An Overview of Generalized Frequency Division Multiplexing (GFDM)
11 An Overview of Generalized FrequencyDivision Multiplexing (GFDM)
Ching-Lun Tai , Tzu-Han Wang , and Yu-Hua Huang School of Electrical and Computer Engineering, Georgia Institute ofTechnology, GA, United States
Abstract
As a candidate waveform for next-generation wireless communications, generalized frequencydivision multiplexing (GFDM) features several decent properties which make it promising. In this paper,we systematically overview the research about GFDM. We start with GFDM transceivers with their maincomponents, which consist of prototype filter design, low-complexity transceiver implementation, andsymbol detection algorithms. Then, we investigate a couple of non-ideal issues of GFDM, including syn-chronization issues, channel estimation, and in-phase/quadrature (I/Q) imbalance compensation. Lastly,we study the applications of GFDM-based cognitive radio and full-duplex radio which boast of a highspectral efficiency.
Index Terms
Generalized frequency division multiplexing (GFDM), transceiver structure, non-ideal issue, cog-nitive radio, full-duplex radio
I. I
NTRODUCTION
Generalized frequency division multiplexing (GFDM) [1] is a promising candidate waveformfor next-generation wireless communications, featuring several advantages such as low latency,low peak-to-average ratio (PAPR), low out-of-band (OOB) emission and low adjacent channelleakage ratio (ACLR), and relaxed requirements of time and frequency synchronization [2].With a flexible transceiver structure, GFDM boasts of a high degree of freedom for transmitterand receiver design. Therefore, GFDM is applicable to a variety of scenarios and its parameterscan be adapted to meet the requirements of specific services. In addition, there is abundant low-complexity implementation of GFDM transceivers, which are hence practical from an economicperspective, and various algorithms can be applied to the GFDM receiver, where the complexityis further reduced while maintaining an allowable performance.In real-world applications, there are a couple of non-ideal issues that affect the performancesof GFDM. However, thanks to its flexible structure, plenty of techniques can be adopted for a r X i v : . [ c s . I T ] A ug GFDM
Transceiver
Prototype filter designLow-complexity transceiver implementationSymbol detection algorithm
Non-ideal issue
Synchronization issueChannel estimationI/Q imbalance compensation
Application
Cognitive radioFull-duplex radio
Figure 1: Organization of GFDM overview in this paper.
GFDM and help with the evaluation and compensation of the adverse effects caused by theseissues.Because of its decent properties, GFDM is suitable for a large number of applications. Amongall potential applications, cognitive radio and full-duplex radio are of great interest due to theirhigh spectral efficiency, which help address the scarcity of bandwidth resources. Accordingly,GFDM-based cognitive radio and full-duplex radio are considered an appealing solution tospectrum management in next-generation wireless communications.In this paper, we provide a systematic overview of GFDM with the following topics (assummarized in Fig. 1): • GFDM transceiver : We briefly review the system model of GFDM. Besides, we studythe important components of GFDM transceivers, including prototype filter design, low-complexity transceiver implementation, and symbol detection algorithms. • Non-ideal issues : We investigate the effects and possible solutions of several non-ideal is-sues of GFDM, including synchronization issues, channel estimation, and in-phase/quadrature(I/Q) imbalance compensation. • GFDM-based cognitive radio and full-duplex radio : We introduce the applicationsof cognitive radio and full-duplex radio and discuss about the research of GFDM-basedcognitive radio and full-duplex radio.
The remainder of this paper is organized as follows. Sec. II introduces GFDM transceiversand their essential components. The non-ideal issues of GFDM are investigated in Sec. III. InSec. IV, we study GFDM-based cognitive radio and full-duplex radio. Finally, Sec. V concludesthe paper.
Notations : Boldfaced capital and lowercase letters denote matrices and column vectors, re-spectively. We use (cid:104) . (cid:105) D to denote the modulo D . We adopt the MATLAB subscripts : and a : b todenote all elements and the elements ordered from a to b , respectively, of the subscripted objects.Given a vector u , we use [ u ] n to denote the n th component of u and diag( u ) the diagonal matrixcontaining u on its diagonal. Given a matrix A , we denote [ A ] m,n , A T , and A H its ( m , n )thentry (zero-based indexing), transpose, and Hermitian transpose, respectively. We define q to bethe q × zero vector, and W q the normalized q -point discrete Fourier transform (DFT) matrixwith [ W q ] m,n = e − j πmn/q / √ q, q ∈ N .II. GFDM T RANSCEIVER
Figure 2: GFDM system model.
