Kilbom Lee

MMSE-Based CFO Compensation for Uplink OFDMA Systems with Conjugate Gradient

In this paper, we present a low-complexity carrier frequency offset (CFO) compensation algorithm based on the minimum mean square error (MMSE) criterion for uplink orthogonal frequency division multiple access systems. CFO compensation with an MMSE filter generally requires an inverse operation on an interference matrix whose size equals the number of subcarriers. Thus, the computational complexity becomes prohibitively high when the number of subcarriers is large. To reduce the complexity, we employ the conjugate gradient (CG) method which iteratively finds the MMSE solution without the inverse operation. To demonstrate the efficacy of the CG method for our problem, we analyze the interference matrix and present several observations which provide insight on the iteration number required for convergence. The analysis indicates that for an interleaved carrier assignment scheme, the maximum iteration number for computing an exact solution is at most the same as the number of users. Moreover, for a general carrier assignment scheme, we show that the CG method can find a solution with far fewer iterations than the number of subcarriers. In addition, we propose a preconditioning technique which speeds up the convergence of the CG method at the expense of slightly increased complexity for each iteration. As a result, we show that the CFO can be compensated with substantially reduced computational complexity by applying the CG method.

CFO Compensation for Uplink OFDMA Systems with Conjugated Gradient

In this paper, we propose an iterative lowcomplexity carrier frequency offset (CFO) compensation algorithm based on the conjugate gradient (CG) method for uplink orthogonal frequency division multiple access systems. In general, a linear minimum mean square error (MMSE) CFO compensation algorithm is simple and efficient, but it requires an inverse operation to compute the MMSE solution of the CFOinduced inter-carrier interference (ICI) matrix whose size equals the number of subcarriers. Thus, the computational complexity becomes prohibitively high when the number of subcarriers is large. To address this issue, we employ the iterative CG method to solve linear equations whose matrix is Hermitian positivedefinite. First, we derive the eigenvalue distribution of the CFOinduced ICI matrix. Based on the distribution, we present several observations which lead to the iteration number required for the convergence. Especially, the analysis shows that for an interleaved carrier assignment scheme, the maximum iteration number to compute an exact solution is at most the same as the number of mobile units. Simulation results exhibit that the proposed scheme can yield almost the same bit error rate performance of the MMSE compensation algorithm with substantially reduced computational complexity and memory requirements.

Sequence Designs for Robust Consistent Frequency-Offset Estimation in OFDM Systems

In this paper, we derive the average pairwise error probability (PEP) of an integer carrier frequency-offset (CFO) estimator with consistent pilots in orthogonal frequency-division multiplexing (OFDM) systems and address several issues based on PEP analysis. In particular, the relationship between the PEP and consistent pilots is established in terms of a diversity gain and a shift gain. Based on the observations, we present new criteria for sequence designs. Simulation results show that the sequence developed from these criteria yields much reduced outliers compared with conventional sequences for consistent CFO estimation in frequency-selective fading channels.

Low Complexity Pilot Assisted Carrier Frequency Offset Estimation for OFDMA Uplink Systems

In this letter, we propose a low complexity pilot aided carrier frequency offset (CFO) estimation algorithm for orthogonal frequency division multiplexing access (OFDMA) uplink systems based on two consecutive received OFDMA symbols. Assuming that the channels and the CFOs are static over the two consecutive symbols, we express the second received OFDMA symbol in terms of the CFOs and the first OFDMA symbol. Based on this signal model, a new estimation algorithm which obtains the CFOs by minimizing the mean square distance between the received OFDMA symbol and its regenerated signal is provided. Also, we implement the proposed algorithm via fast Fourier transform (FFT) operations by utilizing the block matrix inversion lemma and the conjugate gradient method. Simulation results show that the proposed algorithm approaches the average Cramer Rao bound for moderate and high signal to noise ratio (SNR) regions. Moreover, the algorithm can be applied for any carrier assignment schemes with low complexity.

Robust Pilot Designs for Consistent Frequency Offset Estimation in OFDM Systems

Abstract-In this paper, we suggest novel criteria for pilot designs which minimize outliers for consistent carrier frequency offset (CFO) estimation in the orthogonal frequency division multiplexing (OFDM) systems. In order to derive the criteria, we first analyze the average pairwise error probability (PEP) of integer CFO (iCFO) estimation with consistent pilots in the OFDM systems where fadings among subcarriers are correlated, and address several issues based on the PEP analysis. Especially, the PEP reveals the relation between the channel and the minimum Hamming distance of the training sequence which is composed of consistent pilots. Based on the observations made from the PEP, we revise the conventional criteria to make them suitable for systems for correlated fading channels. Simulation results show that the sequence developed from the proposed criteria yields much reduced outliers compared to the conventional sequences for consistent CFO estimation.

