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A PPN Based Low Complexity Transmitter for UFMC
Liu Lupeng, Sun Chunhui, Zhang Yinghai
**
(Information & Electronics Technology Lab, Beijing University of Posts and Telecommunications, 5
Beijing 100876)
Abstract: Universal Filtered Multi-Carrier (UFMC), which is an emerging 5G waveform candidate,
has gained wide attention in recent years. The properties of UFMC is very close to OFDM, while the
former has better spectrum properties than the latter. UFMC is more suitable for short-burst
communication systems than other 5G waveform candidates, for example, Filter-Bank Multi-Carrier 10
(FBMC). However, the complexity of conventional UFMC transmitter is much higher than OFDM. To
solve this problem, this paper firstly present a low complexity transmitter structure based on the
combination of small-size IFFT and time-domain interpolation. On the basis of this, a new Polyphase
Network (PPN) based UFMC transmitter with much lower computational complexity is proposed. Our
PPN based approach eventually brings the complexity of UFMC transmitter down to the same level as 15
OFDM, and makes the complexity of UFMC transmitter even lower than OFDM in some special
conditions. This PPN based low complexity implementation makes UFMC more suitable for the
devices with low computing power.
Key words: UFMC; low complexity;transmitter
20
0 Introduction
Targeting the “Horizon2020”, 5G has raised a hot discussion in recent years. With the
consideration of Internet of Things (IoT), 5G is going to be designed for various kinds of services
and devices. Because of the accession of heterogeneous types of services as well as devices, it will
be extremely difficult to provide strict time and frequency alignment between the transceivers. To 25
solve this problem, many waveform candidates have been proposed. All these candidates are more
suitable for 5G communication system than OFDM. One of the candidates is Filter-Bank
Multi-Carrier (FBMC)
[1]
, which has been thoroughly studied in recent years. In FBMC, each
subcarrier is filtered individually by using a filter bank, and as a consequence, FBMC is not as
sensitive as OFDM to frequency-time misalignment. However, typical FBMC uses a long-size 30
filter which extends the length of the symbol. As a consequence, FBMC is not suitable for
short-burst communication systems. Another novel waveform contender, Universal Filtered
Multi-Carrier (UFMC), is proposed recently
[2]
. UFMC replaces the cyclic prefix of OFDM by
operating the per-subband filtering. By using the per-subband filtering, the side-lobe level of
UFMC is significantly decreased
[3]
. The filter length of UFMC is not as long as FBMC, and this 35
fact makes UFMC more suitable for short-burst communication without strict time-frequency
alignment than FBMC and, of course, OFDM
[4]
. Although UFMC has many advantages as we
have mentioned above, however, the computational complexity of conventional UFMC transmitter
is much higher than OFDM. To solve this problem, a reduced complexity implementation of
UFMC transmitter based on frequency-domain generation was proposed recently
[5]
, and a reduced 40
complexity implementation of UFMC transmitter which implemented by time-domain
approximation was presented recently
[6]
. However, these two methods are all based on the
approximation of the exact UFMC signal, and are both not suitable for the devices which require
the very accurate signals.
As a contrast to the schemes mentioned above, this paper presents two structures of UFMC 45
transmitter implemented in time domain without loss of accuracy. We firstly present a low
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complexity UFMC transmitter by applying the combination of small-size IFFT, time-domain
interpolation, and low-pass filtering. On the basis of this, a novel Polyphase Network (PPN) based
UFMC transmitter was presented, which could further reduce the complexity and make the
complexity mainly depend on the size of the subband, a small number of successive subcarriers, in 50
the overall bandwidth. By using the advanced PPN based low complexity transmitter structure, the
exhibited solution could eventually bring the complexity of transmitter down to the level of
OFDM.
The rest of this work is organized as follows. Section 1 presents the system model of both
conventional UFMC transmitter and the novel low complexity UFMC transmitters. In Section 2, 55
we give some complexity evaluation of both traditional UFMC transmitter and the new low
complexity UFMC transmitters. Finally, we present the simulation results in Section 3 and draw a
conclusion in Section 4.
1 System Model
Conventional UFMC Transmitter 60
The baseband time-domain transmit vector ky for a specific UFMC symbol of user k is
obtained by superimposing several subband-wise components which filtered by FIR filters
individually, with filter length L and IFFT length N.
