SCIENTIA SINICA Informationis, Volume 49, Issue 7: 886-899(2019) https://doi.org/10.1360/N112018-00015

## Design of SR-NYQ prototype filter in an FBMC system

• AcceptedJul 2, 2018
• PublishedApr 30, 2019
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### Abstract

As a candidate for next generation mobile communication, filter bank multicarrier (FBMC) has several advantages over orthogonal frequency division multiplexing (OFDM), such as larger side-lobe attenuation and no requirements of strict orthogonality and synchronization, in which the prototype filter for subcarrier shaping plays an important role. Currently, the commonly used prototype filters include the PHYDYAS filter and the IOTA filter, but in the corresponding design of both, there are few controllable parameters and the filters' flexibility is insufficient. Therefore, a constrained optimization method to directly design the FBMC filter is proposed herein. In this method, the error energy in the stopband is considered the optimization target, which is aimed at reducing the side-lobe leakage of the FBMC waveform. Furthermore, the constraints on the Nyquist (NYQ) condition are implemented in the frequency domain via approximation, through which the control of inter-symbol interference can be achieved. These NYQ constraints contain linear matrix inequalities and a linear inequality for the cut-off frequency point, which circumvent the nonconvex problem caused by the convolution calculation in original constraints. After solving the constrained optimization via semi-definite programming, the designed FIR filter with linear phase can effectively improve stopband attenuation characteristics when the NYQ condition is suitably relaxed, thus improving the frequency selectivity of the FBMC waveform. The bit error rate (BER) simulations indicate that the optimized filters have a certain superiority over the PHYDYAS and IOTA filters. In addition, using the proposed method, the designed filter with shorter length can also result in a BER comparable to that of the PHYDYAS filter, with a multiplication complexity is lower than that of the PHYDYAS filter.

### References

[1] You X H, Pan Z W, Gao X Q, et al. The 5G mobile communication: the development trends and its emerging key techniques. Sci Sin Inform, 2014, 44: 551--563. Google Scholar

[2] Dongming W, Yu Z, Hao W. An overview of transmission theory and techniques of large-scaleantenna systems for 5G wireless communications. Sci Sin inf Sci, 2016, 46: 3-21 CrossRef Google Scholar

[3] Ijaz A, Zhang L, Grau M, et al. Enabling massive IoT in 5G and beyond systems: PHY radio frame design considerations. IEEE Access, 2017, 4: 3322--3339. 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] Agiwal M, Roy A, Saxena N. Next generation 5G wireless networks: a comprehensive survey. IEEE Commun Surv Tut, 2017, 18: 1617--1655. Google Scholar

[6] Ding Z, Liu Y, Choi J. Application of Non-Orthogonal Multiple Access in LTE and 5G Networks. IEEE Commun Mag, 2017, 55: 185-191 CrossRef Google Scholar

[7] Yuan Y F, Zhu L M. Application scenarios and enabling technologies of 5G. China Commun, 2014, 11: 69--79. Google Scholar

[8] Wunder G, Kasparick M, Wild T, et al. 5GNOW: Intermediate frame structure and transceiver concepts. In: Processdings of Globecom Workshops, Austin, 2014. 565--570. Google Scholar

[9] Kasparick M, Wunder G, Chen Y, et al. 5G waveform candidate selection D3.1. 5GNOW, 2013. http://5gnow.eu/wp-content/uploads/2015/04/5GNOW_D3.1.pdf/. Google Scholar

[10] Farhang-Boroujeny B. OFDM Versus Filter Bank Multicarrier. IEEE Signal Process Mag, 2011, 28: 92-112 CrossRef ADS Google Scholar

[11] Nissel R, Rupp M. OFDM and FBMC-OQAM in Doubly-Selective Channels: Calculating the Bit Error Probability. IEEE Commun Lett, 2017, 21: 1297-1300 CrossRef Google Scholar

[12] Schaich F, Wild T, Chen Y. Waveform contenders for 5G-Suitability for short packet and low latency transmissions. In: Proceedings of Vehicular Technology Conference (VTC Spring), Seoul, 2014. 1--5. Google Scholar

[13] Aminijavaheri A, Farhang A, RezazadehReyhani A, et al. Impact of timing and frequency offsets on multicarrier waveform candidates for 5G. In: Proceedings of Signal Processing and Signal Processing Education Workshop, Salt Lake City, 2015. 178--183. Google Scholar

[14] Srinivasan S, Dikmese S, Renfors M. Spectrum sensing and spectrum utilization model for OFDM and FBMC based cognitive radios. In: Proceedings of Signal Processing Advances in Wireless Communications, Cesme, 2012. 139--143. Google Scholar

[15] Dikmese S, Srinivasan S, Shaat M, et al. Spectrum sensing and resource allocation for multicarrier cognitive radio systems under interference and power constraints. EURASIP J Adv Signal Process, 2014, 1: 68--80. Google Scholar

