# Enhanced Next Generation Millimeter-Wave Multicarrier System with Generalized Frequency Division Multiplexing

Authors: Hidekazu Shimodaira; Joongheon Kim; Ali S. Sadri
Journal: International Journal of Antennas and Propagation
 (2016)

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## Abstract

Orthogonal Frequency Division Multiplexing (OFDM) is a popular multicarrier technique used to attain high spectral efficiencies. It also has other advantages such as multipath tolerance and ease of implementation. However, OFDM based systems suffer from high Peak-to-Average Power Ratio (PAPR) problem. Because of the nonlinearity of the power amplifiers, the high PAPR causes significant distortion in the transmitted signal for millimeter-wave (mmWave) systems. To alleviate the high PAPR problem, this paper utilizes Generalized Frequency Division Multiplexing (GFDM) which can achieve high spectral efficiency as well as low PAPR. In this paper, we show the performance of GFDM using the IEEE 802.11ad multicarrier frame structures. IEEE 802.11ad is considered one of the most successful industry standards utilizing unlicensed mmWave frequency band. In addition, this paper indicates the feasibility of using GFDM for the future standards such as IEEE 802.11ay. This paper studies the performance improvements in terms of PAPR reduction for GFDM. Based on the performance results, the optimal numbers of subcarriers and subsymbols are calculated for PAPR reduction while minimizing the Bit Error Rate (BER) performance degradation. Moreover, transmitter side ICI (Intercarrier Interference) reduction is introduced to reduce the receiver load.


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## Body

## 1. Introduction

The demands for wireless data communications have been increasing year by year. Recently, transmitting pictures or movies through a wireless channel is very popular and even 4K resolution ultra-high definition (UHD) video can be transmitted in real-time over the wireless channel. In order to support this kind of massive wireless data transmissions, ultra-wide channel bandwidths are essentially required. Among various candidates, millimeter-wave (mmWave) wireless communication technology is one of promising ultra-wideband wireless communication technologies in order to realize multi-gigabit-per-second (multi-Gbps) ultra-high speed wireless data communications. For instance, 60 GHz mmWave channels have a bandwidth of 2.16 GHz [1].Among several mmWave wireless technologies, this paper mainly focuses on 60 GHz IEEE 802.11ad as it is the most successful standard in mmWave research societies [1, 2]. However, the proposed methodologies are applicable for other mmWave standards including 28 GHz and 38 GHz mmWave frequency bands [3–6]. The IEEE 802.11ad (hereinafter referred to as 11ad) is one of the mmWave wireless communication systems which uses 60 GHz ISM (Industry-Science-Medical) band. In more detail, 57–66 GHz is allocated to the 60 GHz ISM band and 11ad separates this 9 GHz band into four channels of 2.16 GHz bandwidth each. 11ad supports two types of transmission schemes, Single Carrier (SC) and Orthogonal Frequency Division Multiplexing (OFDM) transmission, and theoretical maximum throughput reaches about 7 Gbps using the OFDM transmission scheme. OFDM efficiently utilizes system bandwidth based on (i) subcarrier orthogonality and (ii) intersymbol interference (ISI) mitigation due to the narrow band characteristics in each subcarrier. However, parallel transmission using large number of subcarriers increases Peak-to-Average Power Ratio (PAPR) [7–9]. In 60 GHz communication systems, the demand for power amplifier is more severe than that of microwave systems and hence high PAPR is undesirable. In order to tackle this problem there are two major approaches: (i) applying PAPR reduction techniques for OFDM and (ii) introducing new waveforms.The first approach, that is, the PAPR reduction techniques for OFDM, has been studied extensively in the literature. One such PAPR reduction technique is transmit signal clipping [10–12]. This technique sets a threshold value and just clips the high amplitudes. Since some transmit signals are distorted and undesired signals are radiated by clipping, the clipped signals are filtered before transmission. The other commonly used PAPR reduction technique is signal companding. This technique applies nonlinear compression to the transmit signals to suppress the signal peak values [13–15]. Partial Transmit Sequences (PTS) technique [16–18] divides subcarriers into segments and modulates each block. After modulation, phase rotation factor is applied to each partial sequence in time domain, and the subsegments are combined. Selected Mapping (SLM) technique makes several OFDM modulated signals where each OFDM modulation has its own different phase weight and chooses the best one from candidates [19–21].The second approach, that is, new waveform design for the next generation wireless systems, has been currently investigated actively. From the view point of PAPR reduction, Filter Bank Multicarrier (FBMC) is one of the well-investigated waveforms [22]. FBMC applies pulse shaping filter to each subcarrier. The filter bank structure can be adapted to the clipping technique [23, 24]. However since clipping technique induces not only the out-of-band radiation but also the in-band distortion, the system becomes more complicated. Generalized Frequency Division Multiplexing (GFDM) [25, 26] is also one of the new waveform candidates and it can reduce PAPR efficiently utilizing more straightforward methods. GFDM can flexibly configure the symbol structure; that is, the number of subcarriers can be configured by introducing time domain slicing. Since GFDM can have the characteristics of both single carrier and multicarrier transmission, low PAPR and high spectral efficiency can be achieved simultaneously by applying appropriate configuration.This paper focuses on GFDM and proposes GFDM frame design for 11ad to be fully in compliance with standards. The validity of the proposed frame structure is shown through intensive numerical simulations. Based on the PAPR and Bit Error Rate (BER) simulation results, the best GFDM configuration for 11ad system is determined. The computational complexity of GFDM is analyzed and a low complexity modulator/demodulator is proposed. Using the scheme proposed in this paper, the performance of current multicarrier mmWave standards can be improved in terms of the throughput for various mmWave systems such as backhaul in line-of-sight (LOS), fronthaul in LOS, and access networks in both LOS and non-LOS (NLOS).The remaining sections are organized as follows. Section2 explains OFDM and GFDM briefly and introduces the 11ad OFDM structure. Section 3 proposes a new GFDM frame structure for 11ad. Section 4 introduces a novel low complexity interference canceller for GFDM. PAPR and BER comparison is shown in Section 5. Section 6 analyzes the computational complexity of modulation/demodulation architectures. Finally, conclusion and future work are provided in Section 7.


