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Fig. 3. Performance comparison **of** CFO **estimation**, the algorithm **in** [17], and proposed algorithm **I**; SNR = 10 dB.
Fig. 4. BER comparison for **systems** **with** and without CFO.
**frequency**-domain binary-phase-shift-keying-modulated signal, has ten periods, and each period has 16 samples. The data following the preamble are transmitted **using** a 16-quadratic- amplitude-modulation scheme. The mean square error (MSE) **of** the estimated CFO is used as a performance measure. We first consider the CFO-only **estimation** problem. **In** this case, the first received N samples are discarded. As previously mentioned, we term the proposed approach for this scenario as algorithm **I** (as described **in** Section III). We compare the proposed ML estimator **with** that **in** [17]. One optimum algorithm (algorithm A) and two suboptimum algorithms (algorithm A and B) **in** [17] are simulated. Fig. 3 shows the simulation result for SNR at 10 dB. **In** the figure, we can see that the performances **of** algorithms A and B are poorer. Algorithm A and the proposed algorithm offer a similar level **of** performance that is very close to the CRLB. To evaluate the impact **of** CFO on system perfor- mance, we conduct simulations for **systems** with and without CFO. For the system **with** CFO, we first use the proposed method to estimate CFO and then conduct CFO compensation.

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This chip occupies 4.6×4.6 mm 2 and consumes 62.8 mW at 1.2 V.
**I**. **I** NTRODUCTION
The combination **of** multi-input multi-output (MIMO) transmission, orthogonal **frequency**-division multiplexing (**OFDM**) technology, and space-time block code (STBC) scheme comprises a potential solution for next-generation wireless communications [1]. However, MIMO-**OFDM** **systems** are sensitive to sampling clock **offset** and **carrier** **frequency** **offset** (CFO). **In** addition, direct-conversion receivers suffer from **I**/**Q** **mismatch** (IQM). IQM arises when the phase and gain differences between **I** and **Q** branches are not exactly 90° and 0 dB, respectively. Due to the impairment **in** the analog components, the mismatched low-pass filters result **in** **frequency**-dependent IQM (FD-IQM) [2]. **In** an MIMO-**OFDM** system **with** FD-IQM, the FD-IQM parameters for every subcarrier are different. Moreover, the ability **of** adaptive equalization is required due to time-varying environments. For successful transmissions, obtaining accurate channel **frequency** response (CFR) is extremely important. Owing to the above considerations, an MIMO- **OFDM** modem is proposed for fast timing recovery, anti-IQM **frequency** recovery, FD-IQM **estimation** and adaptive **frequency**-domain equalization.

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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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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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C. Hadamard–Walsh Code **in** the Uplink Transmission **In** the uplink transmission, it is difficult to guarantee that every user transmits his/her signal simultaneously. This will lead to timing **mismatch** among users. If the Hadamard–Walsh code is used **in** the uplink transmission **in** conventional CDMA sys- tems, a small timing **mismatch** among users will result **in** great MAI even if the channel is perfect. For instance, consider the case **with** processing gain . If the fourth user has a delay **of** one chip duration while the other three users are per- fectly synchronized, the receiver cannot distinguish the fourth user from the third one because . There- fore, Hadamard–Walsh code is seldom used **in** the uplink trans- mission unless the timing **mismatch** problem can be well re- solved by some other mechanism. **In** conventional CDMA or MC-CDMA **systems**, quasiorthogonal codes that have less cross correlation such as the Gold code or the Kasami code are usu- ally used to mitigate the timing **mismatch** problem. **In** contrast, since the proposed system is robust to timing **mismatch** [23], we can adopt the low complexity Hadamard–Walsh code **in** the uplink transmission.

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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 (Δ**q** = 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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power **in** dealing **with** a broad range **of** **estimation** problems **with** incomplete observations [12], [13]. **Estimation** **of** the symbol arrival time and the **carrier** phase was considered **in** [14] **with** the transmitted symbol being treated as the missing data. A blind CFO **estimation** scheme **in** MC-CDMA **systems** **using** the EM algorithm was studied **in** [15], where the gradient decent technique was proposed to deal **with** the nonlinear optimization problem **in** the CFO estimate. However, since there exist multiple local optima **in** the cost function, the solution is sensitive to the initialization **of** the optimiza- tion process, which could be problematic for a hill-climbing adaptive algorithm. Besides, all these schemes were operated **in** a block-based manner assuming that the target parameters were time invariant inside this time block. However, timely updates **of** system parameters would be more desirable **in** real time applications, which motivates the development **of** online algorithms to track possibly time-varying unknowns.

