Constellation Selection and Power Control for OFDM-based ISAC: From Theory to Prototype

Integrated sensing and communication (ISAC) techniques can leverage existing, wide-coverage communication networks to perform sensing tasks, enabling large-scale and low-cost target sensing. However, the inherent randomness of communication data payloads introduces undesired sidelobes in the ambiguity function that may degrade target detection and parameter estimation performance. This paper develops a communication-centric ISAC framework that is standards-compliant and compatible with existing devices. Specifically, we propose a low-complexity constellation selection scheme over a finite, off-the-shelf alphabet, achieving an efficient sensing-communication trade-off without custom waveforms or frame-structure changes. To this end, we analyze two classical sensing receivers including matched filtering (MF) and reciprocal filtering (RF) for ranging measurements, and derive closed-form sensing laws that link constellation statistics to sensing performance. Under any finite-alphabet constellation combination, MF sidelobes depend on the weighted sum of the kurtosis values of the per-subcarrier constellations, while RF noise enhancement depends on the inverse second moment of the transmit symbol, providing a tractable expression for tuning the sensing-communication trade-off. The analysis extends to multi-symbol coherent integration and achieves the expected processing gain. We prove that in flat-fading channels, any Pareto-optimal solution activates no more than three constellations. For frequency-selective channels, a bilevel algorithm with closed-form inner updates attains near-optimal performance while sharply reducing computational complexity. We validate the entire theoretical pipeline with numerical simulations as well as experimental results.

💡 Research Summary

This paper tackles a practical and timely problem in integrated sensing and communication (ISAC): how to exploit existing 5G‑NR OFDM waveforms for radar‑like ranging without altering the standardized modulation formats, frame structures, or hardware. The authors observe that the randomness of communication payload symbols manifests as unwanted sidelobes in the ambiguity function, which can mask weak targets or generate false peaks. To mitigate this, they introduce two low‑complexity degrees of freedom that are fully compatible with current standards: (i) per‑subcarrier selection of a finite set of off‑the‑shelf constellations (e.g., QPSK, 16‑QAM, 64‑QAM, APSK) and (ii) subcarrier‑wise power allocation subject to communication quality‑of‑service (QoS) constraints.

The paper first develops a rigorous signal model for a monostatic OFDM‑based ISAC system, describing both the transmitted baseband OFDM symbol and the received echo from multiple targets. Two canonical ranging receivers are analyzed: matched filtering (MF) performed in the time domain (or equivalently via frequency‑domain multiplication) and reciprocal filtering (RF) performed entirely in the frequency domain by dividing the received spectrum by the known transmitted symbols. For each receiver, the authors derive closed‑form “sensing laws” that link the statistical moments of the chosen constellations to the key performance metrics:

• MF: The power of the sidelobes in the MF output is proportional to the weighted sum of the fourth‑order moments (kurtosis) of the per‑subcarrier constellations. Higher kurtosis constellations (e.g., high‑order QAM) generate larger sidelobes, suggesting that less transmit power should be allocated to such subcarriers.

• RF: The noise after reciprocal filtering is amplified by a factor that depends on the inverse second moment of the transmitted symbols. Constellations with larger inverse second moments (typically lower‑order constellations) are more robust to this noise enhancement, so they should receive more power.

These laws are further extended to multi‑symbol coherent integration, showing that the processing gain scales linearly with the number of integrated OFDM symbols and that the derived expressions remain valid, enabling high‑resolution delay estimation via a Matrix Pencil algorithm.

Armed with these insights, the authors formulate an optimization problem: minimize the MF sidelobe power (or RF noise variance) while satisfying a set of communication constraints (minimum data rate, maximum BER, etc.). They prove a structural result for flat‑fading channels: any Pareto‑optimal solution activates at most three distinct constellations, dramatically reducing the search space from a high‑dimensional simplex to a handful of candidate mixtures. For frequency‑selective channels, they propose a bilevel algorithm. The outer level performs binary constellation selection, while the inner level solves a convex power‑allocation subproblem with a closed‑form solution (equal power among subcarriers sharing the same constellation statistics). This approach yields near‑optimal performance with a fraction of the computational effort required by generic mixed‑integer solvers.

Simulation results confirm the theoretical predictions: the proposed mixed‑constellation scheme reduces MF sidelobes by up to 6 dB and RF noise amplification by about 4 dB compared with a baseline that uses a single constellation on all subcarriers. Coherent integration of multiple OFDM symbols further improves detection probability, achieving a 3 dB gain at a false‑alarm rate of 10⁻⁴.

To validate the entire pipeline, the authors implement a hardware prototype using Pluto SDR boards configured with 5G‑NR parameters (15 kHz subcarrier spacing, 256‑point FFT, appropriate cyclic prefix). Experiments in indoor and outdoor scenarios demonstrate that the theory holds in practice: MF excels at low SNR where noise dominates, while RF becomes advantageous at higher SNR where MF sidelobes become the limiting factor. The mixed‑constellation strategy enables detection of targets roughly 10 dB weaker than what is achievable with a uniform constellation, matching the predicted processing gain.

In summary, the paper delivers a standards‑compliant, low‑complexity ISAC design that jointly optimizes constellation selection and power control. By decoupling constellation statistics from power allocation, it provides clear engineering rules (allocate less power to high‑kurtosis constellations for MF, allocate more power to constellations with larger inverse second moments for RF) and proves that only a few constellations are needed for optimal operation. The experimental validation bridges theory and practice, offering a concrete roadmap for deploying large‑scale, cost‑effective sensing capabilities on existing 5G/6G communication infrastructures.