In some applications, however, a preamble with more than two pe- riods is available. A typical example is the IEEE802.11a/g wireless local area network system, which features a ten-period preamble.
Recently, researchers have proposed a maximum likelihood (ML) CFO estimation method for such systems. This approach first estimates the received preamble using a least squares method and then maximizes the corresponding likelihood function. In addi- tion to the standard calculations, this method requires an extra procedure to solve the roots of a polynomial function, which is disadvantageous for real-world implementations. In this paper, we propose a new ML method to solve the likelihood function directly and thereby perform CFO estimation. Our method can obtain a closed-form ML solution, without the need for the root-finding step. We further extend the proposed method to address the STO estimation problem as well as derive a lower bound on the estimation performance. Our simulations show that while the performance of the proposed method is either equal to or better than the existing method, the computational complexity is lower.
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the preamble period, the estimation performance is degraded due to the fact that the received signal model (4) is no longer valid.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 andand 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.
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.
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 frequencyoffset 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 forfrequency-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 frequencyoffset versus the exact CFO value, based on the simulation parameters in Table I. Simulation results indicate that the proposed algorithm can estimate the frequencyoffset more accurately than the two-repeat preamble-based scheme.
Therefore, an accurate estimation of the frequencyoffset is critical.
Existing approaches for the frequency-offsetestimation using the pre- amble data , , the cyclic preﬁx data , , or the cyclostationary property  of the received signals have been proposed. Extensive coverage of techniques for digital synchronization is also provided in textbooks –. Here, we focus on the data-aided maximum-like- lihood (ML) estimationinOFDMsystems. The MLestimation of fre- quency andtime offsets inOFDMsystems using the two sets of iden- tical cyclic preﬁx data has been derived in . In the IEEE 802.11a  standard for wireless LAN communications, the preamble con- tains multiple sets of identical data for channel estimationand syn- chronization. Hence, an extension for the MLestimation 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 , we generalize the ML algorithm for the estimation of frequencyandtime 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.
In this paper, we investigate two EM-based iterative re- ceivers forOFDMand BICM/OFDMsystemsin doubly selective fading channels. By assuming channel varies in a linear fashion, we first analyze the ICI effect infrequency domain and derive a data detection method based on the EM algorithm using the ML criterion. In an effort to reduce complexity, groupwise processing is adopted for the two EM-based receivers. ForOFDMsystems, we implement an ML-EM receiver which iterates between a groupwise ICI canceller and an EM detector. Based on this receiver structure, a TURBO-EM receiver for BICM/OFDMsystems is then proposed to successively improve the performance by applying the turbo principle. Finally, for the initial setting of the two receivers, MMSE-based CE is first performed by using a few pilot tones and it is later improved via the decision feedback methodology. To the best of our knowledge, this is the first work studying an EM approach for joint ICI estimationand data detection in multipath time-varying channels. Our work differs from the previous EM-based approaches , –
adaptive filter bank, copied from the lower branch, performs despreading and MAI suppression, and pilot symbols assisted frequencyoffsetestimation, channel vector estimationand 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 estimationandfrequencyoffset compensation.
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) , . 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 . 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.
Symbol-timing andfrequencyoffsetestimationforOFDM are widely discussed in the literature. However, relatively few results are available for the estimation of sampling clock offset. Sampling clock offsetestimationand 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 offsetsynchronization is an important issue that needs to be solved for a practical OFDM system.
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.
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.
I. I NTRODUCTION
Terrestrial Digital Video Broadcasting (DVB-T) is a next-generation standard for wireless broadcast of MPEG-2 video . 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 OFDMfor 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 . 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, timeandfrequencysynchronization 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 synchronizationand channel estimationin 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
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 frequencyandtime 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.
IV. S IMULATION R ESULTS
Several Monte Carlo simulations were conducted to verify the performance of the proposed approach. In the simulations, the timing andfrequencysynchronization 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 .
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 intime-selective andfrequency-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
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 forsynchronization preamble bits detection. If detected, both frequencyoffsetand sampling time error are es- timated from the FFT results. Symbol timing sychronization is done in a feedforward manner. Carrier frequencyoffset com- pensation is done in a hybrid manner. On one hand, frequencyoffsetestimation 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 synchronizationand data detection process can be un- derstood in more detail by examining the flowchart shown in Fig. 2.
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 estimationandsynchronization 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  and is also the designed bandwidth of the adaptive channel estimation filter . As the demand on wireless service increases rapidly, adaptive transmission techniques, such as Adaptive Modulation and Coding (AMC) , 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.
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.