Calibration of a speckle-based compressive sensing receiver

Optical speckle in a multimode waveguide has been proposed to perform the function of a compressive sensing (CS) measurement matrix (MM) in a receiver for GHz-band radio frequency (RF) signals. Unlike other devices used for the CS MM, e.g. the digital micromirror device (DMD) used in the single pixel camera, the elements of the speckle MM are not known before use and must be measured and calibrated. In our system, the RF signal is modulated on a repetitively pulsed chirped wavelength laser source, generated from mode-locked laser pulses that have been dispersed in time or from an electrically addressed distributed Bragg reflector laser. Next, the optical beam with RF propagates through a multimode fiber or waveguide, which applies different weights in wavelength (or equivalently time) and space and performs the function of the CS MM. The output of the guide is directed to or imaged on a bank of photodiodes with integration time set to the pulse length of the chirp waveform. The output of each photodiode is digitized by an analog-to-digital converter (ADC), and the data from these ADCs are used to form the CS measurement vector. Accurate recovery of the RF signal from CS measurements depends critically on knowledge of the weights in the MM. Here we present results using a stable wavelength laser source to probe the guide.