## 2. System Overview

In this section, we first discuss the OFDM and GFDM symbol structures and then describe the 11ad OFDM system architecture.


### 2.1. Overview of OFDM

OFDM is one of the well-known multicarrier transmission schemes [27–31]. It is widely employed by several wireless systems including Digital Terrestrial Television Broadcasting, LTE (Long Term Evolution), and IEEE 802.11a/g/n/ac/ad. Since OFDM transmits signals in parallel utilizing many subcarriers, each subcarrier bandwidth becomes narrow and thus the ISI is mitigated. Moreover, thanks to the FFT (Fast Fourier Transform) algorithm in OFDM structures, computational and implementation costs can be reduced.The mathematical expression of an OFDM transmission symbol is as follows;(1)xn=∑k=0N-1dkexp⁡j2πnkN,where xn is the transmission symbol of nth time sample and k and N are the subcarrier index and the total number of subcarriers, respectively. dk in (1) is the QAM (Quadrature Amplitude Modulation) modulated symbol transmitted on the kth subcarrier. Equation (1) describes parallel transmission of N modulated symbols (d0,d1,…,dN-1) using N orthogonal subcarriers. Please note that (1) is equivalent to the definition of IDFT (Inverse Discrete Fourier Transform), and hence the transmitted data symbols in (1) can be rewritten as follows:(2)x=FHdx=x0x1⋯xN-1T∈CNF=wN0·0wN0·1⋯wN0·N-1wN1·0wN1·1⋯wN1·N-1⋮⋮⋱⋮wNN-1·0wNN-1·1⋯wNN-1·N-1∈CN×Nd=d0d1⋯dN-1T∈CN,where wN=exp⁡-j2π/N is a primitive Nth root of unity. ·T and ·H represent transpose and conjugate transpose, respectively. Figure 1 shows how to map modulated symbols on the time-frequency resource grid in OFDM.Figure 1
OFDM symbol mapping structure.On the receiver side, received signals can be demodulated using DFT operation.


### 2.2. Overview of GFDM

As the name suggests, GFDM generalizes the multicarrier modulation schemes, SC and OFDM, by controlling the system design parameters. In GFDM, a time-frequency resource grid is sliced in both frequency and time domains. QAM modulated symbols are mapped on each time-frequency resource block. Figure2 shows the mapping illustration of GFDM where K and M stand for the number of subcarriers and number of subsymbols, respectively. Each resource block has K×M sample points. Therefore if K×M=N is satisfied, the amount of transmission data with GFDM will be equivalent to the amount of transmission data with OFDM during same symbol duration in same bandwidth. In order to localize each resource block, pulse shaping filter is applied.Figure 2
GFDM symbol mapping structure.The mathematical expression of GFDM transmission signal is as follows:(3)xn=∑k=0K-1∑m=0M-1dk,mδn-mK∗gnmod⁡Nexp⁡j2πnkK=∑k=0K-1∑m=0M-1dk,mg~n-mK︸xknexp⁡j2πnkK=∑k=0K-1xknexp⁡j2πnkK,where (∗) represents the convolution operation. In (3), g~n-mK≜gn-mKmod⁡N is the pulse shaping filter with mK time shifting. The modulo operation in (3) is equivalent to the tail biting process which makes filter convolution circular [32]. The GFDM modulation procedure is enumerated below and also shown in Figure 3.(1)
Symbol sequence is divided intoK parallel blocks, with each containing M QAM modulated symbols.(2)
The QAM modulated symboldk,m is upsampled by a factor N.(3)
Pulse shaping filter is applied and the subsymbols are summed up in time domain.(4)
Filtered symbols are upconverted to the corresponding subcarrier frequency.(5)
All symbols are summed up.Figure 3
GFDM modulation block diagram.In case ofM=1 and rectangular pulse shaping filter, (3) reduces to (1). In case of K=1, (3) is equivalent to SC transmission. For this reason, this scheme is denoted as GFDM.Equation (3) can be rewritten as a linear equation x=Ad. The matrix A and vector d are as follows:(4)A=G0∘WK⋯GM-1∘WK∈CN×KMGm=g~mg~m⋯g~m︸K∈CN×Kg~m=g~-mKg~1-mK⋯g~N-1-mKT∈CNWK=wK0·0wK0·1⋯wK0·K-1wK1·0wK1·1⋯wK1·K-1⋮⋮⋱⋮wKN-1·0wKN-1·1⋯wKN-1·K-1∈CN×Kd=d0T⋯dmT⋯dM-1TT∈CKMdm=d0,md1,m⋯dK-1,mT∈CK,where the operation (∘) represents the Hadamard product.This paper assumes that the receiver employs correlation detector. The correlation receiver is realized by multiplyingAH to the received GFDM symbols. Since A contains upconversion term for each subcarrier, downconversion can be performed through AH operation. Figure 4 shows normalized absolute value of AHA. As shown in the figure, intercarrier interference (ICI) appears due to the nonorthogonality of subcarriers.Figure 4
ICI effect of the GFDM (Root Raised Cosine filter with roll-off factor 0.1.K=6,M=4).