Small-Size IDFT
Spreader
+P/S
Filter F2,k
With
Length L
Filter FB,k
With
Length L
Baseband
to RF
Channel
RF to
Baseband
Time domain
pre-processing
(.
windowing)
+S/P2N Point-
FFT
Frequency
domain symbol
processing
(
subcarrier
equalization)
Noise n
0
Zeropadding
Filter F1,k
With
Length L
Small-Size IDFT
Spreader
+P/S
Small-Size IDFT
Spreader
+P/S
Other
users
Symbol
estimates
M
M
M
0
0
,kX1
,kX 2
,B kX
,kx1
,kx2
,ky1
,ky2
,B ky
k
y
,B kx
,kx1
,kx2
,B kx
Fig. 1 The system model of small-size IFFT based UFMC transmitter implementation 65
N represents the total number of subcarriers. ky can be represented by:
, , ,
1
B
k i k i k i k
i
y F V X (1)
In (1), ,i kV is an IDFT-matrix. Elements in each column of ,i kV is according to the
respective subband position within the overall frequency range. ,i kF is a Toeplitz matrix
composed of FIR filter impulse response if , which operates the linear convolution. The function 70
of matrix multiplication between ,i kV and ,i kX is just as same as an N-point IFFT which
converts a frequency-domain sequence ,i kX into a time-domain sequence ,i kx . After the above
approaches, ,i kx is then passed through a FIR filter to cut down the side-lobe level in frequency
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domain, and the filtering can be realized by operating a matrix multiplication between ,i kx and
,i kF .Finally, ky , the output signal of UFMC transmitter, is obtained by summing up all of the 75
subband-wise components.
Small-size IFFT Based UFMC Transmitter
In the conventional implementing method of UFMC transmitter, each subband sequence
,i kX is converted into a time-domain signal by an N-point IFFT, while N represents the number of
total subcarriers. This inflexible approach, however, can be replaced by a facile small-size IFFT 80
followed by a time-domain interpolation. The system model of the small-size IFFT based UFMC
tranceiver is shown in .
In Fig. 1, The allocated bandwidth, which carries the data to transmit, is divided into B
subbands. ,i kX represents the ith subband of a UFMC symbol belongs to user k. For simplicity,
we assume that the number of the total subcarriers N is a power of 2, since IFFT requires the length 85
of the input signal should be a power of 2. This time-domain based implementing method is
described in detail in the following passage.
M copyies
( )jX e
2
1
2
1
2
1
low-pass
filter
2
1
( )a ( )b
( )c ( )d
( )jX e
( )jX e
( )jX e
Frequency spectrums corresponding to different time-domain sequences in different steps of the
implementing scheme. (a) depicts the spectrum of
,i kx . (b) depicts the spectrum of
,i kx . (c) depicts the spectrum 90
operation corresponds to per-subband filtering. (d) depicts the spectrum of
,i ky .
First of all, ,i kX is converted into a time-domain sequence ,i kx by a p-point IFFT, while p is
a power of 2 and p satisfies the following equation:
2log
2
Lsubband
p (2)
subbandL is the number of subcarriers within one subband. If p is larger than subbandL , several 95
zeroes should be padded to the tail of ,i kX .
After the small-size IFFT, ,i kx is then interpolated with zeroes in time domain by an M-factor
interpolator. The output of the interpolator is denoted as ,i kx .
As Fig. 2 (a)(b) show, the frequency spectrum of ,i kx is the periodic extension of ,i kx ’s
frequency spectrum, while the amplitude of the frequency spectrum is unchanged. 100
After the time-domain interpolation, ,i kx , the output of interpolator, is then filtered by a
low-pass filter to eliminate the redundant part of the frequency spectrum. This approach is depicted
in Fig. 2 (c)(d). There is an important thing to note is that the filter used in this process should be an
FIR low-pass filter but not an IIR ideal low pass filter, since UFMC is designed to be suitable to the
short-burst communication and the length of the symbol should be short enough. After the low pass 105
filtering, ,i ky is then multiplied by the frequency shifting coefficients to shift the spectrum to the
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中国科技论文在线
correct position.
Finally, all of the subband-wise components are summed up to generate the final output signal
of the UFMC transmitter.
A Novel PPN Based UFMC Transmitter 110
The forementioned UFMC transmitter implementation based on small-size IFFT reduces the
computational complexity by applying the combination of small-size IFFT and time-domain
interpolation. In Fig. 1, an important property of ,i kx should be noted that the time domain of ,i kx
is interpolated by lots of zero values. As a result, only a few number of multipliers have nonzero
inputs. It is obvious that this formentioned implementation does not exploit this fact to minimize 115
the required computational complexity. Fortunately, a polyphase approach, which could give a
more efficient design, was proposed
[7][8]
.
