Advances in Electrical Engineering

Volume 2014, Article ID 482805, 25 pages

http://dx.doi.org/10.1155/2014/482805

## Filter Bank Multicarrier Modulation: A Waveform Candidate for 5G and Beyond

ECE Department, University of Utah, Salt Lake City, UT 84112, USA

Received 7 August 2014; Accepted 11 November 2014; Published 21 December 2014

Academic Editor: Gorazd Stumberger

Copyright © 2014 Behrouz Farhang-Boroujeny. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Recent discussions on viable technologies for 5G emphasize on the need for waveforms with better spectral containment per subcarrier than the celebrated orthogonal frequency division multiplexing (OFDM). Filter bank multicarrier (FBMC) is an alternative technology that can serve this need. Subcarrier waveforms are built based on a prototype filter that is designed with this emphasis in mind. This paper presents a broad review of the research work done in the wireless laboratory of the University of Utah in the past 15 years. It also relates this research to the works done by other researchers. The theoretical basis based on which FBMC waveforms are constructed is discussed. Also, various methods of designing effective prototype filters are presented. For completeness, polyphase structures that are used for computationally efficient implementation of FBMC systems are introduced and their complexity is contrasted with that of OFDM. The problems of channel equalization as well as synchronization and tracking methods in FBMC systems are given a special consideration and a few outstanding research problems are identified. Moreover, this paper brings up a number of appealing features of FBMC waveforms that make them an ideal choice in the emerging areas of multiuser and massive MIMO networks.

#### 1. Introduction

In the past, orthogonal frequency division multiplexing (OFDM) has enjoyed its dominance as the most popular signaling method in broadband wired [1, 2] and wireless [3, 4] channels. OFDM has been adopted in the broad class of DSL standards as well as in the majority of wireless standards, for example, variations of IEEE 802.11 and IEEE 802.16, 3GPP-LTE, and LTE-Advanced. OFDM is known to be a perfect choice for point-to-point communications, for example, from a base station to a mobile node and vice versa. It offers a minimum complexity and achieves very high bandwidth efficiency. However, it has been noted that OFDM has to face many challenges when considered for adoption in more complex networks. For instance, the use of OFDM in the uplink of multiuser networks, known as OFDMA (orthogonal frequency division multiple access), requires full synchronization of the users’ signals at the base station input. Such synchronization was found to be very difficult to establish, especially in mobile environments where Doppler shifts of different users are hard to predict/track. Morelli et al. [5] have noted that carrier and timing synchronization represents the most challenging task in OFDMA systems. To combat the problem, some researchers have relaxed on the need for a close to perfect carrier synchronization among users and have proposed multiuser interference cancellation methods [6–9]. These methods are generally very complex to implement. Their implementation increases the receiver complexity by orders of magnitude [10]. Hence, one of the main advantages of OFDM, the low complexity, will be lost.

Another limitation of OFDM appears when attempt is made to transmit over a set of noncontiguous frequency bands, known as* carrier aggregation*. The poor response of the subcarrier filters in IFFT/FFT filter banks of OFDM introduces significant out-of-band* egress noise* to other users and also picks up significant* ingress noise* from them. The same problem appears if one attempts to adopt OFDM for filling in the spectrum holes in cognitive radios. Methods of reducing OFDM spectral leakage prove to be very limited in performance and may add significant complexity to the transmitter. For instance, the side lobe suppression techniques, like those proposed in [11–13], can achieve an out-of-band emission suppression of only 5 to 10 dB, while they may add significant complexity to the transmitter and they will incur some loss in bandwidth efficiency.

Filter bank multicarrier (FBMC) is an alternative transmission method that resolves the above problems by using high quality filters that avoid both ingress and egress noises. Also, because of the very low out-of-band emission of subcarrier filters, application of FBMC in the uplink of multiuser networks is trivial [14, 15]. It can be deployed without synchronization of mobile user nodes signals. In the application of cognitive radios, the filter bank that is used for multicarrier data transmission can also be used for spectrum sensing [16–20]. On the other hand, compared to OFDM, FBMC falls short in handing multiple-input multiple-output (MIMO) channels, although a few solutions to adopt FBMC in MIMO channels have been reported in the literature; for example, see [21–23]. Nevertheless, as our recent research study has shown (see Section 8, below), in the emerging area of* massive* MIMO, FBMC is found as powerful as OFDM and in some cases superior to OFDM.

