## 5 Results and Analysis
### The Multi-Block Approach  
It is well known that pulse compression degrades with time evolution, as the channel is time variant in practice. In the Section 5.2, the degradation is neglected, where the subsequent adaptive channel equalizers manage to track the channel variations. In the current subsection, the multi-block approach is used to counter for the variations within each data packet. It is understood that the channel can be assumed constant within a short time interval, correspondingly a data block.  
Figure 14 shows an example of performance comparison between one-block and multi-block approaches. For the multi-block approach, the received data packet of 8.128 s was split into eight blocks of 1 s each and one block of 0.128 s. The right panel of Figure 14(a) shows that the single channel DFE encounters difficulties in tracking the channel variations, as the output MSE increases with time. As shown in the left panels of Figure 14, BER is reduced from 4.9% to 2.2%, when the multi-block approach is implemented. As follows for the multi-block approach, each block has time duration of 1 s.  
Figure 15 shows the performance assessment, in which the multi-block approach is used for PPC processing. Performance of PPC-McDFE still consistently approximates that of McDFE, and PPC-DFE achieves the worst performance. McDFE fails in the 14 th period, which may be due to the impropriate parameters for McDFE, while both PPC-McDFE and PPC-DFE succeed in recovering the distorted information. In observation, the MP algorithm shows advantages over the LS method for the multi-block approach. For instance, using the MP algorithm, 4.1 dB improvement (the 11 th period) is obtained by PPC-DFE, and 3.3 dB improvement (the 9 th period) is obtained by PPC-McDFE.  
The multi-block approach operates on the decision directed mode, and hence there is the issue of error-propagation. In the scenario of low input SNR, the LS method is sensitive to errors of detected symbols of the previous block, while the MP algorithm estimates only dominant arrivals with less impact from the errors. Temporal focusing is more enhanced by the MP algorithm, which leads to better performance. Therefore, the MP algorithm is suggested for the multi-block approach.  
Figure 13: Performance in terms of output SNR at a symbol rate of 2 kilo-symbol/s.  
The multi-block approach may be better than the one block approach, but it depends on the rate of channel variation. Figure 16 shows the comparison between using the one block and multi-block approaches. For PPC-McDFE, there is trivial improvement with a maximum improvement of 0.5 dB (the 12 nd period). For PPC-DFE, there is improvement in 11 th periods, with mean improvement of 0.6 dB, and the maximum improvement is 1.4 dB (the 2 nd period). In the current case, only modest  
Figure 14: Performance of PPC-DFE with different approaches. (**a**) One block; (**b**) 9 blocks. The MP algorithm is used, and the symbol rate is 2 kilo-symbol/s.  
Figure 15: Performance of three receiver structures. There are 16 blocks for PPC processing.  
improvement has been obtained when using the multi-block approach, and this can be understood that the collected data were moderately time variant. The multi-block approach cannot avoid the issue of error-propagation, and hence caution should be paid when using this approach, especially in the scenario with low input SNRs.