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.
In the past, orthogonal frequency division multiplexing (OFDM) has enjoyed its dominance as the most popular signaling method in broadband wired [
Another limitation of OFDM appears when attempt is made to transmit over a set of noncontiguous frequency bands, known as
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 [
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 [
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
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
FBMC communication techniques were first developed in the mid-1960s. Chang [
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 [
Chang’s method [
One more interesting observation is that another class of filter banks which were called modified DFT (MDFT) filter bank has appeared in the literature [
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 [
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 [
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
The CMT time-frequency phase-space lattice.
Figure
Magnitude responses of the CMT pulse-shaping filters at various subcarriers and time instants
Let
The synthesis of
It is not difficult to show that
To develop an in-depth understanding of the CMT signaling, it is instructive to explore a detailed derivation of (
When
When
Next, consider the case where
It is also worth noting that some of the recent derivations of FBMC that are presented in discrete-time design the respective prototype filter
To summarize, the above derivations revealed that the following settings of the CMT parameters lead to the real orthogonality of the basis functions The symbol spacing The pulse-shape/prototype filter The above constraints are applied to assure orthogonality of the basis functions that are within the same subcarrier or adjacent subcarriers only. The orthogonality of basis functions that belong to the nonadjacent subcarriers is guaranteed by virtue of the fact that they correspond to filters with nonoverlapping bands. A more advanced design presented in Section The phase shifts indicated in Figure Although in CMT the position of the lattice points is fixed, these points can be moved in the time-frequency plane as long as their relative position and phase differences remain unchanged. We use this point below to arrive at the SMT waveform by applying a simple modification to the CMT waveform (
The above equations may be combined to arrive at the CMT transmitter and receiver structures that are presented in Figure
CMT transmitter and receiver blocks.
SMT may be thought of as an alternative to CMT. Its time-frequency phase-space lattice is obtained from that of CMT (Figure
The SMT time-frequency phase-space lattice.
Magnitude responses of the SMT pulse-shaping filters at various subcarriers and time instants
SMT transmitter and receiver blocks.
FMT waveforms are synthesized following the conventional method of frequency division multiplexing (FDM). The subcarrier channels have no overlap, and thus ICI is resolved through use of well-designed filters with high stopband attenuation. ISI may be compensated for by adopting the conventional method of square-root Nyquist filtering that is used in single-carrier communications. For doubly dispersive channels, we have adopted a more advanced design [
For comparison with the CMT and SMT structures in Figures
FMT transmitter and receiver blocks.
Magnitude responses of an FMT pulse-shaping filter at various subcarriers.
The results of the previous section suggest that linear phase square-root Nyquist filters that have been widely used for single carrier data transmission are the most trivial choice for prototype filter in FBMC systems. This indeed remains an accurate statement as long as the underlying channel is time-invariant or varies slowly. However, in cases where the channel is fast varying, a more general class of square-root Nyquist filters that satisfy the Nyquist condition both along the time and frequency axis should be adopted. In this section, we first review couple of classical Nyquist designs developed by us [
The classical prototype filter for FBMC systems that was suggested in [
Martin [
More recently, we have developed an algorithm for designing SR-Nyquist filters that can balance between the accuracy of the Nyquist constraints and the filter stopband attenuation [
Figure
Magnitude responses of a sampled and truncated SRRC filter and two discrete-time designed SR-Nyquist filters.