Filter Fi,k
With
Length L
Small-Size
-IDFT
Spreader
+P/S
M
M
1z
1z
M
M
0 ( )R z
1( )R z
1( )MR z
,i kX
,i kx
,i ky
,i kx
,i ky
,i kx
Fig. 3 Block diagram of the kernel part of the PPN based implementation.
By taking the advantages of polyphase network, a novel implementation based on polyphase 120
network is proposed in this paper to further reduce the computational complexity of UFMC
transmitter.
The key part of this PPN based transmitter block diagram is depicted in Fig. 3. In Fig. 3, M
represents the up-sampling rate. For simplicity, we assume that the number of total subcarriers N
and the small size of IFFT p are both the power of 2, and M can be expressed as below: 125
/M N p (3)
The impulse response of the FIR filter used for the per-subband filtering is denoted as ( )f n ,
and the M-fold decimated version of ( )f n is denoted as ( )ir n . We denote the z-transform of
( )ir n as ( )iR z . ( )iR z can be expressed as below:
(z) ( 1 ) 0,1, , 1
ni
n
R f Mn M i z i M (4) 130
Noting that the part in the red dotted box in is the key part of the small-size IFFT based
UFMC transmitter that we have proposed before, but in the novel PPN based solution, this part is
substituted by the part circled by a blue dotted box in Fig. 3, which is a form of polyphase network.
The key part of the PPN based implementing method can be divided into four steps as below:
Firstly, ,i kx ,The output of the IFFT module, is pushed into the polyphase network and is then 135
filtered by a small-size FIR filter on each branch of the polyphase network.
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Secondly, the output of the small-size filter on each branch is then interpolated by an M-factor
interpolator.
After the interpolation, the output of interpolator on the ith branch is delayed for i samples.
Finally, after the above processes, all of the outputs on each branch is summed up to generate 140
the subband-wise component ,i ky .
As we will see in the next section, the computational complexity of the PPN based UFMC
transmitter almost no longer depends on the number of total subcarriers by using the polyphase
network. As a consequence, the complexity of UFMC transmitter is cut down significantly. The
complexity assessment of this approach will be discussed in section 2. 145
2 Complexity Assessment
In this section, we analyze and evaluate the computational complexity of different UFMC
transmitter implementations. Noting that, since the implementing complexity of some modules
like encoder and pre-processing module are not considered into the complexity assessment, the
result of complexity assessment presented in this section does not reflect the total complexity of 150
these transmitter implementations. In addition to this, as we all know that adders are considerably
much cheaper to implement than multipliers, the complexity analysis presented in this section is
just based on the number of real multiplications. As we have mentioned before, all of the
implementations presented in this paper can be divided into several IFFT modules and convolution
modules, so the computational complexity of IFFT is essential to the complexity assessment. As a 155
result, we firstly give the complexity assessment of IFFT before estimating the complexity of
UFMC transmitter implementations.
In this paper, IFFT is assumed to be implemented by using the Split-Radix algorithm
[9]
. The
complexity of IFFTN -point IFFT can be written as
2(log ( ) 3) 4 IFFT IFFT IFFTC N N (5) 160
OFDM Complexity Analysis
For OFDM, since the CP does not increase the burden on computation, the transmitter can be
seemed to be implemented directly by an N-point IFFT, and N represents the number of the total
subcarriers. As a consequence, the complexity of the OFDM transmitter can be simply written as
_ 2(log ( ) 3) 4 OFDM TXC N N (6) 165
Conventional UFMC Transmitter Complexity
Let us recall the conventional UFMC transmitter we have mentioned in section . The
conventional transmitter is implemented in time domain. We denote the number of subbands as B,
and the number of total subcarriers is N. To generate the final transmitting symbol, B N-point
IFFTs followed by B convolutions operated between an N-point sequence and an L-point sequence 170
are required, while L represents the length of the impulse response of an FIR filter.
The complexity brought by B N-point IFFTs can be written as:
_ 2( (log ( ) 3) 4) B IFFTC B N N (7)
The complexity brought by B convolutions between an N-point sequence and an L-point
sequence can be written as: 175
4 convolutionsC B N L (8)
convolutionsC denotes the number of real multiplications consumed by B convolutions operated
between an N-point sequence and an L-point sequence. Since the complex multiplication is
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constituted by 4 real multiplications and 2 real additions, so the factor 4 in (8) is needed.
