## 6 Results and Discussion
### Performance Comparison between CMI and R1 for Turbo Coded OFDM in AWGN Channel  
The CMI is designed for turbo coded OFDM scheme. The size of interleaver L is taken as 256 bits. The joint turbo decoding iterations are taken as four in all the simulated results in order to have a fair comparison. The bit error rate (BER) performance of turbo coded OFDM scheme over AWGN channel is estimated by Monte Carlo simulations as shown in Figure 7. The CMI is compared with RI over different modulation schemes such as BPSK, QPSK and 16 QAM. It is evident from Figure 7 that a CMI interleaver not only improves the performance of code in medium to high SNR regime but also lowers the bit \"error floor\" performance significantly. Comparing the simulation results for four-state turbo coded OFDM in BPSK modulation scheme it was observed that the CMI achieves an improvement of 1-dB relative to RI at BER of \(10^{-6}\). Similarly it was observed that CMI out performs its counterpart RI by 1-dB for the same BER in case of QPSK modulation. In the case of 16 QAM, the gap between CMI and RI widens as the SNR increases. This gap widens to its maximum value at the BER of \(8\times 10^{-8}\). At this BER the CMI achieves a gain of 1.5 dB relative to its counterpart RI. Moreover, an error floor  
Figure 6: Joint iterative SISO decoding for turbo coded OFDM with MIMO (2 \(\times\) 2) antennas. performance has been improved considerably in the case of CMI. Furthermore, it is also observed that as the order of modulation increases, the BER performance decreases significantly. As seen from the figure a low-order modulation such as BPSK is more resilient and can tolerate a large amount of noise interference as compared to high-order modulation such as 16 QAM which is more sensitive against bit errors, it can only be useful when the SNR is sufficiently high and the communication system is bandwidth efficient. Performance Comparison between CMI and RI for Turbo Coded OFDM with MIMO (2 \(\times\) 2) Antennas in Fast Rayleigh Fading Channels  
The performance CMI is also analyzed and evaluated under turbo coded OFDM in MIMO antennas scheme over fast Rayleigh fading channels. The said scheme incorporates two transmit antennas at the source-S terminal and two receive antennas at the destination-D terminal. The interleaver size L is taken as 1024 bits. The decoding iteration is taken as four in all the simulated results. The BER performance of turbo coded OFDM in MIMO antennas scheme with CMI and RI is simulated over a fast Rayleigh fading channel as shown in Figure 8. The performance of the selected CMI is evaluated on turbo coded OFDM with MIMO (2 \(\times\) 2) scheme. The digital modulation techniques are chosen as BPSK, QPSK, and 16 QAM. Comparing the simulation results for 4-state turbo coded OFDM with MIMO (2 \(\times\) 2) in BPSK modulation scheme it has been seen that the CMI achieves an improvement of 1.2 dB relative to RI at BER of \(10^{-7}\) over fading channels. Both the interleavers achieve \"error floor\". However, in the case of CMI, the error floor performance has been improved significantly. Similarly, the BER performance of the considered scheme incorporating CMI outperforms RI in QPSK modulation over fading channels. It was observed that CMI performs better especially in medium to high SNR regime (3-6 dB) as compared with its counterpart RI. In this case, CMI achieves 1 dB gain in SNR relative to RI at the BER of \(10^{-6}\). Moreover, the waterfalls region exhibits steeper slope. This is due to fact that CMI ensures that no short cycle events occur. In the case of 16 QAM a similar behavior was observed. An interesting observation is seen from the Figure 8 that the BER performance of the proposed scheme with CMI always decreases rapidly with the increasing SNR. This is due to the fact the CMI increases the minimum free distance of the turbo code which eventually results in the reduced error floor of the code. Figure 7: BER performance of turbo coded OFDM in AWGN channel, \(L=256\) and four decoding iterations.