As seen, and one would expect, SRRC design performs significantly inferior to both of the SR-Nyquist designs. From the two SR-Nyquist designs, the one based on [
When a channel is subject to dispersion both in time (due to multipath effects) and in frequency (due to variation of the channel in time), we say the channel is
The parameter
The design of the prototype filter for time-varying channels is closely tied to the ambiguity function [
Let
We note that the case where
Another key point that one should consider in the selection of
Attempts to design filters that satisfy the orthogonality conditions (
The design procedure proposed by Haas and Belfiore [
Haas and Belfiore’s design [
The basic equations for the design of Hermite pulses are obtained by substituting (
The significant points are the ones at which the constraints ( Once the desired constraints are imposed at the significant points defined in The remaining grid points, indicated by white disks, will satisfy the constraints (
Grid of
We note that to satisfy the constraints (
It should be also noted that since, here, the designed filter is isotropic, with the parameter
To design prototype filters for an orientation that follows the hexagonal lattice, we choose the constrained points according to those depicted in Figure
Grid of
To develop a numerical method for the minimization of
Removing the third term on the right-hand side of (
Figure
Responses of three designs of a prototype filter. (a) The time-domain responses. (b) The magnitude of the frequency-domain responses.
Considering the results presented in Figure Both IOTA and Hermite designs have time-domain responses that are more compact than the time-domain response of the SR-Nyquist filter. In the frequency domain, on the other hand, the SR-Nyquist design gives a more compact response. The compact responses of IOTA and Hermite designs in time will make them less prone to distortion introduced by channel variation with time. The broader responses of IOTA and Hermite design in frequency, on the other hand, make them more prone to the channel frequency selectivity. Considering When channel is time-invariant or varies slowly, the choice of SR-Nyquist results in the maximum immunity to the channel frequency selectivity.
The robust design approach that was presented above was first introduced in [
The impact of a doubly dispersive design and three designs of FMT. “FMT-c” is the case where a SR-Nyquist design is used. “FMT-dd” follows the robust design that was introduced above (the author obtained permission from IEEE to include this figure).
The results presented in Figure
Polyphase structures are commonly used to implement FBMC transmitter and receiver. Direct mimicking of the continuous-time structures of Figures
Polyphase structures for FMT transmitter and receiver also need particular attention to take care of the fact that sampling rate changes in the AFB (at the transmitter side) and in the SFB (at the receiver side) is different from the size of IFFT/FFT block. A method that takes into account this change of sampling rate is presented in a later part of this section.
The basic polyphase SFB block that may be used to construct the SFB blocks in both CMT and SMT transmitter is presented in Figure The inputs The SFB output has a rate of The synthesis is performed based on an IFFT of size The filtering blocks This structure is an efficient implementation of a bank of filters with the respective inputs The commutator at the output serializes the outputs of the polyphase component filters, after arrival of each set of data symbols at the input.
Basic synthesis polyphase filter bank.
Figure
Basic analysis polyphase filter bank.
CMT and SMT systems, as was demonstrated in Section
A rearrangement of the transmitter of SMT.
The structure that is presented in Figure
A rearrangement of the transmitter of SMT.
Looking back at the synthesis polyphase structure of Figure
It is also worth noting that a number of other authors also have taken note of the same symmetry properties in SMT waveform and accordingly proposed methods of reducing the complexity [
Following the same line of thoughts that led to Figure
A rearrangement of the receiver of SMT.
SMT receiver structure. The equalizers are single-tap or multitap. When they are multitap, they have a tap spacing of half a symbol interval.
The receiver structure presented in Figure
The polyphase SFB that is presented in Figure
In FMT, the situation is different. While the symbol rate remains equal to
The fact that
FMT transmitter in discrete-time.
To proceed, we write the time index
Equation (
Polyphase implementation of an FMT transmitter.
Following Figure
FMT receiver in discrete-time.
To proceed, we define
According to Figure
Here, we present a general polyphase structure for computation of the samples of
Following (
Polyphase implementation of an FMT receiver.
