 Research
 Open Access
FBMC receiver for multiuser asynchronous transmission on fragmented spectrum
 JeanBaptiste Doré^{1}Email author,
 Vincent Berg^{1},
 Nicolas Cassiau^{1} and
 Dimitri Kténas^{1}
https://doi.org/10.1186/16876180201441
© Doré et al.; licensee Springer. 2014
 Received: 30 November 2013
 Accepted: 13 March 2014
 Published: 28 March 2014
Abstract
Relaxed synchronization and access to fragmented spectrum are considered for future generations of wireless networks. Frequency division multiple access for filter bank multicarrier (FBMC) modulation provides promising performance without strict synchronization requirements contrary to conventional orthogonal frequency division multiplexing (OFDM). The architecture of a FBMC receiver suitable for this scenario is considered. Carrier frequency offset (CFO) compensation is combined with intercarrier interference (ICI) cancellation and performs well under very large frequency offsets. Channel estimation and interpolation had to be adapted and proved effective even for heavily fragmented spectrum usage. Channel equalization can sustain large delay spread. Because all the receiver baseband signal processing functionalities are proposed in the frequency domain, the overall architecture is suitable for multiuser asynchronous transmission on fragmented spectrum.
Keywords
 FBMC
 FDM
 FDMA
 Equalization
 Synchronization
 Channel estimation
 Asynchronous processing
 Multiuser
 Fragmented spectrum
 Carrier frequency offset
1 Introduction
The current generation of cellular physical layers such as used by Long Term Evolution (LTE) and LTE Advanced have been optimized to deliver highbandwidth pipes to wireless users but require strict synchronism and orthogonality between users within a single cell. The advent of the smart phone and the expected explosion of MachineType Communication (MTC) are posing new and unexpected challenges. Fast dormancy necessary for these types of equipment to save battery power has resulted in significant control signalling growth. Furthermore, as the availability of large amounts of contiguous spectrum is getting more and more difficult to guarantee, the aggregation of noncontiguous frequency bands has to be considered. Therefore relaxed synchronization and access to fragmented spectrum are key parameters for future generations of wireless networks [1]. This requirement of spectrum agility has encouraged the study of alternative multicarrier waveforms such as filter bank multicarrier (FBMC) to provide better adjacent channel leakage performance without compromising spectral efficiency [2]. frequency division multiple access (FDMA) has already been considered for FBMC and provides promising performance without strict synchronization [3] between users. However, efficient frequency domain FBMC receiver algorithms have to be considered to fully benefit from the scheme. A first attempt at a practical implementation in the frequency domain for FBMC has been proposed in [4]. Synchronization and channel estimation are also based on the use of a training sequence but performance is limited by intercarrier interference (ICI) in the presence of large carrier frequency offset (CFO). This paper presents an architecture of a FBMC receiver suitable for asynchronous multiuser FDMA with very relaxed synchronization constraints: timing synchronization, CFO compensation and channel equalization are addressed.
Correction of CFO has been largely documented for orthogonal frequency division multiplexing (OFDM) [5] and FBMC [6]. A coarse CFO compensation in the time domain is necessary prior to a phase tracking in the frequency domain in order to limit ICI. As a different level of frequency offset is associated with each user, these solutions require as many receivers as users and are not suitable for practical implementation. Alternative signal processing methods for CFO compensation in the frequency domain should be developed. Iterative ICI cancellation has been proposed through iterative inversion techniques [7] or turbo processing [8] but is extremely complex to implement. The authors of [9] proposed an interesting method in the context of an orthogonal frequency division multiple access (OFDMA) uplink network. This method compensates CFO after fast Fourier transform (FFT) using a circular convolution. A good tradeoff between performance and complexity is demonstrated. A low complexity CFO compensation method for FBMC  FDMA based on this method has been investigated in this paper.
Channel estimation is a necessary process before demodulation as the radio channel is frequency selective. For multicarrier modulation systems, the estimation is usually performed by sending a training data sequence, called pilot tones, on a set of carriers known to the receiver. The channel is then estimated at the pilot frequencies using the classical least squares (LS) or minimum meansquare error (MMSE) estimators [10]. When pilot tones are not available on every carrier, a process of interpolation is required to recover the complete channel response [11]. The interpolation may be done in the time domain [12]. A timedomain channel impulse response is obtained using an inverse Fourier transform of the channel estimated at the pilot frequencies. A filter may then be applied to reduce noise