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Delay-Doppler Sensing Performance Analysis for MIMO-OFDM ISAC Systems
Peishi Li, Rang Liu, Qian Liu, Ming Li
TL;DR
Communication-centric MIMO-OFDM-ISAC sensing is difficult to characterize because data randomness and beamformed multi-stream illumination shape the RDM, beyond target parameters alone. The paper derives second-order RDM moments and dynamic-range expressions for MF and RF, showing that MF retains a multi-stream floor while RF removes matched-angle target fluctuations but amplifies noise according to reciprocal illumination statistics. The resulting MF/RF tradeoff depends directly on user-target geometry, with numerical results validating these behaviors.
Problem
Multi-antenna communication-centric OFDM-ISAC sensing remains insufficiently characterized because beamformed data streams add randomness to the delay-Doppler response.
Method
The paper analyzes a downlink MIMO-OFDM-ISAC system by deriving RDM second-order moments and dynamic ranges for matched and reciprocal filtering.
Results
MF retains multi-stream, modulation-dependent, and noise floors, whereas RF removes the matched-angle data-induced floor but amplifies noise through reciprocal-power illumination statistics.
Takeaways & Limitations
User-target angular geometry governs the MF/RF tradeoff: MF is comparatively robust under weak illumination, while RF can achieve higher DR when reciprocal-noise amplification is mild.
Abstract
from arXiv · showhide
In communication-centric integrated sensing and communication (ISAC), delay-Doppler sensing reuses data-bearing orthogonal frequency division multiplexing (OFDM) signals rather than dedicated radar probing waveforms. Consequently, the resulting range-Doppler map (RDM) is shaped not only by target parameters, but also by communication-symbol randomness and, in multi-antenna transmissions, by spatial beamforming. While existing analyses have largely focused on single-antenna OFDM-ISAC, the delay-Doppler sensing behavior of multi-antenna OFDM-ISAC remains insufficiently understood. This paper analyzes a multi-input multi-output (MIMO)-OFDM-ISAC system in which multiple data streams jointly illuminate a sensing target. We derive second-order moment expressions for the RDM under matched filtering (MF) and reciprocal filtering (RF), and use them to characterize the dynamic range (DR). The analysis reveals two key multi-stream effects. First, under MF, the random superposition of multiple beamformed streams creates an additional RDM floor beyond the modulation-dependent and receiver-noise terms; therefore, constant-modulus signaling no longer eliminates the data-induced pedestal as in single-antenna OFDM-ISAC. Second, under RF, the matched-angle data-induced floor is removed, but the noise floor is amplified according to the reciprocal-power statistics of the beamformed target illumination. These results show that the user-target angular geometry directly governs the MF/RF tradeoff: MF is more robust under weak illumination, whereas RF can achieve a higher DR when reciprocal-noise amplification is mild. Numerical results validate the analysis and demonstrate the distinct geometry-dependent behaviors of MF and RF.
I. INTRODUCTION
Communication-centric OFDM-ISAC reuses data-bearing waveforms for sensing, but this makes the delay-Doppler response depend on both target parameters and random communication symbols. Existing analyses address these effects mainly for single-antenna systems, leaving multi-antenna behavior insufficiently characterized.
- Communication-centric ISAC reuses data-bearing communication waveforms for sensing, preserving compatibility with existing wireless standards.
- Data reuse makes the sensing waveform random, so the RDM depends on target parameters, information-bearing symbols, and temporal-frequency filtering.
- Single-antenna OFDM-ISAC studies show that constellation moments, pulse shaping, and filtering determine the average sidelobe pedestal and delay-Doppler response.
- Existing single-antenna results do not directly characterize multi-antenna communication-centric ISAC with beamformed multi-stream illumination.
- The paper derives MIMO-OFDM-ISAC RDM second-order moments under MF and RF, characterizes DR, and identifies geometry-dependent differences between the filters.