[16] Farhang-Boroujeny B. Filter bank multicarrier modulation: a waveform candidate for 5G and beyond. Adv Electr Eng, 2014, 2014: 482805. Google Scholar

[17] Sahin A, Guvenc I, Arslan H. A comparative study of FBMC prototype filters in doubly dispersive channels. In: Proceedings of Globecom Workshops, Anaheim, 2012. 197--203. Google Scholar

[18] 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

[19] Chen D, Qu D, Jiang T, et al. Prototype filter optimization to minimize stopband energy with NPR constraints for filter bank multicarrier modulation systems. IEEE Trans Signal Process, 2012, 61: 159--169. Google Scholar

[20] Aminjavaheri A, Farhang A, Doyle L, et al. Prototype filter design for FBMC in massive MIMO channels. In: Proceedings of International Conference on Communications, Paris, 2017. Google Scholar

[21] Viholainen A, Ihalainen T, Stitz T H, et al. Prototype filter design for filter bank based multicarrier transmission. In: Proceedings of European Signal Processing Conference, Glasgow, 2009. 1359--1363. Google Scholar

[22] Viholainen A, Bellanger M, Huchard M. Prototype filter and structure optimization. PHYDYAS, 2009. http://www.ict-phydyas.org/delivrables/PHYDYAS-D5-1.pdf. Google Scholar

[23] Farhang-Boroujeny B. A Square-Root Nyquist (M) Filter Design for Digital Communication Systems. IEEE Trans Signal Process, 2008, 56: 2127-2132 CrossRef ADS Google Scholar

[24] Mirabbasi S, Martin K. Overlapped complex-modulated transmultiplexer filters with simplified design and superior stopbands. IEEE Trans Circ Syst II: Analog and Digital Signal Processing, 2003, 8: 456--469. Google Scholar

[25] Datar A, Jain A, Sharma P C. Design and performance analysis of adjustable window functions based cosine modulated filter banks. Digital Signal Processing, 2013, 23: 412-417 CrossRef Google Scholar

[26] Harris F J. Multirate Signal Processing for Communication Systems. Prentice Hall PTR, 2004. Google Scholar

[27] Lai X, Lin Z. Optimal Design of Constrained FIR Filters Without Phase Response Specifications. IEEE Trans Signal Process, 2014, 62: 4532-4546 CrossRef ADS Google Scholar

[28] K S, Elias E. Prototype Filter Design Approaches for Near Perfect Reconstruction Cosine Modulated Filter Banks - A Review. J Sign Process Syst, 2015, 81: 183-195 CrossRef Google Scholar

[29] Hua J, Wen, J, Lu W, et al. Design and application of nearly Nyquist and SR-Nyquist FIR filter based on linear programming and spectrum factorization. In: Proceedings of Conference on Industrial Electronics and Applications, Hangzhou, 2014. 64--67. Google Scholar

• Table 1   The performances comparison of the optimized SR-NYQ filters with the PHYDYAS filter and the IOTA filter
 $\{M=64,K=4/3\}$ $N_p$ $R_p$ (dB) $A_s$ (dB) $E_s$ ${\rm~ISI}_t$ ${\rm~ISI}_f$ PHYDYAS 257 3.0103 39.8544 $1.3476\times10^{-6}$ $8.14\times10^{-4}$ $6.27\times10^{-4}$ IOTA 257 2.6807 13.8932 $5.6124\times10^{-4}$ $2.70\times10^{-3}$ $4.22\times10^{-2}$ ${\rm~{h1}_A}$ 257 3.0033 49.4834 $4.0514\times10^{-8}$ $8.00\times10^{-4}$ $7.89\times10^{-4}$ ${\rm~{h1}_B}$ 257 3.0429 55.7287 $9.8038\times10^{-9}$ $1.40\times10^{-2}$ $1.16\times10^{-2}$ ${\rm~{h1}_C}$ 193 2.9926 39.7521 $1.2428\times10^{-6}$ $8.10\times10^{-4}$ $8.06\times10^{-4}$
• Table 2   The parameters for the BER simulation of FBMC system
 Parameter Value Subcarrier spacing $\Delta~f$ $15$ kHz Number of subcarriers $64$ FFT size $64$ Number of used subcarriers $32$ Number of users $2$ Sampling rate $0.96$ MHz Modulation $4\text{-}$QAM Overlapping factor $K~\in~\{3,4\}$
• Table 3   The further BER comparison between the ${\rm~{h1}_B}$ and the PHYDYAS filter
 SNR (dB) 0 5 10 15 20 25 PHYDYAS 0.343 0.1755 0.0852 0.0516 0.0377 0.0277 ${\rm~{h1}_B}$ 0.3403 0.1702 0.0814 0.0483 0.0347 0.0243
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