# Linear Approximation Signal Detection Scheme in MIMO-OFDM Systems
## 5 Simulation Results  
This section shows the simulation results for bit error rate (BER) performance and complexity. In the simulation results, the used modulation scheme is 16-QAM. Also, the number of used total subcarriers is 128 and length of the cyclic prefix (CP) is 32. Figure 4 shows the BER performances for the conventional ZF, DFE, and proposed detection scheme in 4 \(\times\) 4 MIMO-OFDM system. In this simulation, the transmit symbols go through 7-path Rayleigh fading channel. The proposed detection scheme uses MMSE based detection for robustness to noise effect and higher error performance. For the MMSE, the estimation of the noise power is very simple and it does not cause high complexity to the overall systems. Also, the BER performance for the ML is shown for comparison. The BER performance for the proposed detection scheme is higher than the conventional ZF because the DFE and QRD-\(M\) stages are helpful for the accurate estimation of transmits symbols with slight addition of the complex multiplications. Also, the BER performance for the proposed detection scheme is slightly lower than the conventional DFE at low SNR because the noise is amplified in the partial ZF and it causes severe error propagations. However, the gap of the BER performances between the conventional DFE and the proposed detection scheme becomes small, according to increased SNR.  
Figure 5 shows the BER performances for the conventional ZF, DFE and proposed detection scheme in 8 \(\times\) 8 MIMO-OFDM system. For various environments, the transmit symbols go through 10-path Rayleigh fading channel. Also, the BER performance for the ML is shown for comparison. Like in 4 \(\times\) 4 MIMO-OFDM system, the BER performance for the proposed detection scheme is higher than the conventional ZF, and is lower than the conventional DFE at low SNR. As a result, the error performance for the proposed detection scheme is slightly decreased, according to the increased number of transmit antennas due to severe noise enhancement in the partial ZF stage. However, the  
Figure 4: The BER performances for the conventional and the proposed detection scheme in 4 \(\times\) 4 MIMO-OFDM system (BER: bit error rate; ML: maximum likelihood).  
complexity for the proposed scheme is increased almost linearly, according to the increased number of transmit antennas. This result is shown in Figure 6.  
For further comparisons, Tables 2 and 3 compare the error performance and the complexity for the proposed detection scheme with the proposed simplified ML decoding (SMLD) in [3]. The number of transmit and receive antennas is four and eight. Also, the used modulation is 16-QAM. The parameter \(V\)  
Figure 5: The bit error rate (BER) performances for the conventional and the proposed detection scheme in 8 \(\times\) 8 MIMO-OFDM system.  
Figure 6: The required number of complex multiplications for the conventional and the proposed detection scheme (QRD-M: QR decomposition-\(M\) algorithm).  
denotes the number of candidate symbols at the top layer in the DFE algorithm. The error performance and complexity increase nonlinearly, according to increased \(V\). Table 2 represents the required SNR to obtain the BER performance for \(10^{-3}\). The required SNR for the SMLD is decreased according to the increased number of transmit antennas. However, the required SNR for the proposed detection scheme is increased according to the increased number of transmit antennas because the noise enhancement is very severe in the partial ZF stage. In a similar way, Table 3 represents the required number of complex multiplications. Like Table 2, the number of complex multiplications for the SMLD is variable according to \(V\). The required number of complex multiplications for the proposed detection scheme increases linearly. according to the increased number of transmit antennas relative to the SMLD due to the partial ZF stage.