稀疏恢复辅助的上行链路OFDMA系统载波频率偏移估计

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"这篇文章提出了一种新颖的盲载波频率偏移(CFO)估计算法，称为稀疏恢复辅助CFO(SR-CFO)估计器，适用于上行正交频分多址(OFDMA)系统。通过利用嵌入在OFDMA数据中的稀疏性，将CFO估计问题转化为具有高分辨率的稀疏恢复优化问题。同时，为了提高CFO的估计精度，通过利用变换观测数据中噪声协方差矩阵的结构以及采样误差的渐近分布来减轻背景噪声和采样误差的影响。此外，文章还提出了一种方法来确定SR-CFO估计器使用的正则化参数，以控制数据拟合误差和解的稀疏性之间的平衡。" 本文主要探讨了在上行OFDMA系统中如何有效地估计载波频率偏移，这是无线通信中一个关键的技术问题。OFDMA系统允许多个用户在同一频段的不同子载波上同时传输数据，但载波频率偏移会导致子载波间的相互干扰，降低系统性能。因此，准确的CFO估计是必要的。作者提出的SR-CFO估计算法是基于稀疏恢复理论的，这是一个在信号处理和信息理论领域广泛研究的概念。稀疏恢复的目标是从有限的观测数据中重构信号，而信号本身在某种基或表示下是稀疏的。在这个场景下，OFDMA数据的稀疏特性被用来提高CFO估计的精度。通过构建优化问题，可以找到最佳的CFO估计，同时保持解的稀疏性，从而减少错误。文章进一步讨论了如何通过分析噪声协方差矩阵的结构和采样误差的统计特性来降低噪声和采样误差对CFO估计的影响。这通常涉及到复杂的统计分析和数学建模，以确保估计的稳健性和准确性。此外，选择合适的正则化参数对于SR-CFO算法的性能至关重要。正则化参数控制了模型复杂度和数据拟合之间的权衡，过大可能导致欠拟合，过小则可能导致过拟合。文中提出的正则化参数选择方法旨在找到最佳的平衡点，使得CFO估计既不会过于简单而忽略重要的信息，也不会过于复杂而捕获噪声。这篇论文为OFDMA系统的CFO估计提供了一个创新的解决方案，利用稀疏恢复技术提高了估计的精度，并通过有效的噪声抑制和正则化策略优化了性能。这种方法对于现代无线通信网络的优化和性能提升具有重要意义，特别是对于需要高效利用频谱资源的5G和未来无线系统。

9592 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 10, OCTOBER 2017

Carrier Frequency Offset Estimation in Uplink OFDMA

Systems: An Approach Relying on Sparse Recovery

Min Huang, Lei Huang, Senior Member, IEEE, Chongtao Guo ,

Peichang Zhang, Jihong Zhang, and Lie-Liang Yang

, Fellow, IEEE

Abstract—This paper proposes a novel blind carrier frequency offset

(CFO) estimator, namely the sparse recovery assisted CFO (SR-CFO)

estimator, for the uplink orthogonal frequency-division multiple access

(OFDMA) systems. By exploiting the sparsity embedded in the OFDMA

data, the CFO estimation is formulated as an optimization problem of

sparse recovery with high-resolution. Meanwhile, in order to enhance the

estimation accuracy of CFOs, background noise and sampling errors are

mitigated by exploiting the structure of the noise covariances matrix in

the transformed observation data, and the asymptotic distribution of the

sampling errors. Furthermore, we propose an approach for deriving the

regularization parameter used by the SR-CFO estimator, so as to control

the tradeoff between the data ﬁtting error and the sparsity of solution.

The performance of the proposed SR-CFO estimator along with other four

existing estimators is investigated and compared. Numerical results show

that the proposed SR-CFO estimator is superior to the state-of-the-art

estimators in terms of the estimation reliability.

Index Terms—OFDMA, carrier frequency offset, estimator, sparse

recovery.

