Orthogonal Time Frequency Space System Research Articles

Secure high-density constellation mapping OTFS modulation scheme with low PAPR

In this paper, a secure orthogonal time-frequency space (OTFS) modulation transmission system based on 3D dense constellation mapping (DCM) geometric shaping is proposed, and a selective reduction amplitude algorithm (SRA) for DCM to reduce peak average power ratio (PAPR) is presented. The DCM is based on regular tetrahedron construction to improve its space utilization efficiency. The proposed SRA involves reducing high PAPRs transmitter and restoring them at the receiving end, which only requires an additional 0.57% of the total transmission capacity. The algorithm reduces PAPR while ensuring the bit error rate performance of the system, so it is suitable for systems that need to process large amounts of transmitted data quickly. By verifying the actual transmission performance on a 2 km of 7-core optical fiber transmission system, the optical transmission with a bit rate of 33.93Gb/s is achieved. The experimental results show that when the bit error rate (BER) reaches the 3.8×10−3 threshold, the OTFS system using DCM and SRA could improve the receiver sensitivity by 3.7 dB compared with the OTFS system using concentric cube mapping and SRA, and 2.7 dB compared with the OFDM system using DCM. After adding the SRA, the PAPR of the OTFS system is reduced by more than 2.2 dB. When the received optical power reaches near the bit error rate threshold, the SRA valid data can be fully recovered by optimizing the SRA.

PAPR analysis in OTFS using the centre phase sequence matrix based PTS method

Orthogonal time–frequency space (OTFS) is a multicarrier modulation technique for high-speed data transfer in wireless communications. In an OTFS system, many subcarriers are used to send the modulated symbols. This makes OTFS signals have a high peak-to-average power ratio (PAPR). We suggest a partial transmit sequence (PTS) approach based on the Centre Phase Sequence Matrix (CPSM) to lower the high PAPR. Furthermore, the suggested method effectively searches for the best possible combination of phase rotation factors to reduce computing complexity. We examine the outcomes regarding bit error rate (BER), power spectral density (PSD), and PAPR to validate the competing transforms in the OTFS system. Along with non-orthogonal multiple access (NOMA), filter bank multi-carrier (FBMC), universal filter multi-carrier (UFMC), and orthogonal frequency division multiplexing (OFDM), the PAPR, BER, and PSD performance of OTFS were also compared. According to the data, the suggested PTS + CPSM reduces PAPR more effectively than the current PTS. It is also mentioned that by increasing the number of sub-blocks (s = 2 and 4), the suggested PTS + CPSM can achieve an even better PAPR rate. According to the experimental results, the suggested approach has dramatically decreased the PAPR while maintaining the BER and PSD performance with the least amount of computational complexity.

DFT-Spread Orthogonal Time Frequency Space System With Superimposed Pilots for Terahertz Integrated Sensing and Communication

Terahertz (THz) integrated sensing and communication (ISAC) is a promising interdisciplinary technology that realizes simultaneously transmitting Terabit-per-second (Tbps) and millimeter-level accurate environment or human activity sensing. However, both communication performance and sensing accuracy are influenced by the Doppler effects, which are especially severe in the THz band. Moreover, peak-to-average power ratio (PAPR) degrades the THz power amplifier (PA) efficiency. In this paper, a discrete Fourier transform spread orthogonal time frequency space (DFT-s-OTFS) system with superimposed pilots is proposed to improve the robustness to Doppler effects and reduce PAPR for THz ISAC. Then, a two-phase sensing parameter estimation algorithm is developed to integrate sensing functionality into the DFT-s-OTFS waveform. Meanwhile, a low-complexity iterative channel estimation and data detection method with a conjugate gradient based equalizer is proposed to recover the data symbols of DFT-s-OTFS. The proposed DFT-s-OTFS waveform can improve the PA efficiency by 10% on average compared to OTFS. Simulation results demonstrate that the proposed two-phase sensing estimation algorithm for THz DFT-s-OTFS systems is able to realize millimeter-level range estimation accuracy and decimeter-per-second-level velocity estimation accuracy. Moreover, the effectiveness of the iterative method for data detection aided by superimposed pilots in DFT-s-OTFS systems is validated by the simulations and the bit error rate performance is not degraded by the Doppler effects.

