According to the proposed iterative approaching algorithm, the global maximum of log-likelihood function can be definitely found to achieve both frequency and time synchronization[r]

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the channel’s maximum delay spread is shorter than the length of the cyclic prefix. Assuming a mobile speed of 100 km/h, cor- responding to a Doppler **frequency** of approximately 463 Hz when the carrier **frequency** is 5 GHz, we plot the corresponding MSE performance **in** Figs. 7 **and** 8. As our derivations assume a quasi-static channel that remain unchanged during the preamble period, the **estimation** performance is degraded due to the fact that the received signal model (4) is no longer valid. **In** sum- mary, Algorithms **and** **and** the MTB estimate render the best performance, followed by Algorithm , **and** then the other correlation-based algorithms. When is small, Algorithms , , **and** yield almost the same MSE performance. The pro- posed methods can be used when an arbitrary number of identical pilot symbols are available.

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A. Residual **Frequency** Tracking Error
**In** the acquisition stage, we assume that the residual fre- quency error after the **frequency** tracking stage is an integral multiple of the subcarrier spacing. However, there exists a residual **frequency** tracking error that introduces ICI **and** de- grades the performance of the acquisition scheme. To explore how the residual **frequency** tracking error affects the acquisi- tion scheme, a computer simulation is taken. Fig. 15 shows the plots of versus the normalized residual **frequency** tracking error. The solid-line curve **and** the dashed-line curve represent the estimated by (22) **for** SNR dB **and** SNR dB, respectively. **In** Fig. 15, the “ ” symbols **and** the “ ” symbols represent the Monte Carlo simulations results **for** SNR dB **and** SNR dB, respectively. To speed up our simulation, the acquisition range is set to ten. We can see that the missed lock probability of the acquisition scheme is still very low even the residual **frequency** tracking error is as large as 0.47 times of the subcarrier spacing. That is, the proposed acquisition scheme is insensitive to the tracking error. As shown **in** Fig. 7, the residual tracking error after the **frequency** detector without averaging process is smaller than 0.15 times of the subcarrier spacing, which is tolerable to the proposed acquisition scheme.

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The carrier frequency offset can he estimated by first calculating the pilot-suhcarrier phase difference between two OFDM symbols, removing the quantity contributed by the [r]

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A typical **OFDM** system based on IEEE 802.11g **for** WLAN was adopted as a reference-design platform to evaluate the per- formance of the proposed algorithm. The parameters employed **in** the simulation platform were **OFDM** symbol length 64 **and** cyclic prefix 16. IEEE 802.11g includes ten short training symbols **for** coarse **estimation**, **and** two long preambles **for** fine **estimation**. A satisfactory accuracy can usually be reached if sufficient data samples are applied to compute the estimate from the short training symbols. Consequently, the proposed method only uses short training symbols to measure the **frequency** **offset** under IQ-M conditions. **In** this experiment, the gain **and** phase errors were set to 2 dB **and** 20 , respectively. The CFO amount was simulated with values **in** the range of ppm to ppm at a carrier **frequency** of 2.4 GHz, **and** the additional P-CFO was set to 30 ppm. Table I lists the simulation parameters **for** **frequency**-selective fading channels. **For** a fair comparison, the two-repeat preamble-based scheme also used three training symbols to estimate the CFO value. Fig. 6 shows the **estimation** of **frequency** **offset** versus the exact CFO value, based on the simulation parameters **in** Table I. Simulation results indicate that the proposed algorithm can estimate the **frequency** **offset** more accurately than the two-repeat preamble-based scheme.