II. SIGNAL MODEL AND DELAY-DOPPLER PROCESSING
The system reuses a downlink MIMO-OFDM frame carrying multiple data streams for monostatic sensing without dedicated probing signals. Angularly hypothesized MF and RF filters process the random beamformed illumination differently, producing a tradeoff between residual signal fluctuations and reciprocal noise enhancement.
- A downlink monostatic MIMO-OFDM transceiver sends K data-bearing streams across N subcarriers and M OFDM symbols, reusing the same frame for communication and sensing.
- The transmit vector combines deterministic beamforming matrices with independent, zero-mean data symbols whose common fourth-order moment is µ4.
- Constant-modulus signaling has µ4 = 1, whereas circular Gaussian signaling has µ4 = 2 under unit average-power normalization.
- The single-antenna sensing receiver and cyclic-prefix-bounded delay isolate transmit-side random illumination effects while retaining angle dependence through the beamformed echo.
- For an angular hypothesis θ, the processor constructs temporal-frequency filtering from the hypothesized beamformed illumination and forms the corresponding RDM.
- MF matches the echo to hypothesized illumination, while RF normalizes it by that illumination using q_RF_n,m(θ) = 1/b_n,m(θ).
- At the matched angle, MF preserves random illumination power and may create a signal-induced floor, whereas RF cancels target fluctuations but can amplify receiver noise.
III. SECOND-ORDER RDM MOMENT ANALYSIS
For any angular hypothesis, the RDM output is a zero-mean complex random variable driven by the target coefficient, receiver noise, and random beamformed data symbols. Consequently, sensing behavior is characterized through second-order moments.
- The RDM output χθ(l, ν) is determined by the target coefficient, receiver noise, and random beamformed data symbols.
- Both MF and RF produce E{χθ(l, ν)} = 0 because the target coefficient and receiver noise are zero mean and independent of transmitted symbols.
- The paper therefore characterizes delay-Doppler sensing behavior through derived second-order moments.
A. MF Processing
MF produces a coherent delay-Doppler mainlobe over three delay-Doppler-independent background contributions: multi-stream superposition, modulation randomness, and receiver noise. The multi-stream floor persists with constant-modulus signaling, while the modulation-dependent floor vanishes for such constellations.
- A. MF Processing: The MF RDM second moment decomposes into a coherent delay-Doppler response and three background floors caused by multi-stream superposition, modulation randomness, and receiver noise.
- A. MF Processing: The stochastic pedestal is obtained by separating diagonal and off-diagonal terms in the RDM second-moment expansion and applying a fourth-order data-symbol identity.
- A. MF Processing: The MF formulation includes coherent accumulation described by the Dirichlet kernel together with the three background contributions.
- A. MF Processing: The multi-stream contribution arises from random superposition of beamformed streams and remains present under constant-modulus signaling.
- A. MF Processing: The modulation-dependent contribution depends on the fourth-order constellation moment and vanishes for constant-modulus constellations.
- A. MF Processing: The receiver-noise contribution is the noise floor after MF weighting.
B. RF Processing
RF normalizes received echoes by hypothesized beamformed illumination and derives the RF-based RDM second moment under arbitrary angular hypotheses. At the matched angle, RF removes target fluctuations but introduces ratio-variance and reciprocal-filtered noise floors governed by illumination statistics.
- RF assumptions: For unregularized RF, reciprocal terms must be well defined and possess finite second-order moments.The condition ξ_n(θ) < ∞ prevents zero-illumination events for the considered discrete constellation.
- RDM second moment: The RF-based RDM second moment comprises the target response and two background floor contributions under an arbitrary angular hypothesis.The proposition explicitly defines the RF second moment together with its two background terms.
- RDM floors: At the matched angle, RF produces a ratio-variance floor from fluctuations in the beamformed-illumination ratio.RF replaces the MF illumination product with a ratio r_n,m(θ0, θ), whose variance contributes P_RF_var(θ0, θ).
- RDM floors: The reciprocal-filtered noise floor is governed by the reciprocal-power moment ξ_n(θ), which increases when hypothesized illumination can approach zero.This dependence makes RF sensitive to the reciprocal-power statistics of the beamformed illumination.
