Figure 6 shows the performance of an uncoded BER averaged over 10,000 multicarrier blocks, from which it can be seen that there is an improvement in the performance of the DFrCT-OCDM system compared to both the OFDM and FrFT-OCDM systems with complexity less than the FrFT-OCDM system. From Figure 6, it is observed that the proposed DFrCT at 10-3 Bit Error Rate provides approximately 10 dB better performance than the OFDM and about 1 dB improvements over the FrFT-OCDM system and at 10-4 Bit Error Rate provides approximately 3 dB improvements over the FrFT-OCDM system.
Same results are obtained when using the low comlexity LDLH factorization equalizer.
DFrCT-OCDM System Performance Using the Low complexity LDLH factorization equaliser:
The low complexity factorization equaliser is used to shown the good performance it provides with the DFrFT-OCDM system, The factorization equaliser can be used with the DFrCT-OCDM system using the same proposed technique. The uncoded BER performance of the DFrCT-OCDM compared to the OFDM system is investigated by means of simulation over 100000 multicarrier blocks. An FrCT-OCDM system with N = 128, NA = 96, L = 8, and QPSK modulation is assumed. The channel simulation parameters are the same as the Rayleigh fading channel used in the clock MMSE equaliser in Figure 6.
Figure 7 shows that the DFrCT-OCDM system performance is superior to the conventional OFDM system with the same low complexity equaliser. In  Cancellation Schemes for BER Performance Improvement of OFDM System is shown, and the itsresults can be compared with these results to show the improvement achieved by DFrCT-OCDM.
DFrCT-OCDM System Performance Using the Low complexity LSMR Equaliser:
The low complexity LSMR equalizer shows almost the same performance as the block MMSE equalizerequaliser in Figure 6 and the factorization
Figure 6. The BER Comparison between DFrCT, DFrFT-OCDM and OFDM using block MMSE equalizer.
Figure 7. The BER Comparison between DFrCT-OCDM and OFDM using the factorization equalizer.
Figure 8. The BER Comparison between DFrCT-OCDM and OFDM using the RLS- LSMR equalizer.
equaliserin Figure 7, but with lower complexity. LSMR equaliser can be used with the DFrCT-OCDM following the same technique that was followed with the DFrFT-OCDM.
Figure 8 indicates that the DFrCT-OCDM system performance is better than both the conventional OFDM system and the DFrFT-OCDM system with the same low complexity equaliser.
The different equaliser techniques that are based on the LSMR method can be used all with the DFrCT-OCDM system and it is predicted that the DFrCT- OCDM system will be better than the DFrFT-OCDM system and the OFDM systems.
A novel multicarrier transceiver based on the Discrete Fractional Cosine Transform (DFrCT) was proposed. The DFrCT is an optimal modulation/demodula- tion basis when the multicarrier system faces doubly selective fading channels. It was shown that the DFrCT-OCDM multicarrier system BER performance is superior to the OFDM and the FrFT-OCDM systems with less computational complexity which make the DFrCT a viable multicarrier transceiver in some practical applications that need low power consumption that can be effective in high speed requirement conditions such as DVB-H and WiMAX.
Our ongoing research includes using of low complexity equalizers, testing the peak to average power ratio, time-frequency synchronization and the anti-jam- ming properties of the new system.
The future work will be directed to investigate the most proper equalizer for the proposed system; moreover, it is important to investigate in more details the effect changing the guard bank with the operation frequency as the basic parameter to mitigate the effect of the Doppler frequency.
Moreover, as total new direction; it is important to go for the downlink communication to investigate this system more with high performance encoders and the ability to apply the new techniques over this system such as Network Coding as it is a band width efficient technique and could help to solve the inefficiency of the bandwidth when increasing the guard band to decrease ICI as a result of the Doppler frequency.
Philadelphia university deserves my true acknowledgements for the good atmosphere they maintain for their researchers and for the financial support for this research.
Moreover, I am always thankful for Dr. Lina Stankovic and Dr. Vladimir Stakovic from the University of Strathclyde, Glasgow, UK, for their support with the technical issues, beside their proof reading and technical modifications in my whole research work. They always add good values to my research work.
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