effects and border effects. An interpolated frequency domain channel is then processed by Fourier transform. Another solution may be to interpolate the channel in the frequency domain. Many algorithms, such as linear interpolation, lowpass filtering and spline cubic interpolation have been proposed [13, 14]. For most interpolation schemes, the channel is poorly interpolated on the carrier located on the edges of the frequency band. This effect may be neglected when the number of carriers per contiguous frequency band is large but may lead to significant performance degradation of the overall system when the multicarrier modulation is applied to a fragmented spectrum. A robust interpolation scheme for the complete spectrum, including the edges is therefore critical. A solution has already been proposed in [12] using interpolation in the time domain. Performance is increased at the price of higher complexity. Furthermore, instability issues are not addressed and may lead to noise enhancement. A stable and robust scheme based on interpolation filters in the frequency domain is proposed in this paper.
Conventional equalization techniques for FBMC are suitable for multiuser reception. Good spectral containment introduced by the matched filter of the receiver helps to avoid distortion from nonsynchronous users. Channel equalization may therefore be independently processed per user. However, if the conventional polyphase network FBMC implementation is employed, then equalization has to be carried out in the time domain. To cope with this issue, frequencyspreading FBMC is considered [15]: at the cost of a significantly larger FFT (the size of the FFT is multiplied by the overlapping ratio), equalization may be efficiently done using a onetap complex coefficient per subcarrier. A highperformance equalization scheme is described in this paper. Performance of the receiver is evaluated and discussed.
The paper is organized as follows: In Section 2, the overall context for a multiuser asynchronous environment is presented and the benefits FBMC waveforms have in this context are developped. Then in Section 3, the complete architecture of a FBMC receiver adapted to these scenarios is described and performance results are given. In Section 4, the main features and results are summarized and some perspectives are provided.
2 Asynchronous multiuser context
2.1 FBMC
Singlecarrier (SC) FDMA has been chosen for the LTE to provide radio resource access for mobile users to the base station. This uplink multiuser access technique provides flexible resource allocation and is spectrally efficient. However, frequency offset between users should be strictly contained and received data signal should be aligned. If these synchronization requirements are not fulfilled, the orthogonality condition is not respected: intercarrier and intersymbol interference dramatically deteriorate performance. In order to guarantee mobility, the base station constantly monitors the time of arrival of received transmission signals. Signaling is sent to the mobile user via the downlink channel in order to synchronize this time of arrival at the base station. This constant exchange of control information introduces an overhead on the network that could be significant for asynchronous data communication services such as web access or machinetomachine communications.
where ${G}_{P}\left(0\mathrm{..}3\right)=\left[1,\phantom{\rule{2.22144pt}{0ex}}0.97195983,\phantom{\rule{2.22144pt}{0ex}}\frac{1}{\sqrt{2}},\phantom{\rule{2.22144pt}{0ex}}1{G}_{P}{\left(1\right)}^{2}\right]$ for an overlapping factor of K=4 and N is the number of carriers. In the following sections, the term carrier will refer to one of these N carriers and the term subcarrier will refer to one of the KN frequency domain FFT outputs at the receiver (see Section 3.1). The larger the overlapping factor K, the more localized the signal will be in frequency. In filter bankbased systems, transmit pulses are localized in time and in frequency. The orthogonality between carriers is maintained by introducing half a symbol period delay between the inphase and the quadrature components of every complex symbol. The welladjusted frequency localization of the prototype filter guarantees that only adjacent carriers interfere with each other. This justifies the use of FBMC waveforms in a nonsynchronous context and particularly for the fragmented scenario. Nevertheless, adjacent carriers significantly overlap with this kind of filtering. In order to keep adjacent carriers orthogonal, real and pure imaginary values alternate on successive carrier frequencies and on successive transmitted symbols for a given carrier at the transmitter side. In order to maximize spectral efficiency of the offset QAM (OQAM) modulation, the symbol period T is halved.
FBMCFDMA access schemes appear therefore to be a very promising flexible multicarrier waveform. Efficient implementations of the FBMCFDMA receivers should thus be considered in such multiuser asynchronous environments. A solution for this context is investigated in this paper.
2.2 Proposed burst structure
2.3 Notations
Bold letters denote vectors and matrices. Uppercase and lowercase letters denote frequency domain and time domain variables, respectively. The following notations are used:

(.)^{ t } Transpose

(.)^{ H } Hermitian transform

E[. ] Expectation operator

t r[. ] Trace operator

. lnorm
where ${w}_{N}={e}^{\phantom{\rule{0.3em}{0ex}}j\frac{2\mathit{\pi}}{N}}$. Matlab notation was used to index the matrix. Therefore, A=B(:,1:U) means that A is built with the first U columns and all the rows of B.
3 Receiver architecture
3.1 Overview
The detection of a start of burst is then achieved on the frequency domain (i.e. at the output of the FFT) using a priori information from the preamble. CFO is first estimated using the pilot subcarrier information of the preamble by computing the phase of the product between two consecutive FBMC symbols at the location of the pilot subcarriers. The propagation channel is assumed static for the duration of the burst. As described in [17], when large CFO correction is required, a first step in the estimation process consists of scanning the subcarriers around the pilot subcarrier locations to determine the subcarrier with the highest energy. A tracking algorithm of the CFO may complete the synchronization process when the duration of the burst is large and the accuracy of the preamblebased detection algorithm does not meet the required level [18]. CFO compensation is then performed in the frequency domain using a feedforward approach.
The channel coefficients may be estimated on the pilot subcarriers of the preamble. Authors of [6, 19] have already considered a similar approach by introducing a phase term to correct the CFO. In Section 3.2, this technique is completed by an efficient algorithm that compensates intercarrier interference. The channel is then estimated on the pilot subcarriers before being interpolated on every active subcarrier. The use of a KNpoint FFT makes the interpolation particularly specific to this receiver and a description of the proposed algorithm is detailed in Section 3.3.
Once the channel is estimated on all the active subcarriers, a onetap per subcarrier equalizer is applied before filtering by the FBMC prototype filter (Section 3.4). Demapping and loglikelihood ratio (LLR) computation complete the inner receiver architecture. A softinput forward error correction (FEC) decoder recovers finally the original message.
The asynchronous frequency domain processing of the receiver combined with the high stopband attenuation of the FBMC prototype filter provides a receiver architecture that allows for multiuser asynchronous reception. FFT and Memory Unit are common modules, while the remaining of the receiver should be duplicated as many times as the number of parallel asynchronous users the system may tolerate.
3.2 Carrier frequency offset compensation
3.2.1 Problem formulation
$q\in \mathbb{Z}$ and $\epsilon \in \mathbb{R}$ with ε∈[−1/(2K);1/(2K)]. Regardless of the integer part, q, ICI is only present when ε≠0. Assuming q is known, the required range of detection for δ may be very small. For instance, in the case of FBMC with a prototype filter of duration K=4, the maximum level of ICI is introduced when ε=12.5%.
3.2.2 Proposed correction scheme
As described in the previous section, CFO may be decomposed into integer and fractional parts. The integer part is easily corrected by a shift of q subcarriers at the output of the KNpoint FFT. The phase term should then be compensated by a phase correction factor. A simple and efficient way to reduce ICI introduced by the factional part of the CFO, ε, may be achieved by complex filtering of the received sequence. In order to derive the complex coefficients of filter W that mitigates ICI, two criteria are considered:

Zeroforcing criterion (): using Equation 5, and omitting the phase term, which has been corrected, we define W such as:$\mathbf{WC}=\mathbf{I}$(9)

By substituting C with the expression in (6), (9) may be rewritten as${\mathbf{WFdF}}^{H}=\mathbf{I}$(10)

As F F^{ H }=F^{ H }F=I and d d^{ H }=I, the filter W may be derived by$\mathbf{W}={\mathbf{Fd}}^{H}{\mathbf{F}}^{H}$(11)

Minimum mean square error criterion (): the filter may also be optimized to minimize the mean square error (MSE), taking the noise level at the receiver into account:${\mathbf{W}}_{\mathbf{\text{est}}}={argmin}_{\mathbf{W}}{\left\left\mathbf{W}{\widehat{\mathbf{R}}}_{\mathbf{m}}{\mathbf{R}}_{\mathbf{m}}\right\right}^{2}$(12)

