ICI and ISI. In addition, with (6)-(8), it can be shown that the SINR is a unimodal function of the STO and CFO, and has the maximum value at the ideal synchronization point. (Due to space limitation, this figure is not shown here). Hence, one can estimate the STO and CFO by intuitively maximizing the SINR estimation (12) as
{
}
, , , ( ( ), ( )) arg max ( , ) f GSA f GSA n l f n l l n ε ε η ε Δ Δ = Δ (13) where nΔ,GSA( )l and , ( ) f GSA lε are the l-th symbol’s STO and
CFO (divided by fc) estimates of the two-dimensional
MSINR-GSA, respectively. This is a complicated two-dimensional search problem. Since the SINR profile is a unimodal function of the STO and CFO, we separate it into two one-dimensional processes, i.e., the STO search and the CFO search, as described by the following equation
{
}
{
}
, , , , ( ) arg max ( , ( 1)) . ( ) arg max ( ( 1), ) f GSA n l f GSA f GSA l GSA f n l n l l n l ε η ε ε η ε Δ Δ Δ Δ ⎧ ′ = ′ − ⎪ ⎨ ′ = ′ − ⎪ ⎩ (14)where nΔ′,GSA( )l and ε′f GSA, ( )l are the STO and CFO (divided by
fc) estimates of the one-dimensional MSINR-GSA.
2) MSINR-ELG ST (MSINR-ELG-ST) Recovery Loop: The
computational complexity of (14) is still high, because the frequency-domain data and their SINRs have to be obtained over all possible synchronization points. To reduce the com-putational complexity, instead of searching the whole range of
Δ
n , it is assumed that the signal is sampled early at
,ELG( ) nΔ l −τΔ and late at ,ELG( ) nΔ l +τΔ , where ,ELG( ) nΔ l is the
estimated STO of the MSINR-ELG-ST, and τ is the time shift Δ
relative to the estimated symbol boundary. The metrics (12) at these two symbol boundaries are subtracted and filtered to form
an error signal ( )e lΔ [6]. The nonzero error signal is produced
to fine-tune the symbol boundary and iteratively make the error signal become zero. The S-curve of the timing discriminator is given by 1 , , 1 , , ( 1) ( ( ) , ( )) ( ( ) , ( )) l ELG f ELG l ELG f ELG e l n l l n l l η τ ε η τ ε Δ + Δ Δ + Δ Δ + = − − + (15)
where εf ELG, ( )l is the estimated CFO (divided by fc) of the l-th
symbol.
The MSINR ST synchronizer implemented by the ELG is shown in Fig. 3(a). An approximated linear model for the ELG timing recovery loop is shown in Fig. 4, where ( )F z is the loop filter, K is the loop filter gain, F K is the timing detector’s I
intrinsic gain, K is the voltage-controlled oscillator (VCO) V
gain, ( )N zΔ is the z-transform of nΔ , N zΔ( ) is the
z-transform of nΔ,ELG( )l
, ( )E zΔ is the z-transform of ( )e lΔ ,
and ( )E zΔ′ is the z-transform of the filtered error signal ( )e lΔ′ .
The ST is iteratively adjusted by the VCO as follows
,ELG( ) ,ELG( 1) V S S ( ).
nΔ l =nΔ l− +K N T e lΔ′ (16)
The closed-loop system equation ( )L z N z N zΔ( ) / Δ( )can be
shown to be
(
)
1 1 1 2 (1 ) ( ) 1 2 (1 ) T T T K z az L z z K z K a − − − − − = + − + − (17) -50 0 50 100 150 200 250 300 0 5 10 15 20 25 STO (a) SI N R (d B ) -0.50 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 5 10 15 20 25CFO Normalized by Subcarrier Spacing (b) SI N R ( d B ) SNR 5dB SNR 10dB SNR 15dB SNR 20dB SNR 5dB SNR 10dB SNR 15dB SNR 20dB
Fig. 2. The estimated SINR profiles against the STO and CFO in a multipath fading channel are shown in (a) and (b), respectively. N = 256. L = 50 symbols.
where KT K K K N TF I V S S is the overall loop gain.