In the past, many attempts have been made to adopt FBMC in various standards. Apparently, the earliest proposal to use FBMC for multicarrier communications is a contribution from Tzannes et al. of AWARE Inc., in one of the asymmetric digital subscriber lines (ADSL) standard meetings in 1993 [24]. The proposed method that was called discrete wavelet multitone (DWMT) was further studied in [25, 26]. Despite enthusiasm from the research community (see [27] and the cited references therein), DWMT was not adopted in the ADSL standard. This was partly because of the perceived complexity of this method as compared to its rival, DMT (discrete multitone, an equivalent name for OFDM in DSL literature). Indeed, the DWMT structure proposed by Tzannes et al. was significantly more complex than that of DMT. The major part of the complexity of DWMT came from the equalization method that was adopted. The detailed discussion presented in [26] assumed that one needs an equalizer that combines signals from each subcarrier band and its adjacent bands. Typical equalizer lengths suggested in [26] were 21 real-valued taps per subcarrier. It was later noted by the author of this paper that if each subcarrier is sufficiently narrow such that it can be approximated by a flat gain, two real taps per subcarrier would be sufficient for equalization [27]. This observation led to further study of DWMT. In power line communications (PLC) community, it has been named wavelet OFDM and was adopted in the IEEE P1901 standard [28]. The main motivation for use of DWMT in DSL and its adoption later in PLC was to deal with ingress and egress noises, since both DSL and PLC use unshielded copper lines that are subject to strong radio interference. Moreover, in 1999, an FBMC method with nonoverlapping subcarrier bands was proposed as a solution for filtering the narrow-band interferences in very high-speed DSL (VDSL) channels [29]. The proposed method was called filtered multitone (FMT). This proposal that was included as an annex in one of the initial draft documents of VDSL [30] was further developed by a number of researchers [31–34]. However, to avoid incompatibility with ADSL, FMT was not included in the final document of the VDSL standard [35]. Another unsuccessful story is an attempt by France Telecom [36] to introduce FBMC in the IEEE 802.22, a cognitive radio standard to access TV bands in wireless rural area networks (WRAN). Up to now, apparently, the only standard for radio transmission that uses FBMC is the TIAs Digital Radio Technical Standard [37].

Recent discussions on the fifth generation (5G) wireless communications have initiated a much stronger wave of interest in deviating from the main stream of OFDM systems. This shift of interest is clearly due to limitations of OFDM in the more dynamic and multiuser networks of future. A number of proposals have been made to adopt new waveforms with improved spectral containment. A good example of such activity is the 5GNOW project in Europe which challenges LTE and LTE-Advanced in coping with the dynamic needs of 5G. The 5GNOW has identified four alternative choices of waveforms to better serve 5G needs. These waveforms that are all built based on some sort of filtering may be thought as adoptions of FBMC method to suit different needs of various applications. We refer interested readers to the documents available at http://www.5gnow.eu for the details of the proposed waveforms by the 5GNOW group. Another major activity that has performed a broad study of FBMC is due to the PYHDYAS project (also in Europe). The PHYDYAS contributors have published heavily on various aspects of FBMC, including prototype filter design, equalization, synchronization, and application to MIMO channels. A summary of the major findings of the PHYDYAS contributors is presented in [21], and a complete list of their publications can be found at http://www.ict-phydyas.org.

The main thrust of this paper is to present a point of view of FBMC and its future applications as seen by the author. While we acknowledge the presence of a large body of works on FBMC, the paper details are geared towards the research outcomes of the author and his students in past 15 years. The paper emphasis is on the recent works of the author and his students. Many shortcomings of OFDM in dealing with the requirement of the next generation of wireless systems are discussed and it is shown how FBMC overcomes these problems straightforwardly. We present a derivation of FBMC systems that reveals the relationships among different forms of FBMC. A method of designing FBMC systems for a near-optimum performance in doubly dispersive channels is presented and its superior performance over OFDM is shown. The example considered is an underwater acoustic channel. Application of FBMC technique to massive MIMO communications is introduced and its advantages in this emerging technology are revealed. Last, but not the least, the problems of channel equalization and synchronization in FBMC systems are also given a special treatment and a number of outstanding research problems in this field, for future studies, are identified.

This paper begins with a historical overview of FBMC methods in Section 2. In order to keep the presentation in this paper a complement to those we have recently reported in [19, 38], the rest of this paper is organized as follows. A summary of the theoretical background based on which the various forms of FBMC are built are presented in Section 3. Methods of designing prototype filters for FBMC are presented in Section 4. Polyphase structures that are used for efficient implementation of FBMC systems are reviewed in Section 5. A few comments on complexity comparison of FBMC and OFDM are also made in this section. Channel equalization in FBMC systems is discussed in Section 6. Methods of carrier and symbol timing acquisition and tracking in FBMC systems are reviewed in Section 7. Here, a few particular features of FBMC systems that need special attention for their successful implementation are highlighted. Section 8 reminds the reader of a number of applications in the literature where FBMC has been found to be a good fit. This section also discusses the opportunities offered by FBMC in the emerging area of massive MIMO. The concluding remarks of the paper are made in Section 9.

*Notations*. The presentations in this paper follow a mix of continuous-time and discrete-time formulations, as appropriate. While refers to a continuous function of time, , is used to refer to its discrete-time version, with denoting the time index. The notation is used as frequency variable in , the Fourier transform of the continuous-time signal , and also as normalized frequency in , the Fourier transform of the discrete-time signal . We use to denote linear convolution, and the superscript to denote complex conjugate.