C. Delay-Doppler Sensing Performance Analysis
At the matched angular hypothesis, MF and RF dynamic range depend on different statistics of random beamformed illumination. MF retains a multi-stream signal-induced floor, while RF removes the matched-angle ratio-variance floor but can amplify noise through reciprocal-power statistics.
- Reciprocal filtering: At the matched angle, RF eliminates the ratio-variance contribution, leaving a noise floor governed by the reciprocal-power moment of target illumination.Near-zero illumination events dominate this reciprocal-power statistic and can amplify the RF noise floor.
- Matched filtering: Constant-modulus symbols minimize the modulation-dependent MF floor, but multi-stream beamformed illumination generally leaves an additional MF floor.The effective illumination is a random beam-domain phasor sum whose magnitude depends on symbol phases and user-target angular geometry.
- SNR behavior: At high sensing SNR, MF approaches a finite dynamic-range ceiling, whereas RF continues increasing linearly when its reciprocal-power moment is finite.MF saturation occurs because its coherent mainlobe and signal-induced floor scale together with target-return power.
- Geometry-dependent tradeoff: The MF/RF tradeoff is governed by average illumination power, the MF signal-induced floor coefficient, and the reciprocal-power moment.These statistics depend on user-target angular geometry in different and generally non-monotonic ways, so no universal MF/RF ordering exists.
- Geometry-dependent tradeoff: MF is more robust at low sensing SNR and under weak or cancellation-prone illumination, whereas RF becomes advantageous when target returns are strong and near-zero illumination events are rare.At low sensing SNR, RF has not yet benefited from removing the signal-induced floor while already incurring reciprocal-noise amplification.
IV. NUMERICAL RESULTS
Numerical results validate the analytical RDM characterization and show that MF and RF exhibit distinct sensing-SNR and target-angle behaviors. MF is comparatively robust to geometry changes, whereas RF is more sensitive to weak or cancellation-prone illumination.
- Validation: Theoretical curves closely agree with Monte Carlo markers, validating the derived second-order moment expressions.The results also exhibit the predicted additional MF pedestal from multi-stream illumination.
- RDM behavior: Even with QPSK, multi-stream illumination visibly elevates the MF sidelobe floor, while 16QAM adds a further modulation-dependent contribution.At the matched angle, RF removes the data-induced fluctuation and its background is mainly governed by receiver noise.
- Sensing-SNR dependence: The MF/RF crossing SNRs are −3.2 dB for QPSK and 1.6 dB for 16QAM, matching the simulated transitions.At high sensing SNR, MF approaches an analytical ceiling, whereas RF continues increasing because its floor remains noise-limited.
- Sensing-SNR dependence: In the low-SNR regime, MF follows the analytical slope controlled by coherent illumination power ρ(θ0), while RF remains shaped by the reciprocal-power moment ξ(θ0).Thus, even under QPSK, MF and RF no longer yield identical dynamic ranges.
- Angular geometry: RF-QPSK can underperform RF-16QAM for some target angles because RF depends on the full beamformed-illumination distribution, not only on the fourth-order modulation moment.Constant-modulus QPSK phasor superposition can create more severe near-zero illumination events for certain geometries.
V. CONCLUSION
The paper analyzes delay-Doppler sensing in MIMO-OFDM ISAC with multi-user beamformed data transmissions and derives matched- and reciprocal-filtering performance expressions. It shows that MF retains multi-stream and modulation-dependent floors, whereas RF removes the matched-angle data-induced floor but is sensitive to reciprocal-power illumination statistics.
- MIMO-OFDM ISAC sensing performance is characterized through closed-form RDM second-order moments and corresponding dynamic-range expressions for MF and RF.
- MF is limited by multi-stream-induced, modulation-dependent, and receiver-noise contributions, while RF removes the matched-angle data-induced floor but depends on reciprocal-power illumination statistics.
- User-target angular geometry directly shapes delay-Doppler target visibility, with MF comparatively robust and RF highly sensitive to weak or cancellation-prone illumination.