Wireless Pers Commun (2017) 96:163–181 DOI 10.1007/s11277-017-4160-0
Time and Frequency Synchronization with Channel Estimation for SC-FDMA Systems Over Time-Varying Channels Hakan Dog˘an1 • Niyazi Odabas¸ ıog˘lu1 • Bahattin Karakaya1
Published online: 29 April 2017 Ó Springer Science+Business Media New York 2017
Abstract The constant amplitude zero autocorrelation sequence based synchronization and its usage in the block-type channel estimation for the single carrier frequency division multiple access (SC-FDMA) systems are vulnerable to the time-varying channels. Therefore, the channel estimation errors limit the performance of SC-FDMA systems in fast fading environments and result an irreducible error floor. In this paper, cyclic prefix based maximum likelihood estimator of time/frequency synchronization with comb-type channel estimation for the SC-FDMA systems are proposed to track the channel variations. Moreover, the residual time/frequency offsets calculations are derived for SC-FDMA systems. Simulation results confirm and illustrate that the proposed receiver is capable of tracking fast fading channel parameters and improving the overall performance as compared with the conventional receiver. Keywords SC-FDMA LTE CAZAC Synchronization Channel estimation Blocktype allocation Comb-type allocation High mobility
1 Introduction To reduce the high peak-to-average power ratio (PAPR) in orthogonal frequency-division multiple access (OFDMA) system, single-carrier frequency division multiple access (SCFDMA) that employs extra discrete Fourier transform (DFT) precoding at the transmitter
& Niyazi Odabas¸ ıog˘lu
[email protected] Hakan Dog˘an
[email protected] Bahattin Karakaya
[email protected] 1
Department of Electrical and Electronics Engineering, Istanbul University, Istanbul, Turkey
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has drawn great attention in the uplink communications [1]. Therefore, the SC-FDMA technology has been standardized as a fundamental air interface for the long term evolution (LTE) systems [2]. The SC-FDMA system requires a cyclic prefix (CP) which has a longer length than the finite impulse response (FIR) of channel memory to avoid the inter-symbol interference (ISI). The CP structure also provides a guard time between two successive SC-FDMA symbols. Therefore, it protects against possible inter-block interference (IBI). Moreover, it avoids the inter-carrier interference (ICI) between subcarriers due to the CP is a copy of the last part of the SC-FDMA symbol. However, the SC-FDMA transmission is very sensitive to receiver synchronization imperfections in wireless channels even the CP is used [3]. Moreover, for the coherent demodulation of SC-FDMA systems, estimation of transmission channel parameters is important to obtain the channel frequency response (CFR) by using the reference signals multiplexed in the transmitted signal [4]. Hence, both synchronization and channel estimation are crucial issues in the SC-FDMA receiver design. Time/frequency synchronization and channel estimation techniques considered for OFDMA could be applied to the SC-FDMA while both have fundamental similarities. Synchronization techniques can be considered in two groups such as data-aided and non data-aided. The data-aided techniques use pilots or preambles [5, 6] while the non-data aided techniques employee the correlation between CP and the last part of the symbol instead of preambles [7, 8]. Traditional synchronization techniques for the SC-FDMA systems focused on the receiver design based on the preamble structure because the constant amplitude zero autocorrelation (CAZAC) property of Zadoff-Chu (ZC) sounding reference sequence (SRS) is exploited in the frame structure of LTE uplink [9–11]. Pun et al. [11], proposed the maximum likelihood (ML) based joint channel and frequency offset estimation algorithm for SC-FDMA system using one training block while its complexity is prohibitively high because of the required matrix inversion calculation, particularly when the number of subcarrier is large. Most of these earlier works consider quasi-static channels while they are most vulnerable to the time-varying channels. Recent works are focused on to enable mobile broadband services at vehicular speeds beyond 100 km/h for OFDM based systems [12, 13]. Therefore, Cheon, [14], also proposed the usage of CP and the two demodulation reference symbols (DMRS) for the SC-FDMA system while the perfect channel state information (CSI) is available at the receiver. The channel estimation in fast time-varying channels is one of the most challenging problems for the SC-FDMA systems similar to the OFDMA. The channel is unsteady during a symbol duration, which ruins the orthogonality between subcarriers and generates the ICI in such a high mobility environment. Block-type pilot arrangement used in the uplink LTE dedicates all frequency channels within a given time slot to either channel estimation or data transmission while it is a suitable strategy for slow time-varying channels. Karakaya et al. [15], used the combination of block-type channel estimation based on the CAZAC pilot sequence and Kalman filter that consider the radio channel as a dynamic process with the path taps and polynomial curve fitting to track of channel estimation variations. However, it requires a high complexity because of polynomial fitting and Kalman equations. Moreover, it also requires predetermined polynomial degrees for different mobilities. To have lower complexity, Huang et al. [16], proposed a sliding windowing based channel estimation. Alternatively, the time variations of the frequency domain transmission function are modeled by the basis expansion model (BEM) is also proposed in [16]. All of these works assume the perfect synchronization is available at the receiver while the channel estimation error in the presence of timing errors should be considered [17, 18].
