# Single-Carrier Rotation-Interleaved Space-Time Code for Frequency-Selective Fading Channels +
## 4 Simulation Results and Discussion
### Number of multipaths is three (\(L=3\))  
In the second part of the simulation, \(L\) is three, both \(M_{T}\) and \(M_{R}\) are two. The block size \(K\) is 132. First, BPSK modulation is considered. In Figure 9, the proposed scheme, Proposed-G\({}_{4}\) scheme, using a 4-state BPSK STTC (with generator \(G_{4}=[011;111]^{T}\)) and fixed rotation (\(\theta=2\pi/5\)), is compared with one of the best 4-state STTCs (with generator \(G_{4^{*}}=[111;101]\) from [21]) designed for frequency-selective channels with 3 taps. Note that the Proposed-G\({}_{4}\) scheme requires 256 ML states whereas the \(G_{4^{*}}\)-STTC requires 16 ML states only, and the performance of the Proposed-G\({}_{4}\) scheme outperforms \(G_{4^{*}}\)-STTC by about 0.25 dB at FER = 0.01. Both schemes deliver the maximum level of diversity performance as seen from the slope of the FER curves, therefore validating the diversity advantage of the proposed scheme for \(L=3\). Next, in order to circumvent the complexity problem of ML detection, the iterative receiver as described in section III.C is used for the proposed scheme when the constituent STTC has a large number of states. Due to the suboptimal nature of the iterative receiver, the performance of the proposed scheme is compromised. Our focus is to assess its diversity performance over the range of desired FER as well as considering the comparison with existing space-time coding schemes of similar decoding complexity. As such, we remark that the major complexity requirement of the iterative receiver stems from the number of states required in the BCJR decoding algorithm rather than the linear FDE which has polynomial complexity and is independent of the STTC design. The proposed scheme, Proposed-G\({}_{16}\), using the 16-state BPSK STTC (with generator \(G_{16}=[11011;0111]^{T}\)) from [34] is then considered. The rotation angle is fixed to \(\theta=2\pi/7\) and its performance is shown in Figure 9. With a comparable number of states (16 states BCJR decoder), it offers a 1 dB gain over the \(G_{4^{*}}\)-STTC (with 16 ML states) at FER = 0.01 while both schemes deliver the same level of diversity gain over the range of desired FER. Thus, it indicates that not only has the iterative receiver delivered the diversity advantage of the proposed scheme, it brings about a considerable amount of improvement over some STTC schemes. Hence, the proposed scheme using iterative receiver may yield good performance with affordable level of complexity. Another comparison is also included in Figure 9, in which the performance of the best 16-state STTC (\(G_{16^{*}}=[11101;1101]^{T}\)) [23] designed for frequency-selective channels is shown. It is slightly better than the Proposed-G\({}_{16}\) scheme but at the expense of larger number of ML states since it requires 64 ML states. Finally, Figure 9 shows the performance of the proposed scheme, Proposed-G\({}_{32}\), with 32-state BPSK STTC (with generator \(G_{32}=[110101;10111]\) from [35]) and \(\theta=2\pi/7\). It outperforms the best 16-state \(G_{16^{*}}\)-STTC code by about 1 dB at FER = 0.01 while requiring only 32 states in the BCJR decoder. Thus, the proposed scheme again yields promising performance with affordable level of complexity. Note that, as shown in Figure 9, the proposed scheme, Proposed-G\({}_{16}\), is simulated for both random and fixed rotation, and they provide comparable performance when the iterative receiver is employed. Next, QPSK modulation is considered. The proposed scheme, Proposed-G\({}_{32}\), using the 32-state QPSK STTC (with generator \(G_{32}=[2012122;2201202]^{T}\) from [36]) is considered. The rotation angle is chosen to be \(\theta=2\pi/19\) and the iterative receiver is employed. In Figure 10, the result is compared to the best 4-state QPSK STTC code for frequency-selective fading channels (with \(G_{4^{*}}=[12;21]\) from [21]) and the gain of the proposed scheme is about 2 dB at FER = 0.01 while both schemes achieve equal diversity performance over the range of desired FER.