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Therefore, an accurate **estimation** of the **frequency** **offset** is critical.
Existing approaches **for** the **frequency**-**offset** **estimation** using the pre- amble data [6], [7], the cyclic preﬁx data [8], [9], or the cyclostationary property [10] of the received signals have been proposed. Extensive coverage of techniques **for** digital **synchronization** is also provided **in** textbooks [11]–[13]. Here, we focus on the data-aided maximum-like- lihood (**ML**) **estimation** **in** **OFDM** **systems**. The **ML** **estimation** of fre- quency **and** **time** offsets **in** **OFDM** **systems** using the two sets of iden- tical cyclic preﬁx data has been derived **in** [8]. **In** the IEEE 802.11a [14] standard **for** wireless LAN communications, the preamble con- tains multiple sets of identical data **for** channel **estimation** **and** syn- chronization. Hence, an extension **for** the **ML** **estimation** algorithm to include **for** multiple sets of identical data is practically useful **and** worth studying. Therefore, **in** this paper, by using the matrix inversion lemma [15], we generalize the **ML** algorithm **for** the **estimation** of **frequency** **and** **time** offsets to include **for** the number of the identical data set more than two. Moreover, we also derive the Cramér–Rao bound **for** the fre- quency-**offset** estimate. Since the resulting **ML** algorithm requires high realization complexity, we further develop a simpliﬁed algorithm that can reduce signiﬁcantly the realization complexity but at the cost of modest performance degradation. Simulations are then carried out to evaluate the performance of all proposed algorithms using the ten short identical symbols **in** the preamble of IEEE 802.11a standard.

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adaptive filter bank, copied from the lower branch, performs despreading **and** MAI suppression, **and** pilot symbols assisted **frequency** **offset** **estimation**, channel vector **estimation** **and** RAKE combining give the desired signal symbols. With signal subtraction **in** the lower branch, the proposed MC-CDMA re- ceiver can achieve nearly the performance of the ideal MSINR receiver within a few iterations. Finally, a low-complexity PA realization of the GSC adaptive filters is presented **for** a multiuser scenario. The new PA receiver is shown to be robust to multiuser channel errors, **and** offer nearly the same perfor- mance of the fully adaptive receiver. **In** summary, the proposed MC-CDMA receiver with PA MAI suppression performs near optimal signal detection with tolerance to large **frequency** offsets **and** resistance to strong MAI. More importantly, it can be initialized **in** the blind mode without the aid of channel **estimation** **and** **frequency** **offset** compensation.

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very high. The distinct feature of the proposed algorithm is that it only requires a root-searching procedure. The main idea is to use a series expansion when evaluating the **ML** function. The performance of the expansion is also analyzed. The operations of the proposed method are simple, **and** the computational complexity is low. Simulations show that the proposed method can approach the CRB. As shown **in** Fig. 1, a large EVS will be induced **in** the full-loaded scenario (Δq = 1), **and** the perfor- mance of the proposed method will seriously be affected. The problem can be solved by an expectation-maximization (EM) algorithm referred to as **iterative** space alternating generalized EM (SAGE) [23], [24]. However, the complexity of the SAGE algorithm can be very high **for** large N s . Note that **in** real- world applications, only a number of users will be activated at a specific **time** [24]. Thus, only the CFOs of the newly activated users have to be estimated, **and** the knowledge of the previously estimated CFOs can be exploited **in** each new **estimation**. It is interesting to incorporate the SAGE algorithm into the proposed method, which may serve as a topic **for** further research.

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Symbol-timing **and** **frequency** **offset** **estimation** **for** **OFDM** are widely discussed **in** the literature. However, relatively few results are available **for** the **estimation** of sampling clock **offset**. Sampling clock **offset** **estimation** **and** compensation are important **in** an **OFDM** system because sampling clock **offset** can cause a severe drift **in** symbol-timing, thus causing inter-carrier **and** inter-**OFDM**-symbol interference. The problem is especially severe when a large number of subcarriers is used. **For** example, **in** DVB-T with 2048 sub-carriers (2K mode), if the sampling clock **offset** is 10 parts per million (ppm) of the sampling **time** duration, the resulting drift is about 77 samples per second. Therefore sampling clock **offset** **synchronization** is an important issue that needs to be solved **for** a practical **OFDM** system.