Following Figure
Being an alternative to the widely adopted OFDM in various standards, it is always of interest and important to compare FBMC methods against OFDM. As noted in Section
We count the complexity of OFDM as one IFFT,
Similarly, for FMT, we find that
Comparing (
In FBMC receivers, equalization is performed at the output of the analysis filter banks. It is often assumed that each subcarrier has a small bandwidth; hence, the channel may be assumed to be flat over each subcarrier band. In that case, a single-tap equalizer per subcarrier would suffice. In cases where the flat gain approximation may be insufficient, a multitap equalizer per subcarrier band may be necessary. For CMT and SMT systems, it is necessary to use a fractionally spaced equalizer. A tap-spacing of half symbol interval is the most convenient choice and, hence, has been suggested in the literature, for example, [
Although, in many scenarios it may appear that a single-tap equalizer per subcarrier is sufficient, in practice, where carrier and clock mismatch between the transmitter and receiver is inevitable, a multitap equalizer can be instrumental. In particular, the difference between the clock used at transmitter to pass the signal samples to a digital-to-analog converter (DAC) and the one used at the receiver to control the rate of samples taken by an analog-to-digital converter (ADC) at the receiver introduces a constant drift in the timing phase of sampled signal. This drift, as explained in the next section, can significantly deteriorate the receiver performance. The use of a multitap equalizer can resolve this problem to a great extent. This is demonstrated through a numerical example in the next section.
Another point that should be emphasized here is the following. Most researchers, who have published in the area of FBMC, have limited their results to the use of one single-tap equalizer per subcarrier band. This has been to emphasize on the simplicity of equalization in FBMC systems and also to stay in par with OFDM. Alternatively, one may look at the use of multitap equalizers in FBMC systems as a mechanism that brings with itself a number of advantages. Firstly, the use of multitap equalizers removes any small frequency selectivity over each subcarrier band and, hence, facilitates adoption of a large symbol constellations and this, in turn, increases the bandwidth efficiency of transmission. Secondly, it allows reducing the number of subcarriers which, in turn, reduces the system (i) complexity (possibly compensating for the added complexity resulting from the use of multitap equalizers), (ii) latency, (iii) sensitivity to carrier frequency offset, and (iv) peak-to-average power ratio (PAPR).
Synchronization methods are necessary in any receiver to compensate for any difference between the carrier frequency of the incoming signal and the local oscillator used to demodulate it as well as to compensate for any clock mismatch between the transmitter and receiver. Pilot aided and blind synchronization methods have been widely studied in the literature from the beginning of development of data modems [
In majority of standards, including those of OFDM and FBMC, the pilot aided approaches have been adopted. For instance, all the OFDM packet formats that have been proposed for WiFi and WiMAX as well as those suggested in LTE and LTE-Advanced start with a short-training periodic preamble, for coarse carrier acquisition. This follows by a long preamble, consisting of two or more similar OFDM symbols, that is used for fine tuning of the carrier, timing acquisition, and channel estimation; for example, see [
A few researchers, who have looked at the packet design for FBMC, have also suggested a similar packet format to those of the OFDM [
Figure
An FBMC data packet with short and long preambles.
There is also some difference in the long preamble proposed in [
Here, to make suggestions to further improve the preamble design, we first note that the preamble is a packet component that constitutes a loss in the bandwidth efficiency of transmission. Clearly, an attempt to reduce the length of the preamble improves the bandwidth efficiency. The research so far in the above cited works has led to the following observations. (i) A preamble with a set of pilot symbols that are well separated in frequency is needed to assure detection and correction of large CFO values. (ii) A longer preamble that allows a more accurate estimate of CFO may be also necessary. On the other hand, one may realize that to obtain the CFO and symbol timing estimates, it is not necessary to send pilots on all the subcarriers. The number of parameters that characterize the channel response (determined by the length of the channel impulse response) is usually much smaller than the number of subcarriers. This means, a fraction of subcarriers, whose number is greater than or equal to the length of the channel impulse response, suffice for pilot subcarriers in the preamble. This, in turn, implies that one may propose to combine the short and long preambles into one preamble, and by taking such approach, obviously, a shorter preamble will result. We note that the preamble proposed in [
Another consideration that needs one’s attention in designing an effective preamble is the choice of the prototype filter that is used for preamble. Assuming that the preamble consists of only a long preamble, the preamble length is determined by the length of the prototype filter and the number of its repetitions. Accordingly, a shorter prototype filter leads to a shorter preamble and thus a more bandwidth efficient packet. The above suggestion to space out the pilot subcarriers in the preamble can be taken advantage of to shorten the length of the preamble. This is because wider subcarrier allows one to increase the bandwidth of each subcarrier and accordingly reduce the symbol period and thus the length of the corresponding prototype filter. Nevertheless, it should be also noted that a broader band of each subcarrier can make it prone to some level of frequency selectivity that should be taken into account while identifying the channel parameters.
