## 5 Experimental Results
### Performance and Computational Complexity of the Low Complexity Demodulation Method
#### 5.2.2 Computational Complexity of Proposed Demodulation Methods  
In this paper, we compared the computational complexity of the conventional schemes [12] and the proposed demodulation schemes. We calculated the number of instruction clock cycles of each demodulation method using the number of additions and multiplications used in the operation. Table 3 provides formulas for the number of addition and multiplication used in each demodulation method. The formula is expressed in terms of the number of antennas and sub-carriers used in the MIMO Wi-Fi backscatter system. The SED method was not formulated because multiplication operation was not utilized. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **\# of additions** & **\# of multiplications** \\ \hline ED & \(4N\times(4C-1)\) & \(4N\times 2C\) \\ SET & \(4N\times(4\hat{C}-1)\) & \(4N\times 2\hat{C}\) \\ TCST & \(N\times(3C+(4\times(4\hat{C}-1)))\) & \(4N\times 2\hat{C}\) \\ SED & \(4N\times(4C-1)\) & - \\ \hline \hline \end{tabular} where \(N\) is the number of antennas, \(C\) is the number of all subcarriers assigned to the CSI data, and \(\hat{C}\) is the average number of subcarriers applied to the Euclidean distance calculation in the SET method and TCST method. ED: Euclidean distance method; SET: Subcarrier energy based threshold method; TCST: Tag’s channel state based threshold method; SED: Similar Euclidean distance.  
\end{table} 
Table 3: Number of additions and multiplications of demodulation methods. Figure 11: BER performance of SED method for the number of received (Rx) antennas (1, 2, 4, and 8). (**a**) The number of Rx antennas is 1; (**b**) the number of Rx antennas is 2; (**c**) the number of Rx antennas is 4 and (**d**) the number of Rx antennas is 8.  
proposed algorithm with respect to BER and throughput, the system was designed by using MATLAB and was tested under the 802.11 TGn channel models. From the simulation results, the proposed backscatter method showed a better performance in terms of both BER and throughput compared to existing algorithms. The proposed system obtained the maximum gain of 15 dB in SNR with the same throughput as the existing power-level algorithm [12] and the maximum gain of 5 dB in SNR with the same BER as the existing threshold method [9], regardless of the distance between the tag sensor and the reader. The throughput performance of the proposed system was better than about 10 dB compared to the power level modulation method [12]. In addition, we presented three low complexity demodulation methods to determine received data symbol in MIMO Wi-Fi backscatter system. The computational complexity, when comparing each method with ED method, was reduced to a maximum of 46%, 32%, 60% and BER performance had a difference of up to 0.001 dB, 0.1 dB, and 1 dB. Since BER performance and computational complexity were in a trade-off relationship with each other, an appropriate method can be used according to the system. The simulation results showed that the proposed backscatter method was very useful for a Wi-Fi backscatter system, in which power saving was an important issue under reliable communication conditions. [PERSON] and [PERSON] designed the algorithm, performed the simulation and experiment, and wrote the paper; [PERSON] and [PERSON] implemented the evaluation platform and performed the experiment; [PERSON] conceived and led the research, analyzed the experimental results, and wrote the paper. All authors have read and agreed to the published version of the manuscript.