# Review of Channel Estimation for Candidate Waveforms of Next Generation Networks
## 3 Fundamentals of Channel Estimation
### Classification of Channel Estimation Schemes
#### 3.1.1 Overview of Pilot Based (Non-Blind) CE
The performances of channel estimators such as LS, FIR, Gauss-Markov (GM), LMMSE and NLMS are analysed in [111] for SC-FDMA systems at three different user speeds of 3 km/h, 50 km/h and 120 km/h. Results obtained in terms of SER demonstrate that all compared CE schemes exhibit similar performances, although the LMMSE estimation scheme offers the best CE performance for SC-FDMA multiplexing schemes at low SNR ranges under very low user speed (3 km/h) conditions. The GM algorithm offers the best CE performance at high SNR values under same conditions. Similarly, at medium user speed (50 km/h), the LMMSE estimator offers the best CE performance at low SNR ranges while GFDM estimator performs best under high SNR conditions. In both low and high SNR conditions, LMMSE CE demonstrates the best performance as compared to all the estimators under very high speed conditions (120 km/h). BFDM is a waveform under potential consideration for next-generation networks which employs well-localised pulse shapes at both transmitter and receiver [37]. The applied transmitter and receiver localised pulse shapes are designed to be bi-orthogonal to each other where the high quality frequency localisation of transmit pulses offer extra robustness against Doppler effects (frequency dispersion). The good time localisation of the pulses gives extra robustness to this multicarrier system against the effects of multipath fading (time dispersion) using OQAM technique. CE for BFDM-OQAM transceivers is still an open research area. In fact, to the best of our knowledge, the only research work documented to analyse the performance of CE schemes for BFDM-OQAM is in [112]. In [112], a low complexity ML based channel estimator is proposed for BFDM-OQAM systems in dispersive time-varying channels which uses the correlation matrix of channel parameters for CE. The performance analysis of the proposed ML-based CE as reported in [112] demonstrates that the estimator offers appreciable robustness against frequency dispersion of channels. UFMC is a novel waveform that combines the simplicity features of CP-OFDM systems in addition to the robustness of FBMC systems. Due to the familiarity of these systems (UFMC) with conventional OFDM systems, UFMC is also known as universal filtered OFDM (UF-OFDM) [113]. CE is also not well researched for UFMC systems in the literature. The authors of [113] studied and analysed the performance of CE in UFMC based systems. In this study, the procedure and performance of pilot-aided CE are investigated for UFMC systems where it is revealed that training based CE and pilot structure is applicable to UFMC systems by pre-compensation of the FIR filter at the transmitter. In the investigated CE method, raw channel estimates are obtained at pilot locations using LS and LMMSE schemes where the obtained estimates are subsequently improved using the sliding window (SW) approach. In the SW approach, the variance of the noise signal is significantly reduced in proportion to the SW size. The performances of the investigated CE schemes are analysed using three kinds of communication channels which include AWGN channel, frequency-flat fading channel (with user travelling at 50 km/h) and frequency-selective fading vehicular-A channel. Simulation results obtained show that the UFMC system achieves the same or slightly better SER performance in comparison to LTE based CP-OFDM systems under all considered channel conditions using SW algorithm.