基于空子载波的多普勒尺度估计和多项式插值，用于超宽带水下声信道上的多载波通信资源-CSDN文库

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标题中提到的“空子载波的多普勒尺度估计和多项式插值”以及“超宽带水下声信道上的多载波通信”指向了一系列专业领域内的高级技术问题。基于这些概念，我们可以展开以下几个知识点： 1. 空子载波技术：在通信系统中，子载波通常指的是频域内多个正交的小频率信号，它们共同构成一个子载波系统。当某些子载波不传输数据时，它们被称为“空子载波”或“零子载波”。在本文中，空子载波被用于估计多普勒尺度。 2. 多普勒尺度估计：多普勒尺度估计是通信系统中用来测量由于收发双方相对运动而产生的频率变化的技术。在水下声信道中，多普勒效应会导致接收到的信号频率发生变化，这种变化需要通过技术手段来估计和补偿。 3. 多项式插值：多项式插值是一种数学方法，它利用已知数据点来构造多项式，以便能够估计未知数据点的值。本文中提到使用多项式插值来提高多普勒尺度估计的精度，且不增加计算复杂度。 4. 超宽带水下声信道：超宽带（Ultra Wideband，UWB）是一种无线通信技术，它使用非常宽的频带以实现高数据率的传输。水下声信道是一种特殊的传输媒介，由于水对声波的吸收和散射，声波在水下的传播具有复杂性。在超宽带条件下，水下声信道的传输特性更是多样化。 5. 正交频分复用（Orthogonal Frequency Division Multiplexing，OFDM）：OFDM是一种多载波调制技术，通过将高速数据流分散到许多子载波上进行传输。每个子载波上的数据率较低，带宽较小，相互间正交。OFDM技术因其能有效抵抗多径效应和频率选择性衰落而广泛应用于无线通信领域，包括水下声通信。在本研究论文中，作者提出了一个利用空子载波能量总和通过离散傅里叶变换（Discrete Fourier Transform，DFT）构造的代价函数。通过识别非均匀多普勒频移下的空子载波频率，证明了代价函数在全局最小值附近可以拟合为二次多项式。准确的多普勒尺度估计是通过多项式插值来实现的，提高了精度同时减少了计算量。文中还进行了浅水实验来演示所提出方法的性能，在相对带宽为67%的超宽带水下声信道中，当发射器和接收器以5节的相对速度移动时，得到了极佳的结果，验证了该方法的有效性。文章探讨了在水下超宽带声通信环境中，利用空子载波进行多普勒尺度估计和多项式插值的新技术。这种技术在提高通信质量的同时，简化了计算过程，尤其适用于运动载体间的通信。论文中还展示了相关实验数据，证明了该方法在实际应用中的可靠性和效率。通过这些研究，有望推动水下通信技术的进一步发展。

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Journal of Systems Engineering and Electronics

Vol. 26, No. 6, December 2015, pp.1177– 1183

Null subcarriers based Doppler scale estimation with

polynomial interpolation for multicarrier communication

over ultrawideband underwater acoustic channels

Yang Chen

, Jingwei Yin

, Ling Zou

, Dan Yang

3,*

, and Yuan Cao

1. School of Information Science and Engineering, Changzhou University, Changzhou 213164, China;

2. College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China;

3. School of Textile and Material Engineering, Wuhan Textile University, Wuhan 430073, China;

4. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore

Abstract:

This paper addresses the extremal problem of the null

subcarriers based Doppler scale estimation in underwater acoustic

(UWA) orthogonal frequency division multiplexing (OFDM) com-

munication. The cost function constructed of the total energy of null

subcarriers through discrete Fourier transform (DFT) is proposed.