GFDM is a block-based multicarrier communication scheme as shown in Fig. 2 [2]. EachGFDM block employs K subcarriers, with each transmitting M complex-valued subsymbols,and therefore a total of D = KM symbols are transmitted within one block.For a GFDM block d ∈ C D , its m th subsymbol on the k th subcarrier [ d ] k + mK is pulse-shapedby a vector g k,m , whose n th entry is [ g k,m ] n = [ g ] (cid:104) n − mK (cid:105) D e j πkn/K , n = 0 , , ..., D − , m =0 , , ..., M − , k = 0 , , ..., K − , where g ∈ C D is called the prototype filter [2]. Let A = [ g , ... g K − , g , ... g K − , ... g ,M − ... g K − ,M − ] (1)be the GFDM transmitter matrix [2] and x = Ad be the transmit sample vector, whose n thentry is [ x ] n = K − (cid:88) k =0 M − (cid:88) m =0 [ d ] k + mK [ g ] (cid:104) n − mK (cid:105) D e j πkn/K . (2) Then, the vector x passes through parallel-to-serial (P/S) conversion and is further added a cyclicprefix (CP) of length L , generating a GFDM digital baseband transmit signal x [ n ] .Consider an N -tap wireless channel, which is a causal linear time-invariant (LTI) system withimpulse response h [ n ] , where h [ n ] = 0 , n < or n > N − . Accordingly, the baseband receivesignal is y [ n ] = h [ n ] ∗ x [ n ] + w [ n ] , where w [ n ] is the complex additive white Gaussian noise(AWGN) with variance N . Denote h = [ h [0] h [1] ...h [ N − T and w = [ w [0] w [1] ...w [ D − T .Note that the combination of a CP and a linear convolution with a frequency-selective multipathchannel can be modeled as a circular convolution [3]. Specifically, after CP removal and serial-to-parallel (S/P) conversion, the receive sample vector is obtained as y = Hx + w = HAd + w = W HD diag ( W D Ad ) F N h + w , (3)where F N = [ √ D W D ] : , N , and H ∈ C D × D is the circulant matrix whose first column is [ h T TD − N ] T .Finally, the estimated GFDM block ˆ d is obtained after the demodulation process, which variesdepending on the target applications. A. Prototype Filter Design
For GFDM, the prototype filter g determines the characteristics of the transmitter matrix A .With the emergence of various services in a heterogeneous network, prototype filter design iscritical in constructing a transmitter that meets the requirements of quality of service (QoS).Classic prototype filters include the raised cosine (RC) filter featuring low inter subsymbolinterference (ISI) [2] and Dirichlet filter (with its variants) causing no inter subcarrier interference(ICI) [4], [5]. Over the past years, a variety of prototype filter design schemes have been proposedbased on different considerations.From an analytical perspective, the conditional number of a transmitter matrix is of greatinterest. Specifically, the conditional number is related to the singularity [6], which affectsthe error rate, and noise enhancement factor (NEF) [7], which indicates the level of noiseenhancement, of a transmitter matrix.When it comes to the radio resource allocation, the OOB radiation, which is related to ACLRand evaluates the energy leak experienced by the outer frequency band in terms of the powerspectral density (PSD), becomes a main concern.Considering the circuit implementation, one of the main focuses is the PAPR, which is definedas PAPR ( x ) = ( max n | [ x ] n | ) / ( (cid:80) D − n =0 | [ x ] n | /D ) ≥ for a transmit sample vector x . A largerPAPR implies that the transmit samples are more subject to the distortion caused by a poweramplifier (PA).Another practical concern is the transmission rate, which determines the number of symbolstransmitted within a fixed time period. In the existing literature, [8] and [9] propose their design based on the conditional number,adopting a frequency shift technique and radix-2 fast Fourier transform (FFT), respectively. Witha different focus, [10] and [11] design their prototype filters by solving optimization problemswhich minimize the PAPR. Instead of dealing with only one consideration, some works proposetheir prototype filter design with multiple considerations taken into account. [12] proposes analgorithm to jointly optimize the OOB radiation and transmission rate; [13] solves an optimizationproblem that minimizes the OOB radiation while satisfying an NEF constraint; [14] minimizesthe approximate PAPR while considering the NEF and OOB radiation by solving an optimizationproblem.
