This paper presents a linear complexity iterative rake detector for the recently proposed orthogonal time frequency space (OTFS) modulation scheme. The basic idea is to extract and coherently combine the received multipath components of the transmitted symbols in the delay-Doppler grid using maximal ratio combining (MRC) to improve the SNR of the combined signal. We reformulate the OTFS input-output relation in simple vector form by placing guard null symbols or zero padding (ZP) in the delay-Doppler grid and exploiting the resulting circulant property of the blocks of the channel matrix. Using this vector input-output relation we propose a low complexity iterative decision feedback equalizer (DFE) based on MRC. The performance and complexity of the proposed detector favorably compares with the state of the art message passing detector. An alternative time domain MRC based detector is also proposed for even faster detection. We further propose a Gauss-Seidel based over-relaxation parameter in the rake detector to improve the performance and the convergence speed of the iterative detection. We also show how the MRC detector can be combined with outer error-correcting codes to operate as a turbo DFE scheme to further improve the error performance. All results are compared with a baseline orthogonal frequency division multiplexing (OFDM) scheme employing a single tap minimum mean square error (MMSE) equalizer.

Low Complexity Iterative Rake Decision Feedback Equalizer for Zero-Padded OTFS systems

We elaborate on the recently proposed orthogonal time frequency space (OTFS) modulation technique, which provides significant advantages over orthogonal frequency division multiplexing (OFDM) in Doppler channels. We first derive the input-output relation describing OTFS modulation and demodulation (mod/demod) for delay-Doppler channels with arbitrary number of paths, with given delay and Doppler values. We then propose a low-complexity message passing (MP) detection algorithm, which is suitable for large-scale OTFS taking advantage of the inherent channel sparsity. Since the fractional Doppler paths (i.e., not exactly aligned with the Doppler taps) produce the inter Doppler interference (IDI), we adapt the MP detection algorithm to compensate for the effect of IDI in order to further improve performance. Simulations results illustrate the superior performance gains of OTFS over OFDM under various channel conditions.

Low-complexity iterative detection for orthogonal time frequency space modulation

This article focuses on a new path division multiple access (PDMA) for both uplink (UL) and downlink (DL) massive multiple-input multiple-output network over a high mobility scenario, where the orthogonal time frequency space (OTFS) is adopted. First, the 3D UL channel model and the received signal model in the angle-delay-Doppler domain are studied. Secondly, the 3D-Newtonized orthogonal matching pursuit algorithm is utilized for the extraction of the UL channel parameters, including channel gains, directions of arrival, delays, and Doppler frequencies, over the antenna-time-frequency domain. Thirdly, we carefully analyze energy dispersion and power leakage of the 3D angle-delay-Doppler channels. Then, along UL, we design a path scheduling algorithm to properly assign angle-domain resources at user sides and to assure that the observation regions for different users do not overlap over the 3D cubic area, i.e., angle-delay-Doppler domain. After scheduling, different users can map their respective data to the scheduled delay-Doppler domain grids, and simultaneously send the data to base station (BS) without inter-user interference in the same OTFS block. Correspondingly, the signals at desired grids within the 3D resource space of BS are separately collected to implement the 3D channel estimation and maximal ratio combining-based data recovery over the angle-delay-Doppler domain. Then, we construct a low complexity beamforming scheme over the angle-delay-Doppler domain to achieve inter-user interference free DL communication. Simulation results are provided to demonstrate the validity of our proposed unified UL/DL PDMA scheme.

A New Path Division Multiple Access for the Massive MIMO-OTFS Networks

: Research in the area of matrix-based signal processing included matric theory, numerical and parallel computing, signal processing and a Very Large Scale Integration implementation. Results of the research are summarized in the final report with details in the publications and proceedings issued during the course of the research.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA231226&Location=U2&doc=GetTRDoc.pdf

Fast Algorithms for Signal Processing

Orthogonal time frequency space (OTFS) is a two-dimensional modulation scheme realized in the delay-Doppler domain, which targets the robust wireless transmissions in high-mobility environments. In such scenarios, OTFS signal suffers from multipath channel with continuous Doppler spread, which results in significant inter-symbol interference and inter-Doppler interference (IDI). In this article, we analyze the interference generation mechanism, and compare statistical distributions of the IDI in two typical cases, i.e., limited-Doppler-shift channel and continuous-Doppler-spread channel (CoDSC). Focusing on the OTFS signal transmission over the CoDSC, our study firstly indicates that the widespread IDI incurs a computational burden for the element-wise detector like the message passing in the state-of-the-art works. Addressing this challenge, we propose a block-wise OTFS receiver by exploiting the structure and characteristics of the OTFS transmission matrix. In the receiver, we deliberately design an iteration strategy among the least squares minimum residual based channel equalizer, reliability-based symbol detector and interference eliminator, which can realize fast convergence by leveraging the sparsity of channel matrix. The simulations demonstrate that, in the CoDSC, the proposed scheme achieves much less detection error, and meanwhile reduces the computational complexity by an order of magnitude, compared with the state-of-the-art OTFS receivers.