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Alternatively, it is more reasonable to use comb-type pilot insertion which employs pilot and data symbols mixed in the frequency domain within each SC-FDMA symbol to track channel variations instead of block type pilot insertion when fluctuations between consecutive transmitted symbols are not negligible [19]. In this case, the channel estimation that employs the comb-type pilot arrangement allows the tracking of fast fading channel parameters with a lower complexity [20, 21]. The coarse time synchronization and comb-type channel estimation are presented for the SC-FDMA and cooperative system in [22] and [23]. In this paper, we address the problem of jointly estimating carrier frequency offsets (CFO), timing offsets, and channel response of SC-FDMA system under timevarying channel. The first step in the proposed algorithm is the joint time and frequency ML estimation offset done by the CP for each SCFDMA symbol. The next step is to employee the least squares (LS) technique to estimate the channel parameters at pilot frequencies and interpolate them by spline interpolation technique. Our purpose is to show advantage of proposed scheme over the CAZAC based synchronization and block type channel estimation for SC-FDMA systems. The rest of paper is organized as follows. In Sect. 2, we introduce the channel model and the signal model for the SC-FDMA systems. This is followed by the synchronization techniques in Sect. 3. Finally, computer simulation results are provided in Sect. 4, while conclusions are given in Sect. 5.
2 System Model 2.1 Channel Model The complex baseband representation regarding to a wireless mobile time variant channel impulse response (CIR) can be illustrated by X ai ðtÞdðt si Þ h0 ðt; sÞ ¼ ð1Þ i
where ai ðtÞ is the time-variant complex tap parameters of the i-th path and si is the analogous path delay. The fading channel parameters ai ðtÞ can be formed as zero mean complex Gaussian random variables. The fading channel parameters in different delay taps are statistically independent depended on the wide sense stationary uncorrelated scattering (WSSUS) assumption. Fading parameters are considered to be correlated in the time domain. These parameters have Doppler power spectrum density formed as in [24] with the following autocorrelation function E½ai ðt1 Þai ðt2 Þ ¼ r2ai J0 ð2pfd Ts ðt2 t1 ÞÞ
ð2Þ h i where r2ai ¼ E jai ðtÞj2 stands for the average power of the i-th path channel parameter, fd is the maximum Doppler frequency in Hertz. Also ð:Þ and E½: denote conjugate and expectation, respectively. J0 ð:Þ is the zeroth order Bessel function of the first kind. The term fd Ts shows the normalized Doppler frequency and Ts is the sampling period. In the practical systems, the pulse shaping filter at the transmitter and matched filter in the receiver are usually the same in terms of frequency response. When we consider the effect of transmitter-receiver pair pulse shaping, Eq. (1) can be written as follows [25]:
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hðt; sÞ ¼ h0 ðt; sÞ cðsÞ X ai ðtÞcðs si Þ ¼
ð3Þ
i
where stands for convolution operation, and cðsÞ ¼ ct ðsÞ cr ðsÞ is the combined impulse response of the transmitter-receiver pair pulse shaping filter. In this paper, the combined impulse response of the transmitter-receiver pair is considered as the raised cosine filter and given by cos pbs Ts s ð4Þ cðsÞ ¼ sinc Ts 1 4b22s2 Ts
where b denotes the roll-off factor. Continuous channel transfer function (CTF) can be picked up from Eq. (3) as follows: Z 1 hðt; sÞej2pf s ds Hðt; f Þ ¼ 1 ð5Þ X ¼ Cðf Þ ai ðtÞej2pf si i
where C(f) is the Fourier transform of impulse response, cðsÞ, of the transceiver pair and it can be written as 8 1b > jfj > > Ts ; < 2Ts pTs 1b 1b 1þb ð6Þ Cð f Þ ¼ Ts > 1 þ cos jfj ; \j f j > > 2T 2T 2T 2 b s s s : 0; otherwise If the synchronization tasks are sufficiently done and an adequately long CP is selected, the discrete subcarrier-related CTF for the LTE uplink system can be depicted as X j2pkl H½n; k ¼ h½n; le N ¼ C½k
X
l
ai ðnTs Þej2pkDf si
ð7Þ
i
where h½n; l,hðnTs ; lTs Þ ¼
X
ai ðnTs ÞcðlTs si Þ
i
ð8Þ
is the CIR which has sample-spaced delays at lTs time instant.
