SCIENCE CHINA Information Sciences, Volume 62, Issue 8: 080301(2019) https://doi.org/10.1007/s11432-018-9808-5

## Fast-convolution multicarrier based frequency division multiple access

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• ReceivedDec 5, 2018
• AcceptedMar 1, 2019
• PublishedJul 11, 2019
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### Abstract

Fast-convolution multicarrier (FCMC), the asynchronous waveform with ultra-low sidelobe, has appeared to be a promising waveform technique for future wireless communications. In this paper, we investigate the filter bank optimization as well as receiver design including low-complexity channel estimator and equalizer for FCMC based frequency division multiple access (FDMA). Starting from the conventional multi-carrier signals, we first derive a vectorized signal model as a framework to systematically design the FCMC transceiver. For nearly perfect reconstruction (NPR) filter banks design, an optimization criterion which consists of minimizing received signal segments' mean square error (MSE) is proposed. From the fact that Toeplitz matrices can be asymptotically diagonalized by discrete Fourier transform (DFT) matrix, the channel equalizer can be simplified to one-tap frequency domain equalizer when DFT size is large enough. The minimum mean square error (MMSE) criterion is then applied to calculate the coefficients of one-tap frequency domain equalizer. In practice, due to the channel fading, the channel estimation has to be performed to obtain the channel state information (CSI) which is required by the channel equalization. To this end, we propose a combined cyclic prefix (CP) and cyclic suffix (CS) pilot structure which facilitates to estimate the frequency domain CSI directly in the receiver end. The proposed FCMC based FDMA features low-complexity receiver, adjustable users' bandwidth and low peak-to-average power ratio. Simulation results confirm the performance of the proposed scheme.

### Acknowledgment

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61320106003, 61761136016, 61631018), Natural Science Foundation of Jiangsu Province (Grant No. BK20170688), National Science and Technology Major Project of China (Grant No. 2017ZX03001002-004), and Civil Aerospace Technologies Research Project (Grant No. D010109).

### References

[1] Ji X, Huang K, Jin L. Overview of 5G security technology. Sci China Inf Sci, 2018, 61: 081301 CrossRef Google Scholar

[2] Li L, Wang D, Niu X. mmWave communications for 5G: implementation challenges and advances. Sci China Inf Sci, 2018, 61: 021301 CrossRef Google Scholar

[3] Wunder G, Jung P, Kasparick M. 5GNOW: non-orthogonal, asynchronous waveforms for future mobile applications. IEEE Commun Mag, 2014, 52: 97-105 CrossRef Google Scholar

[4] Gupta A, Jha R K. A Survey of 5G Network: Architecture and Emerging Technologies. IEEE Access, 2015, 3: 1206-1232 CrossRef Google Scholar

[5] Ma Z, Zhang Z Q, Ding Z G, et al. Key techniques for 5G wireless communications: network architecture, physical layer, and MAC layer perspectives. Sci China Inf Sci, 2015, 58: 041301. Google Scholar

[6] Bellanger M, Ruyet D Le, Roviras D, et al. FBMC physical layer: a primer. PHYDYAS FP7 Project Document. 2010. Google Scholar

[7] Jiang T, Chen D, Ni C X, et al. OQAM/FBMC for future wireless communications: principles, technologies and applications. Pittsburgh: Academic Press, 2017. 25--38. Google Scholar

[8] Kong D J, Xia X G, Jiang T. An Alamouti coded CP-FBMC-MIMO system with two transmit antennas. Sci China Inf Sci, 2015, 58: 102306. Google Scholar

[9] Michailow N, Matthe M, Gaspar I S. Generalized Frequency Division Multiplexing for 5th Generation Cellular Networks. IEEE Trans Commun, 2014, 62: 3045-3061 CrossRef Google Scholar

[10] Zhang X, Jia M, Chen L, et al. Filtered-OFDM - enabler for flexible waveform in the 5th generation cellular networks. In: Proceedings of 2015 IEEE Global Communications Conference, San Diego, 2015. 1--6. Google Scholar

[11] Vakilian V, Wild T, Schaich F, et al. Universal-filtered multi-carrier technique for wireless systems beyond LTE In: Proceedings of 2013 IEEE Globecom Workshops, Atlanta, 2013. 223--228. Google Scholar

[12] Sahin A, Guvenc I, Arslan H. A Survey on Multicarrier Communications: Prototype Filters, Lattice Structures, and Implementation Aspects. IEEE Commun Surv Tutorials, 2014, 16: 1312-1338 CrossRef Google Scholar

[13] Boucheret M L, Mortensen I, Favaro H. Fast convolution filter banks for satellite payloads with on-board processing. IEEE J Sel Areas Commun, 1999, 17: 238-248 CrossRef Google Scholar

[14] Borgerding M. Turning overlap-save into a multiband mixing, downsampling filter bank. IEEE Signal Process Mag, 2006, 23: 158-161 CrossRef ADS Google Scholar

[15] Renfors M, Harris F. Highly adjustable multirate digital filters based on fast convolution. In: Proceedings of 2011 20th European Conference on Circuit Theory and Design, Linkoping, 2011. 9--12. Google Scholar

[16] Renfors M, Yli-Kaakinen J, Harris F J. Analysis and Design of Efficient and Flexible Fast-Convolution Based Multirate Filter Banks. IEEE Trans Signal Process, 2014, 62: 3768-3783 CrossRef ADS Google Scholar