Iterative channel estimation and data detection algorithm for MIMO-OTFS systems

Channel estimation in high-mobility environments is a challenging problem for advanced mobile communication systems (5G and beyond). In this manuscript, we first propose an iterative algorithm for channel estimation and data detection in the delay-Doppler domain for multiple-input multiple-output orthogonal time frequency space system. Then, in order to increase the spectral efficiency of the system, we use a superimposed pilot pattern. The proposed algorithm takes advantage from the sparse nature of the channel in the delay-Doppler domain and iterates between message passing-aided data detection and data-aided channel estimation. For channel estimation, we propose two algorithms. The first one consists in estimating all channel parameters, including the number of path gains, delay taps, Doppler taps, and channel gains by using a mean-field approximation and the variational Bayesian expectation maximization algorithm. The second one, based on the fact that delay and Doppler taps remain unchanged for a rather long period of time, uses an MMSE approach combined with Cholesky decomposition to only estimate channel gains in each transmitted frame. For data detection, we adapt the message-passing algorithm proposed in the literature. We also derive a lower bound on the signal-to-interference-plus-noise ratio of the proposed scheme, and maximize it by optimally allocating power between pilots and data symbols. Finally, we compare the complexity and the performance in terms of normalized mean square error, bit error rate, and spectral efficiency against existing methods. Simulation results, conducted in high-mobility scenarios show that the proposed algorithm achieves a good compromise between complexity and performance.

Joint channel estimation and data detection for high rate orthogonal time frequency space systems

SummaryThis paper proposes a new pilot pattern in the delay‐Doppler (DD) domain for the orthogonal time frequency space (OTFS) system. In contrast to the embedded‐pilot schemes, guard intervals are not used so as increase the spectral efficiency. Also, compared to the superimposed design where data symbols and pilots are arranged on the entire DD grid, in the proposed rearrangement, the number of pilots used is only spread over a subgrid of the DD grid. Hence, the interference of pilots with data symbols is reduced. Afterwards, an algorithm for channel estimation (CE) and symbol detection in the DD domain benefiting from the sparsity of the DD channel is designed. The sparse CE step is formulated as a specific marginalization of the maximum a posteriori (MAP) criterion by providing a Bayesian approach via the mean‐field approximation that involves the variational Bayesian expectation maximization (VB‐EM) algorithm. Detection of data symbols is done using a low complexity MP algorithm. We also propose an interference cancellation (IC) scheme to mitigate contamination of data by pilots that is run after each CE step. To achieve a high CE accuracy, based on the mean mutual incoherence property (MIP), a pilot optimization problem for OTFS is formulated and develop a simulated annealing‐based algorithm to solve it. Finally, simulation results show that the proposed scheme achieves a good compromise between spectral efficiency, complexity, and performance in terms of bit error rate (BER) and normalized mean square error (NMSE) when compared to literature benchmarks.

Spatial-Index Modulation Based Orthogonal Time Frequency Space System in Vehicular Networks

In this paper, a spatial-index modulation (SIM) based orthogonal time frequency space (OTFS) system, named SIM-OTFS, is proposed to enhance the effectiveness and the reliability of high mobility vehicular networks in intelligent transportation systems. The SIM-OTFS system adopts a three dimensional index modulation (IM) technique which utilizes the transmit antenna, delay, and Doppler indexes in the space and delay-Doppler domains, respectively, to achieve a higher transmission rate. Considering the characteristics of vehicular networks, we first present the SIM-OTFS system design and the corresponding signal processing. Then, we derive the average bit error rate (ABER) upper bound of the SIM-OTFS system by the union bound theory. Moreover, the diversity, the coding gain, and the complexity of the SIM-OTFS system are further investigated. Numerical results verify the theoretical analysis of the ABER and the diversity of the SIM-OTFS system, which shows the superiority of the SIM-OTFS system in the ABER performance over the multiple-input and multiple-output (MIMO) based OTFS (MIMO-OTFS) system. Meanwhile, the SIM-OTFS system realizes better performance than the spatial modulation (SM) and IM based orthogonal frequency division multiplexing (SM-OFDM-IM) system in high mobility vehicular communication with reasonable complexity sacrifice. Furthermore, the influence of the resolvable multipaths of the channel in vehicular networks on the ABER performance of the SIM-OTFS system is also illustrated.

