Joint channel estimation and decoding in the
presence of phase noise over time-selective
flat-fading channels
ISSN 1751-8628
Received on 13th May 2015
Revised on 28th October 2015
Accepted on 1st December 2015
doi: 10.1049/iet-com.2015.0453
www.ietdl.org
Qiaolin Shi, Nan Wu
✉
, Hua Wang, Weijie Yuan
School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
✉ E-mail: wunan@bit.edu.cn
Abstract: Oscillator phase noise (PHN) can result in significant performance loss in coherent communication systems if not
compensated appropriately. Most existing studi es focus on either PHN estimation over additive white Gaussian noise
channels or channel impulse response (CIR) estimation in the absence of PHN. In this study, joint CIR estimation and
decoding over time-selective flat-fading channels impacted by PHN is studied. Both the time evolutions of CIR and PHN
are approximated by autoregressive models. Building on thi s, factor graph of the joint aposterioriprobability function
is constructed and the sum–product algorithm is applied to derive messages on factor graph. Due to the non-linearity
of PHN, no closed-form expressions of the messages can be obtained. To this end, the authors use c anonical
distribution approach, which approximates the messages by Gaussian and Tikhonov probability density functions on
the sub-graphs o f CIR and PHN, respectively. Accordingly, the messages can be calculated by updating the parameters
of the canonical distributions. A mixed serial-parallel message passing schedule is presented to implement the
algorithm, which enables the compromise between the bit error rate performance and the processing throughput.
Simulation resul ts sho w t hat t he pr oposed joint estimation and decodi ng algorithm significantl y ou tperforms the
existing methods in fading channels impacted by PHN.
1 Introduction
Oscillator phase noise (PHN) has been one of the major impairments
to the performance of coherent communication systems [1]. It is
originated from the local oscillator instabilities of both the
transmitter and receiver. The problem of data detection in the
presence of PHN has been studied for decades. Recently, much
attention has been attracted due to the demands for high data rate
millimetre wave transmission [2]. This is due to the fact that, on
the one hand, PHN of an oscillator becomes much severe as the
oscillation frequency increases. On the other hand, high order
constellations are more sensitive to carrier phase uncertainties.
Many algorithms have been developed for signal detection and
decoding over additive white Gaussian noise (AWGN) channels
affected by PHN [3–9]. A dynamic phase tracking algorithm
which employs the soft symbols obtained from channel decoder is
studied in [3]. In [4], a code-aided forward–backward recursive
phase estimator is proposed and analysed, which is demonstrated
to be superior to the traditional non-data-aided estimators when the
signal is affected by PHN. On the basis of factor graph and the
sum–product algorithm (SPA) [10], a joint detection and decoding
algorithm in the presence of strong PHN is developed in [5]. The
probability density functions (pdfs) related to carrier phase
computed by the SPA are represented by Tikhonov pdf, which can
be regarded as the canonical distribution approach presented in
[11]. In [6], phase discretisation approach is used to develop a
joint phase estimation and turbo decoding algorithm. Variational
bounding is utilised in [7] to obtain iterative detection algorithms,
where the system model is linearised by Taylor-series expansion
approximation and the soft estimation of PHN is computed by
extended Kalman smoother. For further complexity reduction, Lin
and Lim [8] restricts the free distribution to be a Gaussian density
or Dirac delta function, and also reveals the relation between the
proposed algorithm and the classical approach via the
expectation-maximum (EM) algorithm. In [9], truncated discrete
cosine transform (DCT) expansion is employed to model the PHN
variation in the received data block, and EM algorithm is applied
to estimate the DCT coefficients. All the above papers only
assume AWGN channels, the impact of fading in mobile
communication is not taking into account.
Receiver algorithms for joint channel estimation and data
detection assuming perfect phase synchronisation have been
well-studied for various systems [12–14]. A finite state Markov
model for a quantised version of the fading channel phase is
designed in [12]. The forward–backward algorithm is used to
perform joint channel estimation and turbo decoding in
frequency-flat time-selective Rayleigh fading channels. A practical
joint demodulation and decoding strategy for non-coherent
communication over block fading channels is investigated in [13],
and the comparisons with information-theoretic benchmarks are
also interpreted. In [14], the correlated Rayleigh fading channel is
approximated by a first-order autoregressive (AR) model, building
on which, SPA on factor graph is employed, leading to Kalman
smoothing algorithm. In [15], both the Rayleigh fading as well as
the strong co-channel inference are considered, and parameterised
messages are updated when performing joint channel estimation,
interference mitigation and decoding based on the factor graph and
belief propagation. The computational complexity is tractable
because the number of the components of the mixed Gaussian
densities is limited. Note that although the estimation of complex
channel impulse response (CIR) can implicitly alleviate the impact
of time-varying phase, without taking into account the statistical
information of the dynamic phase, these algorithms result in
significant performance loss in the presence of strong PHN. One
of the few works that consider receiver design over fading
channels impacted by PHN is shown in [16]. However, the CIR is
assumed to be invariant during a block in OFDM system, which
cannot be applied in time-selective fading channels. In [17], low
complexity suboptimal algorithms are proposed for joint phase
estimation and decoding in multiple-input multiple-output system
in the presence of PHN. However, the CIR between transmit and
receive antennas are assumed to be known. To the best knowledge
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