In wireless communication, Orthogonal Frequency Division Multiplexing (OFDM) has been adopted due to its robustness to multipath fading and high data rate transmissions. At the other hand, the performance of OFDM systems severely degraded due to multi-path fading and Doppler frequency shifts in mobile systems, which causes inter-carrier-interference (ICI). Thus, Estimation of channel parameters is required at the receiver using a pre designed estimator where pilot tones are inserted in each OFDM symbol. In this paper, a random pilot data are generated and inserted in each OFDM symbol at equally spaced locations. The performance test of Least Square (LS) and Linear Minimum Mean Square (LMMSE) estimation methods are proposed with Discrete Fourier Transform (DFT) based on both LS and LMMSE, where different ITU channel models are considered in order to compare their performance for data transmission in high mobile systems with different Doppler frequencies exceeds 200 Hz and minimal number of pilots.

Compressive sensing (CS) is a new attractive technique adopted for linear time varying channel estimation. orthogonal frequency division multiplexing (OFDM) was proposed to be used in 4G and 5G which supports high data rate requirements. Different pilot aided channel estimation techniques were proposed to better track the channel conditions, which consumes bandwidth, thus, considerable data rate reduced. In order to estimate the channel with minimum number of pilots, compressive sensing CS was proposed to efficiently estimate the channel variations. In this paper, a novel delay dictionary-based CS was designed and simulated to estimate the linear time varying (LTV) channel. The proposed dictionary shows the suitability of estimating the channel impulse response (CIR) with low to moderate Doppler frequency shifts with acceptable bit error rate (BER) performance.

In this paper, channel overhead is reduced by exploiting channel sparsity for multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) system. Where, compressive sensing (CS) based dictionary design algorithms has been adopted as a channel estimation technique in high mobile systems with minimal number of pilots, such as high-speed train (HST) systems. A novel framework design of the dictionary-based CS was proposed considering both delay and Doppler effects in order to correctly recover the channel response. The channel under consideration is a 2 by 2 space-time block code (STBC) MIMO channel. Simulation tests according to the international telecommunication union (ITU) channel model demonstrated the suitability of the proposed dictionary for estimating the channel impulse response (CIR) of a liner time varying (LTV) channel with a mobility approaches 675 Km/h related to a Doppler frequency of 1500 Hz and 2.4 GHz carrier frequency. Two CS recovery algorithms were applied; orthogonal matching pursuit (OMP) and basis pursuit (BP), where by about 7 dB gain in signal to noise ratio (SNR) was achieved with mobility of 675 Km/h using OMP as compared to BP at a bit error rate (BER) of 10 −3 with 128 OFDM subcarriers.

Channel estimation is an essential part of Orthogonal Frequency Division Multiplexing (OFDM) communication systems. In this paper, two Discrete Fourier Transform (DFT) improvement algorithms are proposed and compared where the 1st one exploits channel sparsity concept while the other considers significant channel coefficients only. In the proposed algorithms; Enhanced and Sparse DFT (E-DFT and S-DFT), different number of significant channel components is selected either by a threshold determining procedure such as in    E-DFT, or through determining channel sparsity level such as in S-DFT. In the presence of Doppler frequency shifts, the Inter Symbol Interference (ISI) effect on channel coefficients is successfully reduced using the proposed estimation algorithms. Vehicular A-ITU channel model is considered with a relatively high vehicle speed up to 68 Km/h in order to test the suitability of the proposed algorithms for mobile systems. E-DFT and S-DFT improves conventional as well as previous DFT improvement methods (I-DFT) suggested by [7], [8], [9], [15]. For 64 subcarriers, S-DFT outperforms E-DFT and I-DFT by about 3dB at a BER of 0.01 with a mobility reaches 45 Km/h, and by about 0.4dB and 2.5dB at a BER of 0.02 with a mobility reaches 68Km/h.