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2. **OFDM** System Model
A simplified **OFDM** system model is shown **in** Fig. 1. **In** the figure, X l ,k / ˜X l ,k is the transmitted/received FD data on the k-th subcarrier of the l-th symbol, 1/T S is the sampling **frequency**, f c is the carrier **frequency**, **and** n Δ is the estimated STO. On the transmitter side, N complex data symbols are modulated onto N subcarriers by using the IFFT. The last N G IFFT samples are copied to 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.

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Kun-Chien Hung **and** David W. Lin, Senior Member, IEEE
Abstract—We consider the phase-rotated linearly interpolative channel **estimation** technique **for** multicarrier transmission. The technique models the channel **frequency** response between two nearby subcarriers as the product of a linear function **and** a linear-phase factor, where the linear-phase factor may be equiv- alently modeled **in** the **time** domain as a reference delay dubbed the anchor delay **in** this work. We show that the performance of the technique is a fourth-order function of the channel path delays **and** the anchor delay. We derive a method to estimate the optimal anchor delay. Analysis **and** simulation **in** a context of Mobile WiMAX downlink transmission show that, with the proposed an- chor delay estimate, we can attain better performance **in** channel **estimation** than conventional linear interpolation **and** a previously proposed method of phase-compensated linear interpolation.

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I. I NTRODUCTION
Terrestrial Digital Video Broadcasting (DVB-T) is a next-generation standard **for** wireless broadcast of MPEG-2 video [1]. **In** order to provide the high data rate required **for** video transmission, concatenated-coded orthogonal **frequency** division multiplexing (**OFDM**) has been adopted into DVB-T. **In** order to cope with a multitude of propagation conditions encountered **in** the wireless broadcast channel, many parameters of **OFDM** **for** DVB-T can be dynamically changed according to channel conditions. **In** particular, the number of **OFDM** subcarriers can either be 2048 (2K) or 8196 (8K) so that the desired trade-off can be struck between inter-symbol interference (ISI) mitigation capability **and** robustness against Doppler-spread [1][2]. As a result, a “mode detector” that detects the number of subcarriers **in** the transmitted **OFDM** symbol is required **in** a DVB-T receiver. Furthermore, **time** **and** **frequency** **synchronization** as well as channel **estimation** are also required as **in** any **OFDM** transmission system. Note that these operations can be performed **and** the transmitted information detected only after the correct number of subcarriers has been determined. Therefore mode detection must be done prior to **synchronization** **and** channel **estimation** **in** a DVB-T receiver. **In** principle, mode detection can be carried out by detecting the positions of pilot subsymbols. However, this method requires the knowledge of the pilot pattern **and** is therefore system-dependent. **In** this paper, a new algorithm is proposed **for** blind mode detection. The proposed algorithm exploits the cyclic nature of **OFDM** signals **and** difference **in** symbol durations to distinguish between different numbers of subcarriers. It will be shown **in** this paper that the proposed algorithm is simple **and** effective. Furthermore, since pilot subsymbols are not required, the proposed method is system-independent

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Example 5—CFO Effect **in** a Multipath Environment: **In** this example, we examine the CFO effect when the channel has the multipath **frequency**-selective fading. The number of multipath is assumed to be **and** , whereas the other param- eters remain the same as those given **in** Example 4. The MAI performance of the four **systems** is shown **in** Fig. 11. **In** a fully loadded situation with the CFO smaller than 0.05, OFDMA has less MAI than the proposed system because OFDMA is com- pletely MAI-free when **frequency** **and** **time** are well synchro- nized. However, as CFO grows, the proposed system slightly outperforms OFDMA system. **In** a half-loaded situation, the proposed system outperforms OFDMA by around 10 dB due to the use of the code selection. The low MAI value of the proposed system with code selection is also beneficial to CFO **estimation**.

