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Orthogonal Time Frequency Space (OTFS) Modulation Based Radar System
P. Raviteja, Khoa T. Phan, Yi Hong, Emanuele Viterbo
TL;DR
The paper addresses whether OTFS can improve radar range and velocity estimation under Doppler conditions that limit OFDM-based radar. It proposes an OTFS matched-filter algorithm using full-frame random data, and numerical results show accurate high-Doppler estimation alongside practical transmission and tracking benefits.
Problem
The paper investigates whether OTFS is suitable for radar processing of target range and velocity in conditions where OFDM suffers Doppler-related limitations.
Method
The paper proposes an OTFS-based matched-filter algorithm that processes random equal-power symbols occupying a full OTFS frame to estimate target ranges and velocities.
Results
OTFS detects both range and velocity without error in the reported 975 m, 80 m/s case and has zero RMSE across the reported high-velocity simulations, unlike OFDM.
Takeaways & Limitations
OTFS-based radar supports longer range, faster tracking, and larger Doppler-frequency estimation than the paper's conventional OFDM-based radar comparison.
Abstract
from arXiv · showhide
Orthogonal time frequency space (OTFS) modulation was proposed to tackle the destructive Doppler effects in wireless communications, with potential applications to many other areas. In this paper, we investigate its application to radar systems, and propose a novel efficient OTFS-based matched filter algorithm for target range and velocity estimation. The proposed algorithm not only exhibits the inherent advantages due to multi-carrier modulation of the existing orthogonal frequency division multiplexing (OFDM-) based radar algorithms but also provides additional benefits to improve radar capability. Similar to OFDM, OTFS spreads the transmitted signal in the entire time--frequency resources to exploit the full diversity gains for radar processing. However, OTFS requires less cyclic prefix, and hence, shorter transmission duration than OFDM, allowing longer range radar and/or faster target tracking rate. Additionally, unlike OFDM, OTFS is inter-carrier interference-free, enabling larger Doppler frequency estimation. We demonstrate the performance of the proposed algorithm using numerical results under different system settings.
I. INTRODUCTION
Existing OFDM-based radar and RadCom systems face Doppler-related limitations, motivating investigation of OTFS for radar processing. The paper proposes an OTFS matched-filter algorithm for estimating target range and velocity while exploiting OTFS's time–frequency spreading, shorter cyclic-prefix overhead, and ICI-free operation.
- High-mobility and dense-traffic applications expose limitations in current RadCom and radar systems.
- OFDM-based radar suffers Doppler intolerance, while OFDM communications degrade under high Doppler environments.
- OTFS multiplexes information symbols over two-dimensional orthogonal basis functions designed for time-varying delay–Doppler channels.
- The paper proposes an OTFS-based matched filter that estimates potential target counts, ranges, and velocities using random equal-power symbols across a full OTFS frame.
- OTFS uses less cyclic-prefix overhead than OFDM, shortening transmission duration and supporting longer range or faster target tracking.
- OTFS radar is ICI-free and can detect Doppler frequencies up to Δf, whereas OFDM exactly detects them only up to 10% of Δf.
II. OTFS-BASED RADAR
This section introduces the OTFS-based radar signal model used to develop the matched-filter radar algorithm.
- The paper describes the signal model that provides the foundation for its OTFS-based matched-filter radar algorithm.
A. Basic OTFS concepts/notations
OTFS discretizes time–frequency and delay–Doppler resources into M×N grids with defined sampling intervals, frame duration, bandwidth, and quantization steps.
- The time–frequency plane is discretized into an M×N grid sampled at intervals T and Δf = 1/T.
- Modulated samples X[n,m] occupy an OTFS frame of duration T_f = NT and bandwidth B = MΔf.
- The delay–Doppler plane is discretized into an M×N grid over delay region (0,T] and Doppler region (−Δf/2,Δf/2].
- The delay and Doppler quantization steps are 1/(MΔf) and 1/(NT), respectively.
B. OTFS-based radar signal model
The radar model maps delay–Doppler symbols through OTFS modulation and transforms, representing targets by channel taps with ranges and velocities on a discretized grid.
- Random delay–Doppler symbols are mapped to time–frequency samples using ISFFT, then transformed into the transmitted radar signal with a transmit pulse.
- The model assumes P targets with ranges R_i and relative velocities V_i, where velocities may be positive or negative.
- Each target is characterized by round-trip delay τ_i and Doppler frequency ν_i, determined using carrier frequency, propagation speed, range, and velocity.
- The delay–Doppler channel represents each target with complex gain h_i and a Dirac delta function at its delay and Doppler.
- Detectable delay and Doppler ranges are (0,1/Δf] and (−1/(2T),1/(2T)], with targets assumed to lie on integer grid multiples of the respective resolutions.
- Received time-domain data are filtered and sampled into Y[n,m], then transformed by SFFT into delay–Doppler symbols y[k,l] for radar processing.
