# Low-Complexity Progressive MIMO-OFDM Receiver for Underwater Acoustic Communication
## 5 Results
### ICI Aware Progressive Iterative Receiver  
#### 5.2.1 Simulation Results  
Adding the effect of the non-uniform Doppler to the four channels of a 2 X 2 MIMO-OFDM system, while using the same simulation parameters as used above. The system was tested in good channel conditions as well as poor channel conditions and it was assumed that the Doppler factor of each path obeyed the uniform distribution with zero mean value and the standard deviations of the relative motion speeds of sending and receiving ends were set to \(\sigma_{v1}=0.15\) m\(\cdot\)s\({}^{-1}\) and \(\sigma_{v2}=0.25\) m\(\cdot\)s\({}^{-1}\) and the corresponding maximum Doppler shift factors are \(b_{\text{max1}}=\sqrt{3}\sigma_{v1}/c=1.15\times 10^{-4}\), \(b_{\text{max2}}=\sqrt{3}\sigma_{v2}/c=2.89\times 10^{-4}\), respectively. The Doppler factor step length is set to \(\Delta b=4\times 10^{-5}\). First, we analyze the influence of the value of D on the ICI equalization effect of non-progressive MIMO-OFDM iterative receiver shown in Figure 6. Figure 6a shows that for \(\sigma_{v1}=0.15\) m\(\cdot\)s\({}^{-1}\), when D is set to 0, the system performance is poor. When D is set to 1, the system performance is significantly improved. The value of D is continuously increased; however, the trend of further improvement in the system performance is not obvious. This shows that even when there is a slight ICI in the MIMO-OFDM system, it cannot be ignored as it will also have a significant impact on BER performance. Therefore in such cases, we can just take value of D = 1 for the ICI equalization. For \(\sigma_{v2}=0.25\) m\(\cdot\)s\({}^{-1}\), similarly if the ICI is not equalized (D = 0), the system performance is poor. With each increase in the value of D, an obvious improvement can be observed as highlighted by the arrows in the Figure 6b, indicating that when there is a more serious ICI in the system, the value of D can be increased accordingly to equalize the ICI. Figure 6 also shows that if we assume the value of D = 2 in the \(\sigma_{v2}=0.25\) m\(\cdot\)s\({}^{-1}\) case, the non-progressive system will stop the iterations while the system will still have a lot of ICI left to be  
Figure 5: Experimental results comparison of the two receivers. equalized. Similarly if the D is taken as 3 in \(\sigma_{v1}=0.15\) m\(\cdot\)s\({}^{-1}\) case, the non-progressive receiver will keep iterating unnecessarily and will increase the complexity. Next, the progressive iterative reception algorithm for MIMO-OFDM systems considering ICI is simulated. Assuming \(D_{\text{max}}=3\), the number of Doppler factors \(N_{b}^{D}\) corresponding to D = 1, 2, and 3 in the iteration process is taken as 6, 10, and 14, respectively. D = 1 iterates 2 times, thus it actually runs 5 times in total. The BER performance at various \(D_{\text{max}}\) values of the iterative MIMO-OFDM progressive iterative receiver is shown in Figure 7. It can be seen from Figure 7 that the progressive iterative receiving algorithm can significantly improve the system performance for a MIMO-OFDM system with ICI. As the iteration progresses, the value of D gradually increases and the BER of the system gradually decreases, which verifies the effectiveness of the progressive MIMO-OFDM iterative receiver. Figure 8 compares the performance of the non-progressive iterative receiver and progressive iterative receiver for \(\sigma\
u\) = 0.25. Initially when the D and Dmax both are 0, i.e., there is no ICI equalization, both the curves are the same. Later on, the performance of the progressive receiver after the fourth progression is compared with the performance of the non-progressive receiver with D = 3; and it can be observed that the performance of the progressive iterative receiver is better than that of non-progressive iterative receiver. Figure 6: BER performance of non-progressive iterative MIMO receiver with different values of D and \(\sigma\
u\). Figure 7: BER performance of progressive MIMO-OFDM iterative receivers with different values of D and \(\sigma\
u\).