# Single-Carrier Rotation-Interleaved Space-Time Code for Frequency-Selective Fading Channels +
Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/)]([https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/))). [PERSON]  
+++ ==WARNING: Truncated because of repetitions==  
++  
Alternatively, other research efforts, such as [17; 18; 19; 20; 21; 22], have been targeting single-carrier STC design for frequency-selective fading channels. However, no important results were obtained in recent years in this direction as most efforts were concentrated on OFDM to combat multipaths. In this paper, we consider single-carrier STC design for frequency-selective fading channels. The reasons are two-fold. Firstly, single-carrier modulation alleviates the problem of PAPR and it is particularly suitable for the uplink transmission in which mobile or lightweight terminals such as an IoT device may use cheaper amplifiers operating with lower power back-off. Secondly, without OFDM, STC design presents a major challenge if exploiting the full space-time-multipath diversity gain is the main concern. This is because the multipath is a form of self-interference which undermines the ability of STC to extract the diversity gain from multipath and more sophisticated design rules are needed. While there exists a fair amount of previous works on single-carrier STC design, most of them suffer from some shortcomings. In [17], a delay diversity scheme was proposed. While it achieves the maximum space-time-multipath diversity gain, it is rate-limited since signal streams from different antennas are replicas of one another with delays. In [19; 20], a single-carrier orthogonal-STBC scheme was devised to achieve maximum diversity order in the frequency-selective fading channel. However, the scheme may suffer from rate loss when there are more than two transmit antennas. In [21], single-carrier STTC construction methods exclusively for BPSK and QAM modulations were proposed. In [22], single-carrier space-frequency block code was proposed with good PAPR property but yet it is limited to four transmit antennas. These previous single-carrier STC schemes are either rate-limited, restricted to a fixed number of antennas or specifically designed for certain types of modulation (see Table 1 for a comparison), and their construction methods may not be easily generalized. Due to the complex nature of multipath interference, they often resort to numerical searches to obtain the codebooks capable of achieving full diversity. Here, a novel construction method, which is based on multiplexing independent streams of STCs in a time-interleaved fashion and applying respective phase rotations, is investigated. The STCs employed in the independent streams are originally designed for flat fading channels and, while they all achieve full spatial diversity gain in the flat fading channel, they may not always do so in the frequency-selective fading channel. The advantage of our approach is that, by simply multiplexing and judiciously rotating the STCs originally designed for flat fading channel while keeping their original structures intact, it is able to support full-rate transmission and extract full space-time-multipath diversity gain with single-carrier modulation. Specifically, with maximum-likelihood (ML) detection, the proposed scheme may achieve a space-time-multipath diversity order of \(M_{T}\cdot M_{R}\cdot L\), where \(M_{T}\), \(M_{R}\) and \(L\) are the number of transmit antennas, receiver antennas and the number of paths in the tapped-delay-line model of the frequency-selective fading channel, respectively. Both theoretical proofs and simulations are provided in this paper to verify this claim.