### 2.3. WiGig/IEEE 802.11ad OFDM Frame Structure

The 11ad OFDM frame is composed of five fields as defined in the standard, that is, Short Training Field (STF), Channel Estimation Field (CEF), Header, OFDM symbols, and optional training fields. Since the header and optional training fields do not impact the performance, these fields are ignored in this paper.The STF is used for the carrier frequency offset (CFO) estimation and autogain control (AGC) configuration. After CFO compensation and AGC, propagation channels are estimated using CEF. These two fields use Golay complementary sequence withπ/2-shift BPSK modulation [33]. Figure 5 shows the STF and CEF structures of control PHY (for control signal transmission), SC PHY, and OFDM PHY.Figure 5
WiGig/IEEE 802.11ad preamble structure.G a 128 and Gb128 in Figure 5 stand for 128-bit Golay complementary sequences. Gu512 and Gv512 are not the 512-bit Golay complementary sequences; however they are constructed with the concatenation of Ga128 and Gb128. The 11ad receiver can distinguish each frame due to the difference between STF and CEF. The last -Ga128 in STF indicates the end of STF or the start point of CEF.The OFDM symbol follows these preamble fields. The number of OFDM symbols within one packet varies according to the transmitted data and MCS (Modulation and Coding Scheme). Table1 shows important parameter configurations and corresponding values of 11ad OFDM. This paper proposes the GFDM frame structure for 11ad based on these parameters.Table 1
WiGig/IEEE 802.11ad OFDM parameters.
Parameter Value Number of IDFT/DFT points 512 Number of data subcarriers 336 Number of pilot subcarriers 16 (±10, 30, 50, 70, 90, 110, 130, 150) Number of DC subcarriers 3 (−1, 0, 1) Number of guard band subcarriers 157 (−256~-178, 178~255) Subcarrier frequency spacing 5.15625 MHz (2640 MHz/512) OFDM sample rate 2640 MHz OFDM symbol period 0.194 usec Cyclic prefix duration 48.4 ns = 0.194 usec× 25%


## 2.1. Overview of OFDM

OFDM is one of the well-known multicarrier transmission schemes [27–31]. It is widely employed by several wireless systems including Digital Terrestrial Television Broadcasting, LTE (Long Term Evolution), and IEEE 802.11a/g/n/ac/ad. Since OFDM transmits signals in parallel utilizing many subcarriers, each subcarrier bandwidth becomes narrow and thus the ISI is mitigated. Moreover, thanks to the FFT (Fast Fourier Transform) algorithm in OFDM structures, computational and implementation costs can be reduced.The mathematical expression of an OFDM transmission symbol is as follows;(1)xn=∑k=0N-1dkexp⁡j2πnkN,where xn is the transmission symbol of nth time sample and k and N are the subcarrier index and the total number of subcarriers, respectively. dk in (1) is the QAM (Quadrature Amplitude Modulation) modulated symbol transmitted on the kth subcarrier. Equation (1) describes parallel transmission of N modulated symbols (d0,d1,…,dN-1) using N orthogonal subcarriers. Please note that (1) is equivalent to the definition of IDFT (Inverse Discrete Fourier Transform), and hence the transmitted data symbols in (1) can be rewritten as follows:(2)x=FHdx=x0x1⋯xN-1T∈CNF=wN0·0wN0·1⋯wN0·N-1wN1·0wN1·1⋯wN1·N-1⋮⋮⋱⋮wNN-1·0wNN-1·1⋯wNN-1·N-1∈CN×Nd=d0d1⋯dN-1T∈CN,where wN=exp⁡-j2π/N is a primitive Nth root of unity. ·T and ·H represent transpose and conjugate transpose, respectively. Figure 1 shows how to map modulated symbols on the time-frequency resource grid in OFDM.Figure 1
OFDM symbol mapping structure.On the receiver side, received signals can be demodulated using DFT operation.


## 2.2. Overview of GFDM

As the name suggests, GFDM generalizes the multicarrier modulation schemes, SC and OFDM, by controlling the system design parameters. In GFDM, a time-frequency resource grid is sliced in both frequency and time domains. QAM modulated symbols are mapped on each time-frequency resource block. Figure2 shows the mapping illustration of GFDM where K and M stand for the number of subcarriers and number of subsymbols, respectively. Each resource block has K×M sample points. Therefore if K×M=N is satisfied, the amount of transmission data with GFDM will be equivalent to the amount of transmission data with OFDM during same symbol duration in same bandwidth. In order to localize each resource block, pulse shaping filter is applied.Figure 2
GFDM symbol mapping structure.The mathematical expression of GFDM transmission signal is as follows:(3)xn=∑k=0K-1∑m=0M-1dk,mδn-mK∗gnmod⁡Nexp⁡j2πnkK=∑k=0K-1∑m=0M-1dk,mg~n-mK︸xknexp⁡j2πnkK=∑k=0K-1xknexp⁡j2πnkK,where (∗) represents the convolution operation. In (3), g~n-mK≜gn-mKmod⁡N is the pulse shaping filter with mK time shifting. The modulo operation in (3) is equivalent to the tail biting process which makes filter convolution circular [32]. The GFDM modulation procedure is enumerated below and also shown in Figure 3.(1)
Symbol sequence is divided intoK parallel blocks, with each containing M QAM modulated symbols.(2)
The QAM modulated symboldk,m is upsampled by a factor N.(3)
Pulse shaping filter is applied and the subsymbols are summed up in time domain.(4)
Filtered symbols are upconverted to the corresponding subcarrier frequency.(5)
All symbols are summed up.Figure 3
GFDM modulation block diagram.In case ofM=1 and rectangular pulse shaping filter, (3) reduces to (1). In case of K=1, (3) is equivalent to SC transmission. For this reason, this scheme is denoted as GFDM.Equation (3) can be rewritten as a linear equation x=Ad. The matrix A and vector d are as follows:(4)A=G0∘WK⋯GM-1∘WK∈CN×KMGm=g~mg~m⋯g~m︸K∈CN×Kg~m=g~-mKg~1-mK⋯g~N-1-mKT∈CNWK=wK0·0wK0·1⋯wK0·K-1wK1·0wK1·1⋯wK1·K-1⋮⋮⋱⋮wKN-1·0wKN-1·1⋯wKN-1·K-1∈CN×Kd=d0T⋯dmT⋯dM-1TT∈CKMdm=d0,md1,m⋯dK-1,mT∈CK,where the operation (∘) represents the Hadamard product.This paper assumes that the receiver employs correlation detector. The correlation receiver is realized by multiplyingAH to the received GFDM symbols. Since A contains upconversion term for each subcarrier, downconversion can be performed through AH operation. Figure 4 shows normalized absolute value of AHA. As shown in the figure, intercarrier interference (ICI) appears due to the nonorthogonality of subcarriers.Figure 4
ICI effect of the GFDM (Root Raised Cosine filter with roll-off factor 0.1.K=6,M=4).


