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On Spectral Shaping of Multicarrier Waveforms
Employing FIR-Filtering and Active Interference
Cancellation
Xiaojie Wang, Kevin Kienzle and Stephan ten Brink
Institute of Telecommunications, Pfaffenwaldring 47,
University of Stuttgart, 70569 Stuttgart, Germany
Email: {xiaojie.wang, kevin.kienzle, tenbrink}@inue.uni-stuttgart.de
Abstract—For next generation wireless communication systems
(also referred to as “5G”), many advanced multicarrier wave-
form techniques have recently been proposed to enhance the
system performance beyond today’s most prominent multicarrier
technique, namely, orthogonal frequency division multiplexing
(OFDM). Despite several advantages of OFDM, its less pro-
nounced frequency localization property and considerable out-of-
band (OOB) emissions make it less suited for many applications
in 5G such as massive machine communications and Internet
of Things. In order to reduce the high OOB emissions, novel
multicarrier modulation techniques like universal filtered multi-
carrier (UFMC) and generalized frequency division multiplexing
(GFDM) employing improved pulse shaping are currently being
investigated. An important aspect is “spectral shaping”, i.e.,
generating spectral notches in OFDM signals, as already explored
in the past for applications in ultra-wideband (UWB) systems.
In this paper, we compare the effectiveness of suppressing
OOB emissions employing FIR-filtering and active interference
cancellation (AIC), respectively, in the context of 5G scenarios.
Moreover, we propose a novel scheme to combine AIC and FIR-
filtering into one multicarrier transmission system, i.e., UFMC
with AIC. The simulation results show that the proposed AIC
algorithm for UFMC reduces OOB emissions more effectively and
introduces less spectral overshoot compared to the conventional
method while hardly increasing computational complexity.
I. INTRODUCTION
With the rollout of future applications such as Internet
of Things (IoT) and tactile Internet, different technical chal-
lenges, e.g., higher data rate, spectral efficiency, supported
number of devices, relaxed synchronization and lower latency,
have to be mastered in the upcoming 5th Generation (5G)
wireless communication network [1]. It is believed that 5G
will be a major paradigm shift compared to the current Long
Term Revolution (LTE) design based on synchronicity and
orthogonality [2]. Disruptive technologies in all layers are re-
quired to realize the manifold improvements. The information-
bearing waveform of the physical channel plays a primary
role in communication systems. Orthogonal frequency division
multiplexing (OFDM) in conjunction with a cyclic prefix (CP)
is the waveform choice of many standards, e.g., LTE and
various wireless LAN standards, because of its simplicity
and efficiency. One of the main well-known drawbacks of
OFDM is the high out-of-band (OOB) emission (“sin (x)/x”
spectrum), which makes it sensitive to synchronization errors.
To enhance the system performance of OFDM, and in order
to support a wider range of traffic types, other multicarrier
waveforms based on filtering approaches have recently been
studied in the context of 5G. Filterbank based multicarrier
(FBMC) dates back to the 1960s [3] [4]. It applies frequency-
well localized pulse shaping per subcarrier, thus generating
very low OOB emissions. However, typically long filters
spanning the length of several multicarrier symbols are re-
quired. Generalized frequency division multiplexing (GFDM)
employs circular pulse shaping for each subcarrier within a
block consisting of several multicarrier symbols. It allows
flexibility in OOB emissions and spectral efficiency. However,
a more complex receiver is required compared to OFDM [5].
Universal filtered multicarrier (UFMC) utilizes much shorter
filters (comparable to the CP length in OFDM, e.g., 8%-15%
of the symbol length) to reduce OOB emissions of a subband,
i.e., a group of subcarriers, while a simple FFT-based receiver
like in OFDM can be used [6].
Generating spectral notches has already been investigated in
the context of ultra-wideband (UWB) technology [7]. In UWB,
a secondary device transmits in a wide frequency band (usually
larger than 500 MHz) with a very low power level. To protect
licensed primary users against interference, the secondary
device has to suppress its power in certain frequency bands
(regulated by, e.g., the FCC or ITU). Due to the flexibility
of OFDM, the so called multi-band OFDM (MB-OFDM)
technique has been considered as promising for UWB. To
further suppress the side-lobe level in MB-OFDM, “spectrum
sculpting” techniques have been proposed in [8][9][10] using
cancellation subcarriers in the frequency domain. In contrast
to frequency domain spectral shaping, classical time domain
pulse-shaping techniques can also be applied, which, though,
appear to be less flexible.
