# Estimation of Compressible Channel Impulse Response for OFDM Modulated Transmissions
## 6 Conclusions  
The new CIR estimation procedure for OFDM transmission was proposed and evaluated in the paper. The clustered coefficients reconstruction was the main idea of the method motivated by the compressibility feature of CIR. The relation between the estimation and approximation components of MSE measure was the entry point to develop the reconstruction procedure. A moving average filter with automatically adjusted length was used as the main processing component. The simulation tests with the benchmark channel models show that for the proposed solution it is possible to achieve the transmission quality results comparable or slightly worse to those obtained for more numerically complex method based on the greedy approach (**R**) and better than in the case of individual coefficients  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**BER** & **Indoor A** & **Indoor B** & **Indoor B Shift** & **Outdoor-to-Indoor A** \\ \hline
0.1 & 0 dB & 0.05 dB & 0.01 dB & 0.1 dB \\
0.01 & 0.04 dB & 0.07 dB & 0.11 dB & 0.05 dB \\ \hline \hline \end{tabular}
\end{table}
Table 6: SNR gap between **G** and **R** methods (\(SNR_{G}-SNR_{R}\)) for the particular BERs and channel models with a resolution 0.01 dB.  
selection (**N**). The estimation gain in the latter case allows the transmitter to save energy in range of 5-7%.  
Future works can cover detailed implementation analysis focusing especially on sorting procedures to fit their time and space complexity to a particular system design platform. In addition, a switching mechanism can be considered that changes the CIR estimation algorithm from the clustered coefficients selection in low and medium SNRs to individual selection in high SNRs. Other interesting research directions are to test the adaptability of the DFT-based channel estimation approach to operate in systems with various CIR characterization and arbitrary subchannel allocation. The latter problem is relevant in OFDM-based cognitive radio systems, where spectrum sensing is performed prior to data transmission to detect unused subchannels [26].  
Conceptualization, G.D.; methodology, G.D.; software, G.D. and M.K.; validation, G.D. and M.K.; formal analysis, G.D.; investigation, G.D.; resources, M.K.; data curation, M.K.; writing--original draft preparation, G.D.; writing--review and editing, M.K.; visualization, G.D. and M.K.; supervision, G.D.; project administration, G.D. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
This work was supported by Statutory Research funds of Department of Telecommunications and Teleinformatics, Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, Gliwice, Poland.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
AWGN Additive White Gaussian Noise  
BER Bit Error Rate  
CIR Channel Impulse Response  
CP Cyclic Prefix  
CS Compressed Sensing  
CSI Channel State Information  
DFT Discrete Fourier Transform  
FFT Fast Fourier Transform  
IoT Internet of Things  
ISI Intersymbol Interferences  
LDPC Low-Density Parity Check  
LMMSE Linear Minimum Mean Square Error  
LS Least Squares  
MIMO Multiple Input Multiple Output  
MSE Mean Square Error  
OFDM Orthogonal Frequency Division Multiplexing  
OMP Orthogonal Matching Pursuit  
QAM Quadrature Amplitude Modulation  
QPSK Quadrature Phase Shift Keying  
SNR Singnal-Noise Ratio  
ZF Zero Forcing