B. Low-complexity Transceiver Implementation
In order to achieve low-cost realizations of GFDM for real-world applications, the complexity,which is defined as the number of complex multiplications (CMs) involved in both modulationat the transmitter and demodulation at the receiver, of GFDM transceivers is of great importance.Note that the complexity is closely related to the amount of computing resources consumed, thedata processing time an application takes, and the latency a user experiences. With the goal offast processing and low latency in next-generation wireless communications [15], low-complexitytransceiver implementation is a critical topic for GFDM researchers.For transceiver design, it could focus on a single side (i.e., the transmitter or receiver side),or it could jointly consider both transmitter and receiver sides.The transmitter is mostly characterized by the transmitter matrix A . Although the matrix A is fully determined once the prototype filter g is explicitly specified, the complexity involved inobtaining the transmit sample vector x , which is equal to Ad , varies depending on the computingprocess. The main reason is that the matrix A can be decomposed into various forms by usingtechniques which transform a matrix into a cascade of smaller sparse matrices and thereforereduce the complexity.Unlike the transmitter, the receiver structure is more flexible and is constructed according tothe specifications of target applications. Among all types of receivers, linear receivers are theones that are commonly used for the low-complexity purpose, including the famous zero forcing(ZF) receiver and linear minimum mean square error (LMMSE) receiver [2], [16]. ZF receiversreverse the cascaded operations performed by the transmitter matrix A and the channel circulantmatrix H , featuring a lower complexity but a poorer performance. On the other hand, LMMSEreceivers require the statistics of noises to minimize the mean square error between the originaland estimated GFDM blocks, d and ˆ d , resulting in a higher complexity but a better performance.Based on the above guidelines and other advanced techniques, there are plenty of low-complexity transceiver schemes proposed for a more efficient implementation. Several worksfocus on the receiver side. [17] and [18] reduce the receiver complexity by employing frequency domain processing. In addition, different techniques have been adopted to achieve low-complexityreceiver implementation, such as sparsification and block diagonalization [19], Taylor series andconjugate gradient [20], and tabu search [21]. Differently, some works focus on the transmitterside, such as [22] reducing the transmitter complexity with the technique of subcarrier-wiseDFT. Combining both transmitter and receiver sides, several low-complexity schemes have beenproposed over the whole transceiver. [23] reduces the complexity of both the transmitter andreceiver by taking advantage of the sparsity in modulation and the block circulant property indemodulation. Unitary transmitter matrices are adopted in [24] for low-complexity transceiverimplementation. In [25], only partial subcarriers are allocated in order to reduce the complexityof the whole transceiver. C. Symbol Detection Algorithms
Apart from conventional demodulation processes (e.g., linear receivers), there are a variety ofalgorithms which can be adopted to provide the estimated GFDM block ˆ d , and these algorithmsare often called symbol detectors.One of the largest differences between conventional demodulation processes and symboldetection algorithms is the tradeoff between complexity and performances. Conventional demod-ulation processes suffer from a higher complexity but provide a (statistically) better performance,while symbol detection algorithms feature a lower complexity but offer an inferior performance.Therefore, symbol detection algorithms are more suitable for applications where a large numberof subcarriers K and/or a large number of subsymbols (within a subcarrier) M are used and thecomplexity of conventional demodulation processes is prohibitively high.Particularly, symbol detection algorithms work for multiple-input-multiple-output (MIMO)systems, where multiple transmitters and multiple receivers are used to provide a benefit ofboth diversity gains (due to the multiple paths created in the system) and multiplexing gains(due to the spatial correlations between transmitters or between receivers) [26]. Note that thecombination of MIMO and GFDM (i.e., MIMO-GFDM) often leads to a large block size whereconventional demodulation processes become infeasible and only symbol detection algorithmswork (despite the sub-optimal performance).Several symbol detection algorithms have been adopted for GFDM in the existing literature.For instance, [27] and [28] use orthogonal approximate message passing (OAMP) and deepconvolutional neural networks (CNNs) to achieve GFDM symbol detection. A couple of symboldetection algorithms have been employed for MIMO-GFDM systems, such as the Markovchain Monte Carlo (MCMC) algorithm [29], MMSE sorted QR-decomposition (SQRD) withsphere decoding (SD) [30], expectation propagation (EP) [31], and MMSE parallel interferencecancellation (PIC) [32]. III. N ON -I DEAL I SSUES OF
GFDMWithin a synthetic simulated environment, we can evaluate the performance limit of a com-munication system over an ideal case. However, in real-world applications, there are a variety ofnon-ideal issues that deteriorate the performances of a communication system. Accordingly, theperformances of a communication system in practical use are expected to be worse than thoseobserved in the ideal case, which provides an upper bound of performances.In the following, we investigate the effects and possible solutions of three typical non-idealissues, including synchronization issues, channel estimation, and I/Q imbalance compensation,of GFDM.
A. Synchronization Issues
Figure 3: An illustration of occurrence of synchronization errors (red dashed box indicates the additional blockcompared with Fig. 2).