## 2.3. WiGig/IEEE 802.11ad OFDM Frame Structure

The 11ad OFDM frame is composed of five fields as defined in the standard, that is, Short Training Field (STF), Channel Estimation Field (CEF), Header, OFDM symbols, and optional training fields. Since the header and optional training fields do not impact the performance, these fields are ignored in this paper.The STF is used for the carrier frequency offset (CFO) estimation and autogain control (AGC) configuration. After CFO compensation and AGC, propagation channels are estimated using CEF. These two fields use Golay complementary sequence withπ/2-shift BPSK modulation [33]. Figure 5 shows the STF and CEF structures of control PHY (for control signal transmission), SC PHY, and OFDM PHY.Figure 5
WiGig/IEEE 802.11ad preamble structure.G a 128 and Gb128 in Figure 5 stand for 128-bit Golay complementary sequences. Gu512 and Gv512 are not the 512-bit Golay complementary sequences; however they are constructed with the concatenation of Ga128 and Gb128. The 11ad receiver can distinguish each frame due to the difference between STF and CEF. The last -Ga128 in STF indicates the end of STF or the start point of CEF.The OFDM symbol follows these preamble fields. The number of OFDM symbols within one packet varies according to the transmitted data and MCS (Modulation and Coding Scheme). Table1 shows important parameter configurations and corresponding values of 11ad OFDM. This paper proposes the GFDM frame structure for 11ad based on these parameters.Table 1
WiGig/IEEE 802.11ad OFDM parameters.
Parameter Value Number of IDFT/DFT points 512 Number of data subcarriers 336 Number of pilot subcarriers 16 (±10, 30, 50, 70, 90, 110, 130, 150) Number of DC subcarriers 3 (−1, 0, 1) Number of guard band subcarriers 157 (−256~-178, 178~255) Subcarrier frequency spacing 5.15625 MHz (2640 MHz/512) OFDM sample rate 2640 MHz OFDM symbol period 0.194 usec Cyclic prefix duration 48.4 ns = 0.194 usec× 25%


## 3. GFDM for IEEE 802.11ad Systems

GFDM has a potential to reduce the PAPR while achieving high throughput performance. However, in order to utilize GFDM in 11ad, transmission system has to be in compliance with the standard. This section proposes the designs of GFDM spectrum and pilot symbols.


### 3.1. GFDM DC Null and Guard Band Design

If there are no constraints, multicarrier transmission systems use entire bandwidth by separating several subcarriers. However if the “transmission system” is considered, DC subcarrier and guard band subcarrier have to be nullified to avoid DC offset and interference for other channels or other systems. Based on Table1, the GFDM transmission system for 11ad is designed.Since GFDM uses small number of subcarriers to reduce PAPR, the subcarrier bandwidth becomes larger than that of OFDM. In the case of OFDM, DC nulling and guard band insertion are just setting zero to the corresponding subcarriers. In the GFDM case, this method results in the waste of frequency resources. Figure6 shows the spectrum of conventional DC nulling and guard band insertion in the case of K=8. Since the subcarrier spacing in this case is 330 MHz (2640 MHz/8), DC null is very wide, and therefore fine-adjustment of guard bands is impossible. In addition, additional guard band insertion is required because this spectrum cannot satisfy 11ad requirement. Consequently, frequency resources are wasted.Figure 6
GFDM spectrum with DC nulling (K=8,M=64).This paper proposes subcarrier upshifting/downshifting methods to avoid the wasting of resources. As shown in Figure3, GFDM modulation has upconversion blocks at the last part. By introducing additional frequency shifting block, wide DC null can be shrunk. This can be done by downshifting the lower side (k=0,1,…,K/2) and upshifting the higher side (k=K/2+1,K/2+2,…,K). Figure 7 shows the result of this process. As evident from the figure, the DC null is reduced. Moreover, this frequency shifting enables the fine-adjustment of guard bands.Figure 7
GFDM spectrum with DC nulling and frequency shift (K=8,M=64).In the case of OFDM, the number of guard band subcarriers is 157; therefore GFDM system should employ the equivalent bandwidth corresponding to guard bands. The bandwidths corresponding to the guard band and the number of guard band subcarriers for GFDM are computed as follows:(5)Bg=157×2640MHz512Ng,GFDM=Bg2640MHz/K,where Bg and Ng,GFDM are the bandwidths corresponding to the guard band and the number of guard band subcarriers for GFDM, respectively. The operation [·] represents rounding function. The proposed 11ad GFDM system employs these values.The mathematical expression of GFDM modulation matrix,A, including the frequency shifting is given below:(6)A=G0∘W~KG1∘W~K⋯GM-1∘W~K∈CN×KMW~K=wK0·0vΔf00⋯wK0·K-1vΔfK0wK1·0vΔf01⋯wK1·K-1vΔfK1⋮⋱⋮wKN-1·0vΔf0N-1⋯wKN-1·K-1vΔfKN-1∈CN×KvΔfk=expsgnk-Ng,GFDM2j2πΔf,where sgn(·) is sign function which returns the sign of the argument. Δf is the frequency shift.


