# Reduced Complexity Detection in MIMO Systems with SC-FDE Modulations and Iterative DFE Receivers
## 4 Performance Results  
This section presents a set of Bit Error Rate (BER) performance results regarding the considered system. The channels have multipath propagation effects, making them frequency-selective. We assume 64 multipath components (similar results were observed for other channels, provided that we have strong multipath effects). We also assume uncorrelated Rayleigh fading on the different multipath components and for the different links between transmit and receive antennas, which are assumed to have low directivity. Perfect synchronization and channel estimation are assumed. The main conclusions apply for other channels, provided that we have rich multipath propagation. Although we are assuming a static channel, with perfect channel estimation and synchronization, the main conclusions of this paper are still valid for time-varying channels and/or in the presence of estimation errors. All the different \(P\) transmitted streams associated with each receiving antenna \(r\) assume that \(\xi_{p,r}=0\) dB. The concern about the ADC effects considers \(m\) bits of resolution with a normalized saturation level of \(A_{M}/\sigma\). In the obtainment of the BER performance results, the detection process involves the computation of the \(\mathbf{F}_{k}\) coefficient, in which the results from either Equations (19) or (31) are indistinguishable. Furthermore, we only show Iterations 1, 2 and 4, since the third iterations does not add relevant information. Lastly, all the performance results are compared with the MFB.  
Figure 4 depicts the system's average BER performance considering \(P=8\) with \(m=2\) and \(m=8\) bits of resolution and different values of \(R\).  
From the figure, it can be seen that when \(R=8\), \(P=8\) and \(m=2\), we have high error floors. However, performing iterations for the cancellation of the residual interference allows one to improve the system's BER. These performance improvements are noticeable for large values of \(R\), provided that \(P\) is fixed. In fact, when \(R=32\) and \(P=8\), the system's performance improves substantially, and the impact of the iterative feedback equalization is accentuated, although we observed that the performance stabilizes after the 4-th iteration. This is comparable to the case where we consider \(P=8\), \(R=8\) and \(m=8\), which corresponds to the case where the effects from quantization are mostly negligible.  
Figure 5 shows the average BER performance of the fourth iteration, considering \(P=8\), ADCs with \(m=2\) bits of resolution and several values of \(R\).  
Figure 4: Average BER performance of all streams considering \(P=8\) with \(m=2\) and \(m=8\) bits of resolution and different values of \(R\). MFB, Matched Filter Bound.  
From the depicted figure, one can note that increasing the number of receive antennas leads to performance improvements if the number of transmit antennas is fixed. In fact, although when \(R=16\) there are high error floors due to the strong nonlinear distortion associated with the use of ADCs with only \(m=2\) bits, when \(R\) increases and \(P\) is maintained fixed, the performance can even get closer to the single-user MFB.  
Figure 6 illustrates the average BER performance of the fourth iteration, considering \(P=16\), \(R=64\) and different values of \(m\).  
As expected, it can be noted that lower resolutions lead to larger performance penalties. However, one can note that when \(R/P=4\), we can employ very low resolution ADCs without sacrificing the performance considerably. This reveals that in scenarios where \(R\gg P\), one can have energy-efficient, low complexity receive branches at the BS, enabling inexpensive, massive MIMO-ready BSs.  
Figure 5: Average BER of all streams considering \(P=8\), \(m=2\) and different values of \(R\) for the fourth iteration.  
Figure 6: Average BER of all streams considering \(P=8\), \(R=64\) and different values of \(m\) for the fourth iteration.