The total complexity of conventional transmitter is obtained by summing _B IFFTC and 180
convolutionsC , and it can be written as:
, 2( (log ( ) 3 4 ) 4) UF conventionalC B N N L (9)
As we can find in the equation above, the complexity of conventional UFMC transmitter
depends mainly on N, which is the total number of subcarriers, and it does not depend on the
number of allocated subcarriers within one subband. 185
When the number of the total subcarriers is large, the complexity of conventional UFMC
transmitter will be very high. This fact leads to the overhead of computation, and as a consequence,
the complexity of conventional UFMC transmitter is, of course, far more than the complexity of
OFDM.
Small-size IFFT Based UFMC Transmitter Complexity 190
This method is implemented based on time domain like the conventional implementation.
Firstly, each subband is processed by a small-size IFFT. And then, the interpolation which
followed by the convolution operated between the output of each small-size IFFT block and an
L-point FIR filter is operated. Finally, the spectrum shifting is operated on the output of the
convolution module. The total complexity can be written as: 195
, _ 2( (log ( ) 3) 4)
4 4 ( 1)
UF small IFFTC B p p
B N L B N L
(10)
In (10), p denotes the small size of IFFT, and N denotes the total number of subcarriers. We
find that the first item in (10) does not depends on the number of total subcarriers any more. As a
consequence, when the number of allocated subcarriers within one subband is much less than the
number of the total subcarriers, the complexity of this new implementation will be far less than the 200
complexity of the conventional UFMC transmitter implementation.
PPN Based UFMC Transmitter Complexity
As same as the previous methods, this PPN based implementation is also based on the
time-domain processing.
Different from the method presented in section , this new implementation only requires B 205
small-size IFFT and B small-size convolution which operated between a p-point small-size
sequence and an L-point sequence. Since the M-factor interpolation does not occupy the
computational resources, the complexity of PPN can be written as:
1
4 ( )
M
PPN
i
L i
C p M
M
(11)
(11) can be approximated as: 210
, 4 PPN apprC p L
(12)
As a consequence, the total complexity of the PPN based UFMC transmitter can be
approximated as:
, 2( (log ( ) 3) 4)
4 4 ( 1)
UF PPNC B p p
B p L B N L
(13)
We find that the complexity of PPN based UFMC transmitter does not mainly depend on the 215
number of total subcarriers anymore, since the first two terms of (13) is never relevant to N, which
is the number of the total subcarriers. The complexity of this novel method is mainly relevant to
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中国科技论文在线
the small size of IFFT, the length of the impulse response of the FIR filter, and the number of
subbands. This fact means that when the number of the subcarriers within one subband only
occupy a small part of the total subcarriers, the complexity of this novel implementation will be 220
cut down significantly, and will be far less than the complexity of conventional UFMC
transmitter.
3 Simulation results
Fig. 4 illustrates the frequency-domain spectrums of the low complexity implementations of
UFMC transmitter with different IFFT sizes. We set 12Q subcarriers in one subband, and we 225
use only one single PRB to transmit data. The number of total subcarriers N is set to 512. The
side-lobe levels of different implementations are shown. As we can see, 12IFFTN exhibits a
very poor side-lobe behavior.
Fig. 4 Spectrum of the novel PPN based generation with different
IFFTN and different side-lobe attenuations; 230
1PRB, 12Q , 512N , 41L .
When IFFTN increases to 32, the performance of side-lobe has not been significantly
improved. It is clear that the side-lobe level of this novel PPN based implementation depends
mainly on the side-lobe attenuation of the FIR filter, which is not enough in the condition of 40dB.
So if we want to make the side-lobe level low enough, we can only increase the side-lobe 235
attenuation while keeping the length of the FIR filter unchanged. When the side-lobe attenuation is
60dB, the side-lobe level becomes acceptable, and when the side-lobe attenuation is increased to
80dB, the side-lobe level becomes much better.
However, there is always a trade-off between the side-lobe attenuation and the main-lobe
width of the filter when the length of impulse response of an FIR filter is constant. So when we set 240
the side-lobe attenuation to 60dB or 80dB from 40dB, the main-lobe width of the FIR filter will
increase, and as a consequence, there could be a degradation on the system performance under the
influence of the frequency offset. The system performance of UFMC transmitter implemented by
different methods is depicted in .
Fig. 5 illustrates the SER of different implementations of UFMC transmitter under the 245
influence of the frequency offset and the noise of the channel. The total number of subcarriers is
set to 512. After QPSK modulation, symbols are mapped onto 10 subbands, while every subband
contains 12 subcarriers. The UFMC symbols are transmitted via an AWGN channel.
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中国科技论文在线
Fig. 5 SER of different UFMC implementations considering frequency offset and channel noise; 12Q , 10 PRB, 250
512N , 41L ,side-lobe attenuation=80dB.