2.2 Signal Model for SC-FDMA Systems The SC-FDMA which has an analogous performance as the OFDMA and can be considered as the DFT-spread OFDMA, where the time-domain data symbols are transformed to frequency domain by the DFT as shown in Fig. 1. We take an M-point DFT to spread the time-domain signal d[m] into the frequency domain:
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Fig. 1 Block diagram for the SC-FDMA system 1 X 1 M D½j ¼ pffiffiffiffiffi d½mej2pmj=M M m¼0
After spreading, D½j is allocated the k-th subcarrier S[k] as follows: D½j; k ¼ CM ½j S½k ¼ 0; k ¼ ðU CM ½jÞ
ð9Þ
ð10Þ
where CM ½j stands for M-point mapping set ðj ¼ 0; . . .; M 1Þ, U is a set of indices whose elements are f0; . . .; N 1g with N [ M. The N output samples of the inverse discrete Fourier transform (IDFT) is extended by a guard interval containing G sample cyclic extension whose length is selected to be longer than the expected channel delay spread to avoid the inter-symbol interference (ISI). The output of the IDFT is a discretetime signal with sampling time Ts ¼ Tn =N. Signal is transmitted with the total symbol duration of T ¼ Tn þ Tg ¼ ðN þ GÞTs where Tn and Tg are durations of data and cyclic prefix respectively. Cyclic prefix duration refers to the prefixing of a symbol with a repetition of the end. The baseband transmitted single carrier signal is given by N1 1 X S½kej2pkDf ðtTg Þ ct ðtÞ s0 ðtÞ ¼ pffiffiffiffi N k¼0 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
ð11Þ
sðtÞ
¼ sðtÞ ct ðtÞ where Df is the subcarrier spacing. The received signal while considering uncertainty in the arrival time and frequency offset can be written as yðtÞ ¼ ðhðt; sÞ sðt qÞÞejð2ptÞ þ wðtÞ
ð12Þ
where q and represent time and frequency offset, respectively. Also, wðtÞ is the additive white Gaussian noise (AWGN) with N ð0; r2w Þ.
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The received signal samples are collected during a fixed length of Ts seconds as follows; y½n ¼ yðnTs Þ for
n ¼ 1; 2; . . .;
ð13Þ
3 Synchronization Techniques Estimation of the symbol timing offset is very crucial, because an incompetent estimate crucially degrades the overall performance of SC-FDMA systems. To overcome the adverse effect of the synchronization errors, precise synchronization is imperative for continuous or burst packet mode transmission systems. The symbol timing is estimated to determine the correct starting position of the fast Fourier transform (FFT) operation at the receiver for the SC-FDMA symbol. In this paper, we compare the conventional CAZAC sequence based symbol time synchronization with the cyclic based symbol time synchronization for SC-FDMA systems in time-varying channel with channel estimation considerations. In the first approach, the CAZAC sequence is placed at the beginning of the frame and the symbol/frame timing is found by searching the CAZAC sequence to find the start of the frame and know where the training symbols are located. In this case, block-type channel estimation is done by the training symbols that are distributed over all subcarriers. It is show that the CAZAC preamble which holds periodic autocorrelation property provides a correct estimate. However, it reduces the bandwidth efficiency and the channel variations could not be tracked between the training symbols for high mobility cases. Alternatively, if the synchronization is done by algorithms that exploit the redundancy of the CP then pilots could be distributed for each SC-FDMA symbol to track the channel variations.