- For rectangular pulses, the OTFS input–output relation is a two-dimensional circular convolution with an additional location-dependent phase shift and additive noise.
III. OTFS-BASED RADAR MATCHED FILTER ALGORITHM
The paper estimates the delay–Doppler radar channel, and therefore target ranges and velocities, using a matched filter applied to known transmit and received OTFS symbols. The gain matrix becomes effectively diagonal for large MN, supporting efficient detection of multiple targets.
- Radar processing estimates h(τ, ν) from known transmit and received OTFS symbols to obtain target ranges and velocities.
- The proposed matched filter computes ˆh = eXHy = Gh + ew to estimate the delay–Doppler channel.The gain matrix is G = eXH eX, and ew represents filtered noise.
- The vectorized model represents y, x, and w as MN-dimensional vectors, with H mapping transmitted symbols and channel coefficients to received symbols.
- The transmit symbols are i.i.d. QPSK symbols with power Ps, enabling analysis of the gain matrix G.
- As MN increases, normalized off-diagonal elements of G converge to zero in the mean-square sense, making G effectively diagonal for sufficiently large MN.This diagonal dominance supports approximating filtered noise as an i.i.d. Gaussian vector.
- The matched-filter detector can locate multiple targets differing in distance or relative velocity, with complexity O((MN)^2).
A. Advantages of OTFS-based radar over OFDM-based radar
OTFS-based radar offers advantages over OFDM-based radar in transmission-time efficiency and tolerance to high Doppler frequencies. These properties support longer-range sensing, faster tracking, and larger Doppler estimation ranges.
- The two principal OTFS radar advantages are reduced time-resource requirements and improved performance under high Doppler interference.
- OTFS radar uses one cyclic prefix for NM symbols, whereas OFDM radar uses N cyclic prefixes.
- OTFS saves (N −1)L symbols of transmission time, supporting longer-range targets and more frequent detection for faster tracking.
- OFDM exactly detects Doppler frequencies only up to 10% of the subcarrier spacing ∆f, while OTFS detects up to ∆f without interference.
IV. SIMULATION RESULTS AND DISCUSSION
Numerical simulations compare OTFS and OFDM radar processing across range, velocity, RMSE, PSLR, and image SNR. OTFS accurately estimates range and velocity under high Doppler, while its PSLR and image SNR remain independent of target velocity.
- Range and velocity profiles: OTFS detects both range and velocity without error for a target at R = 975 m and V = 80 m/s, whereas OFDM has a 19 m/s velocity error.OFDM detects the range without error but suffers high ICI at high Doppler.
- Range and velocity profiles: OTFS has higher PSLR than OFDM for the R = 975 m, V = 80 m/s target.The lower OFDM PSLR is attributed to high ICI caused by Doppler at 65% of ∆f.
- Velocity RMSE: At ±90 m/s, OFDM velocity RMSE exceeds 25%, while OTFS has zero RMSE across the evaluated relative velocities.The evaluation uses 100 Monte Carlo simulations with target velocities set as integer multiples of the velocity resolution.
- PSLR and image SNR: OTFS radar PSLR and image SNR are independent of target relative velocity across the evaluated SNR values.At lower SNRs, image SNR approaches the estimated noise-based value; at high SNR, image SNR saturates to 1/MN.
- PSLR and image SNR: The high-SNR saturation values of OTFS PSLR and image SNR could be improved with more efficient detection algorithms.The paper identifies this improvement as future work.
V. CONCLUSION
The paper proposes an efficient OTFS-based matched-filter algorithm for radar range and velocity determination. Its results indicate improved capability for long-range and high-velocity target detection compared with OFDM-based radar.
- Conclusion: The proposed OTFS-based matched filter determines object range and velocity in radar systems.The conclusion characterizes the algorithm as novel and efficient.
- Conclusion: OTFS-based radar provides longer range, faster tracking rate, and larger Doppler frequency estimation than OFDM-based radar.These benefits accompany the inherent advantages of multi-carrier modulation.
- Conclusion: OTFS-based radar with adequate detection algorithms is presented as a promising robust technique for detecting long-range and high-velocity targets.
APPENDIX PROOF OF LEMMA 1
The appendix proves statistical properties of the matched-filter quantity G[i, j]. It uses independent identically distributed data and index-matching conditions to simplify its mean and variance terms.
- Mean of G[i, j]: The expected value of G[i, j] simplifies to zero for off-diagonal elements using the i.i.d. property of x[k, l].
- Variance of G[i, j]: The variance of G[i, j] is expressed through a decomposition into terms involving MNP^2 and F_i,j.
- Variance of G[i, j]: F_i,j can be non-zero only when four specified modular index-matching conditions on k and l are satisfied.
- Variance of G[i, j]: Under those conditions, F_i,j simplifies to zero, completing the proof.