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IV. S IMULATION R ESULTS
Several Monte Carlo simulations were conducted to verify the performance of the proposed approach. **In** the simulations, the timing **and** **frequency** **synchronization** is assumed to be performed before channel **estimation**. A CP-free **OFDM** system with one transmit antenna **and** one receive antenna is considered. The length of the **OFDM** symbol is chosen as N =16. The data symbols are chosen from the BPSK or QPSK constellation. The maximum number of paths of the CIR is assumed to be L +1 ( L =4). The following exponential power delay profile is applied **for** each channel path [3].

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The main contribution of this paper is that **for** better characterizations of **synchronization** errors under a practical communication environment, that is, **in** doubly-selective fading channels, we analyze joint e ﬀects of the mentioned three major **synchronization** errors, without the assumption of small STO. Another contribution is that compact forms can be derived from our work to gain further insights on the **synchronization** error e ﬀects. To this end, we first analyze the signal model of the combined **synchronization** errors **in** **time**-selective **and** **frequency**-selective fading channels by extending the works **in** [1–15]. Next, based on this model, the theoretical SINR is formulated. The derived SINR can be exploited to obtain all possible combinations of syn- chronization errors that meet the required SINR constraint, knowing that the allowable **synchronization** errors could help design suitable **synchronization** algorithms **and** shorten the design cycle. To gain further insights, some compact

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Assume that we first convert the received signal from radio **frequency** (RF) to baseband **and** the real **and** imaginary compo- nents of the base-band complex signal are **and** . These two signals are oversampled, digitally **frequency** discriminated, **and** low-pass filtered to obtain raw digital data. This data goes through an FFT **for** **synchronization** preamble bits detection. If detected, both **frequency** **offset** **and** sampling **time** error are es- timated from the FFT results. Symbol timing sychronization is done **in** a feedforward manner. Carrier **frequency** **offset** com- pensation is done **in** a hybrid manner. On one hand, **frequency** **offset** **estimation** is fed back to a VCO during the preamble pe- riod. On the other hand, this **estimation** can be used to change the decision threshold **in** a noncoherent detection mode or rotate the signal constellation **in** a coherent detection mode. After syn- chronization is finished, we obtain the demodulated data. The whole **synchronization** **and** data detection process can be un- derstood **in** more detail by examining the flowchart shown **in** Fig. 2.

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Index Terms— **Estimation**, maximum Doppler **frequency**, Ri- cian fading.
I. I NTRODUCTION
I N mobile communication **systems**, multipath propagation usually gives rise to a fading channel. The Doppler spread is induced when a mobile station is moving **in** such a multipath environment. It distorts the transmitted signal, **and** causes difficulties **in** both channel **estimation** **and** **synchronization** at the receiver. The maximum Doppler **frequency** is an essential parameter of the channel. Related to the speed of the mobile station, the maximum Doppler **frequency** provides useful information **in** adaptive handoff [1] **and** is also the designed bandwidth of the adaptive channel **estimation** filter [2]. As the demand on wireless service increases rapidly, adaptive transmission techniques, such as Adaptive Modulation **and** Coding (AMC) [3], are used to enhance the channel capacity by adaptively changing transmission parameters according to the channel state information (CSI). The adaptation rate should be optimized according to the fading rate of the channel that can be directly deduced from the Doppler spread. With its wide applications, the accurate **estimation** of Doppler spread is indispensable **for** the design of a modern mobile communication system.

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Shan-An Yang **and** Jingshown Wu, Senior Member, IEEE
Abstract—**In** this letter, we propose a timing **synchronization** scheme **for** a dual antenna system **in** Rayleigh-fading environ- ments. Instead of assuming the channel gain to be constant during the training duration, we consider the **time**-variant nature of the multiplicative distortions **and** formulate them with linear combinations of eigenfunctions. Then, we derive a formula to find the maximum-likelihood **estimation** of the channel timing **and** simulate the performance with both ideal **and** nonideal channel state information. The results show that this approach outperforms the conventional ones especially when the Doppler spread is severe.

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