In the ideal case, a perfect synchronization is assumed at the GFDM receiver, where thedemodulation process works. However, in practical use, there are plenty of factors that causea synchronization error, which leads to a subcarrier/subsymbol misalignment at the receiverand thus significantly increases the error rate [33], [34]. An illustration of the occurrence ofsynchronization errors is as shown in Fig. 3.Basically, there are two types of synchronization errors, including symbol time offset (STO)and carrier frequency offset (CFO), which correspond to the asynchronization in time domain andfrequency domain, respectively [2]. The main reasons of their occurrence include the Dopplereffect caused by the mobility of users and the multipath effect caused by the obstacles in theenvironment. In order to compensate the adverse effects of synchronization errors, it is criticalto estimate them. Typical approaches include a supervised estimation with the use of trainingsequences and a unsupervised (blind) estimation with the use of statistical methods.
A more complicated scenario happens in an uplink multiuser system, where multiple userstransmit their data to the base station. In addition to synchronization errors, there is also multiuserinterference (MUI) that further deteriorates the demodulation performances. For this case, MUIcancellation methods, which eliminate synchronization errors simultaneously, are essential.Accordingly, a couple of schemes working on synchronization issues have been proposed. Fora supervised estimation of synchronization errors, different structures for training sequences havebeen used, such as embedded midamble [35], scattered pilots [36], pseudo-circular preamble [37],and partial employed subcarriers [38], where training symbols are put in the middle, a specificposition, the front, or all positions of a subcarrier, respectively. In addition, [39] proposes anunsupervised (blind) estimation scheme which derives from the statistical maximum-likelihood(ML) method. For an uplink multiuser system, synchronization errors and MUI need to bejointly addressed. While [40] takes an approach of maximizing signal-to-interference ratio (SIR),[41] adopts the techniques of weighted parallel interference cancellation (WPIC) and adaptiveinterference cancellation filter (AICF).
B. Channel Estimation
Figure 4: An illustration of channel estimation (red dashed boxes indicate the additional blocks compared with Fig.2).
Within an ideal environment, the full channel state information (CSI) about the channel vector h is assumed to be known at the GFDM receiver (which is called Genie-aided condition).However, actually the CSI is hardly known in advance, i.e., such information is seldom a priorknowledge, in real-world applications.Since the receiver is built upon the knowledge of CSI, the channel estimation is an essentialstep before the demodulation process takes place. An illustration of channel estimation is asshown in Fig. 4. In order to achieve channel estimation, we require the pilots, which are symbolswith fixed values that are generated for the estimation purpose, be contained in the GFDM block d . Specifically, we create a concatenation of two subvectors, including the pilot vector d p whichrepresents the pilots for channel estimation and the data vector d d which represents the data symbols to be transmitted, and permute it with a permutation matrix P (which is equivalent to alinear combination of d p and d d ), generating the resulting GFDM block d , i.e., d = P [ d Tp d Td ] T .As a non-orthogonal waveform, GFDM suffers from potential ICI (which can be avoidedif ICI-free prototype filters are used, e.g., the Dirichlet filter) and inherent ISI, resulting in aunique challenge for channel estimation. In order to deal with the effects of interference, the pilotstructure and channel estimator design become the main focuses of GFDM channel estimation.There exist various pilot structures that can be adopted for GFDM channel estimation, includingscattered pilots where pilots are evenly scattered throughout the block, preamble/postamble pilotswhere pilots are in the front/back of the subcarrier, and pilot subcarriers where all positions ofselected subcarriers are reserved for pilots. Besides, there are a variety of channel estimatorsthat one can choose from, including the famous linear channel estimators, e.g., the least square(LS) estimator and LMMSE estimator.Based on different pilot structures and channel estimators, a couple of schemes have beenproposed to achieve channel estimation. Several schemes work on scattered pilots, including[42] adopting the matched filter as the channel estimator, and [43]–[45] performing channelestimation with the use of the LMMSE estimator. In addition, [46] and [47] both employ linearestimators (including the LS and LMMSE estimators), but selecting preamble/postamble pilotsand pilot subcarriers, respectively, as the pilot structures. C. I/Q Imbalance Compensation
Figure 5: An illustration of occurrence of I/Q imbalance (red dashed box indicates the additional block comparedwith Fig. 2).