### 3.2. GFDM Pilot Symbol Design

In 11ad OFDM PHY, pilot symbols are mapped onto the specific subcarriers over all time. The pilot symbols are used for the phase derotation at the receiver side. The pilot symbols have to be inserted since received signals cannot be demodulated under existence of the phase rotation. However, in the case of GFDM, if the pilot symbol is transmitted using specific subcarrier over all time, it results in the waste of resources due to the wide subcarrier bandwidth. This paper introduces a scattered pilot structure similar to the one in LTE packet. Figure8 shows the time-frequency grid of one GFDM symbol. The yellow symbol represents the pilot symbol. The number of pilot symbols is 16 (same as OFDM) and they are mapped onto the lowest subcarrier and the highest subcarrier in a zigzag manner to avoid the ICI effect. Time domain spacing is M/16 to be widely scattered. The phase tracking performance is shown in Figure 9. The upper plot corresponds to OFDM and the lower plot corresponds to GFDM. As expected, there is no significant difference between these two results.Figure 8
Pilot symbol insertion for GFDM symbol (K=8,M=64).Figure 9
Phase tracking performance comparison.


## 3.1. GFDM DC Null and Guard Band Design

If there are no constraints, multicarrier transmission systems use entire bandwidth by separating several subcarriers. However if the “transmission system” is considered, DC subcarrier and guard band subcarrier have to be nullified to avoid DC offset and interference for other channels or other systems. Based on Table1, the GFDM transmission system for 11ad is designed.Since GFDM uses small number of subcarriers to reduce PAPR, the subcarrier bandwidth becomes larger than that of OFDM. In the case of OFDM, DC nulling and guard band insertion are just setting zero to the corresponding subcarriers. In the GFDM case, this method results in the waste of frequency resources. Figure6 shows the spectrum of conventional DC nulling and guard band insertion in the case of K=8. Since the subcarrier spacing in this case is 330 MHz (2640 MHz/8), DC null is very wide, and therefore fine-adjustment of guard bands is impossible. In addition, additional guard band insertion is required because this spectrum cannot satisfy 11ad requirement. Consequently, frequency resources are wasted.Figure 6
GFDM spectrum with DC nulling (K=8,M=64).This paper proposes subcarrier upshifting/downshifting methods to avoid the wasting of resources. As shown in Figure3, GFDM modulation has upconversion blocks at the last part. By introducing additional frequency shifting block, wide DC null can be shrunk. This can be done by downshifting the lower side (k=0,1,…,K/2) and upshifting the higher side (k=K/2+1,K/2+2,…,K). Figure 7 shows the result of this process. As evident from the figure, the DC null is reduced. Moreover, this frequency shifting enables the fine-adjustment of guard bands.Figure 7
GFDM spectrum with DC nulling and frequency shift (K=8,M=64).In the case of OFDM, the number of guard band subcarriers is 157; therefore GFDM system should employ the equivalent bandwidth corresponding to guard bands. The bandwidths corresponding to the guard band and the number of guard band subcarriers for GFDM are computed as follows:(5)Bg=157×2640MHz512Ng,GFDM=Bg2640MHz/K,where Bg and Ng,GFDM are the bandwidths corresponding to the guard band and the number of guard band subcarriers for GFDM, respectively. The operation [·] represents rounding function. The proposed 11ad GFDM system employs these values.The mathematical expression of GFDM modulation matrix,A, including the frequency shifting is given below:(6)A=G0∘W~KG1∘W~K⋯GM-1∘W~K∈CN×KMW~K=wK0·0vΔf00⋯wK0·K-1vΔfK0wK1·0vΔf01⋯wK1·K-1vΔfK1⋮⋱⋮wKN-1·0vΔf0N-1⋯wKN-1·K-1vΔfKN-1∈CN×KvΔfk=expsgnk-Ng,GFDM2j2πΔf,where sgn(·) is sign function which returns the sign of the argument. Δf is the frequency shift.


## 3.2. GFDM Pilot Symbol Design

In 11ad OFDM PHY, pilot symbols are mapped onto the specific subcarriers over all time. The pilot symbols are used for the phase derotation at the receiver side. The pilot symbols have to be inserted since received signals cannot be demodulated under existence of the phase rotation. However, in the case of GFDM, if the pilot symbol is transmitted using specific subcarrier over all time, it results in the waste of resources due to the wide subcarrier bandwidth. This paper introduces a scattered pilot structure similar to the one in LTE packet. Figure8 shows the time-frequency grid of one GFDM symbol. The yellow symbol represents the pilot symbol. The number of pilot symbols is 16 (same as OFDM) and they are mapped onto the lowest subcarrier and the highest subcarrier in a zigzag manner to avoid the ICI effect. Time domain spacing is M/16 to be widely scattered. The phase tracking performance is shown in Figure 9. The upper plot corresponds to OFDM and the lower plot corresponds to GFDM. As expected, there is no significant difference between these two results.Figure 8
Pilot symbol insertion for GFDM symbol (K=8,M=64).Figure 9
Phase tracking performance comparison.


