线性混合双同频8相位移键控信号频率偏移估计

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"这篇研究论文探讨了频率偏移估计在两个同频8相位移键控(8PSK)调制信号线性混合情况下的应用。作者包括杨勇、张东玲和 Peng Hua，他们来自中国国家数字程控交换系统工程技术研究中心。文章于2014年发表在IET Signal Processing期刊上，doi: 10.1049/iet-spr.2014.0079，ISSN1751-9675。" 本文主要关注的是在特定条件下，如何对两个8PSK调制信号的线性混合物进行频率偏移估计。这些条件包括固定帧长度以及帧同步码，同时假设在异步编码的情况下，信号的帧长度是已知的。作者提出了一种基于最大似然准则的频率偏移估计算法。该算法的核心在于优化目标函数，这个函数通过交叉相关计算得出，同时考虑到定时误差、幅度衰减和相位偏移等不确定因素。优化过程采用了层次搜索方法，以求得最佳的频率偏移估计值。层次搜索策略是一种有效的优化工具，它可以在复杂的问题空间中逐步逼近最优解。此外，论文还推导出了混合信号频率偏移估计的Cramer-Rao下界(CRB)，这是一种评估估计性能的标准。CRB提供了理论上的最小方差限制，可以用来比较不同估计算法的性能。通过对比实际的频率偏移估计值与CRB，可以分析所提出的算法在估计精度上的表现。这篇论文的研究成果对于无线通信和信号处理领域具有重要意义，特别是在存在多径传播、载波同步误差或者设备非理想性的情况下，准确估计频率偏移对于正确解调8PSK信号至关重要。通过提供一种有效的频率偏移估计方法，该研究有助于提升通信系统的性能和可靠性。

Published in IET Signal Processing

Received on 21st February 2014

Revised on 27th May 2014

Accepted on 29th July 2014

doi: 10.1049/iet-spr.2014.0079

ISSN 1751-9675

Frequency offset estimation of the linear mixture

of two co-frequency 8 phase-shift keying

modulated signals

Yong Yang, Dongling Zhang, Hua Peng

China National Digital Switching System Engineering and Technological Research Center, Zhengzhou, Henan,

People’s Republic of China

E-mail: yangyong328@163.com

Abstract: A frequency offset estimation (FOE) algorithm based on the maximum-likelihood criterion is proposed for the linear

mixture of two 8PSK modulated signals with ﬁxed frame length and frame synchronisation code on the condition that the frame

length is known when the signals are coded asynchronously. FOE is calculated by optimising the objective function, which is

obtained from cross-correlation computation, given that timing error, amplitude attenuation and phase offset are unknown.

The optimised process is accomplished by utilising hierarchical search. Cramer-Rao bound (CRB) of mixed-signal FOE is

derived to evaluate the performance of the proposed algorithm. The estimation performance of the algorithm can come close

to the CRB performance with low E

. The proposed algorithm is also applied to the FOE of a mixed signal whose power

is asymmetrical.

1 Introduction

Paired carrier multiple access (PCMA) is a new satellite

communication technolog y [1]. The signals sent by two

earth stations are overlapped both in time and frequency

domains. Hence, PCMA can save half of the bandwidth

resources and improve the performance of anti-interception.

The demodulation of PCMA signals is fundamentally a

ﬁeld in single-channel blind source separation [2–5]or

single antenna interference cancellation [6–8]. Therefore

PCMA signals have become a challenge in communication

signal processing.

As a special characteristic of PCMA technology, carrier

synchronisation is the most signiﬁcant link in demodulation,

with signiﬁcant achievements obtained in single digital

modulation signals. The most common method of

demodulation is performed by eliminating the modulated

information through M-power operation and estimating the

frequency offset based on the maximum-likelihood (ML)

criterion [9–11]. This method can also be applied to

low-order modulated PCMA signals, such as those in

binary phase shift keying and quadrature phase shift keying.

However, the presence of too many cross terms after

M-power operation for 8 phase-shift keying (8PSK)

modulated mixed signals renders the ML estimation

algorithm inapplicable. Thus, demodulating the mixed

signal of two 8PSK modulated signals has become a

challenge in signal processing. The frequency offset

estimation (FOE) of two 8PSK modulated signals requires

an immediate solution.

An FOE algorithm based on ML for sync codes is proposed

in this study. The algorithm is applied when two 8PSK

modulated signals are coded asynchronously. The proposed

algorithm has low computational complexity given that

timing error, amplitude attenuation and phase offset

information are unknown. Thus, the algorithm has a good

potential for future application.

This paper is organised as follows. The basic signal model

for the linear mixture of two co-frequency 8PSK modulated

signals is described in Section 2. The FOE algorithm based

on ML is proposed in Section 3. Section 4 focuses on the

derivation of the CRB of the mixed signal. Section 5

provides the simulation results, which show the

effectiveness of the proposed algorithm. Lastly, conclusions

are provided in Section 6.

2 Signal model

The received linear mixture of two co-frequency 8PSK

modulated signals that have the same symbol rate is

considered in satellite communication. The received signal

is sampled at symbol period T, and the discrete-time form

can be written as



i=1

j(2

kT+

)

(i)

+ v

(1)

where v

(k=1, 2, …) is the complex additive white Gaussian

noise (AWGN) sampled sequences with zero mean and

www.ietdl.org

186

The Institution of Engineering and Technology 2015

IET Signal Process., 2015, Vol. 9, Iss. 2, pp. 186–192

doi: 10.1049/iet-spr.2014.0079

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