# Low Power Consumption Signal Detector Based on Adaptive DFSD in MIMO-OFDM Systems
## 5 Simulation Results
### The Bit Error Rate Performance  
Figure 6 shows the error performance comparing the ML, conventional DFSD, adaptive DFSD and DFSD detection scheme using one and four nodes at the \(N_{t}\)-th layer. Also, Figure 7 shows the error performance comparing the ML, conventional DFSD, adaptive DFSD and DFSD detection scheme using one and sixteen nodes at the \(N_{t}\)-th layer. Figure 5: The flowchart for the proposed DFSD detection scheme. As a result of the error performance in Figures 6 and 7, the adaptive DFSD detection scheme has similar error performance compared to the ML and the conventional DFSD detection scheme in the \(2\times 2\) and \(4\times 4\) MIMO-OFDM systems. Also, from the simulation results using the different modulation scheme in Figures 6 and 7, it is shown that the adaptive DFSD detection scheme has suboptimal performance both 16-QAM and 64-QAM. Additionally, Figure 6 shows the DFSD detection schemes using one and four nodes at the \(N_{t}\)-th layer. Also, Figure 7 shows the DFSD detection schemes using one and sixteen nodes at the \(N_{t}\)-th layer. These detection schemes have a worse error performance. Especially, the DFSD detection scheme using one node at the \(N_{t}\)-th layer has the worst error performance among the DFSD  
comparing the conventional DFSD, adaptive DFSD, DFSD detection scheme using one and sixteen nodes at the \(N_{l}\)-th layer, and adaptive QRD-\(M\)[21] in \(4\times 4\) MIMO-OFDM system with 64-QAM. QRD-\(M\) is the non-linear detection algorithm. QRD-\(M\) detection scheme has suboptimal performance and lower complexity compared to the ML detection scheme. The complexity is defined as the number of complex multiplications required to obtain the received symbols at the tree structure. The complex multiplication expressions according to each detection scheme are shown in Table 1. The complex multiplication is calculated from the inverse channel matrix, process of the QR decomposition of channel matrix, multiplication of \(\mathbf{Y}\) and \(\mathbf{Q}^{H}\), and the number of nodes required per layer of tree structure. Especially, the adaptive DFSD detection scheme additionally computes the threshold based on channel condition. Figure 11: The complexity of the detection schemes in \(4\times 4\) MIMO-OFDM system with 64-QAM. Figure 10: The complexity of the detection schemes in \(4\times 4\) MIMO-OFDM system with 16-QAM. It is shown in Figures 10 and 11 that the DFSD detection schemes have lower complexity as the SNR increases. As the SNR increases, the influence of the noise and the initial radius becomes small, and then the complexity becomes low. Also, it can be generally seen that the proposed detection scheme has lower complexity than the conventional DFSD detection scheme. When the proposed detection scheme compares with the adaptive QRD-\(M\)[21], the proposed detection scheme has high complexity compared to the adaptive QRD-\(M\)[21] at less than 8 dB of SNR. On the other hand, the proposed detection scheme has low complexity compared to the adaptive QRD-\(M\)[21] at more than 8 dB of SNR. Because the adaptive QRD-\(M\)[21] has the fixed complexity. Although the proposed detection scheme has high complexity than the adaptive QRD-\(M\)[21] at low SNR, the proposed detection scheme has lower complexity than the conventional DFSD detection scheme at low SNR and lower complexity than the adaptive QRD-\(M\)[21] detection scheme at high SNR. Figure 12 shows the complexity comparing the conventional DFSD, adaptive DFSD, DFSD detection scheme using one and four nodes at the \(N_{l}\)-th layer and adaptive QRD-\(M\)[22] in \(2~{}\times~{}2\) MIMO-OFDM system with 16-QAM. It is shown that the proposed detection scheme has lower complexity than the adaptive QRD-\(M\)[22]. Figures 13 and 14 show the complexity of the detection schemes according to number of transmit antennas and SNR with 16-QAM and 64-QAM respectively. Figures 13 and 14 show the example when SNR is 15 dB and 24 dB.