Usually under an ideal setting, it is assumed that there is no RF impairment in GFDM circuitimplementation. Nonetheless, RF impairments, such as phase noises occurring at the receiver,are inevitable issues when it comes to real-world applications.From an economic perspective toward the design of next-generation wireless communications,direct-conversion transceivers are an appealing option due to its decent properties such as smallsize, low cost, and low energy consumption (low power) [48], [49], involving only a single mixing stage. However, there are several RF impairment issues regarding direct-conversion transceivers,and one of them is the I/Q imbalance, which indicates the misalignment (in amplitudes and/orphases) between the in-phase and quadrature paths over the circuit implementation. An illustrationof the occurrence of I/Q imbalance is as shown in Fig. 5.In order to address I/Q imbalance, it is critical to estimate its level and design the correspondingI/Q imbalance compensation schemes. A couple of works have proposed their schemes aboutanalyzing and compensating the effects of I/Q imbalance. In [50], the authors analyze the I/Q im-balance of GFDM under Weibull fading, which is a statistical model for wireless indoor/outdoorchannels. In order to compensate I/Q imbalance, [51] and [52] propose a supervised scheme withthe use of training sequences and a unsupervised (blind) scheme adopting statistical methods,respectively, to estimate the level of I/Q imbalance.IV. GFDM-B ASED C OGNITIVE R ADIO AND F ULL -D UPLEX R ADIO
Due to its decent properties such as low OOB radiation and low PAPR, GFDM is a promisingsolution to many applications required in next-generation wireless communications. Among allpotential applications, we investigate two of them, including the cognitive radio and the full-duplex radio, which serve as a remedy for the scarcity of bandwidth resources and the congestionin the frequency band.Cognitive radio is a technique of dynamic bandwidth resource management, where unlicensedopportunistic users (also known as secondary users) detect unused channels (which are not oc-cupied by their licensed primary users) and access them, resulting in a higher spectral efficiency.The critical challenges of the cognitive radio include the OOB radiation and ICI, which arecaused by secondary users and affect the primary users in adjacent channels. In this context,GFDM is suitable for cognitive radio since it features low OOB radiation and its ICI can beeliminated with interference cancellation techniques or with the use of ICI-free prototype filters(e.g., the Dirichlet filter). Recent research about GFDM-based cognitive radio mainly focuseson further reduction of OOB radiation and interference cancellation techniques.Full-duplex radio is a duplex technique which allows the simultaneous mutual transmission andreception between two devices in a point-to-point communication, featuring a doubled systemcapacity and a higher spectral efficiency due to the feasibility of bidirectional communication. Thekey challenge of full-duplex radio is the self-interference, where the transmission and receptionprocesses interfere the operations of each other due to the signal leakage resulting from thedeficiency of RF circuits. Although GFDM suffers from inherent ISI, its nice characteristicssuch as low OOB radiation and low PAPR still make itself an appealing choice for full-duplexradio, since these two characteristics mitigate the design complexity of RF circuits. The mainfocus of recent research about GFDM-based full-duplex radio is the self-interference cancellationtechniques. Combining both cognitive radio and full-duplex radio, the full-duplex cognitive radio integratesthe advantages and limits of two radio schemes, featuring an ultra-high spectral efficiency butfacing challenges such as the OOB radiation and self/adjacent interference. Full-duplex cognitiveradio is a rather new concept for GFDM, and the research about GFDM full-duplex cognitiveradio is around the problems derived from the combination