Low-Complexity Detection of Signals under Unknown Bandwidth Constraints

Signal detection in environments with unknown signal bandwidth and time intervals is a basic problem in adversarial and spectrum-sharing scenarios. This paper addresses the problem of detecting signals occupying unknown degrees of freedom from non-coherent power measurements where the signal is constrained to an interval in one dimension or a hyper-cube in multiple dimensions. A Generalized Likelihood Ratio Test (GLRT) is derived, resulting in a straightforward metric involving normalized average signal energy on each candidate signal set. To overcome the inherent computational complexity of exhaustive searches, we propose a computationally efficient binary search method, reducing the complexity from O(N^2) to O(N) for the one-dimensional case. Simulations indicate that the method maintains performance near exhaustive searches and achieves asymptotic consistency, with the interval-of-overlap converging to one under constant SNR as measurement size increases. The simulation studies also demonstrate superior performance and reduced complexity compared to contemporary neural network-based approaches, specifically outperforming custom-trained U-Net models in spectrum detection tasks.