RAND

Due to the rapid development of wireless communication and multimedia systems, which are utilized in many modern applications, such as radar detection, ultra-wide band (UWB) transceivers, and software defined radio (SDR), high-speed and high-resolution analog-to-digital converters (ADCs) are required. In order to achieve the requirements of these modern applications, enhancing the speed and the performance of the available ADCs became a must. However, the physical limits of the traditional ADCs are the main obstacle towards pushing their performance to the GHz-regime. The problem comes from the fact that such ADCs are based on the Nyquist sampling theorem, which guarantees the reconstruction of a band-limited signal when it is uniformly sampled with a rate of at least twice its bandwidth. However, many signals of interest have little information content, and may be called sparse or compressible signals in some transform domain. The standard approach is to sample these signals with a rate higher than the Nyquist-rate, then find the most compact representation of the signal in the digital domain (compression techniques) to increase the transmitted information rate. This leads to a large overhead in the amount of sampled data in the case of sparse signals that can be represented with a small number of coefficients.

Over the past two years, a new theory of compressive sensing (CS) and information recovery has emerged, which exploits this knowledge to achieve signal acquisition using fewer measurements than the number prescribed by the Nyquist theorem for certain classes of signals. In particular, CS allows reconstruction of signals which are compressible by some transform (such as Fourier, wavelet, etc.). By leveraging the CS theory, an analog-to-information converter (AIC) may be designed to acquire samples at a lower rate while successfully recovering the compressible signal of interest. Consequently, this theory relaxes the stringent design constraints, which are the source of the problem in the traditional ADCs. Moreover, sending the same information using fewer samples saves the bandwidth and effectively increases the information transmission rate. Utilizing our design methodology, we have succeeded in implementing the first prototype for a compressive sensing based AIC shown in Figure 1. As shown in Figure 2, our hardware prototype has successfully demonstrated accurate reconstruction of signals that were samples at sub-Nyquist rates (down to 1/12 from Nyquist-rate).

Figure 1: The hardware implementation for our AIC prototype used as transmitter/receiver setup

Figure 2: Measurement data from our AIC prototype show the successful reconstruction for signals with sub-Nyquist acquisition rate