Low-Complexity Factor Graph-Based Iterative
Detection for RRC-SEFDM Signals
Yuan Feng
†
, Yunsi Ma
‡
, Zhengdai Li
§
, Chaoxing Yan
§
, and Nan Wu
‡
†
China Research and Development Academy of Machinery Equipment, Beijing, China, 100089
‡
School of Information and Electronics, Beijing Institute of Technology, Beijing, China, 100081
§
Beijing Research Institute of Telemetry, Beijing, China, 100076
Abstract—Spectrally efficient frequency division multiplexing
(SEFDM) is a promising technique for the next generation
wireless communication due to its high spectral efficiency. Con-
ventional SEFDM detectors suffer from the challenging tradeoff
between computational complexity and bit error rate (BER)
performance. In this paper, we propose a low-complexity iterative
detector using Gaussian message passing (GMP) on factor graph
for coded root raised cosine (RRC) shaped SEFDM signals. By
ignoring the weak intersymbol interference (ISI) imposed by
packing sub-carrier interval, the detection of SEFDM signals is
reformulated into a linear state-space model and a corresponding
Forney-style factor graph (FFG) is constructed. Then, we derive
messages updating expressions based on GMP rules, which enable
low-complexity parametric message passing. Since the Gaussian
approximation employed on the cycle-free factor graph, the
computational complexity of the proposed algorithm increases
linearly with the number of sub-carriers. Simulation results show
that the coded RRC-SEFDM system with the proposed factor
graph-based iterative detection can improve the transmission rate
up to 40% with about 0.5 dB E
b
/N
0
loss.
Index Terms—SEFDM, Spectral efficiency, Gaussian message
passing (GMP), Iterative detection.
I. INTRODUCTION
With the rapid growth of requirements for broadband data
services in the last decade, enhancing spectral efficiency (SE)
utilization of limited spectrum resource becomes a challenging
issue for mobile wireless communication systems. Orthogonal
frequency division multiplexing (OFDM) was one of the best
techniques to increase SE by exploiting multiple overlap-
ping orthogonal sub-carriers, which has been adopted in the
fourth generation ground mobile communication systems [1].
However, traditional OFDM cannot meet the requirements
of ever increasing system throughput in the fifth generation
(5G) networks [2], [3]. In order to achieve high data rate and
spectral efficiency for next generation wireless communication
systems, various non-orthogonal physical layer technologies
have been investigated in recent years [4]–[9].
Spectrally efficient frequency division multiplexing
(SEFDM) was proposed in [10] to enhance SE by reducing
the minimum frequency interval of orthogonal sub-carriers
whilst maintaining the same data rate of single sub-carrier.
Conventional rectangular pulse shaped SEFDM signals result
in high out-of-band power leakage and serious influences on
Corresponding author: Nan Wu (E-mail: wunan@bit.edu.cn). This work
is supported by National Science Foundation of China (NSFC) (Grant Nos.
61471037, 61571041, 61471360).
other users in adjacent frequency bands. In [11], a root raised
cosine pulse (RRC) shaped SEFDM system was investigated
to obtain significant reduction of out-of-band power leakage.
Moreover, the intercarrier interference (ICI) imposed in
RRC-SEFDM is dominated only by the impact of adjacent
sub-carriers, which outperforms rectangular pulse shaped
SEFDM in terms of bit error rate (BER) performance [12].
Spectral efficiency improvement could be achieved at the
cost of imposing intentional ICI, which should be eliminated
effectively with acceptable complexity and performance loss at
the receiver. Several detectors have been proposed to reduce or
compensate interferences for SEFDM system in the literatures.
Optimum maximum likelihood (ML) detection suffers from
exponential algorithmic complexity [13]. In [14], the sub-
optimal linear detectors were discussed, e.g., zero forcing (ZF)
and minimum mean square error (MMSE) detectors, which
only perform well in high signal-to-noise ratio (SNR) regions.
Sphere decoding (SD) [15] and fixed sphere decoding (FSD)
were applied to reduce complexity in SEFDM detectors. In
[16], a hybrid detector combining truncated singular value
decomposition (TSVD) with FSD was developed by apply-
ing TSVD estimates as initializations of the FSD algorithm.
Another hybrid soft detector combining iterative detection (ID)
with FSD achieved a tradeoff between complexity and perfor-
mance for detection of SEFDM signals [17]. However, owing
to computation complexity, aforementioned detectors are only
suitable for SEFDM system with a small number of sub-
carriers. In addition, with increasing number of sub-carriers, a
constant modulus term should be introduced to guarantee the
semi-positive definite condition of Cholesky decomposition in
SD processing [18]. For coded SEFDM system, a fast Fourier
transform (FFT)-based soft detector was proposed in [19],
where the soft information exchanged between time domain
and frequency domain results in relatively high complexity.
In [20], an iterative frequency-domain ICI estimation and
compensation scheme was proposed for turbo-coded SEFDM
system, which could achieve better BER performance than that
of FFT-based detector [19]. However, the complexity of the
frequency-domain detector was still relatively high in practical
applications.
In this paper, we propose a low-complexity iterative detec-
tion for low-density parity-check (LDPC)-coded RRC-SEFDM
system. By reformulating detection of SEFDM signals into a
linear state-space model, we construct a cycle-free Forney-
978-1-5386-6119-2/18/$31.00 ©2018 IEEE
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