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Low Complexity Modem Structure for OFDM-based Orthogonal Time Frequency Space Modulation
Arman Farhang, Ahmad RezazadehReyhani, Linda E. Doyle, Behrouz Farhang-Boroujeny
TL;DR
OFDM suffers interference in doubly dispersive channels, motivating OTFS's Doppler-delay signaling for time-varying wireless channels. The paper formulates OFDM-based OTFS in discrete time, omits transmitter windowing, and combines transform and OFDM blocks to obtain substantially simpler modem structures. Its complexity analysis reports computational savings relative to existing OTFS structures.
Problem
OFDM performs poorly in doubly dispersive channels because Doppler spread imposes interference, while prior OTFS work provided limited guidance on window selection.
Method
The paper develops a discrete-time OFDM-based OTFS formulation, omits transmitter windowing, retains receiver windowing, and combines SFFT operations with OFDM blocks.
Results
The proposed modem structure substantially reduces computational complexity compared with existing OTFS structures.
Takeaways & Limitations
Combining the SFFT and OFDM modulator or demodulator blocks yields low-complexity OTFS transmitter and receiver structures.
Abstract
from arXiv · showhide
Orthogonal time frequency space (OTFS) modulation is a two-dimensional signaling technique that has recently emerged in the literature to tackle the time-varying (TV) wireless channels. OTFS deploys the Doppler-delay plane to multiplex the transmit data where the time variations of the TV channel are integrated over time and hence the equivalent channel relating the input and output of the system boils down to a time-invariant one. This signaling technique can be implemented on the top of a given multicarrier waveform with the addition of precoding and post-processing units to the modulator and demodulator. In this paper, we present discrete-time formulation of an OFDM-based OTFS system. We argue against deployment of window functions at the OTFS transmitter in realistic scenarios and thus limit any sort of windowing to the receiver side. We study the channel impact in discrete-time providing deeper insights into OTFS systems. Moreover, our derivations lead to simplified modulator and demodulator structures that are far simpler than those in the literature.
I. INTRODUCTION
OTFS addresses the difficulty of OFDM in doubly dispersive, time-varying channels by multiplexing data in the Doppler-delay domain. This paper develops a discrete-time OFDM-based formulation, omits transmitter windowing in realistic scenarios, and derives simpler modem structures.
- Motivation: OFDM performs poorly in doubly dispersive channels because channel Doppler spread imposes substantial interference.Shortening OFDM symbols can reduce channel variation within each symbol, but the constant cyclic-prefix length lowers spectral efficiency.
- OTFS approach: OTFS multiplexes transmit data in a two-dimensional Doppler-delay domain and converts a time-varying channel into an equivalent time-invariant one.It adds precoding and post-processing to a multicarrier waveform while seeking time and frequency diversity in doubly dispersive channels.
- Prior work: Prior OTFS work proposed windowing at both transmitter and receiver, but provided little guidance on window selection and mainly evaluated OFDM transmission.The paper identifies limited understanding of window choices and limited numerical coverage as gaps in prior work.
- Paper contribution: The paper formulates OFDM-based OTFS in discrete time and combines its transform operations with OFDM modulation and demodulation to simplify the modem.The study limits time-frequency signal modulation to OFDM and analyzes channel impact in discrete time.
- Windowing choice: Transmitter windowing is omitted because effective windows require packet-specific channel-variation knowledge unavailable at the transmitter.Receiver-side windowing is retained because iterative channel estimation and equalization may enable an effective sparse-channel window; that topic is left for future study.
II. OFDM-BASED OTFS SYSTEM
The OFDM-based OTFS system transforms Doppler-delay QAM symbols into time-frequency samples, processes them through OFDM with cyclic prefixes, and reverses these operations at reception over an LTV channel.
- Transmitter: An M × N block of Doppler-delay QAM symbols is first converted to time-frequency samples through the inverse SFFT.The symbols are indexed by k = 0, . . . , M − 1 and l = 0, . . . , N − 1.
- Transmitter: The time-frequency samples are directly fed into the OFDM transmitter without transmit windowing.The resulting matrix is processed into OFDM time-domain signals, with cyclic prefixes added before vectorization into the baseband transmit signal.
- OFDM realization: The OFDM implementation uses an M × N time-frequency matrix, DFT-based processing, cyclic-prefix addition, serialization, and interleaving.The cyclic-prefix matrix is formed from the last MCP rows of the M-point identity matrix, where MCP is the CP length.
