# 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
An improved time domain CE method based on the principles of spectrum sensing adopted at transmitter and receiver is proposed in [101] in order to improve the performance and reduce noise for NC-OFDM systems. This proposed method outperforms the DFT based and the conventional LS CE methods. On the other hand, the greedy algorithms include matching pursuit (MP), orthogonal matching pursuit (OMP), stagewise orthogonal matching pursuit (StOMP), regularised orthogonal matching pursuit (ROMP), and compressive sampling matching pursuit (CoSaMP). Active research is carried out in the field of CS which finds many applications in mathematics and signal processing communities [106]. The application of CS techniques to sparse CE employs fewer pilot symbols to estimate the channel. Two main classes of algorithms are considered for CE based on CS in [107]: convex optimisers (linear programming) and greedy algorithms. The linear programming method is based on basic pursuit (BP) and gradient projection for sparse reconstruction (GPRSR), subspace pursuit (SP), and sparsity adaptive matching pursuit (SAMP) algorithms. For NC-OFDM systems, sparse CE techniques have been implemented using OMP and SAMP algorithms. In [108], CE based on CS is investigated where the subspace pursuit algorithm is deployed. The authors of [107] investigated CS based CE, where OMP, SAMP and modified adaptive matching pursuit (MAMP) algorithms are adopted to estimate the channel for NC-OFDM based transceivers. Results were obtained in terms of the MSE, where the MAMP, SAMP, and OMP show superior performance in descending order as compared to the LS method. Channel estimation is proposed for SC-FDMA communication systems in [109; 110; 111]. Three novel CE methods are proposed in [109] for estimating the channel fading coefficients of LTE based SC-FDMA systems over time-varying multipath channels. The estimators are named frequency domain LS (FDLS), frequency domain LMMSE (FDLMMSE) and FDLS estimator with constant windowing (FDLS/CWD). The proposed FDLS CE in this research work [109] is different from the conventional LS technique as it consists of three components that include: the FD real CIR on individual sub-carriers over a symbol duration, the inter-channel interference term and the noise term. The proposed FDLMMSE estimator takes into account the channel auto-covariance matrix, the initial FDLS CIR, as well as the transfer domain AWGN power. One significant feature which distinguishes the proposed FDLMMSE estimator from the conventional LMMSE scheme is the assumption that the receiver at any instance of time has an on-time correlation matrix. To enhance the CE performance in noise-dominant environment, the FDLS/CWD channel estimate is proposed by exploiting the correlation of the channel transfer function (CTF). In the CWD approach, a regular sliding window is adopted for smoothening the obtained FDLS channel estimates on sub-carriers. Results obtained demonstrate that the FDLMMSE estimator offers the best performance in terms of MSE, and the FDLS estimator offers the worst performance at low SNR values. The FDLS/CWD shows similar BER performance to FDLMMSE at low SNRs while exhibiting degradation in performance at high SNR values due to the effects of self-interference. Hence, the FDLMMSE channel estimator offers the best performance in both low and high SNR ranges. In [110], an improved CE based on DFT-LS is proposed in comparison to conventional LS and traditional DFT-LS methods. In the proposed improved DFT-LS estimator, conventional LS estimated values are improved upon by time-domain extraction of the CIR length through in and out estimation of the CP which is set to a particular threshold in order to eliminate the system generated noise. The proposed improved DFT-LS CE algorithms demonstrated superior BER performances in low SNR values. At higher SNR values, the proposed estimator performances deteriorate rapidly in proportion to the selection of the threshold value that is employed for the elimination of noise.