# A Low Complexity Channel Estimation and Detection for Massive MIMO Using SC-FDE
## 4 Performance Results
### Channel Estimation with Conventional Pilots  
Figure 4 shows the performance obtained with ideal channel estimation versus conventional pilots. It is assumed a \(4\times 32\) MIMO, with 4 iterations of the interference cancellation.  
Although achieving performances with conventional pilots very close to those obtained with ideal channel estimation, the conventional pilots present the disadvantage that they require reserving a part of the bandwidth for the periodic transmission of pilots or training sequence, used for data detection and equalization.  
As can be seen, the MRC achieves a performance very close to the MFB. Note that the MFB consists of a performance lower bound, corresponding to a curve that quantifies the channel modeled by the sum of delayed and independently Rayleigh-fading rays. Under ideal channel conditions, the ZF is the scheme that follows the MRC in terms of performance, and the worst performance is achieved by the EGC. It is worth noting that the advantage of both MRC and EGC relies on its simplicity, as compared to the ZF. Whereas the ZF requires the computation of the inverse of the channel matrix, for each frequency component, the MRC and EGC do not. Moreover, it is known that the ZF presents noise enhancement, when utilized in post-processing mode, which is the current situation, is the reason why the MRC performs better than the ZF.  
It is worth noting that the proposed technique applies to any constellation. The only difference relies on an adaptation of the interference cancellation receiver. Naturally, the sensitivity to channel estimation errors (and other impairments) increases with the constellation size. However, the main conclusions remain valid [21, 22, 23]. To avoid having duplication, only QPSK results are shown in this article.  
As compared to OFDM, SC-FDE allows lowering the E\({}_{\text{b}}\)/N\({}_{0}\) values required for a certain BER, but the relative positions of curves do not change significantly.  
Figure 5 shows the performance results for \(4\times 32\) MIMO with conventional pilots and different iterations of the interference cancellation. Even with 1 iteration, the MRC performs better than the ZF. As before, although with lower processing complexity, the EGC performs worse than the ZF. Note that, with MRC and with EGC, a certain level of interference is generated, because these receivers are not optimum. In order to mitigate such interference, the proposed receiver incorporates an interference cancellation.  
As can be viewed from Figure 5, the best performances, of both MRC and EGC, are achieved with four iterations. Nevertheless, the performances obtained with four iterations are close to those obtained with three iterations. It is also observed a degradation of performance when a single iteration is assumed. Using the interference cancellation associated with the MRC and EGC, one can choose between three or four iterations, as the difference is residual. Beyond four iterations, the performance improvement was almost negligible (not shown in Figure 5). It is shown that the best performance is achieved by the MRC with 4 iterations.  
Figure 6 compares the performance of the \(4\times 32\) MIMO against \(4\times 256\) MIMO and \(16\times 256\) MIMO. As expected, due to the higher level of receive diversity, the 4x256 MIMO performs better than the \(4\times 32\) MIMO. Nevertheless, it is noticeable that \(16\times 256\) MIMO performs worse than \(4\times 256\) MIMO. This occurs because the \(16\times 256\) MIMO comprises 16 parallel flows of symbols, while \(4\times 256\) MIMO comprises only 4 parallel flows of data, and therefore \(16\times 256\) MIMO corresponds to more data being transmitted, but also to more interference. This is valid for the MRC, EGC and ZF. It can be viewed  
Figure 4: Bit Error Rate (BER) results for \(4\times 32\) MIMO with conventional pilots versus ideal channel estimation.  
that the results obtained with the MRC, for the \(4\times 256\) MIMO, are almost superimposed with the MFB curve.