3) MSINR-ELG CF (MSINR-ELG-CF) Recovery Loop: The
MSINR CF synchronizer is shown in Fig. 3(b) and is similar to the ST synchronizer except that the signal is assumed to be
shifted in frequency early by εf ELG, ( )l −τf
and late by
, ( ) f ELG l f
ε +τ , where τ is the frequency shift relative to the f
estimated CFO. The S-curve of the frequency discriminator is given by , , , , ( 1) ( ( ), ( ) ) ( ( ), ( ) ). f l ELG f ELG f l ELG f ELG f e l n l l n l l η ε τ η ε τ Δ Δ + = − − + (18)
Since the CF synchronizer utilizes a similar ELG recovery loop as the ST synchronizer, it is omitted here.
C. ELG Loop Analysis and Design
Before introducing the loop design, it must be emphasized that there is no unique optimum design that can be applied in all conditions to the well-known compromise problem between the loop jitter and acquisition time. By designing for the case of signal-to-noise ratio (SNR) = 20 dB and considering the
ac-quisition range, we set τ value to 0.25. The intrinsic gain Δ K I
is determined as 32 to best fit the S-curve. The remaining
pa-rameters of the ELG loop are configured as: KF =1 ,
0.9997
a= and 2 103
V S S
K N T = × − . Finally, K
T can be shown
to be 0.064, and the normalized loop bandwidth BN T , where S S
B is the loop bandwidth, can be shown to be 0.02. Therefore,
the rise time of the loop is roughly around 50 symbols.
D. Computational Complexity
The computational complexity is dominated by four FFTs in
Fig. 3. An N-point radix-2 FFT roughly requires log2
2
N
N
complex multiplications. The averaged MSC (11) requires 2N complex multiplications and N absolute operations. Finally, the
total amount of complexity is 2
1
log 2
2
N⎛⎜ N+ ⎞⎟
⎝ ⎠ complex
mul-tiplications and N absolute operations for each (early/late) branch. Two divisions are also required in (11) and (12), which are much less than the FFT operation. The computational complexities of the blind frequency-domain synchronization algorithms of [5] and [6] in terms of complex multiplication are
roughly 2 1 log 1.5 2 N⎛⎜ N+ ⎞⎟ ⎝ ⎠ and 2 1 log 0.75 2 N⎛⎜ N+ ⎞⎟ ⎝ ⎠,
respec-tively. As can be seen, the computational complexity in this work is similar to those in [5] and [6] because the complexity is dominated by the FFT operation, which is the same for all the
(
)
(
)
1 1 1 1 F K az z − − − − 1 I K z− Loop Filter F(z)(
1 1)
V S S K N T z− − VCO Timing Detector ( ) NΔ z ( ) NΔ z + _ ( ) E zΔ(
)
E zΔ′( )(
)
1 1 1 1 F K az z − − − − 1 I K z− Loop Filter F(z)(
1 1)
V S S K N T z− − VCO Timing Detector ( ) NΔ z ( ) NΔ z + _ ( ) E zΔ E zΔ′( )Fig. 4. Approximated discrete-time model of the ELG recovery loop for the ST synchronizer. (b) (a) SINR Estimation N-point FFT SINR Estimation N-pointFFT Early branch Late branch , l n x ′ , , ( , ) l ELG f ELG η nΔ −τ εΔ , , ( , ) l ELG f ELG η nΔ +τ εΔ CP Removal at ,ELG nΔ −τΔ CP Removal at ,ELG nΔ +τΔ Loop Filter of ST ,ELG nΔ VCO of ST SINR Estimation N-point FFT SINR Estimation N-point FFT Early branch Late branch , l n x ′ , , ( , ) l ELG f ELG f η nΔ ε −τ , , ( , ) l ELG f ELG f η nΔ ε +τ , 2 (f ELG f) j π ε τ t e− − , 2 (f ELG f) j π ε τ t e− + CP Removal at ,ELG nΔ Loop Filter of CF , f ELG ε VCO of CF , 2f ELG j πε t e− (b) (a) SINR Estimation N-point FFT SINR Estimation N-pointFFT Early branch Late branch , l n x ′ , , ( , ) l ELG f ELG η nΔ −τ εΔ , , ( , ) l ELG f ELG η nΔ +τ εΔ CP Removal at ,ELG nΔ −τΔ CP Removal at ,ELG nΔ +τΔ Loop Filter of ST ,ELG nΔ VCO of ST SINR Estimation N-point FFT SINR Estimation N-point FFT Early branch Late branch , l n x ′ , , ( , ) l ELG f ELG f η nΔ ε −τ , , ( , ) l ELG f ELG f η nΔ ε +τ , 2 (f ELG f) j π ε τ t e− − , 2 (f ELG f) j π ε τ t e− + CP Removal at ,ELG nΔ Loop Filter of CF , f ELG ε VCO of CF , 2f ELG j πε t e−
Fig. 3. Architecture of the MSINR ELG synchronization recovery loop: (a) ST synchronizer (b) CF synchronizer. Note that the symbol indices l in
,ELG( )
nΔ l and εf ELG, ( )l
are dropped in this figure for notational simplicity.
