Integrated sensing and communication over fragmented 6G spectra: theoretical limits and sparse signal processing

Future sixth-generation (6G) networks are expected to natively integrate sensing and communication (ISAC) by sharing hardware and spectrum. As spectrum scarcity makes large contiguous allocations increasingly impractical, OFDM sensing must operate over fragmented bands. However, non-contiguous allocations generate severe grating lobes in the delay profile, impairing the detection of weak or closely spaced targets.This thesis investigates OFDM radar under strong spectral fragmentation and develops a unified mathematical framework for two complementary regimes: deterministic multiband allocation and stochastic QAM thinning resulting from the suppression of low-power symbols. The effects of spectral geometry are characterized in terms of delay resolution, peak-to-sidelobe ratio (PSLR), and peak-to-noise-floor ratio (PNFR). To mitigate spectral-gap distortions, a computationally efficient two-dimensional orthogonal matching pursuit (OMP) algorithm is developed for joint delay-Doppler estimation in sparse scenarios. It exploits Fourier-transform-based correlations and an efficient least-squares formulation and is combined with an MDL-based criterion for blind target-number estimation. Physical-layer simulations validate the analytical models and show that the proposed sparse reconstruction significantly outperforms conventional periodogram-based estimation. For the same number of active sensing subcarriers, highly fragmented allocations can improve resolution and target-separation capability when paired with appropriate sparse reconstruction. Thus, spectral fragmentation need not be merely a constraint, but can provide an additional design degree of freedom for flexible and efficient resource sharing in future 6G ISAC networks.