# An Overview of FIR Filter Design in Future Multicarrier Communication Systems
## 1 Introduction  
The rapid increase of mobile devices and the emergence of new technologies as well as services demand more efficient wireless cellular networks [1; 2; 3; 4]. The 5 th generation (5G) communication networks need to support abundant business scenarios, such as Internet of Vehicles [5; 6; 7], Internet of Things [8; 9; 10], virtual reality [11; 12], device-to-device communications [13; 14; 15; 16], and so forth. Therefore, plenty of important technologies are worth studying in future communication networks, for example, multicarrier modulation, massive multiple-input multiple-output (MIMO), millimeter wave, and so forth [1; 2; 3; 4]. Due to the critical role of the prototype filter played in multicarrier modulations, that is, it determines the system performance such as stopband attenuation, inter-symbol interference (ISI), inter-channel interference (ICI) and phase noise caused by high operating frequencies, herein various prototype filter design methods in multicarrier communication networks are summarized. It is known that cyclic-prefix orthogonal frequency division multiplexing (CP-OFDM) as the air interface of the 4 th generation (4G) communication networks is capable of avoiding ICI and ISI. The modulated and demodulated signals are respectively generated through inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT), thereby greatly reducing the system complexity and improving the signal transmission rate. OFDM has been used in conjunction with other technologies, for example, wavelet OFDM (WOFDM) [17; 18], orthogonal frequency division multipleaccess (OFDMA) [19; 20; 21], Alamouti coded OFDM (AC-OFDM) [22; 23; 24; 25], and MIMO-OFDM [26; 27; 28]. Although OFDM has been widely applied, it also has the following limitations: serious out-of-band leakage characteristic; strict synchronization and orthogonality among the subcarriers are needed; high peak to average power ratio (PAPR) resulting in non-linear distortion of the signal; sensitive to frequency offset, which has a significant impact on the system performance [29; 30]. The above situations drive the urgency to conceive an appropriate modulation scheme in future communication networks. Faced with the requirements of the ultra-low latency, high spectrum efficiency, high transmission rate and business diversity in the future networks, researchers and practitioners in related fields have exerted a tremendous fascination on a number of alternative single-carrier or multicarrier modulation techniques [31], including CP-Discrete Fourier Transform spread OFDM (CP-DFT-s-OFDM) [32], filter bank multicarrier (FBMC) [33; 34; 35; 36; 37; 38; 39], generalized frequency division multiplexing (GFDM) [40; 41], universal filtered multicarrier (UFMC) [42; 43; 44], and filtered-orthogonal frequency division multiplexing (F-OFDM) [45; 46; 47], and so forth. Apart from typical waveform design methods where waveform parameters are obtained manually, with the development of machine learning, waveform design methods with data-driven models have attracted increasing attention [48; 49]. These modulation waveforms have their own merits and drawbacks in 5G communication scenarios, respectively. The prototype filter determines the performance of a specific modulation waveform, thus the evaluation standard of prototype filter is primarily characterized by minimizing the stopband energy, minimizing the maximum stopband ripple, minimizing the total interference (ISI and ICI) [50; 51], and so forth. Digital filters are very important in digital communications and are generally divided into two categories--infinite impulse response (IIR) filter and finite impulse response (FIR) filter [52]. Based on the fact that only linear phase FIR filters are suitable for wireless communication systems [53], the FIR filter design has been the major research topic to realize prototype filters in the literature. There have already been a few representative survey works related to prototype filters.