One common objective of both 5G and UWB is to suppress
OOB emissions, thus generating less interference to other
frequency bands. In UWB, active interference cancellation
(AIC) has been proposed due to its flexibility. In 5G, pulse-
shaping with well frequency-localized time domain FIR-filters
is, in contrast, more suitable because of the scarce frequency
resource. The contribution of this paper is to build a unified
framework for analyzing and comparing the effectiveness of
AIC and FIR-filtering techniques in terms of suppression of
OOB emissions in the context of 5G multicarrier waveforms.
Additionally, the associated side effects of the two techniques,
i.e., rate loss and SNR loss, are addressed and compared. We
also combine the AIC technique with the novel multicarrier
UFMC-scheme as an option to further enhance the frequency
localization of this waveform. Unlike in [11], wherein AIC
was applied to an “OFDM signal” before FIR-filtering, our
approach also takes into account the subband-wise filtering of
UFMC. Furthermore, a method of optimally combining the
two approaches subject to a rate loss constraint is presented.
II. COMPARISON OF OFDM-AIC WITH UFMC
In this section, we present a unified approach to describe
and analyze the aforementioned two techniques of generat-
ing spectral notches for both OFDM and UFMC signals.
We consider an uplink multiuser frequency division multiple
access (FDMA) scenario. Following the common practice of
waveform analysis in [8], [9], [10], [12], the evaluation is
conducted in baseband. Any RF frontend nonlinearity can be
addressed separately. The total bandwidth is Nsubcarriers,
which is shared by Musers. Each user (or subband) is
allocated with a bandwidth of NBconsecutive subcarriers for
simplicity. We assume that no guard subcarriers are inserted
between subbands, except for Nccancellation subcarriers in
each subband.
In Fig. 1, we show the unified system model of OFDM
and UFMC applying AIC and FIR-filtering to suppress OOB
emissions, considering only one subband. The other subbands
perform the same procedure to satisfy a certain OOB emission
level. We refer to [13][14] for a more detailed system model of
UFMC. Briefly speaking, UFMC is equivalent to OFDM with
subsequent subband-wise FIR-filtering (usually with short fil-
ter length comparable to the CP in OFDM). Without sacrificing
any subcarriers to bear down the side-lobe, i.e., Nc= 0 , the
di
AIC
ci
si
IDFT xiFIR
Filter
fi
yi
fi
NB−Nc
data
subcarriers
Nc
cancellation
subcarriers
Figure 1. Unified system model of AIC and FIR-filtering for OFDM and
UFMC
output signal yiof the considered subband ican be expressed
as
yi[n]=(fi∗xi) [n] =
L−1
X
k=0
N
2−1
X
l=−N
2
fi(k)si(l−k)·ej2πn l−k
N,
(1)
where fi(k)denotes the FIR-filter coefficients with the length
of Lfor subband i. Moreover, xiand siis the time domain
and frequency domain signal of the subband i, respectively.
The output signal yican be considered as an UFMC signal,
if L > 1. Otherwise, it boils down to a normal OFDM signal.
The FIR-filter coefficients fi(k)can be designed according
to various criteria, e.g., raised-cosine (RC), least-squares (LS)
[15] and equiripple (ER) [16], to obtain better spectral prop-
erties. For a better illustration and comparison, we define the
power of the OOB emission as [5]
POOB =Zf∈OOB
|Yi(f)|2df, (2)
where Yi(f)denotes the power spectral density of the trans-
mitted signal yiand OOB is a set containing all frequencies
outside the subband. In Fig. 2, the original OFDM-spectrum
as well as some UFMC-spectra using different filters are de-
Figure 2. Spectrum of OFDM and UFMC (OFDM with FIR-filtering) with
least-squares, raised-cosine and equiripple filter design
picted, where the total number of subcarriers is set to N= 64,
the considered subband occupies NB= 12 subcarriers and
the FIR-filter length is constrained to L= 14. The frequency
response of the designed FIR filters is also shown by green
solid lines. With (2), the total power of OOB emission is
calculated to be −22.3 dB for OFDM without any suppression
mechanism. With FIR-filtering in UFMC, OOB emissions
are significantly reduced. 15.9 dB lower OOB emissions are
attainable using the ER filter design, while the RC and LS
filter designs yield in 14.7and 14.4 dB lower emissions,
respectively. However, an attenuation of the data carrying tones
at the borders of the subband is noticeable due to the short
filter length. We will deal with this problem later in this
section.