Tracking of channel variation (including variations due to CFO and clock timing drift), during the payload transmission, is usually made through distributed pilots that are transmitted along with the data symbols. This topic, as noted above, has been well studied for OFDM. However, it has received very limited attention in the FBMC literature. Stitz et al. [
In [
As noted above, any difference between the clock frequency at the transmitter and its counterpart at the receiver introduces a timing drift. The common method of compensating for this timing drift is to add a timing recovery loop to the system. In a single carrier receiver, the addition of a timing recovery loop as part of the receiver processing is a relatively straightforward task and is well understood [
To demonstrate the impact of per subcarrier fractionally spaced equalizers on resolving the problem of timing drift, we consider a CMT/SMT transceiver system which we simulate following the schematic diagram presented in Figure
An FBMC transceiver with timing drift and the corresponding compensator block.
For the purpose of demonstration here, we consider the case where channel is absent. In that case, the effect of using a pair of DAC and ADC with different clock rates is like resampling the generated waveform with a resampling ratio
SIR variation as a function of symbol index (equivalently, timing drift) in a CMT transceiver.
Another possible solution that may be adopted to resolve the difference between the DAC clock at the transmitter and ADC clock at the receiver may be proposed by taking note of the following observation. An FBMC waveform (being CMT, SMT, or FMT) is a cyclostationary signal whose statistics are repeated every
In [
Massive MIMO, in essence, is a multiuser technique, somewhat similar to code division multiple access (CDMA). In its simplest form, each mobile terminal (MT) has a single antenna, but the base station (BS) has a large number of antennas. The spreading code for each user is then the vector of channel gains between the respective MT antenna and the multiple antennas at the BS. Accordingly, by increasing the number of antennas at the BS, the processing gain of each user can be increased to an arbitrarily large value. In the pioneering work of Marzetta [
Motivated by Marzetta’s observations [
In a recent work [ The complexity of both transmitter and receiver will be reduced, since the underlying polyphase structures will be based on smaller size IFFT/FFT blocks. The system latency will be reduced. This is because the length and, thus, the corresponding group delay of the underlying prototype filter are reduced. The system sensitivity to CFO will be reduced. The PAPR of the transmit signal will be reduced.
The preliminary research results that are presented in [
This paper presented a tutorial review of the class of filter bank multicarrier (FBMC) communication systems, with emphasis on the recent results of the authors research laboratory. It was noted that by building FBMC systems based on well-designed prototype filters, the spectrum of each subcarrier can be contained within a limited bandwidth. This, in turn, allows transmission over noncontiguous bands, a property that makes FBMC an ideal choice for many applications, including the uplink of multiuser multicarrier networks and cognitive radios. It was also pointed out that FBMC systems can be adopted to doubly dispersive channels to achieve a performance far superior to that of OFDM. The polyphase structures that have been proposed for efficient implementation of FBMC systems were reviewed and their complexities were compared with that of a standard OFDM system. It was noted that the complexity of FBMC transmitters is close to (but less than) twice their OFDM counterpart, and the complexity of FBMC receivers is close to (but less than) three times that of their OFDM counterpart. However, it was also noted that, in some applications, for example, in the uplink of multiuser systems where synchronization cannot be made perfectly, hence, multiuser cancellation techniques should be applied, OFDM can be far more complex than FBMC. Moreover, it was noted that more research is needed to better understand the problems related to synchronization, equalization, and tracking of channel variations in FBMC systems. Possible application of FBMC in the emerging area of massive MIMO was also highlighted, and a number of advantages that FBMC offers in this application were identified.
The author declares that there is no conflict of interests regarding the publication of this paper.