Estimation and Compensation of IQ Imbalance for OTSM Systems

Recently, orthogonal time sequency multiplexing (OTSM) waveform was proposed using Walsh Hadamard transform (WHT) for doubly-dispersive channels at a lower modulation/demodulation complexity than orthogonal time frequency space (OTFS) waveform. At high frequencies, hardware imperfections such as in-phase and quadrature (IQ) imbalance is prominent at the transceiver. In this letter, the input-output (I/O) relation in the delay-sequency domain is derived under these impairments at the receiver. The impairment parameters are estimated in the delay-time domain and are compensated in the time domain using proposed dual pilot approach. The normalized mean square error (NMSE) of the estimated imbalance parameters is evaluated and it is observed that NMSE reduces with increase in SNR and with reduction in mobility. The results are evaluated with OTFS system and it is observed that the NMSE performance of OTSM is similar to OTFS under high pilot power and high SNR at no excess pilot power. The bit error rate performance of the compensated system is evaluated and its performance is close to the ideal system.

Analysis, Estimation and Compensation of Hardware Impairments for CP-OTFS Systems

Orthogonal time frequency space (OTFS) waveform, which is robust to doubly-selective fading channels is a strong contender for the Fifth generation (5G) communications. At high frequencies, hardware imperfections are prominent in practice at the transceivers. In this letter, we consider impairments such as carrier frequency offset (CFO), direct current (DC) offset and in-phase and quadrature (IQ) imbalance at the transmitter (Tx) and receiver (Rx) for cyclic prefix (CP) OTFS system. We derive the input-output (I/O) relation in the delay-Doppler (DD) domain under these impairments and show that due to the DC offset and IQ imbalance, image Doppler interference (IDI) appears along the Doppler domain and the CFO becomes part of the channel parameters. We estimate impairment parameters in the DD domain and compensate these at Tx and Rx in the time domain. The normalized mean square error (NMSE) of the estimated imbalance parameters are evaluated and it is observed that NMSE reduces with increase in, pilot power, number of Doppler bins and with windowing techniques applied in time-frequency (TF) domain.

Nonlinear companding transforms for reducing the PAPR of OTFS signal

In this paper, two non-linear companding transforms, namely exponential and sine hyperbolic, are proposed to reduce the peak to average power ratio (PAPR) of the orthogonal time frequency space (OTFS) modulation signal. The companding transforms are normalized such that the average power remains the same before and after companding. The resulting transforms have a saturation kind of characteristics for larger amplitudes of a signal while enhancing the smaller amplitudes slightly, which leads to a reduction of PAPR significantly. To validate the companding transforms in the OTFS system, we analyze the results in terms of PAPR, transform gain, attenuation factor, and bit error rate (BER). Also, compared the PAPR and BER performance of OTFS with OFDM, and the existing μ-law and clipping methods in OTFS. The results signify that the proposed companding transforms outperform the existing μ-law and clipping methods for PAPR reduction.

Design and analysis of spatial modulation based orthogonal time frequency space system

In this paper, we design a spatial modulation based orthogonal time frequency space (SMOTFS) system to achieve improved transmission reliability and meet the high transmission rate and high-speed demands of future mobile communications, which fully utilizes the characteristics of spatial modulation (SM) and orthogonal time frequency space (OTFS) transmission. The detailed system design and signal processing of the SM-OTFS system have been presented. The closed-form expressions of the average symbol error rate (ASER) and average bit error rate (ABER) of the SM-OTFS system have been derived over the delay-Doppler channel with the help of the union bounding technique and moment-generating function (MGF). Meanwhile, the system complexity has been evaluated. Numerical results verify the correctness of the theoretical ASER and ABER analysis of the SM-OTFS system in the high signal-to-noise ratio (SNR) regions and also show that the SM-OTFS system outperforms the traditional SM based orthogonal frequency division multiplexing (SM-OFDM) system with limited complexity increase under mobile conditions, especially in high mobility scenarios.

