Spectral techniques for high-resolution thermal characterization with limited sensor data

Elevated chip temperatures are true limiters to the scalability of computing systems. Excessive runtime thermal variations compromise the performance and reliability of integrated circuits. To address these thermal issues, state of the art chips have integrated thermal sensors that monitor temperatures at a few selected die locations. These temperature measurements are then used by thermal management techniques to appropriately manage chip performance. Thermal sensors and their support circuitry incur design overheads, die area, and manufacturing costs. In this paper, we propose a new direction for full thermal characterization of integrated circuits based on spectral Fourier analysis techniques. Application of these techniques to temperature sensing is based on the observation that die temperature is simply a space varying signal, and that space varying signals are treated identically to time varying signals in signal analysis. We utilize Nyquist-Shannon sampling theory to devise methods that can almost fully reconstruct the thermal status of an integrated circuit during runtime using a minimal number of thermal sensors. We propose methods that can handle uniform and non uniform thermal sensor placements. We develop an extensive experimental setup and demonstrate the effectiveness of our methods by thermally characterizing a 16-core processor. Our method produces full thermal characterization with an average absolute error of 0.6% using a limited number of sensors.