The frequencies of null subcarriers are identiﬁed from non-uniform

Doppler shift at each tentative scaling factor. Then it is proved that

the cost function can be ﬁtted as a quadratic polynomial near the

global minimum. An accurate Doppler scale estimation is achieved

by the location of the global scarifying precision and increas-

ing the computation minimum through polynomial interpolation,

without complexity. A shallow water experiment is conducted to

demonstrate the performance of the proposed method. Excellent

performance results are obtained in ultrawideband UWA channels

with a relative bandwidth of 67%, when the transmitter and the

receiver are moving at a relative speed of 5 kn, which validates the

proposed method.

Keywords: underwater acoustic (UWA) communication, orthogo-

nal frequency division multiplexing (OFDM), Doppler scale estima-

tion, polynomial interpolation.

DOI: 10.1109/JSEE.2015.00128

1. Introduction

Underwater acoustic (UWA) orthogonal frequency divi-

sion multiplexing (OFDM) communication has been ex-

tensively investigated in recent years [1 – 5]. Unlike the ra-

dio channel which has relatively short delay spread and

slow time variation, UWA channels suffer from long de-

lay spread and fast time variation. And fast time variation

Manuscript received September 09, 2014.

*Corresponding author.

This work was supported by the National Natural Science Foundation

of China (61201096; 61471137; 61501061), the Qing Lan Project of

Jiangsu Province, the Science and Technology Program of Changzhou

City (CJ20130026; CE20135060; CE20145055), and the State Key Lab-

oratory of Ocean Engineering (Shanghai Jiao Tong University) (1316).

brings signiﬁcant Doppler effects to UWA communication

systems, so estimation of the Doppler scaling factor is of

critical importance [6 – 9].

The methods of the Doppler scale estimation can be di-

vided into three categories. In the ﬁrst category, Doppler

scale estimation is accomplished by inserting waveforms

known to the receiver during the data transmission. One

example is to detect the time-of-arrival of the pream-

ble and postamble which is Doppler-insensitive such as

the linear-frequency-modulated (LFM) waveform and the

hyperbolic-frequency modulated (HFM) waveform.

The second is with pilot assisted. Different algorithms

are adopted for the different channel models [10 – 12]. In

[10], the least-squares (LS) channel estimator assumes the

channel to be non-sparse. Reference [11] is based on the

basis expansion model. Reference [12] relies on a discrete-

path model, which employs both the orthogonal matching

pursuit (OMP) and basis pursuit (BP) algorithms.

The third category makes use of null subcarriers. Null

subcarriers are of multi-purpose in OFDM communica-

tion systems. In [13], the power spectrum of the inter-

carrier interference (ICI) plus noise is approximated by ﬁt-

ting the measurements on the null subcarriers embedded

in each OFDM symbol. Pre-whitening is then applied to

each OFDM symbol and impressive performance gains are

found whenever the signal is signiﬁcantly colored. In [14]

and [15], null subcarriers are inserted between pilot and

data subcarriers to protect from the inﬂuence of each other.

The Doppler estimating with null subcarriers is based on

block-by-block processing, and does not rely on channel

dependence across OFDM blocks. Thus it is suitable for

fast-varying UWA channels, and increasingly drawing re-

searchers’ attention.

1178 Journal of Systems Engineering and Electronics Vol. 26, No. 6, December 2015

As an extension of the blind carrier frequency offset

(CFO) estimation method [14], using the energy on the null

subcarriers to ﬁnd the best ﬁt becomes a popular Doppler

scaling factor estimation method in UWA OFDM commu-

nication [15 – 18]. It is essentially an extremal problem of

the cost function formulated from the total energy of null

subcarriers. In [10], a two-step approach is proposed. First,

the received signal is resampled according to the Doppler

scaling factor. The factor is roughly measured by preamble

and postamble, followed by resolution of residual Doppler

which is considered to be uniform. The rough measure-

ment makes it only suitable for ofﬂine processing due to

the processing delay and complexity. The residual Doppler

is also frequency related when the carrier frequency is

low to achieve long range communication, where normally

the relative bandwidth is very large. In [15] the total en-

ergy of frequency measurements at null subcarriers of the

block is resampled with different tentative scaling factors,

thus the computation complexity is extremely large. As an

improvement, in [17], the cost function is sampled spo-

radically to ﬁnd the rough place of the global minimum.