In UWB cognitive radio, devices are required to be able to
adapt their transmission according to the channel occupation
(so called “detect and avoid” approach). Thus, time-domain
filtering is considered as less efficient. A more adaptive
solution is to generate spectral notches in the frequency do-
main using cancellation subcarriers (CS) or to simply disable
several subcarriers (tone nulling). Denote the data-carrying
and cancellation subcarriers by vector diand ˜
cirespectively,
the resulting transmitted symbol vector of the i-th subband is
represented by si=di+˜
ci. It is worth noting that sicontains
merely NBnon-zero elements, since only NBsubcarriers are
allocated to the subband. For simplicity, all non-zero elements
in ˜
cicompose the vector ciwhich shall be optimized. ciis
as depicted in Fig. 1 and contains Nc
2non-zero elements at
each border of the subband. In order to observe the side-lobes
and then suppressing them, oversampling is essential for the
AIC component in Fig. 1. For this purpose, we introduce a
matrix Pwith the dimension pN ×N, where pdenotes the
oversampling factor. The element in the i-th row and k-th
column of the matrix is given by
[P]lk =
1
N·ejπ(k−l
p)−e
−j2π1
2+Ncp
N(k−l
p)
ej2π1
N(k−l
p)−1
k6=l
p
1k=l
p
,(3)
where Ncp is the length of the inserted CP in OFDM to
avoid ISI for transmissions over multipath channels. Hence,
the upsampled spectrum is represented by ˜
si=Pdi+e
Pci,
where e
Pis obtained by deleting all the k-th columns of Pwith
[e
ci]k= 0. The target of AIC is to find the optimal values of
cancellation subcarriers ciwhich suppress the emission of the
data vector diwithin certain frequency ranges. In this paper,
we consider all the frequencies outside of the subband as op-
timization range denoted by the set OOB =nl|l
p>NB
2o.
The optimization problem is thus formulated as [8]
ci,opt =arg min
ciX
l∈OOB
|[˜si]l|2(4)
and this optimization problem can be solved in a closed-form,
which is given by
ci,opt =−¯
e
P
+¯
P
|{z}
C
·di,(5)
where ¯
Pand ¯
e
Pis composed of all the rows of Pand e
Pthat
belong to the set OOB, and (·)+denotes the Moore-Penrose
Pseudoinverse. It should be noted that upsampling is merely
required for the calculation of the AIC matrix C, which can be
computed offline, so that solely a multiplication of respective
data symbols diwith Cis required to determine the values
of the CSs during transmission.
In Fig. 3, the spectra of OFDM with Nc= 2 and Nc= 4
AIC CSs are shown. The cancellation signals Pci,opt are
also illustrated with red lines, which are obtained by solving
(5). The average OOB emission can be reduced by 13.2 dB
and 31.9 dB for Nc= 2 and Nc= 4 respectively. It is
obvious that AIC is very effective in reducing OOB emissions.
However, one main problem is its spectral overshoot due to
the unconstrained power of CSs. The CSs exhibit 3.0 dB and
7.5 dB spectral overshoot, respectively (compare to interactive
webdemo illustrating these effects in [17]).
Both frequency domain AIC and time domain FIR-filtering
sacrifice time and frequency resources, respectively. This in-
duces a rate loss. For a fair comparison, we keep the net
Figure 3. Spectrum of OFDM with AIC, 2 CSs (left), 4 CSs (right)
information rate equal for OFDM-AIC and UFMC, which
means NB−Nc
N+Ncp =NB
N+L−1. We obtain
L=Nc
NB−Nc
N+Nc
NB−Nc
Ncp + 1.(6)
For the considered scenario, with NBallocated subcarriers out
of Ntotal subcarriers per user, the maximum achievable rate
is proportional to Rmax =NB
Ndepending on the modulation
and coding scheme (neglected for simplicity). The insertion of
CSs in the frequency domain and the FIR-filtering in the time
domain lead to a rate loss, which is defined as γloss = 1−R
Rmax
with R=NB−Nc
N+L−1for UFMC-AIC or R=NB−Nc
N+Ncp for OFDM-
AIC. Furthermore, we consider and quantify the spectral
overshoot problem of the AIC approach in terms of SNR loss.