3.1 Time Synchronization 3.1.1 CAZAC Sequence Based Coarse Time Synchronization The SC-FDMA based LTE receivers employ ZC sequence that is a periodic complexvalued signal with modulus one and out-of-phase periodic (cyclic) autocorrelation equal to zero. The u-th root ZC sequence is defined by zu ½n ¼ ej
punðnþ1Þ Z
;
0nZ 1
ð14Þ
where Z is the length of ZC sequence [26]. The CAZAC sequence based coarse time synchronization is carried out with correlation searching by the help of ZC sequence as shown in Fig. 2. On the received signal, initial point (q0c ) of frame is detected coarsely by Pðq0c Þ ¼
NþG1 X k¼0
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y½q0c þ k zu ½k
ð15Þ
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Fig. 2 Frame synchronization techniques
q0copt ¼arg max Pðq0c Þ
ð16Þ
q0c
where q0c is the first point of observation window (OW) and slides along all received symbols.
3.1.2 Cyclic Based Coarse Time Synchronization For a cyclic based coarse time synchronization, we employed the ML estimation that basically correlates the received samples. In this case, the algorithm could detect the position of the cyclic prefix as shown in Fig. 2. Initial point (q0c ) is estimated coarsely by Pðq0c Þ ¼
G1 X
y ½q0c þ k y½q0c þ k þ N
ð17Þ
k¼0
Eðq0c Þ ¼
G1 X y½q0 þ k2 þ y½q0 þ k þ N2 c c
ð18Þ
k¼0
q0copt
Pðq0c Þ ¼ arg max Eðq0c Þ q0c
ð19Þ
where Pðq0c Þ is the correlation value of cyclic prefix, and Eðq0c Þ is energy term of cyclic prefix. Also note that, q0c is a time index corresponding to first sample in the first observation window. As shown in Fig. 2, the observation window slides over time and searches the received data packets. To write the received signal after the coarse time synchronization, we substitute Eq. (11) in Eq. (12) and take the convolution integral with the help of Eq. (5), we get:
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170 N1 ejð2ptÞ X yc ðtÞ ¼ pffiffiffiffi S½kH ðt; kDf Þej2pkDf ðtðqqc ÞTg Þ N k¼0
ð20Þ
þ wðtÞ where qc ¼ q0copt Ts . Please note that, both techniques give the start of the frame and symbol timing, but there is still a plateau may lead to some uncertainty as to the start of the frame. Moreover, these techniques estimate the symbol timing in order of Ts while the delay may not be the exact order of Ts . A precise timing in a symbol duration must be done to increase the system performance. Therefore, an additional fine synchronization is also applied at the receiver.
