## 3 Simulation Results and Analysis  
The performance of the UWA communication, in terms of bit error rate (BER), is evaluated making use of Monte Carlo simulations, associated with SC-FDE block transmission technique and m-MIMO. The error probability, using BER as performance index, was evaluated as a function of \(E_{b}/N_{0}\), where \(E_{b}\) is the energy of the transmitted bits, and \(N_{0}\) is the one-sided power spectral density of the noise. A block length of \(N=256\) QPSK symbols was assumed. LDPC codes of length 32,400 were adopted, with a code rate of \(\frac{1}{2}\). This corresponds to 64,800 coded bits, whose sequence is generated as defined in [24]. A severe Rayleigh fading channel was considered with 20 uncorrelated equal power paths. This corresponds to a highly demanding channel, which can be viewed as a worst-case scenario for underwater propagation. The high number of multipaths and having all of them with the same average power makes this channel very destructive in terms of the creation of intersymbol interference, which can be viewed as the most disruptive cause that limits UWA communications. Channel estimation with training sequences is assumed. Multi-layer MIMO is assumed (spatial multiplexing). Except for the ZF, the other receivers are iterative, canceling the residual interference generated in the decoding algorithm. Nevertheless, while the ZF is much more computationally demanding, the other receivers are not. We considered four iterations of the iterative receivers, as the performance improvement was almost negligible beyond four iterations. As defined in Section 2.3, the Markov chain, binary state model, was assumed to simulate the impulsive noise (in addition to other impairments, such as fading and AWGN noise), typically present in underwater scenarios. We considered \(p_{1,0}=0.1\) and \(p_{0,1}=0.8\). Moreover, we have defined the following probabilities: Prob(Good\(>\)Bad) = 0.1; Prob(Good\(>\)Good) = 0.9; Prob(Bad\(->\)Bad) = 0.2; Prob(Bad\(->\)Good) = 0.8, while in [11] a probability of \(p_{1,0}=0.0098\) was assumed (i.e., Prob(Good\(->\)Bad). Note that Prob(Good\(->\)Bad) stands for the probability of transition from Good to Bad state. Impulsive noise [11,12] may vary from symbol to symbol. Moreover, we assumed a variance of the impulsive noise (when in a bad state) 20 dB higher than the variance of AWGN noise. Table 1 presents a list of baseline simulations utilized in the different graphics of this section. Figure 3 (baseline 1) shows the performance results for UWA communications with and without impulsive noise, with 4 \(\times\) 32 MIMO, without LDPC codes, for four different receivers: the ZF, MRC, EGC, and IB-DFE. The matched filter bound (MFB) curve is a way to measure the channel modeled by the sum of delayed and independently Rayleigh-fading rays, which can be viewed as a lower bound. This graphic considers that the channel correlation between adjacent antenna elements of the MIMO system does not exist (correlation 0). Therefore, results with ideal channel estimation are considered in this graphic. As expected, the results obtained with impulsive noise are much worse than those only with AWGN noise for all the receivers. Nevertheless, it is known that the marine environment is characterized by the existence of impulsive noise generated by sea life activity, making this scenario more realistic. When comparing the different receiver types, it is viewed that the MRC is the one that tends to achieve the best performance (while being less computational demanding than the ZF), while the EGC achieves the worst performance. The ZF and IB-DFE present the same results (these curves are superimposed, with and without impulsive noise). It is worth noting that such superposition of the IB-DFE over the ZF curves occurs in all  
Figure 2: The Markov chain, binary state model [13]. graphics of this article.