By taking the derivative of the expectation of the trace, the minimization problem becomes:$\begin{array}{c}\frac{\partial}{\partial \mathbf{W}}E\left[\text{tr}\left({\mathbf{\text{WCR}}}_{\mathbf{m}}{{\mathbf{R}}_{\mathbf{m}}}^{H}{\mathbf{C}}^{H}{\mathbf{W}}^{H}+{\mathbf{\text{WZ}}}_{m}{{\mathbf{Z}}_{\mathbf{m}}}^{H}{\mathbf{W}}^{H}\right.\right.\\ \phantom{\rule{2em}{0ex}}\phantom{\rule{3em}{0ex}}\left.\left.{\mathbf{\text{WCR}}}_{\mathbf{m}}{{\mathbf{R}}_{\mathbf{m}}}^{H}{\mathbf{R}}_{\mathbf{m}}{{\mathbf{R}}_{\mathbf{m}}}^{H}{\mathbf{C}}^{H}{\mathbf{W}}^{H}\right)\right]=0\end{array}$(13)

In the presence of the additive white Gaussian noise (AWGN), $E\left[{\mathbf{Z}}_{\mathbf{m}}{{\mathbf{Z}}_{\mathbf{m}}}^{H}\right]={\sigma}_{n}^{2}\mathbf{I}$ and if Ω_{ R } is defined by E[R_{ m }R_{ m }^{ H }]=Ω_{ R }, (13) becomes$\mathbf{C}{\mathbf{\Omega}}_{\mathbf{R}}{\mathbf{C}}^{H}{\mathbf{W}}^{H}+{\sigma}_{n}^{2}{\mathbf{W}}^{H}\mathbf{C}{\mathbf{\Omega}}_{\mathbf{R}}=0$(14)

When ${\mathbf{\Omega}}_{\mathbf{R}}={\sigma}_{R}^{2}\mathbf{I}$, the solution is straightforward, and can be expressed by:$\mathbf{W}=\frac{{\sigma}_{R}^{2}}{{\sigma}_{R}^{2}+{\sigma}_{n}^{2}}\mathbf{F}{\mathbf{d}}^{H}{\mathbf{F}}^{H}$(15)
For both cases, the matrix W is Toeplitz and is therefore characterized by only KN complex coefficients. In general, Ω_{ R } is not a diagonal matrix but rather a band diagonal matrix and depends on the considered FBMC prototype filter. A closedform expression of W may be obtained if and only if Ω_{ R } is invertible. However, W may be derived by a nonlinear optimization process or by a using a pseudoinverse based for instance on singular value decomposition.
3.2.3 Performance and practical implementation of the CFO correction algorithm
RMSE is a measure of the signal to interference level as seen on the constellation. In the example, a QPSK modulation has been considered and RMSE decreases as Q becomes larger.
When Q=0, the algorithm only performs phase correction. The benefit of ICI mitigation is clearly demonstrated. Parameter Q could be chosen as a function of the system signaltonoise ratio (SNR) so as to limit the system by thermal noise but not by interference.
In case of Q=3 and P=4, 28 complex coefficients must be stored. A correction range of [−15%;15%] is then possible. As an example, a CFO of 11.7% is corrected by setting MUX0 =1, MUX1 =1, MUX2 =0 and MUX3 =1. The effective CFO corrected is 1%+2%+8%=11%.
A technique to mitigate ICI generated by CFO has been introduced in this section. All the operations have been carried out in the frequency domain and the scheme has given satisfactory performance results while being adapted for implementation.
3.3 Channel estimation and interpolation
Another important function that should be performed in the frequency domain is to recover the channel coefficients on each active subcarrier. This operation is achieved after the channel coefficients have been estimated on the pilot subcarrier location.
3.3.1 Problem formulation
One of the main advantages of multicarrier modulation techniques over singlecarrier modulation is a greatly simplified equalization process. In the case of OFDM, as long as the duration of the channel impulse response is shorter than the guard interval and the channel is constant over the duration of the OFDM symbol, a frequencyselective wideband channel converts to a number of subcarrier channel with flat fading. For FBMC, Hirosaki [20] showed that this property may be preserved if the equalizer at each subcarrier channel is fractionally spaced.
where diag(H) is a N_{ H }×N_{ H } diagonal matrix of the channel frequency response, X the N_{ H }×1 vector of symbols to transmit and Z the N_{ H }×1 vector of additive white Gaussian noise. N_{ H } is the number of active subcarriers.
In this example, the power distribution of matrix W coefficients is mainly located around the diagonal. It should be noted that the coefficients located at the center of the matrix have very similar values. On the contrary, at the edges of the matrix, the coefficients are significantly different. This property has been exploited to construct a new optimization criterion. The criterion imposes complexity constraints on matrix W coefficients as a function of their location within the matrix.
From a practical point of view, implementing a complex filter with a large set of complex coefficients may be extremely costly. The overall complexity should often be kept under control in order to fit implementation area constraints. The following constraints have thus been added to the minimization problem:

W is a matrix with real Q coefficients per row instead of complex N_{ p } coefficients per row

The pilot carrier distribution follows a regular pattern, i.e. the sampling of the channel is uniform^{a}

At least Q pilots are active per set of contiguous subcarriers
where W_{ l } is the N_{ l }×Q matrix representing the left subfilter block, W_{ m } is the N_{ m }×Q matrix representing the middle subfilter block and W_{ r } is the N_{ r }×Q matrix representing the right subfilter block.
The minimization problem of (27) may then be decomposed into three constraint minimization problems function of the three subfilter blocks W_{ l }, W_{ m } and W_{ r }. Further constraints on the coefficients may be added on the minimization algorithm to guarantee stability. This optimization process may be computationally demanding but allows for a control of the complexity of the implemented interpolation process.
By applying (27) into (30), the minimization may be realized considering an a priori knowledge of the autocorrelation matrix of the time domain channel impulse response. By applying this constraint, the level of implementation complexity may be traded off against the target performance of the channel estimation module.
The optimization process is not necessarily implemented on the real time system. A stable and efficient interpolation scheme adapted to the channel conditions is provided while complexity is kept under control.
3.3.2 Application to the proposed preamble structure
The estimation of the channel coefficients is performed before applying the FBMC prototype filtering. The LS estimates of the channel coefficients are computed by applying a CFO phase correction on the received signal according to the location of the pilot symbol on the prototype filter. Performance may be further improved by considering all the positions of the prototype filter and by applying a maximum ratio combining algorithm after interpolation.
3.3.3 Performance results
The following parameters have been taken for a numerical evaluation:

K=4

D=4

N=1,024
Filters have been first optimized for Q=10, a channel duration of 64 samples and a SNR of 15 dB. The performance is estimated using a Monte Carlo simulation based on the draw of 1,000 randomly generated channels with rectangular time profiles.
The RMSE is below the noise level for the three filter blocks. However, only a marginal gain is achieved for the right filter block. This is explained by the pattern considered in the pilot scheme; on the right edge, K D+K−1 channel coefficients have to be interpolated while no pilot subcarriers are located at the edge.
The proposed method gives a performance improvement of up to 7 dB on the RMSE of the estimated channel. Interpolation errors at the edge of the fragment dominate the RMSE. For large frequency fragment the gain becomes negligible. Performance improvement is mainly due to the small number of pilot subcarriers located in the frequency fragment making the proposed approach particularly adapted to multiuser asynchronous fragmented spectrum usage.
3.4 Inner receiver architecture
3.4.1 Proposed architecture
When the channel is short, the power is located on the diagonal term validating the proposed assumption. When the channel is longer, power spreads over the diagonal term of the matrix, and as a result, performance of the onetap equalizer starts showing its limitations.
where ${\sigma}_{X}^{2}\left(k\right)$ is the expectation of the power of X on subcarrier k and ${\sigma}_{Z}^{2}$ is the expectation of the power of Z on subcarrier k. For the following, noise power is assumed to be constant over all the subcarriers.
Further, complexity simplification of (42) may be considered with negligible performance loss such as the techniques described in [21].
3.4.2 Simulations results
Simulated system parameters
Parameter  Value 