I. INTRODUCTION

In wireless communications, orthogonal frequency-division multi-

plexing (OFDM) has been widely employed to support the downlink

and uplink transmissions, and to support multiuser communications

via assigning different subcarriers to different users, forming the or-

thogonal frequency division multiple access (OFDMA). In OFDMA

systems, the achievable performance is very sensitive to the carrier fre-

quency offsets (CFOs) induced by the mismatch between transceiver

oscillators. CFOs lead to strong multiple-access interference ( MAI),

which may signiﬁcantly degrade the system performance if it is not

Manuscript received January 18, 2017; revised April 3, 2017 and May

16, 2017; accepted May 21, 2017. Date of publication May 24, 2017; date

of current version October 13, 2017. This work was supported in part by

the Natural Science Foundation of China under Grants U1501253, 61601300,

6160010632, 61501300, 61601304, and 61601307, in part by the Natural Sci-

ence Foundation of Guangdong Province under Grant 2015A030311030, in

part by the Foundation of Shenzhen under Grants JCYJ20150324140036835,

JCYJ20160520165659418, and JCYJ20160422102022017, in part by the

National Science Foundation under Grant CCF-1218388, in part by the

China Postdoctoral Science Foundation under Grant 2016M592535, in part

by the Shenzhen Key Laboratory Establishment Foundation under Grants

ZDSYS201507081625213 and KC2015ZDYF0023A, and in part by the China

Scholarship Council. The work of L.-L. Yang was supported by the EPSRC,

U.K. The review of this paper was coordinated by Prof. R. Dinis. (Corresponding

author: Lei Huang.)

M. Huang, L. Huang, C. Guo, P. Zhang, and J. Zhang are with the Col-

lege of Information Engineering, Shenzhen University, Shenzhen 518060,

China (e-mail: mhuang@szu.edu.cn; lhuang@szu.edu.cn; ctguo@szu.edu.cn;

zpc1029384756@hotmail.com; zhangjh@szu.edu.cn).

L.-L. Yang is with the School of Electronics and Computer Science, Uni-

versity of Southampton, Southampton SO17 1BJ ,U.K. (e-mail: lly@ecs.

soton.ac.uk).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TVT.2017.2707671

effectively mitigated. Hence, in practical systems, the CFOs need to be

estimated with sufﬁcient accuracy which are then compensated or used

for MAI mitigation.

In literature, maximum likelihood algorithm [1] and its variant ver-

sions [2], [3] have been proposed for estimation of the CFOs in OFDMA

systems. The common drawbacks of these methods are the high imple-

mentation complexity and the requirement of pilots, which reduces the

attainable spectral efﬁciency. In order to combat these problems, a blind

CFO estimation scheme has been proposed in [4]. Specially, by ex-

ploiting the periodic structure of the received signals in the interleaved

OFDMA uplink systems, the multiple signal classiﬁcation approach

referred to as MUSIC has been adopted in [4] to estimate the CFOs.

It is shown in [4] that the MUSIC algorithm has a low computational

complexity, and is capable of achieving a good estimation performance.

However, when the CFOs of the signals from different users are close

to each other in the frequency domain, and when the signal-to-noise

ratio (SNR) is relatively low, it is usually hard to separate the CFOs

by the MUSIC approach. Furthermore, in order to identify the CFOs,

the MUSIC approach has to resort to a highly involved spectral search-

ing procedure, which is rather computationally intensive. Due to these

issues, the MUSIC estimator has been replaced by the estimators de-

signed based on the rotational invariance technique, such as the ESPRIT

[5]. Moreover, in order to further reduce the computational complex-

ity, an improved ESPRIT, namely the Unitary-ESPRIT, has been pro-

posed in [6] for estimation of CFOs. More recently, a unitary subspace

improved minimum output variance (U-SIMOV) estimator has been

introduced in [7] for CFO estimation. By combining the unitary trans-

formation with the subspace projection technique, the U-SIMOV is able

to improve the CFO estimation performance of the Unitary-ESPRIT,

provided that the CFOs with respect to different users are sufﬁciently

separated from each other.

In order to attain high-resolution estimations for the closely located

CFOs, especially, in low SNR region, we propose a novel CFO estima-

tor in this paper, with the main contributions as follows.

1) A novel CFO estimation algorithm designed based on the sparse

recovery is proposed in this paper, which is referred to as the

sparse recovery assisted CFO (SR-CFO) estimator. Our high-

resolution CFO estimator is formulated as a sparse optimization

problem without relying on requiring pilots. Furthermore, with

the aid of the Lagrangian duality theory [8], [9], an approach is

proposed for deriving the regularization parameter required by

our SR-CFO estimator.

2) A selection matrix is designed for mitigating the effect of additive

Gaussian noise by exploiting the structure of the noise variances

in the transformed observation data.

3) A whitening ﬁlter is designed for coping with the sampling er-

rors by exploiting the asymptotic distribution of the sampling

errors.

4) The performance of our SR-CFO estimator is investigated by

simulations, which is also compared with four existing CFO

estimators. Our studies and simulation results show that the pro-

posed SR-CFO estimator outperforms all the benchmark CFO

estimators by providing a higher resolution and also a higher

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