Low-Dimensional Subspace Estimation of Continuous-Doppler-Spread Channel in OTFS Systems

Orthogonal time frequency space (OTFS) has shown to be a promising modulation technology that achieves the robust wireless transmission in high-mobility environments. The high mobility incurred Doppler effect in OTFS system, is represented as a continuous and relatively large band in the Doppler frequency. It yields the equivalent channel responses (ECRs) in the system change significantly within one symbol block, posing a challenge to channel estimation (CE) or tracking. In order to tackle this issue, in this paper, a set of transform-domain basis functions is designed to span a low-dimensional subspace for modeling the OTFS channel. Then, the CE can be performed by estimating a few projection coefficients of ECRs in the developed subspace, with training pilots. According to the individual transmission characteristic of OTFS signal, we propose a corner-inserted pilot pattern, which targets the low pilot overhead and satisfactory CE performance. Moreover, an OTFS signal detector, leveraging the time-domain channel equalization, linear-complexity interference cancellation and delay-Doppler domain maximal ratio combining detection, is developed to retrieve the transmitted data symbols. The simulations show the precisely estimated ECRs enable the detector to ideally demodulate 256-ary quadrature amplitude modulation signaling, under a velocity of 550 km/h at 5.9 GHz carrier frequency.

Low-Complexity Linear Equalization for OTFS Modulation

In this letter, we propose low-complexity linear equalizers for orthogonal time frequency space (OTFS) modulation that exploit the structure of the effective channel matrix in OTFS. The proposed approach exploits the block circulant nature of the OTFS channel matrix to achieve significant complexity reduction. For an $N\times M$ OTFS system, where $N$ and $M$ are the number of Doppler and delay bins, respectively, the proposed approach gives exact minimum mean square error (MMSE) and zero-forcing (ZF) solutions with just $\mathcal {O}(MN \log MN)$ complexity, while MMSE and ZF solutions using the traditional matrix inversion approach require $\mathcal {O}(M^{3}N^{3})$ complexity. The proposed approach can provide low complexity initial solutions for local search techniques to achieve enhanced bit error performance.

High Throughput Mobile Communication Based on OTFS System with the Delay-Doppler Compensation

In this paper, we like to propose a high throughput mobile communication system that can work even at the very high vehicular speed. Generally, mobility and data throughput has inverse relationship. Also, very complicated receiver structure is required and takes a long time processing for compensating the Doppler frequency due to the high speed mobility. Seriously, the communication performance becomes degraded with the increase of the dimension of multiple input and multiple output (MIMO), since the delay Doppler problem becomes bigger the higher dimension of MIMO. So, it is greatly important to design the very robust mobile communication that can provide the high throughput even at the very high vehicular speed system. Design and performance evaluation of the orthogonal time frequency space (OTFS) modulation system and OTFS-based MIMO system are described and analyzed at the very high mobility environment. OTFS modulation can concisely compensate the delay-Doppler spreading effect by using two dimensional inverse discrete Fourier transform and discrete Fourier transform operation. It enables OTFS system to transmit high-speed data. Especially, OTFS-MIMO system can transmit data stream of each antenna without the communication performance degradation even in the high Doppler frequency environments. As simulation results, it is confirmed that the capacity of 1 × 1 OTFS system is a similar to each stream of 2 × 2 OTFS-MIMO system. That is, 2 × 2 MIMO system can completely double the communication capacity in comparison with 1 × 1 OTFS system even in the very high Doppler frequency channel such as high speed mobile environments. This remarkable performance can continue in the very high dimensional MIMO system and simultaneously in the high mobility situation.

OTFS(Orthogonal Time Frequency Space) 변조를 사용하는 MIMO(Multiple Input Multiple Output) 시스템 설계와 성능 평가

In this paper, we have evaluated and analyzed OTFS(Orthogonal Time Frequency Space) modulation and OTFS-MIMO(Multiple Input Multiple Output) system. OTFS modulation can concisely compensate delay-Doppler spreading effect by using 2D(2-Dimension) iDFT (inverse Discrete Fourier Transform) and DFT(Discrete Fourier Transform) operation. It enables OTFS system to transmit high-speed data. Especially, OTFS-MIMO system can transmit all data streams without performance degradation on high Doppler frequency channel. As simulation results, we have confirmed that 1×1 OTFS system’s achievable rate is a similar to each stream of 2×2 OTFS-MIMO system. That is, we have also confirmed that 2×2 MIMO system can completely achieve double achievable rate in comparison with OTFS system on high Doppler frequency channel.