3.1.3 Fine Time Synchronization Coarse time synchronization is carried out by the techniques in Sects. 3.1.1 and 3.1.2, for the CAZAC based structure and proposed CP based structure, respectively. With the coarse time synchronization, initial point of frame that is necessary for the FFT process is found coarsely. The point which is found by the coarse time synchronization is located at where the multiples of Ts . To get a precise initial point, fine time synchronization will be explained in this section. Without loss of generality, the noiseless received signal can be written as y0 ðtÞ ¼ sðtÞ cðtÞ
ð21Þ
Equation (21) can be written as follows if a random time offset, q, is occured: y0 ðt qÞ ¼ sðt qÞ cðtÞ ¼ sðtÞ cðt qÞ
ð22Þ
These Eqs. (21) and (22) tell us that, after the sampling at nTs , Eq. (21) is equivalent to s(t) convolves with dðtÞ which is the sampled version of c(t) and has a peak point of one while others are zero; but for Eq. (22), the equation becomes a convolution with multi tap signal cðnTs qÞ which causes causes an energy degradation as compare with the perfect case. In this case, the total energy will be maximum for the fine-tuned case. X X 2 2 jððsðtÞ cðtÞÞjt¼nT s Þj [ jððsðt qÞ cðtÞÞjt¼nT s Þj ð23Þ n
n
So the fine synchronization could also be applied for SC-FDMA system based on searching the time offset which maximizes the energy of y(t) at oversampled coarsely synchronized signal. After the coarse time synchronization Eq. (20) is acquired. Then resolution of searching is increased by Ts0 ¼ Ts =f where f is the oversampling factor for fine-time synchronization process. Due to the nature of pulse shaping filter applied for SC-FDMA system, peak point of the filter is located before or after from nTs with multiples of Ts0 . Position of the filter is changed within Ts with q0f Ts0 for ðf=2Þ q0f \ðf=2Þ and fined initial point, q0f , is obtained with energy term from Eq. (20) as follows [27]:
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( q0f opt
¼ arg max q0f
X n
171
2
)
jðyc ðtÞjt¼nT s þq0 Ts0 Þj f
ð24Þ
With Eq. (24), the coarse time synchronization, q0copt , is fined as q0opt ¼ q0copt þ q0f opt . After the fine time synchronization, Eq. (20) can be rewritten as N 1 ejð2ptÞ X ^ gÞ yf ðtÞ ¼ pffiffiffiffi S½kH ðt; kDf Þej2pkDf ðtðqqÞT N k¼0
ð25Þ
þ wðtÞ where q^ ¼ q^0opt Ts . As in [7], cyclic prefix is exploited by the ML estimation algorithm.
3.2 Frequency Offset Estimation Under the assumption the received signal is only corrupted by frequency offset, the time domain received signal could be written as; yH ðtÞ ¼ sðtÞej2pt
ð26Þ
When the received signal is sampled at t ¼ n=fs , where fs is the sampling frequency, Eq. (26) can be rewritten as yH ½n ¼ s½nej2pn=fs
ð27Þ
With a normalized frequency offset, 0 , Eq. (27) can be rewritten as 0
yH ½n ¼ s½nej2pN n
ð28Þ
where ¼ 0 Df . Let, Eq. (28) is a received cyclic prefix sample at n, so the corresponding received data sample which N samples apart at n þ N can be expressed as 0
yH ½n þ N ¼ s½n þ Nej2pN ðnþNÞ 0
0
¼ s½neðj2p þj2pN nÞ
ð29Þ
In Eq. (29), the definition of the cyclic prefix is exploited that the cyclic prefix is just a copy of the last G samples of a symbol and so s½n þ N ¼ s½n. The phase difference, between the cyclic prefix and its corresponding data samples, is specified by 2p0 ¼ \ ðyH ½n yH ½n þ NÞ
ð30Þ
Then ^0 of 0 can be estimated from Eq. (30) as follows: ^0 ¼
1 \ ðyH ½n yH ½n þ NÞ 2p
ð31Þ
With the nTs sampled version of Eq. (25), the CP based average frequency offset estimation could be written as ^0 ¼
G1 1 X ðy ½n y½n þ NÞ \ 2p n¼0
ð32Þ
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3.3 Residual Time and Frequency Offsets After the correction of these offsets, there are still residual time and frequency offset, which are q~ ¼ q q^ and ~ ¼ ^, respectively where ^ ¼ ^0 Df . Equation (25) can be rewritten as N 1 ejð2p~tÞ X ~ gÞ S½kH ðt; kDf Þej2pkDf ðtqT y~ðtÞ ¼ pffiffiffiffi N k¼0
ð33Þ
þ wðtÞ By sampling with fs , Eq. (33) can be written after the cyclic prefix removal as follows: N1 j2pð~0 þkÞn j2pkq~0 1 X y~½n ¼ pffiffiffiffi S½kH½n; ke N e N N k¼0
ð34Þ
þ w½n where q~ ¼ q~0 Ts and ~ ¼ ~0 Df . Thus the FFT output at k-th subcarrier can be shown in the following scheme N 1 j2pnk 1 X Y½k ¼ pffiffiffiffi y~½ne N þ w½n N n¼0
ð35Þ
¼ H½k þ I ½k þ W ½k where H½k is the obtained signal of S[k] signal transmitted at k-th subcarrier by all time offset, frequency offset and channel effects. H½k ¼
N 1 j2pkq~0 X j2p~0 n 1 S½ke N H½n; ke N N n¼0
ð36Þ
I[k], ICI caused by the time-varying nature of the channel along with time and frequency offset, is given by I½k ¼
N 1 N 1 j2pðkm~0 Þn j2pmq~0 X 1X N S½me N H½n; me N m¼0 n¼0
ð37Þ
m6¼k
and W[k] shows the Fourier transform of noise vector w[n] as follows: W½k ¼
N 1 X
w½ne
j2pnk N
:
ð38Þ
n¼0
There is an irreducible error floor even in the training sequences since pilot symbols are also corrupted by the ICI due to the I[k] term. The orthogonality between subcarriers is corrupted because of the Doppler frequency caused by the time-varying channel. Therefore, a channel estimation should be carried out before the FFT block. A high quality estimate of the CIR, synchronization of time offset and CFO is compulsory to compensate the ICI effects at the receiver. We accept that equalization is carried out in frequency
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domain after the subcarrier demapping block. Data are acquired after the demapping as illustrated below: X½j ¼ Y½k ¼ H½k þ I½k þ W½k:
ð39Þ
where k ¼ CM ½j and and j ¼ 0; . . .; M 1.