of two radio schemes.In the existing literature, there are several works dedicated to the realizations of GFDM-basedcognitive radio and full-duplex radio. Focusing on GFDM-based cognitive radio, [53] and [54]cancel the ICI with a double-sided serial interference cancellation technique and by insertingadditional subcarriers, respectively. Moreover, several related issues such as the detection ofunused spectrum [55], experimental testbeds [56], and power allocation along with PA non-linearity alleviation [57] have been addressed over the past years. For GFDM-based full-duplexradio, both [58] and [59] deal with the self-interference cancellation when non-ideal issues suchas synchronization errors and I/Q imbalance are present. Extended from [58] and [59], the authorsof [60] focus on the self/adjacent interference cancellation of GFDM-based full-duplex cognitiveradio in the presence of non-ideal issues.V. C
ONCLUSION
In this paper, we present a systematic overview of GFDM, covering three main topics: GFDMtransceivers, non-ideal issues of GFDM, and GFDM-based cognitive radio and full-duplex radio.For GFDM transceivers, we provide a brief review on the GFDM system model and introducetheir essential components, which consist of prototype filter design, low-complexity transceiverimplementation, and symbol detection algorithms. In addition, we investigate non-ideal issues ofGFDM, including synchronization issues, channel estimation, and I/Q imbalance compensation.Lastly, we study the applications of GFDM-based cognitive radio and full-duplex radio, pointingout the research challenges and recent advancements involved.R
EFERENCES [1] G. Fettweis, M. Krondorf, and S. Bittner, “GFDM - Generalized Frequency Division Multiplexing,” in
Veh. Technol. Conf.,2009. VTC Spring 2009. IEEE 69th , Apr. 2009, pp. 1–4.[2] N. Michailow, M. Matth´e, I. S. Gaspar, A. N. Caldevilla, L. L. Mendes, A. Festag, and G. Fettweis, “GeneralizedFrequency Division Multiplexing for 5th Generation Cellular Networks,”
IEEE Transactions on Communications , vol. 62,no. 9, pp. 3045–3061, 2014.[3] D. Tse and P. Viswanath,
Fundamentals of wireless communication . Cambridge university press, 2005.[4] M. Matth´e, N. Michailow, I. Gaspar, and G. Fettweis, “Influence of pulse shaping on bit error rate performance and outof band radiation of Generalized Frequency Division Multiplexing,” in
Proc. IEEE ICC Workshop , 2014, pp. 43–48.[5] C. Tai, B. Su, and C. Jia, “Frequency-domain Decoupling for MIMO-GFDM Spatial Multiplexing,” in
ICASSP 2019 -2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , 2019, pp. 4799–4803.[6] D. W. Lin and P. S. Wang, “On the configuration-dependent singularity of GFDM pulse-shaping filter banks,”
IEEECommun. Lett. , vol. 20, no. 10, pp. 1975–1978, Oct. 2016. [7] M. Towliat, M. Rajabzadeh, and S. M. J. A. Tabatabaee, “On the Noise Enhancement of GFDM,” IEEE WirelessCommunications Letters , pp. 1–1, 2020.[8] A. Yoshizawa, R. Kimura, and R. Sawai, “A Singularity-Free GFDM Modulation Scheme with Parametric Shaping FilterSampling,” in , 2016, pp. 1–5.[9] A. Nimr, M. Matth´e, D. Zhang, and G. Fettweis, “Optimal Radix-2 FFT Compatible Filters for GFDM,”
IEEECommunications Letters , vol. 21, no. 7, pp. 1497–1500, 2017.[10] Z. A. Sim, R. Reine, Z. Zang, F. H. Juwono, and L. Gopal, “Reducing the PAPR of GFDM Systems with QuadraticProgramming Filter Design,” in , 2019, pp. 1–5.[11] K. Liu, W. Deng, and Y. Liu, “Theoretical Analysis of the Peak-to-Average Power Ratio and Optimal Pulse Shaping FilterDesign for GFDM Systems,”
IEEE Transactions on Signal Processing , vol. 67, no. 13, pp. 3455–3470, 2019.[12] S. Han, Y. Sung, and Y. H. Lee, “Filter Design for Generalized Frequency-Division Multiplexing,”
IEEE Transactions onSignal Processing , vol. 65, no. 7, pp. 1644–1659, 2017.[13] P. Chen and B. Su, “Filter optimization of out-of-band radiation with performance constraints for GFDM systems,” in , 2017, pp.1–5.[14] C. L. Tai, B. Su, and P. C. Chen, “Optimal filter design for gfdm that minimizes papr under performance constraints,” in , April 2018, pp. 1–6.[15] P. Popovski, “Ultra-reliable communication in 5G wireless systems,” in , 2014, pp. 146–151.[16] M. Matth´e, L. Mendes, and G. Fettweis, “Generalized Frequency Division Multiplexing in a Gabor Transform Setting,”
