Improved modeling and bounds for NQR spectroscopy signals

Nuclear Quadrupole Resonance (NQR) is a method of detection and unique characterization of compounds containing quadrupolar nuclei, commonly found in many forms of explosives, narcotics, and medicines. Typically, multi-pulse sequences are used to acquire the NQR signal, allowing the resulting signal to be well modeled as a sum of exponentially damped sinusoidal echoes. In this paper, we improve upon the earlier used NQR signal model, introducing an observed amplitude modulation of the spectral lines as a function of the sample temperature. This dependency noticeably affects the achievable identification performance in the typical case when the substance temperature is not perfectly known. We further extend the recently presented Cramér-Rao lower bound to the more detailed model, allowing one to determine suitable experimental conditions to optimize the detection and identifiability of the resulting signal. The theoretical results are carefully motivated using extensive NQR measurements.