[17] Shao K, Alhava J, Yli-Kaakinen J, et al. Fast-convolution implementation of filter bank multicarrier waveform processing. In: Proceedings of 2015 IEEE International Symposium on Circuits and Systems, Lisbon, 2015. 978--981. Google Scholar

[18] Renfors M, Yli-Kaakinen J, Levanen T, et al. Fast-convolution filtered OFDM waveforms with adjustable CP length. In: Proceedings of 2016 IEEE Global Conference on Signal and Information Processing, Washington, 2016. 635--639. Google Scholar

[19] Yli-Kaakinen J, Levanen T, Valkonen S. Efficient Fast-Convolution-Based Waveform Processing for 5G Physical Layer. IEEE J Sel Areas Commun, 2017, 35: 1309-1326 CrossRef Google Scholar

[20] Yli-Kaakinen J, Renfors M. Flexible fast-convolution implementation of single-carrier waveform processing for 5G In: Proceedings of 2015 IEEE International Conference on Communication Workshop, London, 2015. 1269--1274. Google Scholar

[21] Chen D, Qu D M, Jiang T. Novel prototype filter design for FBMC based cognitive radio systems through direct optimization of filter coefficients. In: Proceedings of 2010 International Conference on Wireless Communications and Signal Processing, Suzhou, 2010. 1--6. Google Scholar

[22] Chen D, Qu D, Jiang T. Prototype Filter Optimization to Minimize Stopband Energy With NPR Constraint for Filter Bank Multicarrier Modulation Systems. IEEE Trans Signal Process, 2013, 61: 159-169 CrossRef ADS Google Scholar

[23] Tian Y, Chen D, Luo K, et al. Prototype filter design to minimize stopband energy with constraint on channel estimation performance for OQAM/FBMC systems. IEEE Trans Broadcast, 2018. doi: 10.1109/TBC.2018.2847453. Google Scholar

[24] Renfors M, Yli-Kaakinen J. Channel equalization in fast-convolution filter bank based receivers for professional mobile radio. In: Proceedings of the 20th European Wireless Conference, Barcelona, 2014. 1--5. Google Scholar

[25] Zhao J C, Wang W J, Gao X Q. Transceiver design for fast-convolution multicarrier systems in multipath fading channels. In: Proceedings of 2015 International Conference on Wireless Communications and Signal Processing, Nanjing, 2015. 1--5. Google Scholar

[26] Haykin S, van Veen B. Signals and Systems. New York: Wiley, 1999. Google Scholar

[27] Vaidyanathan P. Multirate Systems and Filter Banks. Upper Saddle River: Prentice-Hall, Inc., 1993. Google Scholar

[28] Yli-Kaakinen J, Renfors M. Optimized Reconfigurable Fast Convolution-Based Transmultiplexers for Flexible Radio Access. IEEE Trans Circuits Syst II, 2018, 65: 130-134 CrossRef Google Scholar

[29] Gray R. On the asymptotic eigenvalue distribution of Toeplitz matrices. IEEE Trans Inform Theor, 1972, 18: 725-730 CrossRef Google Scholar

• Figure 1

(Color online) Overlap-save processing on the transmitter side.

• Figure 2

(Color online) FCMC transceiver processing flow in uplink transmission

• Figure 3

(Color online) FCMC and DFTS-OFDM PSD comparison.

• Table 1   SCM simulation configurations
 Channel model Configurations Scenario Urban micro Velocity $5~\text{km/h}$ Carrier frequency $2~\text{GHz}$ Cell radius $500~\text{m}$
•

Algorithm 1 Proposed FC-FB optimization algorithm

Require:Subcarriers number of the $u$th subband: $N_{a,u}$; bandwidth of the $u$th subband: $M_{b,u}$; the allowed maximum error between optimized transmitted and received filter bank: $\epsilon$; ${\boldsymbol{\lambda}}_t^{(0)}$ and ${\boldsymbol{\lambda}}_r^{(0)}$ as RRC filters which satisfies subband bandwidth $M_{b,u}~$ and subcarrier number $N_{a,u}$ constraints.

Output:The optimized transmitted and received filter bank: ${\boldsymbol{\lambda}}$.

while $||{\boldsymbol{\lambda}}_t-{\boldsymbol{\lambda}}_r||_2>\epsilon$ do

Fix ${\boldsymbol{\lambda}}_t$, calculate $\boldsymbol{F}$ by (37).

Let ${\boldsymbol{F}}_r=[~\begin{matrix} \left({\rm~Re}({\boldsymbol{F}})\right)^{\rm~T}&\left({\rm~Im}({\boldsymbol{F}})\right)^{\rm~T} \end{matrix}~]^{\rm~T}$. Find SVD of ${\boldsymbol{F}}_r{\boldsymbol{F}}_r^{\rm~T}$, and the corresponding right singular vector of minimum positive eigenvalue is the optimized ${\boldsymbol{\lambda}}_r^{(i)}$ with fixed ${\boldsymbol{\lambda}}_t^{(i-1)}$.

Update ${\boldsymbol{\lambda}}_t$: ${\boldsymbol{\lambda}}_t^{(i)}=\beta{\boldsymbol{\lambda}}_t^{(i-1)}+(1-\beta){\boldsymbol{\lambda}}_r^{(i)}$.

end while

Set ${\boldsymbol{\lambda}}={\boldsymbol{\lambda}}_t^{(i)}$.

return ${\boldsymbol{\lambda}}$.

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