1000 IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 8, NO. 4, AUGUST 2019
Short Prototype Filter With Constrained Frequency Spreading
for OQAM/FBMC Systems
Yuan Tian, Da Chen ,DaimingQu , Kai Luo , and Tao Jiang , Fellow, IEEE
Abstract—In this letter, we propose a short filter (i.e., the
overlapping factor is one) with constrained frequency spreading
(CFS) for offset quadrature amplitude modulation-based filter
bank multicarrier (OQAM/FBMC) systems. In detail, a system
of equations in the filter’s frequency coefficients is formulated and
solved in the sense of least squares, then the filter is obtained
through an inverse discrete Fourier transform. Simulation results
reveal that the proposed CFS filter is able to achieve comparable
performance to existing short filters in the presence of differ-
ent channel impairments with less frequency spreading, which
leads to lower implementation complexity of OQAM/FBMC using
frequency spreading structure, thus it is a valuable choice when
considering both the CFS and a near perfect reconstruction of
the OQAM/FBMC signal.
Index Terms—OQAM/FBMC, filter design, frequency
spreading.
I. INTRODUCTION
O
FFSET quadrature amplitude modulation based filter
bank multicarrier (OQAM/FBMC) is considered as a
promising alternative to the conventional orthogonal frequency
division multiplexing (OFDM) [1]–[3]. Allowing for usage
of prototype filters well-localized in the time and frequency
domains, the OQAM/FBMC system is able to overcome some
shortcomings of OFDM, including the poor out-of-band emis-
sion, the loss of capacity due to the cyclic prefix (CP), and
the sensitivity to synchronization errors [4]–[7].
However, the advantages of OQAM/FBMC are gained at
the cost of implementation complexity [8]. Taking the OFDM
receiver as reference, the additional complexity brought by the
OQAM/FBMC receiver is proportional to the prototype filter
length L = KM, where M is the number of sub-carriers and
K is the overlapping factor of the filter. Note that, for K = 1,
we denote the prototype filters as short filters, with which the
additional complexity is largely reduced. In addition, short fil-
ters are preferred in scenarios that require short frame sizes
to reduce system latency. Moreover, OQAM/FBMC systems
with short filters are more robust to time-varying channels [9].
Although short filters would lead to some rise in out-of-band
Manuscript received January 26, 2019; accepted March 1, 2019. Date of
publication March 6, 2019; date of current version August 21, 2019. This
work was supported in part by the National Science Foundation of China under
Grant 61601191 and Grant 61571200, in part by the National High Technology
Development 863 Program of China under Grant 2015AA01A710, and in part
by the Open Research Fund of National Mobile Communications Research
Laboratory, Southeast University under Grant 2014D09. The associate editor
coordinating the review of this paper and approving it for publication was
J. Mietzner. (Corresponding author: Daiming Qu.)
The authors are with the School of Electronic Information and
Communications, Huazhong University of Science and Technology,
Wuhan 430074, China (e-mail: yuan_tian@hust.edu.cn; chenda@hust.edu.cn;
qudaiming@hust.edu.cn; kluo@hust.edu.cn; tao.jiang@ieee.org).
Digital Object Identifier 10.1109/LWC.2019.2903473
emission compared to long filters, which indicates slightly
more spectrum overhead is needed, the OQAM/FBMC still
has much lower out-of-band emission than OFDM [9].
In the literature, some styles of short filters have been
proposed. In [9], the short Time-Frequency Localization (TFL)
filter was designed to achieve the optimal TFL property. The
Quadrature Mirror Filter (QMF) widely used in the sub-
band coding of speech was employed in the Lapped-OFDM
system [10] and for FBMC with pulse-amplitude modula-
tion [11]. Recently, a short filter was proposed in [12] called
Near Perfect Reconstruction 1 (NPR1) with “1” referring to
the overlapping factor of one. Compared to the TFL and QMF
filters, the NPR1 filter exhibits better robustness to channel
impairments like multipath channels, carrier frequency off-
sets (CFO) and timing offsets (TO). Moreover, the frequency
spreading (i.e., the number of non-zero frequency coefficients
which are next to each other) of the NPR1 filter is much
less, which leads to lower implementation complexity of
OQAM/FBMC using the frequency spreading structure [8].
However, the NPR1 filter is formulated by inverting the time
and frequency lattice of the filter-bank impulse response of
the Martin-Mirabassi-Bellanger (MMB) filter with K = 4.
Even though the NPR1 filter is shown to be a good short
prototype filter by experiments [12], there still remains the
question whether the NPR1 filter is the best short filter with
consideration of both constraining the frequency spreading
and maintaining the near perfect reconstruction (NPR) of the
OQAM/FBMC signal.
In this letter, we propose a short filter design for
OQAM/FBMC systems to address above question, where
the filter is generated by an inverse discrete Fourier trans-
form (IDFT) of its frequency response with limited non-zero
frequency coefficients. Based on the perfect reconstruction
(PR) conditions on short filters [13], we formulate a system
of equations in the filter’s frequency coefficients and solve
it in the sense of least squares, resulting in the Constrained
Frequency Spreading (CFS) filter. In contrast to the NPR1
filter design approach, we are able to flexibly designate the
frequency spreading of the CFS filter in our design and at
the same time achieve the best NPR performance. Numerical
results reveal that, with 7 or even 5 frequency coefficients,
the CFS filter is able to achieve good NPR performance. In
addition, the CFS filter with 7 frequency coefficients and the
NPR1 filter nearly coincide and they share similar robust-
ness against multipath channels, CFO and TO. Moreover,
the CFS filter with 5 frequency coefficients could lead to
much lower implementation complexity of OQAM/FBMC
using the frequency spreading structure due to its reduced
frequency spreading. Thus, one could choose an appropri-
ate CFS filter based on requirements of complexity and NPR
performances.
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