The loss of SNR using AIC is due to the fact that some portion
of the total signal power is wasted on AIC CSs instead of
data transmission [9], which is given by the ratio between total
signal power and power spent on AIC CSs. Spectral overshoot
is, on the contrary, hardly an issue for the time domain filtering
approach of UFMC. But the filtering, in particular using short
filters, brings (inband) frequency selectivity into UFMC, i.e.,
subcarriers at the borders are usually slightly attenuated, which
is also addressed in terms of SNR loss for UFMC.
In Fig. 4, the OOB emissions and the SNR losses are
compared between OFDM-AIC and UFMC systems each with
the same rate loss. Depending on the number of used CSs
as well as the length of the inserted CP in OFDM-AIC, the
filter length Lfor UFMC is determined by (6) to ensure the
same net information rate. The SNR loss, induced either by the
wasted power on the CSs for OFDM-AIC or by the frequency
selectivity of the filters in UFMC systems, is depicted as well
on the secondary y-axis. Without CP, OFDM-AIC performs
significantly better than UFMC in suppressing OOB emissions,
whereas the SNR loss of OFDM-AIC is very high compared to
UFMC. Due to the effect of spectral overshoot, the SNR loss
of OFDM-AIC grows up to 6.7 dB for a large number of CSs.
In contrast, the SNR loss of UFMC induced by the filtering
is negligible and decreases for longer filters due to the better
defined frequency response. Because of multipath propagation,
the insertion of a CP is essential for an interference-free
OFDM transmission. Thus, Ncp = 9 CP samples are inserted
into the OFDM-AIC scheme. The insertion of CP has two
consequences: on the one hand, the AIC algorithm shows an
inferior performance compared to OFDM systems without CP;
(a) UFMC versus OFDM-AIC with Ncp = 0
0.27 0.42 0.56 0.71 0.85
rate loss γloss
-160
-140
-120
-100
-80
-60
-40
-20
POOB in dB
0
3
6
9
SNR loss in dB
γloss
(b) UFMC versus OFDM-AIC with Ncp = 9
Figure 4. OOB emission and SNR loss of OFDM-AIC and UFMC
on the other hand, slightly longer filters can be applied in
UFMC, see (6), which improves the performance of UFMC.
Consequently, UFMC, especially with the LS filter design, is
capable of higher OOB emission reduction while resulting in
a lower SNR loss, compared to CP-OFDM-AIC for small rate
losses, e.g., γloss <0.56.
III. UFMC WITH AIC
UFMC and OFDM are similar in nature, thus many known
signal processing methods, which have been developed for
OFDM, can be reused with some modification in UFMC [18].
In [11], AIC was firstly introduced to UFMC in the context
of suppressing inter-subband interference. In this section, we
introduce the AIC algorithm to UFMC in the context of
suppressing OOB emissions and present an extended AIC
algorithm for UFMC.
A. Separate AIC and FIR-filtering
The novelty of UFMC is to filter a subband composed
of several consecutive subcarriers, thus it combines the ad-
vantages of OFDM and FBMC while avoiding their main
drawbacks. Before the subband filtering, the signals remain
“OFDM signals”. Thus, the AIC algorithm can be applied to
UFMC without any modification, since the AIC is performed
in the “OFDM-domain”. After FIR-filtering, each UFMC
symbol yi, see (1), has a length of N+L−1. Stacking all yi’s
in a vector and then padding with N−L+1 zeros (L < N +1)
to form a vector ˜
yi, the spectrum of UFMC Yiwith separate
AIC and FIR-filtering is given by
Yi=Q˜
yi=FiPdi+Fie
Pci,(7)
where Qdenotes the DFT-Matrix with the dimension of pN ×
2N, and Fi=diag Q˜
fiis a diagonal matrix which contains
the FIR-filter coefficients in the frequency domain, with ˜
fi
being a vector composed of the LFIR-filter coefficients and
2N−Lzeros (it is always assumed that short FIR-filters are
applied, i.e., L<N). The coefficients for the AIC tones ci,opt
are computed according to (5).