## 4. Interchannel Interference Cancellation

As described in Section2.2, the received GFDM symbol can be demodulated by multiplying AH. However as shown in Figure 4, the ICI effect is significant and it degrades the Bit Error Rate (BER) performance. The ICI reduction schemes for GFDM have been studied and the algorithm named Double Sided Serial Interference Cancellation (DSIC) [34] shows good performance results. However, this ICI reduction scheme is affected by channel equalization errors and noise effects. Moreover, the special blocks for ICI reduction are needed because ICI estimation is done per subcarrier. This complexity comes from the assumption that ICI should be mitigated at the receiver side. The ICI of GFDM is completely different from the problem in OFDM. This ICI in GFDM is self-interference arose due to subcarrier nonorthogonality. Therefore, the transmitter should be able to estimate the ICI values before the wireless transmission without any noise effects. This paper introduces a transmitter side ICI reduction scheme for GFDM. The proposed ICI reduction block is illustrated as shown in Figure 10.Figure 10
Transmitter side ICI reduction brock diagram.d and d¯ are original QAM modulated symbol and ICI subtracted symbol, respectively. In addition, iterative calculation is desired in order to reduce ICI effects effectively because ICI subtraction leads to another ICI. This ICI reduction block is constructed with GFDM modulator, GFDM demodulator, and adder. According to the fact that the device which has GFDM should have both modulator and demodulator, this ICI reduction block does not require special additional block.


## 5. Simulation Study

### 5.1. DerivingM and K for Improved Performance

As presented in previous sections, 11ad GFDM system performance is evaluated in terms of PAPR and BER. The simulation parameters are provided in Table2. The second term of the cyclic prefix is for the symbol length adjustment when K×M≠512. For the simple derivation, GFDM with K subcarriers and M subsymbols is derived as (K,M)-GFDM hereafter.Table 2
IEEE 802.11ad GFDM parameters.
Parameter Value Number of subcarriersK 4, 6, 8, 16, 32, 128 Number of subsymbolsM 512 / K Number of pilot symbols 16 Number of DC subcarriers 1 Number of guard band subcarriers N g , G F D M GFDM sample rate 2640 MHz GFDM symbol period K × M / 2640 usec Cyclic prefix duration 48.4 ns +512-K×M/2640 MHz Channel model 11ad cubicle LOS/NLOS (far laptop) [35] Carrier frequency offset 0–10 MHz (random generated) Pulse shaping filter Root Raised Cosine Roll-off factorα 0.1, 0.2, 0.3, 0.4 Modulation and coding scheme 11ad MCS 16, 20, 24 [33] Number of ICI canceler iterations 1–4


#### 5.1.1. PAPR Comparison

Figure11 shows the complementary cumulative distribution function (CCDF) of PAPR. This simulation assumes QPSK transmission with the roll-off factor α=0.1. Although the PAPR value changes if other modulation schemes are employed, relativity is not changed. In the view point of PAPR, (4,128)-GFDM achieves the best performance due to the small number of subcarriers. However, in this case, the number of guard band subcarriers is 1; that is, Ng,GFDM=1. Therefore, the effective number of subcarriers is only two. It means that one (4,128)-GFDM symbol can only transmit 2×128=256 symbols. To make matters worth, it contains pilot symbols. Consequently, (4,128)-GFDM can only transmit 240 data symbols with one GFDM symbol. Therefore (4,128)-GFDM degrades throughput performance. On the other hand, in (6,85)-GFDM and (8,64)-GFDM case, they still show good PAPR performance. From the throughput point of view, 324 and 240 data symbols can be transmitted using (6,85)-GFDM and (8,64)-GFDM, respectively. Therefore (6,85)-GFDM can achieve the best PAPR performance while it maintains throughput performance. If there is no guard band insertion, it is obvious that the throughput performances are same between all configurations and PAPR performance can be improved by decreasing the number of subcarriers. Therefore only from the view point of PAPR, SC is the best solution. However, SC is strongly affected by the multipath effect. Based on these issues, this paper concludes that (6,85)-GFDM is the best in order to maintain high throughput as well as good PAPR performance. Hereafter, performance evaluation focuses the (6,85)-GFDM.Figure 11
PAPR comparison between OFDM and GFDM (QPSK,α=0.1).Figure12 shows PAPR dependency on roll-off factor α. As shown in Figure 12, 16QAM and 64QAM show no significant difference, while QPSK shows remarkable performance improvement. If α=0.4 is considered, PAPR performance reaches the performance of (4,128)-GFDM.Figure 12
PAPR dependency on roll-off factor.
(a)
QPSK (b)
16QAM (c)
64QAM


#### 5.1.2. BER Performance Comparison

Figure13 compares the BER performance of OFDM and several GFDM configuration systems in LOS environment. As shown in Figure 13, there is no significant difference in the BER values for different iterations. Two iterations are sufficient to achieve good BER performance. In addition, the OFDM and GFDM show similar BER performances in the best case. These performance results indicate that (6,85)-GFDM can reduce PAPR up to 3 dB without compromising the system throughput.Figure 13
BER comparison between OFDM and GFDM (MCS 16, 20, and 24,α=0.1, LOS).Figure14 shows the BER performance in NLOS environment. It can be seen that the GFDM is significantly better than the OFDM system. This is because of the channel equalization error effect becoming more dominant in NLOS conditions. This error causes frequency selectivity. Since OFDM uses narrow band subcarriers, this effect degrades BER performance. On the other hand, GFDM is relatively more robust to this effect because of the wide bandwidths of the subcarriers.Figure 14
BER comparison between OFDM and GFDM (MCS 16, 20, and 24,α=0.1, NLOS).