Zadoff-Chu Sequence Based Signature Identification for OFDM

A signature identification algorithm is a method to obtain the cell identification information for wireless cellular systems or determine the intended user for wireless local area network. In this paper, we propose a simple and efficient signature identification algorithm on the basis of Zadoff-Chu sequence in orthogonal frequency division multiplexing systems. In addition, we prove that the proposed algorithm achieves a maximum likelihood solution if the receiver knows the channel length. Also, the exact probabilities of signature identification failures of the proposed algorithm are provided for different power delay profiles. To demonstrate efficacy of the proposed algorithm in fading channels, we derive the failure probability at high signal-to-noise ratio (SNR). Through a high SNR expression, it is shown that the proposed algorithm fully exploits frequency selective fadings. Especially, we reveal that the slope of the failure probability curves at high SNR is determined by the channel length regardless of power delay profiles. Simulation results show that the proposed algorithm outperforms conventional signature algorithms in frequency selective fading channels. Also, we confirm that our analysis matches well with the empirical results of the proposed signature identification algorithm.

Low-Complexity Leakage-Based Carrier Frequency Offset Estimation Techniques for OFDMA Uplink Systems

Abstract-In this paper, we propose an efficient carrier frequency offset (CFO) estimation technique based on the space alternating generalized expectation-maximization (SAGE) for uplink orthogonal frequency division multiple access (OFDMA) systems. In general, the SAGE method transforms a multidimensional search problem into a sequence of one-dimensional searches, which greatly simplifies the estimation procedure. However, the conventional algorithms based on the SAGE method require a large amount of computations to estimate the CFO due to exhaustive grid search. To reduce the computational burden, we exploit the leakage on the fast Fourier transform (FFT) output of the received signal after the multiple access interference is removed by the SAGE method. Then, this leakagebased approach reduces the complexity of the conventional SAGE algorithm regardless of an employed carrier assignment scheme by avoiding grid search. Simulation results show that our modified SAGE algorithm approaches the Cramer Rao bound at all signal to noise ratio (SNR) region with greatly reduced complexity compared to the conventional SAGE algorithms.

SLNR-Based User Scheduling for MISO Downlink Cellular Systems

In this paper, we consider a user scheduling problem which maximizes the weighted sum-rate (WSR) in multicell multiple input single output (MISO) downlink systems. Since an exhaustive search algorithm requires high computational complexity, we propose a low complexity algorithm which finds a user set in terms of WSR maximization. We first consider a greedy user selection algorithm which almost achieves the system performance of the exhaustive search algorithm in high SNR regime. Next, a distributed user scheduling algorithm is proposed by employing the maximized signal-to-leakage-and-noise ratio (SLNR) in the selection criteria. This leads to a reduction of the system overhead of exchanging channel state information and computational complexity. From simulation results, we show that the performance of our proposed scheme is very close to the conventional greedy user scheme with lower overhead.

A Pilot-Aided Frequency Offset Estimation Algorithm for OFDMA Uplink Systems

In this paper, we propose a pilot aided carrier frequency offset (CFO) estimation algorithm for orthogonal frequency division multiplexing access (OFDMA) uplink systems based on two consecutive received OFDMA symbols. Assuming that the channels and the CFOs are static over the two consecutive symbols, we express the second received OFDMA symbol in terms of the CFOs and the first OFDMA symbol. Based on this signal model, a new estimation algorithm which obtains the CFOs by minimizing the mean square distance between the received OFDMA symbol and its regenerated signal is provided. The simulation results show that the proposed algorithm approaches the average Cramer Rao bound for moderate and high signal to noise ratio regions. Moreover, the algorithm can be applied for any carrier assignment schemes.

A Low-Complexity Semi-Blind Joint CFO and Data Estimation Algorithm for OFDM Systems

In this paper, we propose a low-complexity semi-blind joint carrier frequency offset (CFO) and data estimation algorithm for orthogonal frequency division multiplexing (OFDM) systems. Given channel information, we first provide a new iterative algorithm which jointly estimates the CFO and data based on pilots by minimizing the mean square error between the received OFDM symbol and its regenerated signal. By using the matrix inversion lemma, the joint CFO and data estimator is divided into a CFO estimator and a data detector without loss of optimality, which significantly reduces the computational complexity. Also, we present a decision feedback strategy to select reliable data from previously detected data by adopting the probability metric which evaluates the reliability. Then, the simplified CFO estimator can utilize the selected reliable data as pilots in the next iteration step. Simulation results show that the simplified CFO estimator can achieve the average Cramer Rao bound in moderate and high signal to noise ratio (SNR) regions within a few iterations even for a small number of pilots with the help of the proposed decision feedback strategy.