#### 2. Review of FBMC Methods

FBMC communication techniques were first developed in the mid-1960s. Chang [39] presented the conditions required for signaling a parallel set of PAM symbol sequences through a bank of overlapping filters within a minimum bandwidth. To transmit PAM symbols in a bandwidth-efficient manner, Chang proposed vestigial sideband (VSB) signaling for subcarrier sequences. Saltzberg [40] extended the idea and showed how Chang’s method could be modified for transmission of QAM symbols in a double-sideband- (DSB-) modulated format. In order to keep the bandwidth efficiency of this method similar to that of Chang’s signaling, Saltzberg noted that the in-phase and quadrature components of each QAM symbol should be time staggered by half a symbol interval. Efficient digital implementation of Saltzberg’s multicarrier system through polyphase structures was first introduced by Bellanger and Daguet [41] and later studied by Hirosaki [42, 43]. Another key development appeared in [44], where the authors noted that Chang’s/Saltzberg’s method could be adopted to match channel variations in doubly dispersive channels and, hence, minimize intersymbol interference (ISI) and intercarrier interference (ICI).

Saltzberg’s method has received a broad attention in the literature and has been given different names. Most authors have used the name offset QAM (OQAM) to reflect the fact that the in-phase and quadrature components are transmitted with a time offset with respect to each other. Moreover, to emphasize the multicarrier feature of the method, the suffix OFDM has been added, hence, the name OQAM-OFDM. Others have chosen to call it staggered QAM (SQAM), equivalently SQAM-OFDM. In [38] we introduced the shorter name staggered multitone (SMT).

Chang’s method [39], on the other hand, has received very limited attention. Those who have cited [39] have only acknowledged its existence without presenting much detail, for example [41, 45, 46]. In particular, Hirosaki who has extensively studied and developed digital structures for the implementation of Saltzberg’s method [43, 47] has made a brief reference to Chang’s method and noted that since it uses VSB modulation, and thus its implementation requires a Hilbert transformation, it is more complex to implement than Saltzberg’s method. This statement is inaccurate, since as we have demonstrated in [38] Chang’s and Saltzberg’s methods are equivalent and, thus, with a minor modification, an implementation for one can be applied to the other. More on this is presented in Section 5. Also, as noted earlier, a vast literature in digital signal processing has studied a class of multicarrier systems that has been referred to as DWMT. It was later noted in [27, 48] that DWMT uses the same analysis and synthesis filter banks as the cosine modulated filter banks (CMFB) [49]. CMFB, on the other hand, may be viewed as a reinvention of Chang’s method, with a very different application in mind [38]. In [38], we also introduced the shorter name cosine modulated multitone (CMT) to be replaced for DWMT and/or CMFB.

One more interesting observation is that another class of filter banks which were called modified DFT (MDFT) filter bank has appeared in the literature [50]. Careful study of MDFT reveals that this, although derived independently, is in effect a reformulation of Saltzberg’s filter bank in discrete-time and with emphasis on compression/coding. The literature on MDFT begins with the pioneering works of Fliege [51] and later has been extended by others, for example [52–55].

Finally, before we proceed with the rest of our presentation, it should be reiterated that we identified three types of FBMC systems: (i) CMT: built based on the original idea of Chang [39]; (ii) SMT: built based on the extension made by Saltzberg [40]; and (iii) FMT: built based on the conventional method frequency division multiplexing (FDM) [34].

#### 3. Theory

The theory of FBMC, particularly those of CMT and SMT, has evolved over the past five decades by many researchers who have studied them from different angles. Early studies by Chang [39] and Saltzberg [40] have presented their finding in terms of continuous-time signals. The more recent studies have presented the formulations and conditions for ISI and ICI cancellation in discrete-time, for example, [46, 50]. On the other hand, a couple of recent works [19, 38], from the author of this paper and his group, have revisited the more classical approach and presented the theory of CMT and SMT in continuous time. It is believed that this formulation greatly simplifies the essence of the theoretical concepts behind the theory of CMT and SMT and how these two waveforms are related. It also facilitates the design of prototype filters that are used for realization of CMT and SMT systems. Thus, here, also, we follow the continuous-time approach of [19, 38]. Moreover, to give a complement presentation to those of [19, 38], an attempt is made to discuss the underlying theory mostly through the* time-frequency phase-space*, with minimum involvement in mathematical details. It is believed that this presentation also provides a new intuition into the relationship between SMT and CMT. Interested readers who wish to see the mathematical details are referred to [20, 38].

##### 3.1. CMT

In CMT, data symbols are from a pulse amplitude modulated (PAM) alphabet and, hence, are real-valued. To establish a transmission with the maximum bandwidth efficiency, PAM symbols are distributed in a time-frequency phase-space lattice with a density of two symbols per unit area. This is equivalent to one complex symbol per unit area. Moreover, because of the reasons that are explained below a 90-degree phase shift is introduced to the respective carriers among the adjacent symbols. These concepts are presented in Figure 1. Vestigial side-band (VSB) modulation is applied to cope with the carrier spacing . The pulse-shape used for this purpose at the transmitter as well as for matched filtering at the receiver is a square-root Nyquist waveform, , which has been designed such that is a Nyquist pulse with regular zero crossings at time intervals. Also, , by design, is a real-valued function of time and . These properties of , as demonstrated below, are instrumental for correct functionality of CMT.