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National Taiwan University, Taipei 10617, Taiwan
Abstract – Sampling clock **offset** **estimation** and compensation are important problems **in** an **OFDM** system. Sampling clock **offset** can cause a severe drift **in** symbol-timing, thus causing inter-**carrier** and inter-**OFDM**-symbol interference. **In** this paper, we propose a novel sampling clock **offset** estimator for **OFDM** **systems** that use scattered pilots. The proposed algorithm makes use **of** the received pilot phases and the least-squares algorithms. Simulation results show that when applied to the DFB-T standard, the performance **of** the proposed estimator is very accurate and robust against multipath fading and Doppler Spread.

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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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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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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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Received: 4 March 2008 / Revised: 4 August 2009 / Accepted: 6 August 2009 / Published online: 8 September 2009
# 2009 Springer Science + Business Media, LLC. Manufactured **in** the United States
Abstract The effects **of** variation **in** RF, such as **I**/**Q** imbalance and filter **mismatch**, are extremely important for **OFDM** wireless accesses. This work presents a low- computational **estimation** **of** **I**/**Q** imbalances **with** filter mismatches to improve performance **in** MIMO-**OFDM** receivers. For N×N MIMO-**OFDM** **systems**, the proposed cross-validation **estimation** is such that, only N+1 preambles are required to extract the mismatches **of** filters, gains and phases. **With** the estimated parameters, **frequency**-domain filters are exploited to correct **frequency**-dependent **I**/**Q** imbalances. Through performance evaluation **of** a 2 ×2 MIMO-**OFDM** system, **with** ideal channel estimations this study incurs a SNR loss **of** 1–1.2 dB to maintain a 10% PER at 1-dB gain error, 10°-phase error and the worst 180°-filter **mismatch**. **In** addition, this algorithm is well-matched to IEEE 802.11n and new specifications discussed **in** IEEE 802.11 VHT study group.

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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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With its low hardware complexity and accurate estimation performance, the raised-cosine frequency- domain interpolation channel estimator will find many appli- cations in OFDM co[r]

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Fig. 7. BEP comparison among block detection scheme **with** L = 4, iterative detection scheme **with** **I** = 3 and L = 4, and TSA-4PSK detection scheme **with** R = 1/8.
Digital simulation has been conducted to evaluate the BEP performance **of** the iterative detection scheme for demodu- lating the Gray-labeled data phasor block-modulated signals composed by the transform **in** Example One **of** Table **I**. It is found by the author that the iterative scheme can provide better performance by increasing iterations. Particularly, significant performance improvement is achieved by making final deci- sion at the second iteration than at the first iteration and the improvement become infinitesimal by making final decision after more than three iterations. Figs. 7 and 8 illustrate the sim- ulated BEP results **of** the iterative detection scheme **with** **I** = 3 for L = 4 and 8, respectively, and compare the results **with** the approximate bound results **of** the block detection scheme.

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Fig. 7. BEP comparison among block detection scheme **with** L = 4, iterative detection scheme **with** **I** = 3 and L = 4, and TSA-4PSK detection scheme **with** R = 1/8.
Digital simulation has been conducted to evaluate the BEP performance **of** the iterative detection scheme for demodu- lating the Gray-labeled data phasor block-modulated signals composed by the transform **in** Example One **of** Table **I**. It is found by the author that the iterative scheme can provide better performance by increasing iterations. Particularly, significant performance improvement is achieved by making final deci- sion at the second iteration than at the first iteration and the improvement become infinitesimal by making final decision after more than three iterations. Figs. 7 and 8 illustrate the sim- ulated BEP results **of** the iterative detection scheme **with** **I** = 3 for L = 4 and 8, respectively, and compare the results **with** the approximate bound results **of** the block detection scheme.

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V. C ONCLUSION
This paper has used the V-shaped curve method to analyze the failure probability **of** ACF packages **in** which the upper and lower pads have a different side length and are subject to alignment errors. **In** formulating the V-shaped curve, the opening probability has been modeled **using** a Poisson function, suitably modified to take into account the effects **of** the pad- width difference and the misalignment **offset** on the effective conductive area between opposing pads. Meanwhile, the bridg- ing probability has been modeled **using** an enhanced bridging model, modified to take into account the effects **of** asymmetry and misalignment on the lengths **of** the bridging paths between neighboring pad pairs. The major findings **of** this paper can be summarized as follows.

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