Wireless Communications

The recently proposed orthogonal time–frequency–space (OTFS) modulation technique was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) over delay-Doppler channels. In this paper, we first derive the explicit input–output relation describing OTFS modulation and demodulation (mod/demod). We then analyze the cases of: 1) ideal pulse-shaping waveforms that satisfy the bi-orthogonality conditions and 2) rectangular waveforms which do not. We show that while only inter-Doppler interference (IDI) is present in the former case, additional inter-carrier interference (ICI) and inter-symbol interference (ISI) occur in the latter case. We next characterize the interferences and develop a novel low-complexity yet efficient message passing (MP) algorithm for joint interference cancellation (IC) and symbol detection. While ICI and ISI are eliminated through appropriate phase shifting, IDI can be mitigated by adapting the MP algorithm to account for only the largest interference terms. The MP algorithm can effectively compensate for a wide range of channel Doppler spreads. Our results indicate that OTFS using practical rectangular waveforms can achieve the performance of OTFS using ideal but non-realizable pulse-shaping waveforms. Finally, simulation results demonstrate the superior error performance gains of the proposed uncoded OTFS schemes over OFDM under various channel conditions.

Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation

Orthogonal time frequency space (OTFS) modulation is a recently introduced multiplexing technique designed in the 2-dimensional (2D) delay-Doppler domain suited for high-Doppler fading channels. OTFS converts a doubly-dispersive channel into an almost non-fading channel in the delay-Doppler domain through a series of 2D transformations. In this paper, we focus on MIMO-OTFS which brings in the high spectral and energy efficiency benefits of MIMO and the robustness of OTFS in high-Doppler fading channels. The OTFS channel-symbol coupling and the sparse delay-Doppler channel impulse response enable efficient MIMO channel estimation in high Doppler environments. We present an iterative algorithm for signal detection based on message passing and a channel estimation scheme in the delay-Doppler domain suited for MIMO-OTFS. The proposed channel estimation scheme uses impulses in the delay-Doppler domain as pilots for estimation. We also compare the performance of MIMO-OTFS with that of MIMO-OFDM under high Doppler scenarios.

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MIMO-OTFS in High-Doppler Fading Channels: Signal Detection and Channel Estimation

Orthogonal time-frequency space (OTFS) is a two-dimensional (2D) modulation technique designed in the delay-Doppler domain. A key premise behind OTFS is the transformation of a time-varying multipath channel into an almost non-fading 2D channel in the delay-Doppler domain such that all symbols in a transmission frame experience the same channel gain. It has been suggested in the recent literature that the OTFS can extract full diversity in the delay-Doppler domain, where full diversity refers to the number of multipath components separable in either the delay or Doppler dimension, but without formal analysis. In this paper, we present a formal analysis of the diversity achieved by the OTFS modulation along with supporting simulations. Specifically, we prove that the asymptotic diversity order of the OTFS (as SNR $\rightarrow \infty $ ) is one. However, in the finite SNR regime, the potential for a higher order diversity is witnessed before the diversity one regime takes over. Also, the diversity one regime is found to start at lower BER values for increased frame sizes. We also propose a phase rotation scheme for the OTFS using transcendental numbers and show that the OTFS, with this proposed scheme, extracts full diversity in the delay-Doppler domain.

On the Diversity of Uncoded OTFS Modulation in Doubly-Dispersive Channels

Orthogonal time frequency space (OTFS) modulation is a 2-dimensional (2D) modulation scheme designed in the delay-Doppler domain, unlike traditional modulation schemes which are designed in the time-frequency domain. Through a series of 2D transformations, OTFS converts a doubly-dispersive channel into an almost non-fading channel in the delay-Doppler domain. In this domain, each symbol in a frame experiences an almost constant fade, thus achieving significant performance gains over existing modulation schemes such as OFDM. The sparse delay-Doppler impulse response which reflects the actual physical geometry of the wireless channel enables efficient channel estimation, especially in high-Doppler fading channels. This paper investigates OTFS from a signal detection and channel estimation perspective, and proposes a Markov chain Monte-Carlo sampling based detection scheme and a pseudo-random noise (PN) pilot based channel estimation scheme in the delay-Doppler domain.

On OTFS Modulation for High-Doppler Fading Channels

The focus of this paper is on the performance of orthogonal frequency division multiplexing (OFDM) signals in mobile radio applications, such as 802.11a and digital video broadcasting (DVB) systems, e.g., DVB-CS2. The paper considers the evaluation of the error probability of an OFDM system transmitting over channels characterized by frequency selectivity and Rayleigh fading. The time variations of the channel during one OFDM symbol interval destroy the orthogonality of the different subcarriers and generate power leakage among the subcarriers, known as inter-carrier interference (ICI). For conventional modulation methods such as phase-shift keying (PSK) and quadrature-amplitude modulation (QAM), the bivariate probability density function (pdf) of the ICI is shown to be a weighted Gaussian mixture. The large computational complexity involved in using the weighted Gaussian mixture pdf to evaluate the error probability serves as the motivation for developing a two-dimensional Gram-Charlier representation for the bivariate pdf of the ICI. It is demonstrated that its truncated version of order 4 or 6 provides a very good approximation in the evaluation of the error probability for PSK and QAM in the presence of ICI. Based on Jakes' model for the Doppler effects, and an exponential multipath intensity profile, numerical results for the error probability are illustrated for several mobile speeds

/pdf/performance-degradation-of-ofdm-systems-due-to-doppler-28wre4f459.pdf

E. Masry

Papers

Performance degradation of OFDM systems due to Doppler spreading