Then, an accurate estimation is conducted by the method of

steepest descent. However, it suffers from the conﬂict be-

tween precision and computation complexity, as the com-

plexity of resampling increases proportionally to the accu-

racy of the interpolation.

In this paper, a new efﬁcient method of Doppler scal-

ing estimation is proposed. The cost function is formulated

from the total energy of null subcarriers through discrete

Fourier transform (DFT) instead of the resampling method.

The frequencies of null subcarriers are identiﬁed accord-

ing to nonuniform Doppler shifts at each tentative scaling

factor. Beneﬁtting from that DFT has much less computa-

tion complexity than the resampling method, the proposed

method is more efﬁcient. The cost function is investigated

and proved to be ﬁtted by a quadratic polynomial near the

global minimum. The accurate location of the global min-

imum can be achieved through polynomial interpolation.

To verify this approach, an experiment was carried out in

Lianhua lake of Heilongjiang province. Over a bandwidth

of 4 kHz with a relative bandwidth of 67%, quaternary

phase-shift keying (QPSK) modulation and rate 2/3 con-

volutional coding are adopted. Excellent performance is

achieved when the relative speed is up to 5 kn, at which

max Doppler shift is greater than the OFDM subcarrier

spacing. The experiment results validate our approach’s

validity and effectiveness.

2. Cylic preﬁx OFDM over underwater

acoustic channels

Let T denote the OFDM symbol duration and T

the cylic

preﬁx. The total OFDM block duration is T



= T + T

The frequency spacing is Δf =1/T. The kth subcarrier is

at the frequency

= f

+ kΔf, k = −K/2,...,K/2 − 1 (1)

where f

is the carrier frequency and K subcarriers are

used so that the bandwidth is B = KΔf.

Consider one CP-OFDM block. Let d(k) denote the in-

formation symbol to be transmitted on the kth subcarrier.

The nonoverlapping sets of active subcarriers S

and null

subcarriers S

satisfy S

∪S

= {−K/2,...,K/2−1}.

The transmitted signal in passband is then given by

s(t)=



k∈S

d(k)e

jk2πΔft

j2πf

,t∈ [T

,T]. (2)

Consider a multipath underwater channel that has the

impulse response

c(τ,t)=



(t)δ(τ − τ

(t)) (3)

where A

(t) is the path amplitude and τ

(t) is the time-

varying path delay. To develop our receiver algorithms, the

following assumptions are adopted.

(i) All paths have a similar Doppler scaling factor a such

that

(t) ≈ τ

− at. (4)

In general, different paths could have different Doppler

scaling factors. The method proposed here is based on the

assumption that all the paths have the same Doppler scal-

ing factor [10,15,17 – 19]. However, when this is not true,

part of useful signals are treated as additive noise, which

increases the overall noise variance. However, we ﬁnd that

as long as the dominant Doppler shift is caused by the di-

rect transmitter/receiver motion, as it is the case in our ex-

periments, this assumption seems to be justiﬁed.

(ii) The path delays τ

(t), the gains A

(t), and the

Doppler scaling factor a are constant over the block du-

ration.

The received signal in passband is

˜y(t)=



(t)



k∈S

d(k)e

jk2πΔf (t+at−τ

)

j2πf

(t+at−τ

)

+˜n(t) (5)

where ˜n(t) is the additive noise.

Base on the expression in (5), each subcarrier experi-

ences a Doppler-induced frequency shift (f

+ kΔf)a,

which depends on the frequency of the subcarrier. Since the

bandwidth of the OFDM signal is comparable to the center

frequency, the Doppler-induced frequency shifts on diffe-

rent OFDM subcarriers differ considerably; i.e. the nar-

rowband assumption does not hold true.

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