/pdf/low-complexity-symbol-detection-and-interference-32q870nco3.pdf

Low-Complexity Symbol Detection and Interference Cancellation for OTFS System

Orthogonal time frequency space modulation is a two dimensional (2D) delay-Doppler domain waveform. It uses inverse symplectic Fourier transform (ISFFT) to spread the signal in time-frequency domain. To extract diversity gain from 2D spreaded signal, advanced receivers are required. In this work, we investigate a low complexity linear minimum mean square error receiver which exploits sparsity and quasi-banded structure of matrices involved in the demodulation process which results in a log-linear order of complexity without any performance degradation of BER.

Low complexity LMMSE Receiver for OTFS

Low Complexity LMMSE Receiver for OTFS

In the last few years, orthogonal time frequency space (OTFS) modulation has received significant attention as an alternative to OFDM especially for high mobilty scenarios. In this work, we develop a delay-Doppler domain embedded pilot based time domain channel estimation for cyclic prefix (CP)-OTFS in the presence of residual frame timing offset, carrier frequency offset and fractional multiple Doppler. One of the reasons for time domain processing is that the time domain channel representation is relatively more sparse as compared to its delay Doppler domain representation in the presence of residual synchronization errors. We also describe a time domain low complexity linear minimum mean square error (MMSE) equalization and successive interference cancellation (SIC) receiver for LDPC (low density parity check) coded CP-OTFS in this work. We further show the impact of residual frame timing offset, carrier frequency offset and fractional multiple Doppler on OTFS symbols. It is seen from the extensive Monte Carlo simulation results that the estimation and compensation methods presented here provide necessary resilience properties to OTFS. We bring out the tolerance of OTFS to such residual synchronization errors. It is further observed that the SIC is able to improve the performance of the system such that it almost matches that of the ideal knowledge based MMSE equalization. We also show the performance of RCP (reduced CP)-OTFS when used with the developed channel estimation and equalization algorithms. A unified signal processing flow for OTFS and orthogonal frequency division multiplexing (OFDM) is also described in this work to motivate studies on coexistence between the two as well as to encourage investigations on a seamless transition between OFDM and OTFS based systems for future adaptive air interface design.

/pdf/time-domain-channel-estimation-and-equalization-of-cp-otfs-3rwyubr1s4.pdf

Time Domain Channel Estimation and Equalization of CP-OTFS Under Multiple Fractional Dopplers and Residual Synchronization Errors

Orthogonal time–frequency space (OTFS) is being pursued in recent times as a suitable wireless transmission technology for use in high-mobility scenarios. In this article, we propose nonorthogonal multiple access (NOMA) based OTFS which may be called NOMA-OTFS system and evaluate its performance from a system-level and link-level perspective. The challenge lies in the fact that while OTFS transmission technology is known for its resilience to high-mobility conditions, while NOMA is known to yield high spectral efficiency (SE) in low-mobility scenarios in comparison to orthogonal multiple access (OMA). We present a minimum mean square error (MMSE)-successive interference cancellation based receiver for NOMA-OTFS, for which we derive expression for symbol-wise postprocessing SINR in order to evaluate system sum SE. We develop power allocation schemes to maximize the sum SE in the high-mobility version of NOMA. We further design a realizable codeword-level SIC (CWIC) receiver using low-density parity check (LDPC) codes along with MMSE equalization for evaluating link-level performance of such practical NOMA-OTFS system. The system-level and link-level performance of the proposed NOMA-OTFS system are compared against benchmark OMA-OTFS, OMA-orthogonal frequency division multiplexing (OMA-OFDM) and NOMA-OFDM schemes. From system-level performance evaluation, we observe interestingly that NOMA-OTFS provides higher system sum SE than OMA-OTFS. When compared to NOMA-OFDM, we find that outage SE of NOMA-OTFS is improved at the cost of decrease in mean SE. The link-level results additionally show that the developed CWIC-based NOMA-OTFS receiver performs significantly better than NOMA-OFDM in terms of block error rate, goodput, and throughout.

Nonorthogonal Multiple Access With Orthogonal Time–Frequency Space Signal Transmission

Orthogonal time frequency space (OTFS) modulation is a recently proposed waveform for reliable communication in high-speed vehicular communication scenarios. It has better resilience to inter-carrier interference (ICI) than orthogonal frequency division multiplexing (OFDM). In this work, we describe OTFS as block-OFDM with a cyclic prefix and time interleaving. This interpretation helps one visualize OTFS in the light of OFDM as well as it also helps in analyzing the gain obtained by OTFS over OFDM. Further, we compare the performance of OTFS with its contender 5G new radio (NR)'s OFDM configuration of variable subcarrier bandwidth (VSB-OFDM) while considering practical forward error correction codes and 3GPP high-speed channel model. This provides realistic performance comparison, which is highly desired for technology realization. Considering practical channel estimation, we find that OTFS outperforms VSB-OFDM with 5G NR parameter by about 5dB. We also present results on peak to average power ratio (PAPR) due to specific pilot structure used in OTFS for channel estimation.

Vivek Rangamgari

Papers

Low complexity LMMSE Receiver for OTFS

Low Complexity LMMSE Receiver for OTFS

Time Domain Channel Estimation and Equalization of CP-OTFS Under Multiple Fractional Dopplers and Residual Synchronization Errors

Nonorthogonal Multiple Access With Orthogonal Time–Frequency Space Signal Transmission

OTFS: Interleaved OFDM with Block CP