# Research on Co-Channel Interference Cancellation for Underwater Acoustic MIMO Communications
## 3 Experimental Results
### Results and Analysis  
Figure 3 shows the channel estimates. The channel length was set at 62.5 ms, and the observation length \(S\) was set to be three times the channel length to achieve accurate channel estimates. The channel estimation method was LSQR [31] in both the traditional channel estimation model and the proposed channel estimation model. Before channel estimation, the Doppler estimation and Doppler compensation were performed. The channel estimate in Figure 3c was obtained by the traditional channel model without IC. From Figure 3c, one may observe that the multipath is obviously rich and the relative delay is more than 20 ms. One also may observe that, in Figure 3c, more estimated noise is caused by CoI. Focusing on Figure 3d, obtained by the proposed method, we can see that the multipath outline is much clearer, and the noise level is much lower. The reason for this is that the proposed channel estimation model projects the CoI to a specific subspace where the CoI is free; thus, it does not suffer from interference, which results improved SNR and lower MSE, as (26) shows. In addition, the multipath from transmitter 2 is much richer than that from transmitter 1. The communication performance is compared in terms of output SNR. The lengths of feedforward filters, feedback filters, and IC filters for CE-DFE-based receivers were 125 ms (400 symbols), 62.2 ms (199 symbols), and 62.2 ms, respectively. The lengths of feedforward filters, feedback filters, and IC filters for DA-DFE based receivers were 18.75 ms (60 symbols), 9.37 ms (30 symbols), and 9.37 ms, respectively. The forgotten factor for RLS_DADFE was 0.9985; the IPNLMS_DADFE step is 0.25; the remaining parameters for IPNLMS_DADFE are the same as in Ref. [12]. The parameters for RLS_DADFE and IPNLMS_DADFE were chosen carefully to achieve the best communication performance. In the CE-DFE-based receivers, the Doppler was estimated via match filtering [11], while in RLS_DADFE and IPNLMS_DADFE, the phase lock loop was used, and the phase lock loop parameters were the same as in Ref. [19]. Figure 4 shows the output SNR in training mode. In training mode, the input of feedback filter and IC filters is known in advance; in other words, the interference is known. One may observe that the CE_NoIC+DFE_IC receiver and CE_NoIC+DFE_NoIC receiver obtained the lowest output SNR. The reason for this is that, because the traditional channel estimation does not cancel the CoI, the channel estimates contain more estimated noise. The feedforward filters and feedback filters, which are directly measured via channel estimates, also contain a large amount of noise. As shown in (33), the excess error is significant, so the output SNR from channel equalization is low for both the CE_NoIC+DFE_NoIC receiver and CE_NoIC+DFE_IC receiver. Meanwhile, theCE_NoIC+DFE_IC receiver has IC filters; this introduces more noise to the channel equalizer than the CE_NoIC+DFE_NoIC receiver does. In addition, the output from equalizers in the CE_NoIC+DFE_IC receiver is fed to the different branches shown in Figure 1, while the output from the equalizer from CE_NoIC+DFE_NoIC receiver is fed to its own branch. If the equalizer output is not correct, the CE_NoIC+DFE_IC receiver introduces much more noise. As a result, the output SNR obtained by the CE_NoIC+DFE_IC receiver is lower than that obtained by the CE_NoIC+DFE_NoIC receiver. For example, the average output SNR from CE_NoIC+DFE_NoIC and CE_NoIC+DFE_IC for transmitter 1 is 5.71 dB and 3.99 dB, while for transmitter 2 it is 7.80 dB and 4.59 dB, respectively. Looking at the output SNR obtained by the CE_IC+DFE_NoIC receiver in Figure 5, it can be seen that the output SNR is not significantly improved. Although the channel estimation performs interference cancellation, and the CE-DFE filters are more accurate, the interference is not canceled in equalizers. The average output SNR from CE_IC+DFE_NoIC receiver is 5.67 dB for transmitter 1 and 7.65 dB for transmitter 2.