- Channel model: Assuming MCP ≥ L, received OFDM symbols are free of intersymbol interference before demodulation.Here L is the channel length and the received signal has passed through a linear time-varying channel with additive noise.
- Receiver: At the receiver, OFDM-demodulated samples are windowed and transformed by the SFFT back to the Doppler-delay domain.The resulting OTFS receiver output is described as a two-dimensional circular convolution of the data symbols with a time-invariant Doppler-delay channel response.
III. CHANNEL IMPACT
The channel-impact analysis expresses OTFS input-output relations in matrix form and characterizes when the Doppler-delay channel becomes a two-dimensional circular convolution. The resulting linear system also supports standard and soft detection methods.
- III. CHANNEL IMPACT: The discrete-time formulation expands the SFFT-based OTFS model to analyze how the channel affects transmitted data symbols.This expansion provides insight into OTFS and supports derivation of the modem structure.
- III. CHANNEL IMPACT: With separable receiver windowing, the receiver output is represented using a two-dimensional window matrix applied to the time-frequency samples.The window coefficients separate into factors that window the columns and rows of the intermediate matrix.
- III. CHANNEL IMPACT: When each OFDM-symbol channel matrix is circulant, the matrix relation realizes a 2D circular convolution between the windowed Doppler-delay channel response and the data matrix.This follows because the relevant matrices are block circulant with circulant submatrices, preserving that structure under multiplication.
- III. CHANNEL IMPACT: The Doppler-delay channel response is formed from the first columns of the OFDM-symbol channel matrices after windowing.Its elements are specified through the corresponding windowed channel-matrix entries.
- III. CHANNEL IMPACT: The resulting linear system can serve as a basis for ZF, MMSE, and soft detectors or equalizers.It relates the vectorized received data to the vectorized transmitted data through the channel model and noise.
IV. PROPOSED MODEM STRUCTURE
The proposed OFDM-based OTFS modem combines Fourier operations that otherwise appear separately in the OTFS and OFDM blocks. This yields simplified transmitter and receiver implementations, with receiver windowing restricted to a separable form.
- IV. PROPOSED MODEM STRUCTURE: Receiver-side windowing is considered channel independent, separable, and applied only at the receiver.The paper notes that frequency-domain windowing can increase delay-domain channel support and degrade sparsity.
- IV. PROPOSED MODEM STRUCTURE: The inverse SFFT’s M-point DFT and the OFDM modulator’s IDFT cancel, allowing transmission through M size-N IDFTs applied to the rows of X.Cyclic prefixes are then added to the columns of the resulting matrix.
- IV. PROPOSED MODEM STRUCTURE: The proposed transmitter distributes QAM symbols across M size-N IDFT blocks, serializes and interleaves their outputs, and adds a cyclic prefix to each block.Its output is the vectorized form of the matrix S.
- IV. PROPOSED MODEM STRUCTURE: At the receiver, the OFDM demodulator’s DFT and the SFFT’s IDFT cancel, reducing the demodulator to window scaling and size-N DFTs on rows.The serialized output sequence is formed from the elements of the receiver matrix.
V. COMPLEXITY ANALYSIS
The complexity analysis compares the proposed modem with existing OTFS and OFDM structures using complex multiplication counts. Combining Fourier blocks substantially reduces the proposed OTFS modem’s computational burden.
- V. COMPLEXITY ANALYSIS: Existing OTFS modem structures require significantly more complex multiplications than their OFDM counterparts.The paper attributes this difference to the separate inverse SFFT and SFFT blocks in those structures.
- V. COMPLEXITY ANALYSIS: Because the number of OFDM symbols N is much smaller than the FFT size M in practical packets, the proposed OTFS modem may be less complex than OFDM.The proposed design combines the inverse SFFT and SFFT with the OFDM modulator and demodulator blocks.
VI. CONCLUSION
The paper formulates OFDM-based OTFS in discrete time, studies channel effects, and combines OTFS Fourier processing with OFDM operations. The resulting modem structures provide substantial computational savings over existing designs.
- VI. CONCLUSION: The paper’s analysis shows that the SFFT−1/SFFT and OFDM modulator/demodulator blocks can be combined.This combination leads to low-complexity OTFS modulator and demodulator structures.
- VI. CONCLUSION: The proposed OTFS modem structure offers substantial computational-complexity savings compared with existing structures.