3.4 Channel Estimation Channel estimation is essential for the coherent receiver to equalize the received information correctly. It is shown that two dimensional (2D) Wiener filter interpolation is optimal for multi-carrier systems such as OFDM [28]. However, it requires channel statistics and its complexity is too high for practical implementation. To achieve the tradeoff between complexity and accuracy, the one dimensional (1D) channel estimations are satisfactory alternative for OFDM systems. Block-type pilot based channel estimation and comb-type pilot based channel estimation are two basic 1D channel estimations. In blocktype pilot arrangement, the pilot signals are inserted to the particular SC-FDMA symbol and sent periodically in time domain while the pilot signals are uniformly distributed within each SC-FDMA symbol in comb-type pilot arrangement. The LS channel estimation is initially done over the pilot subcarriers. After the subcarrier demapping process, Eq. (36) can be rewritten at pilot subcarriers as H½k ¼
N 1 j2pkq~0 X j2p~0 n 1 D½ke N H ½n; ke N N n¼0
ð40Þ
where k ¼ CM ½j; j 2 Cp and Cp is the set of pilot indices. D[k] is pilot symbol which is known by the receiver. CFR, which corresponds to pilot symbol, can be found by the following equation
X ½kD ½k H~ ½k ¼ jD½kj2
ð41Þ
~ is interpolated by chosen interpolation method due to obtain estimated H½k ^ Then, H½k where k ¼ CM ½j; j 2 f0; 1; . . .; M 1g. In this paper, the spline interpolation method is applied for the proposed frame structure to enhance the channel estimation performance. ^ H½k where k ¼ CM ½j; j 2 f0; 1; . . .; M 1g can be found without any interpolation method in CAZAC based frame structure due to use one SC-FDMA symbol as a pilot sequence.
4 Simulation Results This section presents the bit error rate (BER) performance of the proposed time and frequency synchronization with channel estimation methods in SC-FDMA systems for time-varying mobile radio channels. Minimum mean square error (MMSE) equalization technique is used for all simulations. While binary phase shift keying (BPSK) is simulated for uncoded SC-FDMA system, quadrature phase shift keying (QPSK) is used for coded SC-FDMA system to preserve the bandwidth efficiency.
