This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information into the standard recovery procedure by maximizing the correlation between the prior knowledge and the desired signal. We then establish performance guarantees (in terms of the number of measurements) for the proposed method under sub-Gaussian measurements. Specific structured signals including sparse vectors, block-sparse vectors, and low-rank matrices are also analyzed. Furthermore, we present an interesting geometrical interpretation for the proposed procedure. Our results demonstrate that if prior information is good enough, then the proposed approach can (remarkably) outperform the standard recovery procedure. Simulations are provided to verify our results.

This paper reports a side-by-side comparison of two wireless and passive sensing systems: inductive and electromagnetic (EM) couplings for an application of in-situ and real-time monitoring of wafer cleanliness in the rinsing process at semiconductor/microelectromechanical system (MEMS) manufacturing facilities. A MEMS sensor is designed to measure the resistivity of water, corresponding to the ionic concentration, to evaluate the rinsing process inside the micro-features. The transponder, containing the MEMS sensor, receives power from an external interrogator, modulates the resistivity data, and emits back the modulated signal to the interrogator, in all wireless and battery-free operation. Two wireless systems based on inductive and EM couplings have been implemented on 4-inch glass wafers, maintaining the wafer form factor. Inductive coupling system has parasitic electric field coupling. The working distance of the inductive coupling system is attenuated in water and is likely limited by signal-to-noise ratio (SNR), while that of the EM coupling is primarily limited by the coupled power. Hence, inductive coupling is suitable for a short distance measurement that allows more sophisticated functionality with sufficient power, whereas EM coupling could be optimized for long distance detection but has a tight power budget. The implemented on-wafer wireless monitoring units achieve a working distance of 6 and 25 cm with a concentration resolution of less than 2% (4 ppb for a 200 ppb solution) for inductive and EM couplings, respectively.

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