B. Combined AIC and FIR-filtering
The effect of subsequent FIR-filtering can be taken into ac-
count while computing the AIC coefficients ci,opt. We extend
the optimization problem of (4) to UFMC considering also the
filtering effect. The optimization problem is expressed as
ci,opt,UF =arg min
ciX
l∈OOB
|[Yi]l|2(8)
and with (7) its solution can be obtained as
ci,opt,UF =−¯
e
P
+
UF ¯
PUF ·di,(9)
and, similarly, ¯
PUF and ¯
e
PUF are composed of all the rows of
FiPand Fie
Pthat belong to the set OOB, respectively.
Fig. 5 shows a comparison between separate AIC and FIR-
filtering and the proposed combined approach, where a LS
(a) UFMC+AIC LS, separate (b) UFMC+AIC LS, combined
Figure 5. Spectrum of UFMC+AIC with LS filtering
filter of length L= 14 is applied and Nc= 2 subcarriers
are used for AIC. It is observed that the spectral decay at the
edges of the subband is steeper for the combined approach,
resulting in an average OOB emission of −56.3 dB, which is
7.7 dB lower than for the separate approach. The complexity
of the proposed approach is almost identical to the separate
approach since it requires only one more matrix multiplication
with merely diagonal nonzero elements so that the complexity
of the pseudo inverse operation still dominates.
C. Joint Optimization of AIC tones and FIR-length
Usually, a certain amount of time and frequency resources
have to be sacrificed for other purposes, e.g., lower OOB emis-
sion. Next, we consider the question about how to efficiently
make use of the two methods in terms of suppressing OOB
emissions for a given rate loss. Given a certain percent γloss
of the information rate that can be sacrificed to reduce OOB
emissions, we formulate the optimization of FIR-filter length
and number of AIC CS as follows
(Nc, L) = arg min
Nc,LPOOB
s.t. NB−Nc
N+L−1≥(1 −γloss)·Rmax
where POOB is defined in (2). Since Ncand Lare integers
and shall be kept comparatively small, there exist only a few
possible combinations. Thus, this optimization problem can be
easily solved using a brute-force search with low to moderate
complexity for practical systems.
IV. SIMULATION RESULTS
For numerical evaluation, we assume a subband with NB=
12 subcarriers and an FFT size of N= 64. The upsampling
factor for the computation of the AIC matrix is set to p= 64.
The adopted filters in UFMC have a transition width of one
subcarrier, and the power is normalized for a fair comparison.
First of all, we compare the performance of the conventional
AIC algorithm for OFDM and UFMC to the proposed com-
bined AIC and FIR-filtering approach for UFMC. In Fig. 6,
the total power of OOB emissions POOB is shown for UFMC
with separate AIC tone calculation (blue) and the proposed
combined scheme (red). The used FIR-filter is of length
Figure 6. UFMC-AIC separate versus combined approach with LS filter of
length L= 10
L= 10 with LS design. For comparison, OFDM-AIC with CP
is also depicted in green. The length of the CP for OFDM is
chosen to be Ncp =L−1=9such that both systems have the
same rate loss. Because of the additional filtering, UFMC-AIC
in general outperforms CP-OFDM-AIC by more than 20 dB.