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174 Table 1 CAZAC based frame structure system parameters
Table 2 Comb type based frame structure system parameters
Table 3 Channel coding parameters
Parameters
Value
DFT size(M)
304
FFT size(N)
512
Subcarrier spacing
Df ¼ 15 kHz
Carrier frequency
fc ¼ 2:4 GHz
Cyclic prefix length
128
Subcarriers mapping
Localized
Channel model
COST-207(TUx6)
Modulation
BPSK, QPSK
Mobility
V ¼ 30; 150 km/h
Parameters
Value
DFT size(M)
228
Pilot numbers
76
FFT size(N)
512
Subcarrier spacing
Df ¼ 15 kHz
Carrier frequency
fc ¼ 2:4 GHz
Cyclic prefix length
128
Subcarriers mapping
Localized
Channel model
COST-207(TUx6)
Interpolation technique
Spline
Modulation
BPSK, QPSK
Mobility
V ¼ 30; 150 km/h
Parameters
Value
Component encoders
Convolutional codes
Code rate
1/2
Constraint length
7
Code generator polynomials (octal)
[171 133]
Interleaver
Random interleaver
Time and frequency offsets are assumed to be uniformly distributed between 0 40 ls and 0 7:5 kHz, respectively. System parameters for the simulation are summarized in Tables 1, 2 and 3 for the CAZAC frame structure, comb type frame structure, and channel coding parameters, respectively. While expressing simulation results, some abbreviations which are shown in Table 4 are used in figures’ legends. It is important that very high mobility is one of the key features of the 3rd generation partnership project (3GPP) in the form of the LTE project. Meanwhile, broadband communications with mobilities more than 120 km/h are potential applications, particularly for high speed trains.
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Abbreviation
175
Definition
No TS
No Time Synchronization
Coarse TS
Coarse Time Synchronization
Fine TS
Fine Time Synchronization
PDI
Perfect Delay Information
No FS
No Frequency Synchronization
FS
Frequency Synchronization
PFI
Perfect Frequency Information
Fig. 3 The BER performance of uncoded BPSK SC-FDMA system for V ¼ 30 km/h
Figure 3 compares the uncoded BER performance of the CAZAC based synchronization algorithms with the proposed comb type based synchronization for V ¼ 30 km/h. It is shown that the reliable communication is not possible when the delay estimation (DE) is not done at the receiver. Moreover, an importance of the fine DE over the course DE is also observed. The SC-FDMA systems are vulnerable to channel variations even for lowmobility cases. Therefore, it is seen that the proposed receiver is also slightly better than the conventional receiver in the case of perfect delay estimation (PDE). Computer simulations show that the BER performance of the proposed receiver consist of comb-type estimation and CP based ML synchronization is slightly better than the CAZAC based conventional receiver for Typical Urban (TU) channel with the 6-taps. While SC-FDMA based system continue to provide essential wide-area coverage, it also should support high-mobility users. In Fig. 4, it is seen that the proposed receiver has a better uncoded BER performance than the CAZAC based conventional receiver for V = 150 km/h. It is observed that there is a point after which the curve does not fall as quickly as before for the conventional receiver for high mobility cases because of residual time and frequency offsets derived in Sect. 3.3.
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Fig. 4 The BER performance of uncoded BPSK SC-FDMA system for V ¼ 150 km/h
Fig. 5 The BER performance of frequency synchronization for uncoded BPSK SC-FDMA system V ¼ 30 km/h
Carrier frequency offset generally observed when the local oscillator of SC-FDMA system for down-conversion in the receiver does not exactly synchronize with the carrier signal contained in the received signal. When CFO occurs, the received signal will be shifted in frequency and cause the ICI because of the orthogonality among sub carriers. Therefore, we investigated the BER performance of the frequency synchronization for
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Fig. 6 The BER performance of frequency synchronization for uncoded BPSK SC-FDMA system V ¼ 150 km/h
Fig. 7 The BER performance of coded QPSK SC-FDMA system for V ¼ 30 km/h
uncoded proposed receiver in Figs. 5 and 6 for V = 30 and V =150 km/h respectively. It is obviously seen from these figures that the frequency synchronization algorithm is not affected by the high mobility effect. Practical SC-FDMA based communication systems exploit channel coding techniques to obtain better BER performance while it transmits enough redundant data to allow
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Fig. 8 The BER performance of coded QPSK SC-FDMA system for V ¼ 150 km/h
receiver to recover errors. It is clear that if a forward error correction code is used, the bandwidth efficiency is reduced according to the uncoded modulation case. Therefore, in following figures, QPSK is used by the code rate = 1 / 2 to preserve the bandwidth efficiency. In Figs. 7 and 8, coded BER performance of proposed comb-type based structure and the CAZAC based structure are compared. It is demonstrated that the proposed receiver structure is also better than the CAZAC based receiver for channel coded cases. In other words, it is shown that the channel coding does not help to solve the error floor problem for the conventional receiver in the case of practical high mobility channel impairments.