## 5.1. DerivingM and K for Improved Performance

As presented in previous sections, 11ad GFDM system performance is evaluated in terms of PAPR and BER. The simulation parameters are provided in Table2. The second term of the cyclic prefix is for the symbol length adjustment when K×M≠512. For the simple derivation, GFDM with K subcarriers and M subsymbols is derived as (K,M)-GFDM hereafter.Table 2
IEEE 802.11ad GFDM parameters.
Parameter Value Number of subcarriersK 4, 6, 8, 16, 32, 128 Number of subsymbolsM 512 / K Number of pilot symbols 16 Number of DC subcarriers 1 Number of guard band subcarriers N g , G F D M GFDM sample rate 2640 MHz GFDM symbol period K × M / 2640 usec Cyclic prefix duration 48.4 ns +512-K×M/2640 MHz Channel model 11ad cubicle LOS/NLOS (far laptop) [35] Carrier frequency offset 0–10 MHz (random generated) Pulse shaping filter Root Raised Cosine Roll-off factorα 0.1, 0.2, 0.3, 0.4 Modulation and coding scheme 11ad MCS 16, 20, 24 [33] Number of ICI canceler iterations 1–4


### 5.1.1. PAPR Comparison

Figure11 shows the complementary cumulative distribution function (CCDF) of PAPR. This simulation assumes QPSK transmission with the roll-off factor α=0.1. Although the PAPR value changes if other modulation schemes are employed, relativity is not changed. In the view point of PAPR, (4,128)-GFDM achieves the best performance due to the small number of subcarriers. However, in this case, the number of guard band subcarriers is 1; that is, Ng,GFDM=1. Therefore, the effective number of subcarriers is only two. It means that one (4,128)-GFDM symbol can only transmit 2×128=256 symbols. To make matters worth, it contains pilot symbols. Consequently, (4,128)-GFDM can only transmit 240 data symbols with one GFDM symbol. Therefore (4,128)-GFDM degrades throughput performance. On the other hand, in (6,85)-GFDM and (8,64)-GFDM case, they still show good PAPR performance. From the throughput point of view, 324 and 240 data symbols can be transmitted using (6,85)-GFDM and (8,64)-GFDM, respectively. Therefore (6,85)-GFDM can achieve the best PAPR performance while it maintains throughput performance. If there is no guard band insertion, it is obvious that the throughput performances are same between all configurations and PAPR performance can be improved by decreasing the number of subcarriers. Therefore only from the view point of PAPR, SC is the best solution. However, SC is strongly affected by the multipath effect. Based on these issues, this paper concludes that (6,85)-GFDM is the best in order to maintain high throughput as well as good PAPR performance. Hereafter, performance evaluation focuses the (6,85)-GFDM.Figure 11
PAPR comparison between OFDM and GFDM (QPSK,α=0.1).Figure12 shows PAPR dependency on roll-off factor α. As shown in Figure 12, 16QAM and 64QAM show no significant difference, while QPSK shows remarkable performance improvement. If α=0.4 is considered, PAPR performance reaches the performance of (4,128)-GFDM.Figure 12
PAPR dependency on roll-off factor.
(a)
QPSK (b)
16QAM (c)
64QAM


### 5.1.2. BER Performance Comparison

Figure13 compares the BER performance of OFDM and several GFDM configuration systems in LOS environment. As shown in Figure 13, there is no significant difference in the BER values for different iterations. Two iterations are sufficient to achieve good BER performance. In addition, the OFDM and GFDM show similar BER performances in the best case. These performance results indicate that (6,85)-GFDM can reduce PAPR up to 3 dB without compromising the system throughput.Figure 13
BER comparison between OFDM and GFDM (MCS 16, 20, and 24,α=0.1, LOS).Figure14 shows the BER performance in NLOS environment. It can be seen that the GFDM is significantly better than the OFDM system. This is because of the channel equalization error effect becoming more dominant in NLOS conditions. This error causes frequency selectivity. Since OFDM uses narrow band subcarriers, this effect degrades BER performance. On the other hand, GFDM is relatively more robust to this effect because of the wide bandwidths of the subcarriers.Figure 14
BER comparison between OFDM and GFDM (MCS 16, 20, and 24,α=0.1, NLOS).


