# On the Performance of LDPC-Coded Large Intelligent Antenna System
## 4 Simulation Results and Analysis  
This section studies the BER performance results obtained with Monte Carlo simulations, using LIS systems, in the uplink direction, associated with SC-FDE block transmission technique and LDPC codes. \(E_{b}\) stands for the energy of the transmitted bits, and \(N_{0}\) is the one-sided power spectral density of the noise. The BER is calculated as a function of \(E_{b}/N_{0}\). A block size of \(N=256\) symbols was used for the QPSK modulation (identical results were seen for different values of \(N\), given that \(N>>1\)). With a code rate of \(\frac{1}{2}\), LDPC codes 32,400 long were considered in the simulations. The LIS system comprises several panels, whereas each panel includes several antenna elements. The distance between the antenna elements is \(\lambda/2\). The channel correlation between the antenna elements allows for the creation of the above-described beam. Five statistically independent equal power paths were considered in the Monte Carlo simulation to translate for an extreme Rayleigh fading channel. The simulations considered four receiver types: ZF, MMSE, MRC, and EGC. The following graphics include, in some cases, results with and without equalization for the MRC and EGC receivers, while ZF and MMSE receivers cannot avoid equalization. This makes MRC and EGC even simpler, besides the possibility of avoiding the channel matrix inversion for each frequency component of the channel. Except for ZF, all other receivers did not consider equalization (and iterations were not considered). Comparing these not-equalized receivers with iterative receivers that include equalization (in this case, we took into account the repetitive receivers in four iterations), the results are the same, as equalization does not bring any added value when the number of antennas is sufficiently high, which is the generic case of the LIS system. It is worth noting that the other receivers do not compute the channel matrix inverse for each frequency component, whereas the ZF does [25]. This makes the ZF significantly more computationally intensive. For comparison purposes, the Matched Filter Bounds (MFB) curves are considered in different performance graphics, representing lower bounds. In general, the MFB for a frequency selective channel (i.e., a channel with Inter-Symbol Interference) is the performance when a single symbol is transmitted, which means there is no ISI-related degradation, experiencing only fading-related degradation. This can be regarded as a lower bound on the performance of a given receiver, although in many cases even an ideal equalizer (for instance, for a Viterbi equalizer) cannot achieve the MFB. This means that a receiver whose performance is a fraction of dB from the MFB will be close to an optimum receiver. Table 2 presents a list of baseline simulations utilized in the different graphics of this section. Figure 4 shows the performance results for 4X25 LIS system (four panels, each with 25 antennas, making a total of 200 antennas), with five users, without LDPC codes, with and without equalization, for the ZF, MRC, EGC, and MMSE, four distinct receivers. Note that only the MRC and EGC may avoid equalization, while ZF and MMSE receivers cannot get rid of this. This makes MRC and EGC even simpler, besides the possibility of avoiding the channel matrix inversion for each frequency component of the channel. As can be seen, for the MRC and EGC receivers and 4X25 LIS system, the equalization does not bring any added value in terms of performance improvement, as compared to the results without equalization. Moreover, in this scenario, channel estimation is not required. From these results, we can conclude that the LIS system allows the use of very simple processing, as equalization and channel estimation are avoided, at least for this LIS configuration. Moreover, the MMSE and ZF are the receivers that achieve the best performance, and their curves are almost superimposed.