5 Conclusions A considerable amount of research has been done to develop the SC-FDMA receivers based on the CAZAC sequences by assuming a quasi-static fading model. In this paper, we proposed a time/frequency synchronization and channel estimation method in the presence of time varying wireless channels for SC-FDMA systems. We presented a discussion which compares the block-type and comb-type approaches for the SC-FDMA systems when both synchronization and channel estimation issues to be solved. It has been shown that the proposed receiver has comparable performance to the CAZAC based conventional receiver for low mobility while it has significant advantages for high mobility cases. In conclusion, we showed comb-type pilot aided SC-FDMA are more appropriate if we apply the CP based ML time/frequency synchronization for fast fading channels. Acknowledgements This work is supported in part by the Turkish Scientific and Technical Research Institute (TUBITAK) under Grant 114E001. This work is also supported in part by the Research Fund of the University of Istanbul. Project Number: 45861
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25. Akhtman, J., & Hanzo, L. (2005). ‘‘Sample-spaced and fractionally-spaced cir estimation aided decision directed channel estimation for OFDM and MC-CDMA,’’ VTC-2005-Fall. 2005 IEEE 62nd Vehicular Technology Conference, 2005. pp. 1916–1920 26. 3GPP TS 36.211 V12.6.0 (2015–07), ‘‘3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation ’’ (Release 12). 27. Yu, J.-Y., Chung, C.-C., & Lee, C.-Y. (2008). A symbol-rate timing synchronization method for low power wireless OFDM systems. IEEE Transactions on Circuits and Systems II: Express Briefs, 55(9), 922–926. 28. Hoeher, P., Kaiser, S., & Robertson, P. (1997). Two-dimensional pilot-symbol-aided channel estimation by Wiener filtering. In Acoustics, speech, and signal processing, 1997. ICASSP-97, 1997 IEEE international conference on vol. 3. IEEE, pp. 1845–1848. Hakan Dog˘an was born on December 10, 1979, in Istanbul, Turkey. He received the B.S.E in Electronics Engineering in 2001, and the M.S.E. and Ph.D. degrees in Electrical Electronics Engineering in 2003 and 2007, respectively, all from the Istanbul University. From 2001 to 2007 he was employed as a research and teaching assistant at the faculty of the Department of Electrical and Electronics Engineering, Istanbul University. In 2007, he joined the same faculty as an Assistant Professor, where he is presently an Associate Professor. He has been also an adjunct professor in the Turkish Air Force academy since 2008. His interests lie in the areas of estimation theory, statistical signal processing, and their applications in wireless communication systems. His current research areas are focused on wireless communication concepts with specific attention to synchronization, equalization and channel estimation for single carrier, spread-spectrum and multicarrier systems. He was a visiting scholar at the Purdue University, Fort Wayne, USA from May 15, 2010 to 16 August, 2010. Niyazi Odabas¸ ıog˘lu received the B.S., M.S. and PhD degrees from Istanbul University in 1999, 2002 and 2006 respectively all in Electrical and Electronics Engineering. From 1999 to 2006, he was a Research Assistant with the Istanbul University, Electrical and Electronics Engineering Department, Istanbul, Turkey. After he finished PhD, Dr. Odabasioglu has performed research as a postdoctoral research fellow from 2006 to 2007 in Arizona State University, Tempe,AZ,USA. In 2007, he joined the faculty of the Department of Electrical and Electronics Engineering at Istanbul University as an Assistant Professor and now he is an Associate Professor. His general research interests cover various physical layer aspects of communication systems: cooperative communication, free space optical communication, modulation techniques, diversity techniques and channel coding.
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Bahattin Karakaya received his B.S., M.S. and Ph.D. degrees in Electrical and Electronic Engineering from Istanbul University, Istanbul, Turkey, in 1998, 2002 and 2010, respectively. During his Ph.D. study, he collaborated with the WCSP research group in University of South Florida, FL, USA. He worked as a Postdoctoral researcher in a project at Qatar University from 2011 to 2014. He is currently working as an Assistant Professor in Istanbul University since May 2015. His research interests include channel estimation, OFDM and SC-FDMA based systems, cooperative communication, underwater acoustic communications.
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