The side-lobe attenuation of the FIR filter is set to 80dB to cut down the side-lobe level. In
the case of limited length of the FIR filter, the cutoff frequency of the low-pass FIR filter is
relatively high. As a result, the size of IFFT should be increased to make the frequency-domain
duplicate images, which are caused by the interpolation, beyond the cutoff frequency of the FIR 255
low-pass filter, and to eliminate the redundant part of the frequency spectrum completely.
Fig. 6 Complexity of PPN based implementations with different
IFFTN compared to OFDM and conventional
UFMC; 12Q , 1024N , 72L
As we can observe, the performance of the PPN based UFMC system becomes better while 260
increasing the size of IFFT. When 64IFFTN , the performance of this PPN based
implementation reaches the same level as the performance of the conventional UFMC transmitter.
When IFFTN goes up, the system performance of the PPN based implemetion is more and more
close to the performance of conventional UFMC transmitter, since the conventional
implementation itself can be seemed as a special case of the PPN based implementation with 265
512IFFTN .
Fig. 6 shows the complexity in terms of real multiplications, based on the complexity
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中国科技论文在线
assessment presented in section 2. The complexities of OFDM and conventional UFMC are not
relevant to the size of IFFT. As we can observe, when we use one single PRB to transmit data, the
complexity of the “brute force” UFMC is about times more than the complexity of OFDM, 270
while the complexity of the PPN based implementation is about times of the complexity of
OFDM, and is less than the level of OFDM. When B becomes larger, for example, B=25 which
corresponds to 300 subcarriers, the complexity of the conventional implementation will reach
about 610 times of OFDM while the complexity of the PPN based implementation will only reach
about 24 times of OFDM. The computational complexity is reduced significantly. 275
Fig. 7 illustrates the complexity of PPN based UFMC transmitter normalized over
conventional UFMC transmitter complexity with different number of total subcarriers. As we can
see, with the same size of IFFT, the complexity of the PPN based implementation normalized over
conventional UFMC decreases a lot when we increase the number of total subcarriers. This is
because the number of total subcarriers is dominating the complexity of the conventional UFMC, 280
while the number of total subcarriers has little influence on the PPN based UFMC complexity
since the complexity of PPN based UFMC mainly depends on the small size of IFFT. When we
maintain the size of IFFT and increase the number of total subcarriers, the complexity of
conventional UFMC increases rapidly while the complexity of the novel PPN based
implementation maintains the original level. As a consequence, the complexity ratio of PPN based 285
UFMC to conventional UFMC decreases a lot when the number of total subcarriers increases from
512 to 1024 and 2048.
Fig. 7 complexity of PPN based UFMC normalized over conventional UFMC transmitter complexity with
different
IFFTN ; 12Q ,1 PRB. 290
4 Conclusion
In this paper, we proposed a novel PPN based time-domain implementing method to cut
down the complexity of UFMC transmitter. When the side-lobe attenuation is set to 80dB, we use
64IFFTN to bring the complexity down to the same level as OFDM without loss of system
performance. This novel time-domain based method presented in this paper is easy to be 295
implemented, and could be widely applied into the hardware implementations. Future work will
focus on the decreasing of the side-lobe level, and the future work should also consider the size of
IFFT which is not a power of 2 to realize the further reduction of computational complexity.
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基于多相网络的低复杂度 UFMC 发射
机 320
刘鲁鹏，孙春晖，张英海
（信息与电子技术研究室，北京邮电大学，北京 100876）
摘要：作为一种备选的 5G 空口技术，通用滤波器多载波技术（UFMC）近年来来得到了学术
界的广泛关注。UFMC 相比于 OFDM 具有更加良好地频谱特性。相对于其他备选的 5G 空口技
术方案如滤波器组多载波技术（FBMC）而言，UFMC对短帧通信具有更强的适应性。虽然 UFMC325
具有上述诸多优点，然而其自身的计算复杂度却远比 OFDM 高。为了降低 UFMC 的计算复杂度，
本文首先提出了一种新型的基于轻量化快速傅里叶变换的 UFMC 发射机实现原理，并在此基
础上进一步提出了基于多相网络（PPN）的 UFMC发射机实现原理。通过利用多相网络技术，
UFMC发射机的计算复杂度得到了显著的降低并在某些特定情况下低于 OFDM发射机的计算复
杂度。本文所提出的基于多相网络的 UFMC 发射机有利于 UFMC 技术在低计算能力设备上的部330
署与应用。
关键词：UFMC；低复杂度；发射机
中图分类号：
