OFDM技术综述与无线通信应用深度解析

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OFDM（正交频分复用）因其卓越的抗符号间干扰(ISI)能力，在无线通信领域中得到了广泛应用。这篇由IEEE的四位专家——Taewon Hwang、Chenyang Yang（高级会员）、Gang Wu（成员）和Shaoqian Li、Geoffrey Ye Li（院士）合作完成的综述论文，于2009年发表在《车辆技术交易会》(IEEETRANSACTIONSONVEHICULARTECHNOLOGY)第58卷第4期，共20多页的内容深度探讨了OFDM的基本原理及其在无线通信中的关键技术和优化策略。论文首先介绍了OFDM的基本概念，它是一种多载波调制技术，通过将数据信号分配到多个正交子载波上，有效地降低了ISI的影响。OFDM的优势在于其频谱效率高、抗多径衰落能力强，特别适合于存在严重延迟扩散的无线环境。为了进一步提升OFDM在无线通信中的性能，作者详细阐述了一系列关键技术和改进方法。这包括： 1. **信道估计与信号检测**：OFDM系统的性能很大程度上依赖于准确的信道状态信息(CSI)。信道估计技术如基于训练序列的估计方法和自适应算法，对于估计频率和时域上的变化至关重要。 2. **时间-频率偏移估计与校正**：无线信道中的多径传播可能导致信号的时间和频率同步问题。论文讨论了如何精确估计这些偏移，并提出相应的补偿策略来减小它们对信号质量的影响。 3. **峰均功率比(PAPR)降低**：由于OFDM信号通常具有较高的峰值功率，PAPR问题是其应用的一个挑战。文中可能介绍了各种技术，如循环前缀、 Tone Reservation等，用于降低PAPR，提高信号的功率效率。 4. **MIMO技术的应用**：多输入多输出(MIMO)技术是OFDM的重要扩展，它通过利用多个天线进行空间多路传输，增强了系统的容量和可靠性。论文详细讨论了MIMO-OFDM系统的设计、编码和解码技术。此外，论文还概述了OFDM在当前无线通信系统和标准中的实际应用，例如Wi-Fi、LTE（长期演进）以及即将到来的5G网络，展示了OFDM技术在这些系统中的关键角色。总结来说，这篇论文为读者提供了一个全面的OFDM技术概览，涵盖了理论基础、技术优化和实际应用，是研究者和工程师深入理解OFDM及其在无线通信中作用的宝贵参考资料。

HWANG et al.: OFDM AND ITS WIRELESS APPLICATIONS: A SURVEY 1677

It can easily be seen that ML estimation is the same as least-

square (LS) estimation in this case. Direct calculation yields

that LS estimation of the channel frequency response vector is

= S

−1

x. (7)

To reduce the computational complexity of ML or LS channel

estimation, S

−1

in (7) can be calculated ofﬂine. Estimation in

this case neither needs nor exploits the information of channel

statistics. Consequently, estimation performance is usually not

good enough; thus, it is often applied as initial estimation.

By exploiting channel statistics, channel estimation can sig-

niﬁcantly be improved. With the correlation matrix of the

channel frequency response vector R

= E{HH

}, linear

minimum mean square error (LMMSE) channel estimation

can be obtained. For LMMSE estimation, channel frequency

responses are regarded as random variables. Estimation of the

channel frequency response vector is found to minimize the

mean square error (MSE), i.e., E

H − H

. Consequently

LMMSE

= R



+ σ





−1



−1

= R



+ σ





−1



−1

Compared with ML or LS estimation, LMMSE estimation has

much better performance; however, it requires channel statistics

and has higher computational complexity.

With a minor modiﬁcation, the principle of the aforemen-

tioned LMMSE estimation can also be used to estimate channel

frequency responses other than pilot subchannels as in PACE,

which is also called optimal interpolation in [45] and [46].

