# Low-Complexity QRD-\(M\) with Path Eliminations in MIMO-OFDM Systems
## 6 Conclusions  
This paper proposes a low-complexity QRD-\(M\) which eliminates unnecessary survival paths by comparing the ASEDs and the calculated threshold at each layer. For efficient path eliminations, the proposed QRD-\(M\) calculates thresholds adaptively considering the used modulation scheme. In the simulation results, the BER performances for the proposed QRD-\(M\) is the same as conventional QRD-\(M\) and ML, despite a high modulation order. Additionally, the average number of metric operations for the proposed QRD-\(M\) is approximated to the conventional QRD-\(M\) (\(M=1\)) with respect to increased SNR. In order to justify the better performance for the proposed QRD-\(M\), the complexity for several QRD-\(M\) algorithms is compared with the proposed QRD-\(M\). The complexity for the proposed QRD-\(M\) is lower than several QRD-\(M\) algorithms in [6; 7; 8; 9; 10; 11; 12] because the proposed QRD-\(M\) eliminates many unnecessary survival paths due to adaptively calculated thresholds at all layers considering the used modulation scheme. For further comparisons, the complexity for the E-DFE in [16] which has poor error performance is also compared with the proposed QRD-\(M\). The complexity for the E-DFE is higher than the proposed QRD-\(M\) at 10 dB SNR for 16-QAM and 20 dB for 64-QAM. However, the BER performance for the proposed QRD-\(M\) is decreased with respect to increased SNR, and it has lower BER performance than the E-DFE at 20 dB SNR for 16-QAM and 30 dB SNR for 64-QAM. Thus, the proposed QRD-\(M\) can be useful for practical implementation in huge MIMO-OFDM systems which require optimal error performance.  
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2016R1D1A1B03931160) and Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIT) (No. 2017-0-00217, Development of Immersive Signage Based on Variable Transparency and Multiple Layers).  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Detection Scheme**} & **The Decreased or Increased** & **The Increased Ratio in [6; 7; 8; 9]** \\  & **Ratio Compared to the** & **Compared to the Proposed** \\  & **Conventional QRD-\(M\)** & **QRD-\(M\) with Different SNR** \\ \hline Simplified QRD-\(M\) & About 21\% decreased & About 55\% increased (10 dB) \\  & & About 63\% increased (20 dB) \\ \hline Combined QRD-\(M\) and Kalman filter & About 59\% decreased & About 17\% increased (10 dB) \\  & & About 25\% increased (20 dB) \\ \hline Pseudo-inverse based QRD-\(M\) & About 50\% decreased & About 26\% increased (10 dB) \\  & & About 34\% increased (20 dB) \\ \hline Advanced QRD-\(M\) & About 26\% increased & About 102\% increased (10 dB) \\  & & About 110\% increased (20 dB) \\ \hline Proposed QRD-\(M\) & About 76\% decreased (10 dB) & \\  & About 84\% decreased (20 dB) & \\ \hline \hline \end{tabular}
\end{table}
Table 3: The comparisons for the complexity ratio using 16-QAM modulation in a \(4\times 4\) system. SNR: signal-to-noise ratio.  
**Author Contributions:** [PERSON] proposed an algorithm for low complexity QRD-\(M\) and performed computational simulations; [PERSON] and [PERSON] supplemented an algorithm for more high error performance and low complexity to make an proposed algorithm more competitive compared with existing algorithms; [PERSON] gave feedbacks about an modified algorithm and all simulation results. Also, [PERSON] provided the experimental materials for better computational simulations and revised critical errors of the manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.