## 5.1.1. PAPR Comparison

Figure11 shows the complementary cumulative distribution function (CCDF) of PAPR. This simulation assumes QPSK transmission with the roll-off factor α=0.1. Although the PAPR value changes if other modulation schemes are employed, relativity is not changed. In the view point of PAPR, (4,128)-GFDM achieves the best performance due to the small number of subcarriers. However, in this case, the number of guard band subcarriers is 1; that is, Ng,GFDM=1. Therefore, the effective number of subcarriers is only two. It means that one (4,128)-GFDM symbol can only transmit 2×128=256 symbols. To make matters worth, it contains pilot symbols. Consequently, (4,128)-GFDM can only transmit 240 data symbols with one GFDM symbol. Therefore (4,128)-GFDM degrades throughput performance. On the other hand, in (6,85)-GFDM and (8,64)-GFDM case, they still show good PAPR performance. From the throughput point of view, 324 and 240 data symbols can be transmitted using (6,85)-GFDM and (8,64)-GFDM, respectively. Therefore (6,85)-GFDM can achieve the best PAPR performance while it maintains throughput performance. If there is no guard band insertion, it is obvious that the throughput performances are same between all configurations and PAPR performance can be improved by decreasing the number of subcarriers. Therefore only from the view point of PAPR, SC is the best solution. However, SC is strongly affected by the multipath effect. Based on these issues, this paper concludes that (6,85)-GFDM is the best in order to maintain high throughput as well as good PAPR performance. Hereafter, performance evaluation focuses the (6,85)-GFDM.Figure 11
PAPR comparison between OFDM and GFDM (QPSK,α=0.1).Figure12 shows PAPR dependency on roll-off factor α. As shown in Figure 12, 16QAM and 64QAM show no significant difference, while QPSK shows remarkable performance improvement. If α=0.4 is considered, PAPR performance reaches the performance of (4,128)-GFDM.Figure 12
PAPR dependency on roll-off factor.
(a)
QPSK (b)
16QAM (c)
64QAM


## 5.1.2. BER Performance Comparison

Figure13 compares the BER performance of OFDM and several GFDM configuration systems in LOS environment. As shown in Figure 13, there is no significant difference in the BER values for different iterations. Two iterations are sufficient to achieve good BER performance. In addition, the OFDM and GFDM show similar BER performances in the best case. These performance results indicate that (6,85)-GFDM can reduce PAPR up to 3 dB without compromising the system throughput.Figure 13
BER comparison between OFDM and GFDM (MCS 16, 20, and 24,α=0.1, LOS).Figure14 shows the BER performance in NLOS environment. It can be seen that the GFDM is significantly better than the OFDM system. This is because of the channel equalization error effect becoming more dominant in NLOS conditions. This error causes frequency selectivity. Since OFDM uses narrow band subcarriers, this effect degrades BER performance. On the other hand, GFDM is relatively more robust to this effect because of the wide bandwidths of the subcarriers.Figure 14
BER comparison between OFDM and GFDM (MCS 16, 20, and 24,α=0.1, NLOS).


## 6. Computational Complexity

Theoretically, GFDM modulation and demodulation can be realized by simply multiplying the modulation matrixA as described in Section 2.2. However this simple approach requires high computational costs, that is, the large number of complex multiplications. In addition, constructing modulation matrix A also requires high computational costs because it is constructed with the Hadamard product of complex matrix. In order to reduce the number of complex multiplications, modulation and demodulation blocks should be reconfigured so that FFT can be used. Equation (3) can be rewritten as follows:(7)xn=∑k=0K-1∑m=0M-1dk,mg~n-mKexp⁡j2πnkK=∑m=0M-1g~n-mK∑k=0K-1dk,mexp⁡j2πnkK︸IDFT=∑m=0M-1g~n-mKDmnmod⁡K,where Dmnmod⁡K is IDFT of dk,m. Since n=0,1,…,KM-1, Dm[n] becomes circular repetition sequence. Equation (7) shows that x[n] can be computed using IDFT and summing up the filtered M sequences. The total number of the complex multiplications involved in GFDM modulator is (Klog⁡KIFFT+MK(Filtering))×M=(log⁡K+M)MK.Similarly, GFDM demodulation can be described as follows:(8)d^k′,m′=∑n=0KM-1g~n-m′Kxnexp⁡-j2πnk′K=∑l=0M-1∑n=lKl+1K-1g~n-m′Kxnexp⁡-j2πnk′K=∑l=0M-1∑n′=0K-1g~n′+lK-m′Kxn′+lKexp⁡-j2πk′n′+lKK=∑l=0M-1g~n′+lK-m′Kxn′+lK︸Correlation  receiver∑n′=0K-1exp⁡-j2πk′n′K=∑n′=0K-1Dm′n′exp⁡-j2πk′n′K︸DFT.Thus, the total number of the complex multiplications involved in GFDM demodulator is(Klog⁡K(FFT)+MK(Filtering))×M=(log⁡K+M)MK.The modified modulation and demodulation blocks according to these equations are as illustrated in Figure15.Figure 15
GFDM modulator and demodulator block.
(a)
GFDM modulator (b)
GFDM demodulatorOriginally, the computational costs of matrix multiplication areM2K2. Therefore, the computational cost of this modulation/demodulation blocks becomes (log⁡K+M)MK/M2K2=(log⁡K+M)/MK=0.17 for (K,M)=(6,85). Thus, the proposed structure can reduce about 83% of the computational cost. In [36], the proposed GFDM transceiver architecture cannot apply the FFT/IFFT blocks. In contrast, our proposed architecture can utilize the FFT/IFFT blocks and it can drastically reduce the computational cost.


## 7. Concluding Remarks and Future Work

This study has investigated the methodology for adapting GFDM to one of the most successful standards, that is, IEEE 802.11ad. It shows that the proposed GFDM frame structure is fully in compliance with the existing IEEE 802.11ad. Moreover, this study extends the ICI reduction technique to be suitable for IEEE 802.11ad wireless systems. The intensive performance evaluation results in this paper reveal that (6,85)-GFDM could achieve good PAPR and throughput performance simultaneously. The proposed efficient GFDM modulation/demodulation block can reduce computational costs by about 83%. The proposed method is applicable for other mmWave standards in IEEE 802.11ay and 5G mmWave cellular networks.As a future research direction, it is possible to conduct more intensive performance evaluation considering the radio frequency (RF) impairments including power amplifier nonlinearity, IQ imbalance, phase noises, and so forth.



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*Source: 9269567-2016-12-15.xml*