多尺度多时延信道下OFDM系统性能深度探讨

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本文主要探讨了在多尺度多时延（Multi-scale Multi-lag, MSML）信道环境下，正交频分复用（Orthogonal Frequency Division Multiplexing, OFDM）系统的性能分析。水下声学（Underwater Acoustic, UWA）信号由于水中的低声速以及相对运动接收器之间存在的时延变化，通常会遭受明显的尺度效应。在一般情况下，单个尺度下的时延失真可以通过采样操作进行校正。然而，在浅水区域等复杂环境中，不同信道路径的尺度系数可能存在显著差异。近年来，MSML模型被广泛用于描述高速移动的UWA信道特性，它能够捕捉到信道中多尺度和多时延的特点。作者针对这个模型，对OFDM系统进行了深入的研究。他们将每个子载波通道视为一个独立的尺度参数处理单元，从而转化为了等效的MSML信道模型。在这个过程中，他们考虑了尺度效应对OFDM信号传输的影响，包括频率选择性衰落、符号间干扰(ISI)以及多径效应的加剧。性能分析主要集中在以下几个方面： 1. **误码率分析**：通过对MSML信道下OFDM信号的调制与解调过程进行仿真，研究不同尺度和时延条件下，OFDM系统的误码率如何随带宽、子载波间隔以及信道编码策略的变化而变化。 2. **功率效率**：评估OFDM在多尺度信道上的功率效率，讨论如何通过优化子载波分配或采用自适应调制技术来提高能源利用效率。 3. **抗干扰能力**：分析OFDM在MSML信道中的抗多径干扰能力，以及如何通过均衡技术如分集接收或多用户检测来增强系统的鲁棒性。 4. **同步问题**：鉴于多尺度可能导致的同步挑战，研究了如何在OFDM系统中实现有效的时间和频率同步算法。 5. **性能极限与优化**：探讨了在考虑到物理层限制（如信号传播延迟、信道估计误差）的情况下，OFDM在MSML信道上的性能优化方法。结论部分可能提出未来研究方向，比如开发新的OFDM变种或联合编码技术，以进一步提升在多尺度多时延信道上的性能。这篇文章提供了深入了解OFDM在动态UWA环境下的关键性能指标及其优化策略，对于通信系统设计者和水下通信研究人员具有重要的理论参考价值。

Performance Analysis of OFDM over

Multi-scale Multi-lag Channels

Yun Liu

∗†

, Fei Ji

∗

, Fangjiong Chen

∗

, Miaowen Wen

∗

, Hua Yu

∗

, and Yinming cui

∗

School of Electronic and Information Engineering, South China University of Technology,

Guangzhou, China. Email: {eefeiji,eefjchen,eemwwen, yuhua, ymcui}@scut.edu.cn

†

School of Information Science and Technology, Zhongkai University of Agriculture and Engineering,

Guangzhou, China. Email: l.y95@mail.scut.edu.cn

Abstract—Due to the low speed of sound in water, the under-

water acoustic (UWA) signal suffers obvious time scaling when

relative motion exists between the transceivers. In general, given

a single scale, the scaling-induced distortion can be rectiﬁed by

a resampling operation. However, the scaling coefﬁcients of the

channel paths may be different from each other, especially in

shallow water. In recent years, a multi-scale multi-lag (MSML)

model has been used to describe the high speed mobile UWA

channels in the literature. In this paper, we analyze the per-

formance of OFDM system under this model. Considering the

resalmper as a part of the channel, we get a an equivalent MSML

channel. We ﬁrst derive the sub-channel gains in closed form, and

then get the analytical expression of the average channel gains

and inter-carrier interference (ICI) under given statistics of the

channel paths. Finally, we discuss the average achievable rate of

the system and get a lower bound of that in closed form.

I. INTRODUCTION

UWA channels are generally recognized as one of the most

challenging communication media in use today because of

the low speed of sound in water, time-varying propagation,

strong attenuation that increases with frequency, as well as

the relatively high Doppler spreading and shifting induced

by mobility [1]. Recent measurement campaigns and analyses

of acoustic propagation effects indicate that, in the presence

of relative motion, the received signal should be modeled as

the superposition of differently scaled, delayed, and attenuated

versions of the transmitted signal [2], [3].

Orthogonal frequency division multiplexing (OFDM) has

been widely investigated to implement reliable high data rate

communications in UWA channels [2]–[4]. The main advan-

tage of OFDM is that it can decompose a static frequency-

selective channel into a set of independent and intersym-

bol interference (ISI) free sub-channels, which enable low-

complexity frequency-domain channel equalization.

OFDM transmission over mobile multipath channels is

highly sensitive to Doppler distortion, which destroys the

orthogonality of the subcarriers, thus causing ICI. For OFDM

signals, the scaling effect in the time domain introduces

Doppler shifts/spreads on the subcarriers. A single scale can

be described by a scaling factor α, which is the ratio of the

relative-motion speed to the propagation speed of the sound.

For the nth subcarrier of frequency f

, a single scale results

a frequency shift of αf

. In narrowband systems, with N

subcarriers spaced at ∆F , f

≫ B = N∆F , the Doppler shift

can be approximated as equal for all the subcarriers and can

be compensated by adjusting the local carrier frequency [5].

In wideband OFDM systems, such as UWA communications,

however, the time scale causes different carriers to experience

substantially different frequency offsets.

Since the Doppler distortion induced by relative motion

can be modeled as time scaling of the signal, resampling has

been adopted as an effective front-end processing technique to

mitigate the ICI induced by mobility in much previous work

on UWA communications [2]–[4], [6]. The optimal resampling

rates for OFDM systems were proposed under deterministic

and statistical MSML channels in [2] and [3], respectivly.

Since resampling with a single rate cannot compensate dif-

ferent time-scaling factors simultaneously, the ICI cannot be

eliminated completely even with the optimal resampling, and

residual ICIs always exist in the OFDM signal under MSML

channels [3]. In this paper, with the given statistical parameters

of the path gain, delay and Doppler scale of the UWA channel,

we accurately derive the closed-form expression of the average

power gain and ICI coefﬁcient on each subcarrier. Then we

derive a lower bound on the average achievable rate of the

system in analytical expression.

The remainder of this paper is organized as follows. In

the next section, we discuss the OFDM system model and

propose an equivalent MSML model for the resampled OFDM

signals at the receiver. In Section III, the channel response

and average achievable rate are analyzed. In Section IV, the

theoretical analysis is validated by computer simulations. This

paper concludes with remarks in Section V.

Notation: Let x be a random variable. E[x] is the expecta-

tion; (·)

∗

denotes complex conjugate; x ∼ CN(0, σ

) means a

circularly symmetric complex Gaussian random variable with

zero mean and variance E[xx

∗

] = σ

II. SYSTEM MODEL

An OFDM system with N subcarriers is considered, where

N is an integer power of two. The transmitted signal in time

domain within an OFDM symbol can be written as

x(t) =



n=1

j2πf

u(t),

u(t) =



1, t ∈ [−T

, T ]

0, elsewhere

, (1)

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