Furthermore, the proposed combined AIC approach provides
additional 8.6 dB gain compared to the separate approach for
the case Nc= 2, at hardly increased complexity. Another
advantage of the combined approach is the lower SNR loss for
all number of CS, which indicates that the spectral overshoot
is slightly reduced using the proposed approach. A more
insightful comparison including other filter designs and the
resulting gains of the combined AIC computation approach is
given in Table I. It can be concluded that the LS filter design is
Table I
OOB EMISSIONS IN dB FO R CP-OFDM-AIC AN D UFMC-AIC WITH
DI FFER EN T FILTER D ES IGN S
Number of CSs Nc2 4 6 8 10
OFDM-AIC CP −27.8−35.8−53.6−82.0−118.0
UFMC-AIC RC sep. −50.6−70.4−92.8−121.0−159.8
UFMC-AIC RC comb. −59.0−78.8−101.0−132.0−168.3
gain of comb. approach 8.4 8.4 8.3 11.0 8.6
UFMC-AIC LS sep. −50.8−70.6−92.9−121.2−160.0
UFMC-AIC LS comb. −59.3−79.1−101.4−132.5−168.8
gain of comb. approach 8.6 8.5 8.5 11.3 8.8
UFMC-AIC ER sep. −49.2−69.5−91.1−120.2−158.5
UFMC-AIC ER comb. −49.2−70.3−91.5−122.2−159.9
gain of comb. approach 0.0 0.8 0.4 2.0 1.4
most appropriate for minimizing OOB emissions and provides
the best additional gain for the combined AIC approach. Thus,
in the following solely the LS filter design is further examined.
Secondly, we investigate the impact of filter length and
number of CS on the performance gain of the combined
AIC algorithm according to Sec. III-B. The additional gain
of the combined AIC calculation for UFMC, compared to the
separate AIC approach, is quantified in terms of OOB emission
power difference for filter length Lin the range of 1to 65,
and different amount of CSs. Furthermore, the filter length is
normalized to L−1
N. The numerical results are shown in Fig. 7.
Figure 7. Gain of combined AIC calculation
Briefly speaking, the gain tends to increase for longer filters,
e.g., the curve for Nc= 8. However, it does not increase
linearly with the normalized filter length and shows some
variation. This is due to the fact that the FIR-filter design, e.g.,
the LS criterion, does not take the effect of AIC into account.
It can be concluded that the proposed combined approach is
capable of reducing the OOB emissions by at least 6 dB for
most scenarios, where the normalized filter length is longer
than 0.1compared to a separate AIC calculation. Similarly,
a larger gain can be achieved if Ncincreases, e.g., for the
case where the normalized filter length equals 0.9. Also, the
curve for Nc= 10 behaves differently, because this is a corner
case with only OOB emissions of 2 data subcarriers to be
compensated.
Lastly, we simulate all possible combinations of Ncand L
for a variety of rate losses γloss for the optimization according
to Sec. III-C. The result is shown in Fig. 8 for UFMC-
(a) separate AIC calculation (b) combined AIC calculation
Figure 8. OOB emissions for various combinations of Land Nc
AIC using separate as well as combined AIC. The simulation
results show that for the separate AIC and filtering approach
as much resources as possible should be allocated to the
AIC calculation in most cases, which, in turn, leads to the
highest OOB reduction. Exceptions from this guideline are
for γloss = 0.17 as well as for very high rate loss scenarios
(γloss &0.8). Almost the same trend can be observed for the
combined approach. The main reason behind this is the fact
that CSs of the AIC consume more power to mitigate OOB
emissions, thus it is more effective but causes higher SNR
loss. Moreover, these results also allow to obtain the minimum
required rate loss for achieving a certain OOB emission level.
If POOB ≈ −60 dB shall be achieved, using the separate
AIC approach for UFMC, the minimum required rate loss is
about 0.36. However, the required rate loss for UFMC with
combined AIC calculation equals 0.27. Consequently, 9% time
and frequency resources can be saved for data transmission.
These results can be directly compared to UFMC without
AIC (Nc= 0, dark green line), where the required rate loss
amounts to 0.54.
V. CONCLUSIONS
In this paper, we reviewed active interference cancellation
(AIC) for OFDM, which was originally proposed for the ap-
plication in ultra wideband scenarios. Then, the AIC approach
was combined with a recently proposed multicarrier modula-
tion technique, namely, universal filtered multicarrier (UFMC).
Additionally, we proposed a novel combined AIC and filtering
approach for UFMC which allows a more effective suppression
of out-of-band (OOB) emissions at hardly increased complex-
ity. Numerical results show that the proposed method behaves
better than the conventional approach in terms of spectral
overshoot. Also, a lower SNR loss can be achieved. Finally, we
showed how to optimally combine FIR-filtering and the AIC
scheme in a UFMC system under a given rate loss constraint.
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