IEEE Commun. Lett. , vol. 18, no. 8, pp. 1379–1382, Aug. 2014.[17] I. Gaspar, N. Michailow, A. Navarro, E. Ohlmer, S. Krone, and G. Fettweis, “Low complexity gfdm receiver based onsparse frequency domain processing,” in
Veh. Technol. Conf. (VTC Spring), 2013 IEEE 77th , June 2013, pp. 1–6.[18] W. D. Dias, L. L. Mendes, and J. J. P. C. Rodrigues, “Low Complexity GFDM Receiver for Frequency-Selective Channels,”
IEEE Communications Letters , vol. 23, no. 7, pp. 1166–1169, 2019.[19] A. Farhang, N. Marchetti, and L. E. Doyle, “Low complexity gfdm receiver design: A new approach,” in , June 2015, pp. 4775–4780.[20] S. Tiwari and S. S. Das, “Low-Complexity Joint-MMSE GFDM Receiver,”
IEEE Transactions on Communications , vol. 66,no. 4, pp. 1661–1674, 2018.[21] J. Jeong, I. Jung, J. Kim, and D. Hong, “A New GFDM Receiver with Tabu Search,” in , 2019, pp. 1–5.[22] H. Lin and P. Siohan, “Orthogonality improved GFDM with low complexity implementation,” in , Mar. 2015, pp. 597–602.[23] A. Farhang, N. Marchetti, and L. E. Doyle, “Low-complexity modem design for GFDM,”
IEEE Trans. Signal Process. ,vol. 64, no. 6, pp. 1507–1518, Mar. 2016.[24] P. C. Chen, B. Su, and Y. Huang, “Matrix Characterization for GFDM: Low Complexity MMSE Receivers and OptimalFilters,”
IEEE Transactions on Signal Processing , vol. 65, no. 18, pp. 4940–4955, Sept 2017.[25] A. Nimr, M. Chafii, and G. Fettweis, “Low-Complexity Transceiver for GFDM systems with Partially AllocatedSubcarriers,” in , 2019, pp. 1–6.[26] Lizhong Zheng and D. N. C. Tse, “Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels,”
IEEE Transactions on Information Theory , vol. 49, no. 5, pp. 1073–1096, 2003.[27] S. Zhang, C. Wen, K. Takeuchi, and S. Jin, “Orthogonal approximate message passing for GFDM detection,” in , 2017, pp. 1–5.[28] M. Turhan, E. ¨Ozt¨urk, and H. A. C¸ ırpan, “Deep Convolutional Learning-Aided Detector for Generalized Frequency Division Multiplexing with Index Modulation,” in , 2019, pp. 1–6.[29] D. Zhang, M. Matth´e, L. L. Mendes, and G. Fettweis, “A Markov chain Monte Carlo algorithm for near-optimumdetection of MIMO-GFDM signals,” in
Personal, Indoor, and Mobile Radio Commun. (PIMRC), 2015 IEEE 26th AnnualInt. Symposium on , Aug 2015, pp. 281–286.[30] M. Matth´e, I. Gaspar, D. Zhang, and G. Fettweis, “Near-ML Detection for MIMO-GFDM,” in
Veh. Technol. Conf. (VTCFall), 2015 IEEE 82nd , Sep. 2015, pp. 1–2.[31] D. Zhang, L. L. Mendes, M. Matth´e, I. S. Gaspar, N. Michailow, and G. P. Fettweis, “Expectation Propagation forNear-Optimum Detection of MIMO-GFDM Signals,”
IEEE Trans. Wireless Commun. , vol. 15, no. 2, pp. 1045–1062, Feb2016.[32] M. Matth´e, D. Zhang, and G. Fettweis, “Low-Complexity Iterative MMSE-PIC Detection for MIMO-GFDM,”
IEEETransactions on Communications , vol. 66, no. 4, pp. 1467–1480, 2018.[33] D. Gaspar, L. Mendes, and T. Pimenta, “GFDM BER Under Synchronization Errors,”
IEEE Communications Letters ,vol. 21, no. 8, pp. 1743–1746, 2017.[34] N. Sharma, A. Kumar, M. Magarini, S. Bregni, and D. N. K. Jayakody, “Impact of CFO on Low Latency-Enabled UAVUsing ”Better Than Nyquist” Pulse Shaping in GFDM,” in , 2019, pp. 1–6.[35] I. Gaspar and G. Fettweis, “An embedded midamble synchronization approach for generalized frequency divisionmultiplexing,” in , Dec. 2015, pp. 1–5.[36] M. Matth´e, L. L. Mendes, and G. Fettweis, “Asynchronous multi-user uplink transmission with generalized frequencydivision multiplexing,” in , Jun. 2015, pp. 2269–2275.[37] I. Gaspar, A. Festag, and G. Fettweis, “Synchronization using a pseudo-circular preamble for generalized frequencydivision multiplexing in vehicular communication,” in
Veh. Technol. Conf. (VTC Fall), 2015 IEEE 82nd , Sep. 2015, pp.1–5.[38] K. Lee, M. Kang, E. Jeong, D. Park, and Y. H. Lee, “Use of training subcarriers for synchronization in low latency uplinkcommunication with GFDM,” in , 2016, pp. 1–6.[39] P. S. Wang and D. W. Lin, “Maximum-likelihood blind synchronization for GFDM systems,”