0 5 10 15 20 25 10-7 10-6 10-5 10-4 10-3 10-2 10-1 SNR M S E N o rm lize d b y N MSINR-ELG-ST MSINR-GSA Min-ITF 1 Min-ITF 2 TD-NDA CRB
Fig. 5. MSEs of the compared ST synchronizers against the SNR.
0 5 10 15 20 25 10-7 10-6 10-5 10-4 10-3 10-2 10-1 SNR M SE N o rm liz e d b y Su b c a rr ie r Sp a c in g MSINR-ELG-CF MSINR-GSA TD-NDA CRB
compared frequency-domain algorithms.
IV. PERFORMANCE ANALYSIS
The variance of the tracking loop is approximately
propor-tional to the SINR estimation variance with 1/ 2
I
K′ factor,
where KI′ is the slope of the S-curve at the ideal
synchroniza-tion point. Further, if we assume that the ST estimasynchroniza-tion error is a wide-sense stationary white-noise process, after being filtered by L(z), the mean-squared error (MSE) of the synchronizer can be written as
(
)
2 2 1 1 , 2 2 ( ) ( ) ( ) 2 ELG C I E n l n L z L z z dz j K η σ π − − Δ Δ ⎡ − ⎤ ≥ ⎢ ⎥ ⎣ ⎦ ′∫
>
(19) where j= − , and 1 2 ησ is the Cramér-Rao lower bound (CRB)
of the SINR estimate in [12, Eq. 67]. The factor 2 in the RHS of (19) comes from the subtraction of the SINR estimates at the early and late synchronization points. The MSE of the CF synchronizer uses the same inequality as (19) except that the characteristic of the S-curve and the closed-loop system equa-tion are replaced with those used for the CF synchronizer.
V. SIMULATIONS
We use Monte Carlo simulations to evaluate the performance of the synchronizers, and consider an OFDM system of N = 256
subcarriers and a guard interval of NG = N/8 = 32 samples. Only
data subcarriers are assumed. The simulated modulation scheme is quadrature phase-shift keying (QPSK). The signal bandwidth is assumed to be 2.5 MHz and the radio frequency is 2.4 GHz. The subcarrier spacing is 8.68 kHz. The OFDM
symbol duration is 115.2 sμ . The CFO is 10% of subcarrier
spacing, i.e., 0.87 kHz, in all simulations. To verify the per-formance of the proposed technique, the channel is assumed to
have NG paths. The channel taps are randomly generated by
independent zero-mean, complex Gaussian variables. In each simulation run, 10,000 OFDM symbols are tested.
