# Single-Carrier Rotation-Interleaved Space-Time Code for Frequency-Selective Fading Channels +
We emphasize that this design is universal in the sense that it can be readily applied in frequency-selective fading channels with any number of transmit antennas or any type of modulation provided that there exists a corresponding STC design for the flat fading channel with equal number of transmit antennas. Furthermore, our design can in principle be used to construct both single-carrier space-time trellis code and space-time block code, and some examples of both types are given in the simulations. Note that our focus here is on STC but the same construction can be applied by multiplexing other MIMO-techniques such as space-time modulation designed for the flat fading channel. When ML detection is employed in the proposed single-carrier scheme, the receiver complexity may increase exponentially with the number of multipaths and the number of STC streams. Complexity is a common problem in many space-time trellis schemes designed for the frequently-selective fading channel [21]. Alternatively, by noting that the multi-stream interleaved structure of the proposed scheme lends itself easily to an iterative stream-based decoding structure, we propose a frequency-domain iterative detection and decoding method based on [24] which requires only moderate complexity that does not scale exponentially with the number of multipaths or STC streams. This approach is particularly effective for the proposed scheme and may alleviate the complexity problem inherent in the MIMO detection over frequency-selective fading channels. Simulation results show that the proposed scheme using such detection method may outperform other existing approaches of similar level of complexity. In summary, our contributions are as follows:  
* A novel single-carrier-based full-rate space-time code construction scheme capable of attaining the maximum space-time-multipath diversity order is investigated. Without resorting to common OFDM-based design, this approach is low in PAPR. In principle, the proposed scheme is general and broadly applicable in the sense that, with proper rotation, it can be adopted for any number of transmit antennas or any type of modulation as well as flexible transmission rate, unlike the previous approaches which are fixated on certain transmission modes. * In conjunction with the proposed space-time coding scheme, an efficient frequency-domain iterative receiver is developed. This receiver delivers good diversity performance while lowering the receiver complexity significantly. Thus, the proposed scheme may potentially employ powerful STC designed for flat fading channels as its constituent code. In particular, it is capable of outperforming some existing STTCs of comparable complexity which are designed for frequency-selective fading channels. * Theoretical proofs, especially concerning the construction of our STC scheme and the desired rotations required to achieve full diversity gain, are provided. Simulation results are used to verify the performance gain of the proposed scheme. We remark that unlike previous works such as signal space diversity which also employ rotations to exploit space diversity, the approach taken here differs in several aspects. First, one of our goals is to exploit multipath diversity, and a _sequence_ of distinct rotations are judiciously chosen which are assigned to the input streams in the absence of channel state information (except the maximum channel length). Second, we show that mere time-interleaving the input streams alone does not guarantee maximum multipath diversity gain as the delayed streams are superimposed in the time domain. It therefore poses challenges and only through proper rotations on different delayed streams can it achieve the maximum diversity gain. The conference paper version of this paper first appeared in [25] where only Proposition 1 pertaining to the random rotation was included. We have significantly expanded