Training or pilot symbols can be designed to facilitate chan-

nel estimation. For example, if they are with constant modulus,

that is, |s

= σ

for k =0,...,N − 1, then S

= σ

)

−1

=(σ

/σ

)I, and no matrix inversion operation

is required. Furthermore, if the training or pilot symbols are

identical, that is, s

= s for k =0,...,N − 1, then even S

sI and S

−1

=(1/s)I. As indicated in [54], the coefﬁcient

matrix for LMMSE estimation can be computed with the help

of transform domain processing, such as Fourier transform or

singular value decomposition. The correlation matrix of the

channel frequency response vector is determined by the power

delay proﬁle (PDP) of the wireless channel. Therefore, if the

accurate PDP is known in advance, then the coefﬁcient matrix

for LMMSE estimation can be calculated ofﬂine. When the

accurate PDP is unknown in advance, different solutions have

been suggested. For example, channel estimation may set up

coefﬁcients according to a uniform or an exponential PDP [21],

[46], [54], [56].

Estimation performance can further be improved by a 2-D

LMMSE estimator exploiting the time-domain correlation of

channels in addition to the frequency-domain correlation. To

reduce the computational complexity of the 2-D LMMSE esti-

mator, several methods have been proposed, and some of them

bear the same spirit of the 1-D algorithms discussed before. By

exploiting the separable feature of channel correlation at time

and frequency domains [45], [56], 2-D LMMSE estimation is

decoupled into two cascade 1-D LMMSE estimations. Another

solution partitions the 2-D time–frequency region into several

small regions and performs LMMSE estimation by only consid-

ering the correlation among adjacent subchannels in each small

region [54].

1) Pilot-Aided Channel Estimation: Using pilot tones to

estimate channel coefﬁcients was ﬁrst proposed in [57]. The

two major issues of pilot-aided channel estimation are pilot

design and interpolation.

The optimal design for the pilot pattern, power allocation,

and number of pilots has extensively been studied [57]–[63],

which critically depends on a proper criterion and the channel

model. The impact of pilots on system performance for time-

varying channels has ﬁrst been analyzed in [58]. The optimal

pilot design for frequency-selective channels has been inves-

tigated in [59] and [60], whereas that for doubly selective

channels has been investigated in [61]. The pilots have been

designed to minimize the MSE of channel estimation [57]

or CRB [62], maximizing the channel capacity [59]–[61] and

minimizing the symbol error rate [63]. An extensive review on

the topic has been addressed in [47].

As indicated before, LMMSE estimation can be applied for

joint channel estimation and interpolation. However, it requires

channel statistics and high computational complexity [45],

[46]. This motivates us to develop low-complexity interpolation

algorithms.

Two of the simplest ways are piecewise constant and linear

interpolation [2], [64]. However, more pilots are required for

them to achieve acceptable performance in frequency-selective

channels. If the statistics of channel variation either in the

frequency domain (PDP) or in the time domain (Doppler

spectrum) are known apriori, a high-order polynomial can be

applied to accurately ﬁt wireless channels [64], [65].

In addition to the linear and high-order polynomial-based in-

terpolation, pilot-aided channel estimation can also be based on

FFT [46], [66]. FFT-based channel estimation essentially uses

a low-pass ﬁlter as an interpolater, and the ﬁlter is implemented

in a transform domain [55]. Instead of using a low-pass ﬁlter,

we may catch signiﬁcant taps in the transform domain and turn

off those trivial taps, which can improve the performance of

channel estimation, particularly when the SNR of the system

is low. However, when turning off trivial taps or using a low-

pass ﬁlter, a useful component may also be removed, which will

cause a large estimation error for those subchannels on the edge

[55], [56].

2) DDCE: For DDCE, CSI at the preamble block(s) is ﬁrst

estimated and then used to demodulate and detect the symbols

at the next data block. CSI can be tracked by using detected

symbols or data, either hard decision or soft decision, as shown

in [67]–[69]. For systems with error-correction coding, redun-

dancy in coding can be exploited by iteratively performing soft

symbol decision and channel estimation [68], [70].

A major problem of DDCE is error propagation, which is

particularly severe for a system with a large Doppler frequency.

This can be solved by periodically inserting training blocks

[71]. Comb pilots may also be applied instead of training blocks

[46], and channel tracking or prediction can be used for further

performance improvement [72].

For coded OFDM systems, expectation–maximization algo-

rithms can improve estimation performance by exploiting the

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