# Performance Comparisons of Broadband Power Line Communication Technologies
## 4 BER Comparisons and Discussion
### Simulation Results and Discussion  
The CTC decoder decodes the input block by an iterative algorithm. The CTC decoder has two soft-input soft-output (SISO) decoders, which compute a posteriori log-likelihood ratio (LLR) for information bits. With soft-decision inputs and a priori LLR of information bits, a SISO decoder also produces an extrinsic information. The extrinsic information is provided to the other SISO decoder as an updated a priori LLR. This process is done iteratively. As the iteration continues, a posteriori LLR values become more reliable with the updated a priori LLRs. Detailed descriptions of the iterative decoding algorithm are given in [35; 36; 37]. After each iteration, errors in the decoded bits are reduced. The BER results for IoT PLC with QPSK modulation are shown in Figure 13. The number of information  
Figure 12: PLC channel: (**a**) magnitude frequency response of the channel; and (**b**) channel impulse response for IoT PLC. bits for subblocks \(A\) and \(B\) used in the simulation is about \(10^{6}\). The diversity number \(DV_{n}\) of IoT PLC is 1-15. The SNR in dB is defined as \(10 log_{10}(S_{p}/N_{p})\), where \(S_{p}\) and \(N_{p}\) are the signal power and noise power at the receiver, respectively. In Figure 13, the results for diversity numbers of 3 and 15 are shown as examples. In the figures, the BER value decreases as the number of iterations increases. In the second iteration, the BER performance is greatly improved. However, the BER improvement becomes saturated when the iterations are large. The difference between the BER results at Iterations 6 and 8 is very small. In addition, the BER drops rapidly when SNR \(\geq-5\) dB and \(DV_{n}=3\). However, when \(DV_{n}\) increases to 15, the rapid fall of the BER begins at a much lower SNR of \(-13.5\) dB. When \(DV_{n}=3\) and 15, the required SNR to obtain \(10^{-3}\) for the BER is \(-3.3\) dB and \(-12.8\) dB at six iterations, respectively. The BER results for IoT PLC with 16 QAM modulation are shown in Figure 14. The shape of this figure is similar to that of Figure 13. However, the beginning SNR for a rapid BER fall is very large. For example, the BER drops rapidly when SNR \(\geq 5\) dB and \(DV_{n}=3\). When \(DV_{n}=15\), the BER shows rapid fall at SNR \(\geq-5.5\) dB. In addition, as \(DV_{n}\) increases, the slopes of the falling portion of the curves are steeper, which is also seen in Figure 13.  
The BER results for IoT PLC with \(\pi/4\)-DQPSK modulation are shown in Figure 15. For \(\pi/4\)-DQPSK mode, noncoherent detection is used. The channel equalizer is not applied for this mode. The differential detection is performed with symbols adjacent in time in the same subchannel. On static or slowly changing channels, distortions caused by the channel can be compensated with differential detection. When \(DV_{n}=3\), an irreducible error floor is observed. The subchannel located at the deep notch of the channel has unrecoverable bit errors. If the diversity number is not large, the bit  
Figure 14: BER results for IoT PLC with 16 QAM modulation: (**a**) \(DV_{n}=3\); and (**b**) \(DV_{n}=15\). Figure 13: BER results for IoT PLC with QPSK modulation: (**a**) \(DV_{n}=3\); and (**b**) \(DV_{n}=15\). copies are not spread enough to be corrected, which results in error floor. When \(DV_{n}=15\), the error floor is not present and the BER decreases rapidly as the SNR increases owing to the rich diversity. With the channel used in the simulation, the error floor is not observed in the range down to \(10^{-5}\) when \(DV_{n}\geq 4\). Next, the BER results for Mini DF are shown in Figure 16. In Mini DF mode, QPSK modulation is used and the block size is \(N=48\). Since the block size is smaller than that of DF, the BER shows a relatively slow decrease with increasing SNR, which is commonly observed in systems with CTC of small processing blocks. However, for Mini DF mode with many copies of coded bits (16 copies), the BER begins to fall at a low SNR of \(-14\) dB.