稀疏感知非等间距导频布置与正交频分复用系统的信道估计

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"这篇文章是关于在正交频分复用(Orthogonal Frequency Division Multiplexing, OFDM)系统中，利用稀疏感知、信道顺序盲的导频放置策略进行信道估计的研究论文。作者指出，非等间距的导频布局可能优于等间距布局，特别是在考虑无线信道固有的脉冲响应稀疏性时。研究中提出了一种基于相干准则的稀疏感知导频排列方案，以解决由此产生的非确定性问题。在OFDM系统中，导频辅助传输是最常见的方法，等间距的导频安排是最常见的策略。然而，文章指出，由于无线信道的脉冲响应通常具有稀疏特性，即大部分系数接近零，只有少数几个系数具有显著值，因此，这种特性可以被有效地利用来优化导频的布局。该研究探索的稀疏感知导频布置方案旨在最大化信道估计的准确性。通过利用信道的稀疏性，可以减少所需的导频数量，从而降低系统的开销，同时提高频谱效率。提出的非等间距策略能够更好地适应信道的变化，因为它允许导频根据信道的特性动态地分布在子载波上。文章中提到的"coherence criterion"（相干准则）是指在信道估计过程中，选择那些能提供最大信息量或最小化估计误差的导频位置。这种准则有助于减少因信道估计错误导致的系统性能损失。此外，文章还讨论了如何在不预先知道信道顺序的情况下设计这种导频布局，即“信道顺序盲”这一概念。这是一项挑战，因为通常信道的频率响应排序是未知的。通过这种方式，系统可以变得更加灵活，并且对信道的未知特性具有更强的鲁棒性。尽管研究提出的方法有其优势，但实现非等间距导频布局和信道顺序盲的信道估计会带来计算复杂度的问题。因此，文章可能还涉及了解决这些复杂性问题的技术和算法优化，以确保在实际应用中的可行性。这篇研究论文为OFDM系统中的高效导频布置提供了新的视角，强调了利用信道的稀疏性和无序性，以及如何通过优化导频布局来提升系统性能。这种方法对于未来的无线通信系统，尤其是在高数据速率和低功耗需求的5G及更高级别的网络中，具有重要的理论和实践意义。"

Sparsity-aware, channel order-blind pilot

placement with channel estimation in

orthogonal frequency division multiplexing

systems

ISSN 1751-8628

Received on 2nd September 2014

Accepted on 15th January 2015

doi: 10.1049/iet-com.2014.0857

www.ietdl.org

Xiaoqing Peng

, Weimin Wu

✉

, Jun Sun

, Yingzhuang Liu

, Frank Yong Li

Department of Electronic and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074,

People’s Republic of China

Department of Information and Communication Technology, University of Agder, Grimstad 4898, Norway

✉ E-mail: wuwm@hust.edu.cn

Abstract: Equispaced pilot arrangement is the most popular scheme for pilot-aided transmission in orthogonal frequency division

multiplexing systems. In this study, the authors argue that a non-equispaced pilot pattern may outperform its equispaced

counterpart, if they fully take into account the sparsity of the channel impulse response which is inherent in wireless channels.

More specifically, a sparsity-aware pilot arrangement scheme based on the coherence criterion is investigated in this study. To

address the resulting non-deterministic polynomial (NP)-hard combinatorial optimisation problem, they propose an efficient

local search algorithm. For channel estimation, they convert it to a sparse recovery problem. To enhance the applicability of

the authors scheme, that is, when there is no prior knowledge about the channel order, they propose to employ the Bayesian

information criterion to estimate the channel order first and then recover the sparse channel vector via existing low-complexity

methods, for example, orthogonal matching pursuit. By combining the above pilot arrangement scheme with channel

estimation, their scheme exhibits substantially better performance in comparison with the conventional equispaced schemes

with linear (or spline) interpolation, in terms of total number of pilot symbols and bit error rate.

1 Introduction

Channel estimation is an essential technique in orthogonal frequency

division multiplexing (OFDM) systems. In spite of being a

well-explored topic in the literature, what is the fundamental

performance of channel estimation and how to achieve it are still

unclear to date. It is commonly understood that the best pilot

pattern should be equispaced for pilot assisted channel estimation

and this statement has actually been adopted by many international

standards, such as 802.11, LTE etc. However, we observe that such

pilot placement is sensitive to the structure of channel impulse

response (CIR). Essentially, the equispaced pilot placement is just a

realisation of the well-known equispaced (or periodic) sampling

framework pioneered by Shannon and Nyquist. Therefore, to

ensure acceptable channel estimation accuracy, the minimum

number of pilots is required to be of the order of maximum delay

spread (i.e. the inverse of the coherence bandwidth). However, if

we take into account the sparsity of the CIR vector which is quite

common in wideband wireless systems, it might be possible to

assign pilots whose total number is just of the order of the sparsity

of the CIR vector. This fact has been predicted by the compressive

sensing (CS) theory [1–4] since this number is usually smaller than

the maximum delay spread of the CIR vector. Therefore, the

sparsity-aware pilot arrangement with channel estimation is of great

signiﬁcance in order to save pilot overhead and improve system

performance in comparison with the conventional equispaced pilot

arrangement with linear (or spline) interpolation of channel

estimation. As an effort to analyse and approach the fundamental

performance of channel estimation in OFDM systems, this paper

proposes a sparsity-aware channel order-blind pilot placement

scheme with channel estimation and investigates its performance.

1.1 Pilot placement

The optimal assignment of pilots in OFDM systems has received so

far little attention in the literature. One of the few studies within this

topic is [5]. It studied the multiple-input–multiple-output

(MIMO)-OFDM system and reached a conclusion that

equipowered, equispaced and phase-shift-orthogonal pilot

sequences are optimal in terms of mean square error (MSE), by

assuming that ‘linear’ channel estimation is employed. Therefore

their criterion is not applicable to the sparsity-based channel

estimation, which requires in essence a ‘non-linear’ method. Other

related work on pilot placement can be found in [6–11]. A discrete

Fourier transform (DFT) sub-matrix deterministically constructed

via the additive character sequences was considered in [6].

However, this method is based on the cases where the size of DFT

is an integer power of an odd prime. In [7, 8], an algorithm using

modiﬁed discrete stochastic approximation (DSA) was proposed to

arrange the pilot. However, it does not fully exploit the fact that

both the length of the cyclic preﬁx (CP) and the size of DFT are an

integer power of two in realistic OFDM systems. Furthermore, pilot

allocation for MIMO-OFDM systems was also studied in [10, 11].

For CS-based channel estimation, the pilot placement problem

boils down to a problem of optimally selecting rows from a DFT

matrix which plays the role of the measurement matrix in the CS

terminology (this point will be explained in Section 2).

Unfortunately, the optimal row selection is a tedious task because

of the combinatorial nature of the problem. Therefore, we resort to

the suboptimal sparse recovery methods and introduce a succinct

index which is critical for row selection.

1.2 Sparsity-based channel estimation

Sparse recovery is a central procedure for sparsity-based channel

estimation. In fact, if we could recover precisely the sparse

time-domain CIR, the frequency-domain CIR could be easily

obtained. Broadly speaking, the existing sparse recovery

algorithms could be categorised into two classes: one class is the

convex optimisation method (say, ℓ

optimisation method) [12,

13] and the other one is the greedy pursuit method [14–18].

Although the convex optimisation method could provide better

IET Communications

Research Article

IET Commun., 2015, Vol. 9, Iss. 9, pp. 1182–1190

1182

The Institution of Engineering and Technology 2015

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