1) ST Estimation Performance: For the ST estimation, we
compare the proposed technique with the following blind or NDA techniques: (a) Blind minimum-interference ST syn-chronizer (Min-ITF 1) [6], (b) Blind minimum-interference ST synchronizer (Min-ITF 2) [5], and (c) NDA ML ST synchro-nizer (TD-NDA) [1]. The MSE of the estimated ST against SNR in multipath fading channels is shown in Fig. 5. In addi-tion to the MSEs of the MSINR-ELG-ST and MSINR-GSA (13), the CRB (19) is also shown. As can be seen, the MSINR synchronizer achieves smaller MSE than the compared syn-chronizers. In addition, the performance of the MSINR-GSA is better than the MSINR-ELG-ST. However, their performances are not too far apart. Therefore, the complexity can be greatly reduced by the ELG technique while not losing too much per-formance.
2) CFO Estimation Performance: For the CFO estimation,
we compare the proposed technique with the TD-NDA CFO estimation in [1]. The MSE of the estimated CFO (normalized
by the subcarrier spacing) against SNR in multipath fading channels is shown in Fig. 6. As can be seen, the ELG technique greatly reduces the complexity of the MSINR-GSA with a close performance to it.
Due to space limitation, the figures that demonstrate the acquisition time are not shown. However, by simulations, it is roughly around 50 symbols as targeted.
VI. CONCLUSION
In literature, the synchronization problem has been treated by the viewpoint of the estimation theory, for example, the ML approach. In this work, we intuitively deal with this problem by maximizing the SINR. The proposed technique is NDA and independent of the signal structure. It has been shown that the proposed ELG tracking loop is a good compromise between the performance and complexity.
ACKNOWLEDGEMENT
This work is supported in part by the grants NSC 95-2219-E-009-004 and MOEA 95-EC-17-A-01-S1-048, Taiwan.
REFERENCES
[1] J. J. van de Beek, M. Sandell, and P. O. Börjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Process., vol.45, no.7, pp. 1800-1805, Jul. 1997.
[2] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchro-nization for OFDM,” IEEE Trans. Commun., vol.45, no.12, pp.
1613-1621, Dec. 1997.
[3] H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and fre-quency synchronization for OFDM systems,” IEEE Trans. Wireless Commun., vol.2, no.4, pp. 822-839, Jul 2003.
[4] M. Speth, S. Fechtel, G. Fock, and H. Meyer, “Optimum receiver design for OFDM-based broadband transmission-part II: a case study,” IEEE Trans. Commun., vol.49, no.4, pp. 571-578, Apr. 2001.
[5] Q. Zhu and Z. Liu, “Minimum interference blind time-offset estimation for OFDM systems,” IEEE Trans. Wireless Commun., vol.5, no.8, pp.
2136-2142, Aug. 2006.
[6] A. J. AI-Dweik, “A novel non-data-aided symbol timing recovery tech-nique for OFDM systems,” IEEE Trans. Commun., vol.54, no.1, pp.
37-40, Jan. 2006.
[7] M. Speth, S. Fechtel, G. Fock, and H. Meyer, “Optimum receiver design for wireless broad-band systems using OFDM-part I,” IEEE Trans. Commun., vol.47, no.11, pp. 1668-1677, Nov. 1999.
[8] J. Li and M. Kavehrad, “Effects of time selective multipath fading on OFDM systems for broadband mobile applications,” IEEE Commun. Letters, vol.3, no.12, pp. 332-334, Dec. 1999.
[9] Y. Mostofi and D. C. Cox, “Mathematical analysis of the impact of timing synchronization errors on the performance of an OFDM system,” IEEE Trans. Commun., vol.54, no.2, pp. 226-230, Feb. 2006.
[10] G. C. Carter, C. H. Knapp and A. H. Nuttall, “Estimation of the magni-tude-squared coherence function via overlapped fast Fourier transform processing,” IEEE Trans. Audio Electroacoust., vol.AU-21, no.4, pp.
337-344, Aug. 1973.
[11] R. W. Lowdermilk and F. J. Harris, “Synthetic instruments extract masked signal parameters,” IEEE Instrum. Meas. Audio Mag., vol.8,
Is-sue 3, pp. 40-46, Aug. 2005.
[12] D. R. Pauluzzi and N. C. Beaulieu, “A comparison of SNR estimation techniques for the AWGN channel,” IEEE Trans. Commun., vol.48,
