Performance Analysis of Orthogonal Time Frequency Space Modulation in High-Doppler Channels

Abstract

Next generation wireless systems are envisioned to offer dependable and consistent user experience across a wide range of environments, including high-mobility scenarios involving high-speed trains, aircrafts, and vehicle-to-vehicle and vehicle-to-infrastructure communications. In such dynamic environments, wireless channels become doubly-dispersive due to the combined effects of multipath propagation causing time dispersion and Doppler shifts causing frequency dispersion. The doubly-dispersive nature of the channels poses significant challenges to traditional multicarrier modulation techniques like orthogonal frequency division multiplexing (OFDM), which suffer from performance degradation due to loss of orthogonality among subcarriers in the presence of high Dopplers. Orthogonal time frequency space (OTFS) modulation is a recently proposed modulation technique that has been shown to be resilient to high Dopplers and deliver significantly improved bit error performance compared to OFDM in high-mobility scenarios. The distinctive feature of OTFS modulation is that it multiplexes information symbols in the delay-Doppler (DD) domain, which is different from multiplexing in the time-frequency domain done in conventional multicarrier modulation schemes like OFDM. Also, the channel is viewed in the DD domain in OTFS. A consequence of this is that rapidly time-varying channels appear as slowly time-varying sparse channels in the DD domain. This, in turn, reduces the DD channel estimation overhead and complexity at the receiver. In this thesis, our main focus is on performance analysis of OTFS modulation under various scenarios. The performance analyses carried out in the thesis consider various aspects of OTFS systems, including antenna selection, decode and forward relaying, role of reconfigurable intelligent surfaces (RIS), and index modulation (IM).

Performance analysis with antenna selection: In the first part of the thesis, we analyze the performance of multi-antenna OTFS systems that employ antenna selection at the receiver and transmitter. The antennas are selected based on the maximum channel Frobenius norms in the DD domain. For receive antenna selection (RAS), we consider single-input multiple-output OTFS (SIMO-OTFS), multiple-input multiple-output OTFS (MIMO-OTFS), and space-time coded OTFS (STC-OTFS) systems. In these systems, we choose $n_s$ antennas from the available $n_r$ receive antennas. We investigate these systems with and without phase rotation (PR). Our diversity analysis results show that, with no PR, SIMO-OTFS and MIMO-OTFS systems with RAS are rank deficient, and therefore they do not extract the full receive antenna diversity as well as the diversity present in the DD domain. Also, Alamouti coded STC-OTFS system with RAS and no PR extracts the full transmit antenna diversity, but it fails to extract the DD diversity. On the other hand, SIMO-OTFS and STC-OTFS systems with RAS become full-ranked when PR is used, because of which they extract the full spatial as well as the DD diversity present in the system. Also, when PR is used, MIMO-OTFS systems with RAS extract the full DD diversity, but they do not extract the full receive antenna diversity because of rank deficiency. In the case of transmit antenna selection (TAS) in MIMO-OTFS systems, $n_s$ antennas are selected out of $n_t$ available transmit antennas. Our analysis for a single resolvable path in the DD channel (i.e., $P=1$) demonstrates that, when $n_s=1$, full spatial diversity of $n_r n_t$ is achieved, meaning full receive diversity of $n_r$ and full transmit diversity of $n_t$ are achieved, due to the underlying symbol difference matrix being full rank. However, when $n_s > 1$, only $n_r$th order receive antenna diversity is achieved because of rank deficiency. For $P>1$, diversity orders are predicted based on the rank of the difference matrices, and these predictions are validated through the computation of pairwise error probability (PEP) bounds and simulations. Our simulation results confirm the analytically predicted diversity performance for RAS and TAS based OTFS systems.

Performance analysis with decode-and-forward relaying: In the second part of the thesis, we consider the performance analysis of MIMO-OTFS systems with decode-and-forward relaying. Cooperative relaying is a widely recognized means to enhance the range and coverage in wireless communications. Amplify-and-forward (AaF) and decode-and-forward (DaF) protocols are widely studied owing to their simplicity and practicality. The performance of communication systems in cooperative relaying environments degrade in the presence of node mobility. The inherent robustness of OTFS can alleviate this issue in cooperative communications with node mobility. Therefore, performance analysis OTFS in cooperative communication systems with node mobility is of interest. Towards this, we consider the performance of OTFS with decode-and-forward (DaF) relaying using multiple antennas at the transmitter, receiver, and relay nodes. Two DaF schemes are considered. The first scheme is a basic DaF scheme, where there is no direct link between source and destination, and communication happens through a single relay in two hops. The second scheme is a selective DaF scheme, where a direct link is present, and there are multiple relays out of which some selected relays aid the communication. We analyze these two schemes, derive closed-form expressions for the end-to-end pairwise error probabilities, and characterize the asymptotic diversity orders achieved in these schemes. We also analyze the considered systems when phase rotation is used to improve the diversity performance. Simulation results are presented to validate the analytically predicted diversity performance for both basic DaF and selective DaF OTFS schemes.

RIS-aided OTFS: Reconfigurable intelligent surface (RIS) assisted communication is a promising new technology. Reconfigurable intelligent surfaces comprising of an array of tunable reflecting elements can be placed in the propagation environment to aid communication by reflecting the incident electromagnetic waves towards the receiver. In the third part of the thesis, we propose an RIS-aided OTFS scheme and investigate the role of RIS in enhancing the performance in OTFS systems. We derive the end-to-end DD domain input-output relation for an RIS-aided OTFS system. The analysis considers the use of bi-orthogonal pulses at the transmitter and receiver with integer DDs, as well as rectangular pulses at the transmitter and receiver with fractional DDs. In the case of rectangular pulses with fractional DDs, we carry out the derivation for two types of OTFS receivers, namely, 1) a two-step receiver, where the received time domain (TD) signal is converted into a DD domain signal in two steps, viz., TD to time-frequency (TF) domain using Wigner transform and TF domain to DD domain using symplectic finite Fourier transform, and 2) a single-step Zak receiver, which uses Zak transform to directly convert the received TD domain signal to DD domain. We maximize the Frobenius norm of the effective end-to-end DD channel matrix of the RIS-aided OTFS system to choose the phase tuning vector at the RIS. Our simulation results demonstrate that RIS-aided OTFS outperforms OTFS without RIS and achieves superior performance compared to RIS-aided OFDM.

OTFS with index modulation: In the fourth part of the thesis, we consider OTFS with index modulation (IM). In IM, information bits are conveyed through indexing of transmission entities such as transmit antennas, time slots, and subcarriers. IM offers the advantages of increased data rates and enhanced performance. In OTFS systems, the information can be conveyed through the indexing of the DD bins. We investigate OTFS with IM (OTFS-IM) in two parts. In the first part, we propose an RIS-aided OTFS scheme in which IM is carried out in the DD domain. We call the proposed scheme as RIS-aided OTFS-IM scheme. We develop an end-to-end DD domain input-output relation for the proposed RIS-aided OTFS-IM scheme and evaluate its bit error performance. We compare different phase selection schemes at the RIS. Our simulation results show that the performance of RIS-aided OTFS improves with the proposed DD domain indexing and increased number of RIS elements. In the second part, we analyze the performance of OTFS-IM in a DaF relaying system. The communication involves two hops between the source and destination nodes through a relay node. We derive a closed-form expression for the end-to-end pairwise error probability in OTFS-IM with DaF relaying and assess the achieved asymptotic diversity order. Our analytical and simulation results show that the use of DD domain indexing improves the performance of OTFS with DaF relaying.