# 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  
Non-blind CE can either be data-aided (training-based) or decision directed CE, as depicted in Figure 12. In training-based CE, also known as pilot-assisted CE, training sequences called pilot symbols, which are known to the receiver, are transmitted along with the data symbols for efficient estimation of the channel [83; 84; 85]. If the density of the training symbols used is high, the system CE accuracy improves tremendously; however, the spectral efficiency of the system is decreased due to the introduction of overhead by the pilot symbols [83]. Several works have been reported in the literature to address the challenges of pilot-assisted CE schemes for various telecommunication techniques such as SISO-OFDM, NC-OFDM and MIMO-OFDM schemes. In [86], the performances of two time domain CE techniques named least square (LS) and minimum mean square error (MMSE) CE schemes are investigated for OFDM systems in a slow fading multipath channel. The basic LS and MMSE channel  
Figure 12: Classification of CE techniques. estimates as reported in [86] are modified and estimated through multipath fading channel assuming different number of taps. It is observed from results obtained in [86] that the MMSE CE scheme demonstrates superior performances over LS in terms of mean square error (MSE) and symbol error rate (SER) at various levels of signal-to-noise ratio (SNR). In [73], the performances of three CE schemes (LS, linear MMSE (LMMSE) and least mean square (LMS)) are investigated for SISO-OFDM based transceivers under two channel types: auto-regressive based fading channel and multi-path Rayleigh fading channel. In addition, [73] assumed different kinds of pilot arrangements while adopting \(M\)-ary quadrature amplitude modulation (\(M\)-QAM), where \(M\)=16, quadrature phase shift keying (QPSK), binary phase shift keying (BPSK) and differential QPSK (DQPSK) as the underlying modulation schemes. In [87], the challenges of pilot-aided CE in OFDM systems are addressed using time domain channel statistics on an additive white Gaussian noise (AWGN) channel. Channel estimation schemes such as LS, MMSE and DFT based CE were deployed in [87]. In addition, in [87], the autocorrelation matrix of the channel and the noise variance are obtained using noise suppressed channel impulse response where results are analysed in terms of MSE and SER. From the results obtained, the MMSE estimation scheme demonstrates the best performance in comparison to the LS and DFT based CE schemes, and the LS offered the worst performance. A comparison of two pilot-aided CE techniques is analysed in [88] for OFDM systems, where the performances of maximum likelihood estimator (MLS) and Bayesian MMSE estimator (BMMSEE) are investigated. The MLE does not require information of the SNR and channel statistics while the BMMSEE exploits prior information about the channel. This makes the MLE simpler to implement but the BMMSEE demonstrated a better accuracy at low SNR. However, it is concluded that, at higher and intermediate SNR, the performances of both schemes are comparable. The CP that is inserted into the conventional OFDM system offers enhanced robustness for combating the undesirable effects of multipath fading. OQAM is adopted in digital communication systems for maintaining the orthogonality of sub-carriers as they transmit their signals over the wireless fading channels. The inclusion of CP to OFDM systems using OQAM modulation (that is, CP-OQAM-OFDM) can be used to ensure quality signal reception at the receiver end. In [89], the performances of two estimators named weighted least squares (WLS) and pairs of pilots (PoP) are analysed for CP-OQAM-OFDM system, where corresponding Cram\(\acute{e}\)r-Rao bounds (CRB) are used for comparison. The proposed PoP channel estimator in [89] offers lower computational complexity at the receiver as compared to the transmitter. This estimator offered good and similar bit error rate (BER) CE performance in comparison with WLS estimator.