Reducing the Analog and Digital Bandwidth Requirements of RF Receivers for Measuring Periodic Sparse Waveforms

In this paper, a prototype setup for measuring wideband periodic waveforms whose bandwidth surpasses the analog bandwidth of a radio-frequency receiver is presented. Three major challenges arise in the analog-to-digital stage when measuring such wideband waveforms: the availability of a high sampling rate based on a good amplitude resolution; the availability of the required analog bandwidth to capture the full waveform; and achieving the previous requirements in a cheap way. Those challenges are more pronounced when using wideband modulated signals to test nonlinear devices and when measuring/sensing wideband spectra for cognitive radio applications. For periodic signals, undersampling techniques based on the evolved harmonic sampling can be used to reduce the sampling rate requirements while satisfying a good amplitude resolution. For sparse signals, a technique based on channelization and signal separation is proposed. This technique splits the spectrum of the waveform into parallel channels, downconverts them to the analog frequency band of the analog-to-digital converter (ADC), spreads the channel information, sums them, and then digitizes with a single ADC. Using reconstruction algorithms based on l
₁
-norm minimization, the information of the parallel channels can be separated. The original wideband spectrum can be then reconstructed after de-embedding of the channelization process.