Prototype filter  
K  4 
G  $\{0.235147,\sqrt{2}/2,0.97196,1$ 
$0.97196,\sqrt{2}/2,0.235147,0\}$  
Modulation  
N  1,024 
F _{ e }  15.36 MHz 
Active carriers  601 (9 MHz) 
Type  QPSK 
FEC  
Type  CC 1/2, k=7 
N _{FEC}  1,944 bits 
R  2/3 
Decoding algorithm  SOVA 
Channel estimation  
Q  8 
The MSE on the constellation depends on the timing offset. The worstcase MSE is found when k is equal to N /4; in this case, the receiver is affected the most by the interference from the previous or next multicarrier symbols. The best case comes as expected when the FFT is perfectly aligned, i.e. timing offset is close to p×N/2 ∀p. This confirms that the proposed frequency domain equalizer scheme combined with channel estimation does not require FFT synchronization and is therefore adapted to asynchronous multiuser reception.
The performance obtained with the interpolation filter optimized for a channel delay spread length of N / (4F_{ e }) time domain samples is of particular interest as it demonstrated the limitations of the proposed scheme. When the delay spread of the channel is greater than 0.15×N/F_{ e }, performance is limited by the proposed equalization scheme rather than the channel estimation processing as the onetap equalizer becomes inefficient. On the other hand, for channel delay spread below 0.15×N/F_{ e }, onetap equalization is sufficient and channel estimation performs beyond requirement when an appropriate interpolation filter is considered. These results compare with the performance of an OFDM receiver with a guard interval length of at least 1/8×N. In Figure 19, the guard interval length for an equivalent OFDM system with a FFT size of N is given. Performance of the receiver may be further improved by considering multitap equalization.
The choice of the interpolation filter also impacted on performance. When a filter optimized for a channel exhibiting a large delay spread is applied to a channel with a short delay spread, a significant amount of noise is not filtered. Performance is then better if the interpolation filter is adapted to the actual channel delay spread.
The proposed frequency domain receiver architecture seems very attractive for asynchronous multiuser processing. Fair performance has been obtained by the proposed equalizer scheme; the receiver is robust for large delay spread environment. As a comparison, the normal LTE guard interval is set to 4.69A μs or approximately 1/14×N.
4 Conclusion
This paper presented a novel architecture and algorithms for FBMC reception. All the baseband signal processing functions are implemented in the frequency domain and no strict synchronization requirement on the FFT, the first element of the receiver, is required. This asynchronous frequency domain processing of the receiver combined with the high stopband attenuation of the FBMC prototype filter provides a receiver architecture that allows for multiuser asynchronous reception.
Particular attention has been paid to CFO compensation in order to relax synchronism requirements beyond one carrier spacing. An algorithm to mitigate ICI has been proposed and simulated. The performance of a practical reduced complexity implementation is simulated. Depending on the receiver target SNR, complexity may be traded off to keep RMSE introduced by CFO below thermal noise. Channel interpolation has also been carefully considered. As multiuser asynchronous FDMA generates heavily fragmented spectrum blocks, channel estimation should be optimized for the edges of the receiver active carrier bands. A performance improvement of up to 7 dB on the RMSE of the estimated channel may result on some simulated scenarios. Finally, a new equalizer scheme has been thoroughly presented. Its complexity is contained while good performance for channel exhibiting large delay spread is achieved. As a comparison, using the 10MHz LTE parameters, the receiver performs well for channels with delay spread of up to 8.3 μs. This compares with standard LTE that has been designed for channels with delay spread of up to 4.7 μs. Moreover, we have demonstrated that the proposed equalizer does not require FFT synchronization and is therefore adapted to asynchronous multiuser reception.
Further work should consider implementation performance and complexity estimation with a comparison to similar flexible systems using traditional OFDM techniques. Eventual cost overhead of FBMC implementation and finite precision effects in this context would further complete the study. At the system level, radio resource simulations are necessary to understand the benefits of the multiuser asynchronous approach. Its potential gains in system capacity and energy consumption compared to already existing solutions could be evaluated.
Endnotes
^{a} The proposed method also applies to nonuniform sampling, but the problem is more complex to formulate.
^{b} Channel delay spread is the time delay between the arrival of the first received signal component and the last received signal component associated with a single transmitted pulse.
Declarations
Acknowledgements
The research leading to these results has received funding from the European Commission’s seventh framework program FP7 ICT Call8 under grant agreement 318555 also referred to as 5GNOW.
Authors’ Affiliations
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