IEEE Signal Process. Lett. ,vol. 23, no. 6, pp. 790–794, Jun. 2016.[40] B. Lim and Y. Ko, “Optimal receiver filter for GFDM with timing and frequency offsets in uplink multiuser systems,” in , 2018, pp. 1–6.[41] ——, “Multiuser Interference Cancellation for GFDM With Timing and Frequency Offsets,”
IEEE Transactions onCommunications , vol. 67, no. 6, pp. 4337–4349, 2019.[42] U. Vilaipornsawai and M. Jia, “Scattered-pilot channel estimation for GFDM,” in , April 2014, pp. 1053–1058.[43] Y. Akai, Y. Enjoji, Y. Sanada, R. Kimura, H. Matsuda, N. Kusashima, and R. Sawai, “Channel estimation with scatteredpilots in GFDM with multiple subcarrier bandwidths,” in , Oct 2017, pp. 1–5.[44] S. Ehsanfar, M. Chafii, and G. Fettweis, “Time-Variant Pilot- and CP-Aided Channel Estimation for GFDM,” in
ICC2019 - 2019 IEEE International Conference on Communications (ICC) , 2019, pp. 1–6.[45] C. Tai, B. Su, and C. Jia, “Interference-Precancelled Pilot Design for LMMSE Channel Estimation of GFDM,” in , 2020, pp. 1–5.[46] S. Ehsanfar, M. Matthe, D. Zhang, and G. Fettweis, “Theoretical Analysis and CRLB Evaluation for Pilot-Aided ChannelEstimation in GFDM,” in , Dec 2016, pp. 1–7. [47] ——, “Interference-Free Pilots Insertion for MIMO-GFDM Channel Estimation,” in , March 2017, pp. 1–6.[48] S. Mirabbasi and K. Martin, “Classical and modern receiver architectures,” IEEE Communications Magazine , vol. 38,no. 11, pp. 132–139, 2000.[49] Y. Pan and S. Phoong, “A Time-Domain Joint Estimation Algorithm for CFO and I/Q Imbalance in Wideband Direct-Conversion Receivers,”
IEEE Transactions on Wireless Communications , vol. 11, no. 7, pp. 2353–2361, 2012.[50] M. Lupupa and J. Qi, “I/q imbalance in generalized frequency division multiplexing under weibull fading,” in
Personal,Indoor, and Mobile Radio Commun. (PIMRC), 2015 IEEE 26th Annual Int. Symposium on , Aug 2015, pp. 471–476.[51] N. Tang, S. He, C. Xue, Y. Huang, and L. Yang, “IQ Imbalance Compensation for Generalized Frequency DivisionMultiplexing Systems,”
IEEE Wireless Communications Letters , vol. 6, no. 4, pp. 422–425, Aug 2017.[52] H. Cheng, Y. Xia, Y. Huang, L. Yang, and D. P. Mandic, “A Normalized Complex LMS Based Blind I/Q ImbalanceCompensator for GFDM Receivers and Its Full Second-Order Performance Analysis,”
IEEE Transactions on SignalProcessing , vol. 66, no. 17, pp. 4701–4712, 2018.[53] R. Datta, N. Michailow, M. Lentmaier, and G. Fettweis, “GFDM interference cancellation for flexible cognitive radioPHY design,” in
Veh. Technol. Conf. (VTC Fall), 2012 IEEE , Sep. 2012, pp. 1–5.[54] R. Datta and G. Fettweis, “Improved aclr by cancellation carrier insertion in gfdm based cognitive radios,” in , May 2014, pp. 1–5.[55] D. Panaitopol, R. Datta, and G. Fettweis, “Cyclostationary detection of cognitive radio systems using gfdm modulation,”in , April 2012, pp. 930–934.[56] M. Danneberg, R. Datta, and G. Fettweis, “Experimental testbed for dynamic spectrum access and sensing of 5g gfdmwaveforms,” in , Sept 2014, pp. 1–5.[57] A. Mohammadian, M. Baghani, and C. Tellambura, “Optimal Power Allocation of GFDM Secondary Links With PowerAmplifier Nonlinearity and ACI,”
IEEE Wireless Communications Letters , vol. 8, no. 1, pp. 93–96, 2019.[58] A. Mohammadian and C. Tellambura, “Full-Duplex GFDM Radio Transceivers in the Presence of Phase Noise, CFO andIQ Imbalance,” in
ICC 2019 - 2019 IEEE International Conference on Communications (ICC) , 2019, pp. 1–6.[59] A. Mohammadian, C. Tellambura, and M. Valkama, “Analysis of Self-Interference Cancellation Under Phase Noise, CFO,and IQ Imbalance in GFDM Full-Duplex Transceivers,”
IEEE Transactions on Vehicular Technology , vol. 69, no. 1, pp.700–713, 2020.[60] A. Mohammadian and C. Tellambura, “GFDM-Modulated Full-Duplex Cognitive Radio Networks in the Presence of RFImpairments,” in2019 IEEE 30th Annual International Symposium on Personal, Indoor and Mobile Radio Communications(PIMRC)