# A Low Complexity Channel Estimation and Detection for Massive MIMO Using SC-FDE
## 4 Performance Results
### Channel Estimation with Superimposed Pilots  
For the purpose of channel estimation, this section considers superimposed or implicit pilots, i.e., pilots added to the data. The advantage of this approach relies on the fact that there is no need to reserve a certain bandwidth to send pilots or training sequences. Nevertheless, using superimposed pilots, data represents interference to the channel estimate obtained with the pilots, and the pilots represent interference to the channel estimate obtained with the data, which leads to a degradation of performance. This can be mitigated by employing pilots with relatively low power and average  
Figure 5: BER results for \(4\times 32\) MIMO with conventional pilots and different iteration of interference cancellation. Figure 6: BER results for \(4\times 32\) MIMO versus \(4\times 256\) MIMO and \(16\times 256\), with conventional pilots. the pilots over a large number of blocks, so as to obtain accurate channel estimates (the window size should be such that the channel should be constant within it). We propose the receiver shown in Figure 3, which consists of the following phases:  
1. Perform an initial channel estimation using the pilots (added to the data). 2. Remove the pilots (that represent interference), detect the data, and perform an initial channel estimate using the data. 3. Combine the channel estimate obtained from step 1. with that of step 2. 4. Repeat steps 1 to 3 iteratively, with the new improved channel estimates, and removing the estimated data from the pilots of step 1. Figure 7 considers the performance results obtained with superimposed pilots compared with those obtained with conventional pilots. The superimposed pilots consider pilots power of 0 dB (pilots with the same power as the data), with a block length of five blocks of data symbols used to estimate the channel, and four iterations of the iterative channel estimator. As can be viewed, although the performances obtained with conventional pilots are slightly better than those obtained with superimposed pilots, the differences are residual. Nevertheless, superimposed pilots present the advantage of not having to reserve a certain bandwidth for the purpose of estimating the channel. Regardless of whether superimposed or conventional pilots are employed, the best overall performance is obtained with the MRC, being followed by the ZF and, finally, by the EGC. Once again, the ZF performs worse than the MRC because the former presents noise enhancement. Figure 8 presents the performance results obtained superimposed pilots, with two versus four iterations of the channel estimator, with pilots power of 0 dB. As previously described, two iterations simply consider one initial estimation from the pilots and another estimation from the data (after removing the pilots). These two estimates are combined, and the result is used to detect the data. In the case of four iterations of the channel estimator, this process is repeated, i.e., a third iteration considers the channel estimate from the pilots (after removing the data) and a fourth iteration, where the channel estimate is obtained from the data (after removal of the pilots). In this scenario, the estimates obtained in the third and fourth iterations are combined, and the result is used to perform data detection. The interference between pilots and data is mitigated by employing pilots with relatively low power and average the pilots over a large number of blocks,  
Figure 7: BER results for \(4\times 32\) MIMO with conventional pilots versus superimposed pilots. so as to obtain accurate channel estimates (the window size should be such that the channel should be constant within it). In this case, we have assumed a block of five symbols. As expected, the performance results with four iterations are always better than those obtained with two iterations. This is valid for both MRC, ZF and EGC. As before, the best overall performance is obtained with the MRC (with 4 iterations).