Moshe Mishali

Xampling: Analog to Digital at Sub-Nyquist Rates

Based on the papers:

M. Mishali and Y. C. Eldar, "From Theory to Practice: Sub-Nyquist sampling of Sparse Wideband Analog Signals", IEEE Journal of Selected Topics on Signal Processing, vol. 4, no. 2, pp. 375-391, April 2010. (Talk).
M. Mishali, Y. C. Eldar and A. Elron, " Xampling: Signal Acquisition and Processing in Union of Subspaces", CCIT Report #747 Oct-09, EE Pub No. 1704, EE Dept., Technion - Israel Institute of Technology; [Online] arXiv 0911.0519, Oct. 2009.
M. Mishali, Y. C. Eldar, O. Dounaevsky and E. Shoshan, "Xampling: Analog to Digital at Sub-Nyquist Rates", IET Circuits, Devices & Systems, vol. 5, no. 1, pp. 8–20, Jan. 2011.

The circuit work was presented in SiPS 2010, San-Francisco, CA:
M. Mishali, Y. C. Eldar, O. Dounaevsky and E. Shoshan "Sub-Nyquist Acquisition Hardware for Wideband Communication", IEEE Workshop on Signal Processing Systems (SiPS), pp. 156 -161, October 2010.
The poster can be downloaded from here.
Additional material is found on the software page.

Sub-Nyquist Signal Acquisition Hardware

The Modulated Wideband Converter (MWC) samples multiple narrowband transmissions, at a low rate, proportional to the actual bandwidth occupation, without knowledge of the carrier positions. Photos of the hardware boards appear below. Our hardware can treat 2 GHz Nyquist-rate input signals with spectrum occupancy up to 120 MHz. The sampling rate can be made as low as 280 MHz, which is only 14\% of the Nyquist rate, approaching the lowest possible rate for multiband signals with unknown carrier positions. This web page summarizes a series of lab experiments which verify the circuit design and prove that the system accommodates a wide dynamic range of input powers, reaching up to 50 dB. Read more in [3]. A GUI package that demonstrates the MWC capabilities is available online. Additioanl software packages can be downloaded from the software page.

The analog board (left pane) realizes 4 sampling channels, including the amplification path, mixing with a given set of periodic functions (connectors on the rear), and lowpass filtering.The digital board (right pane) provides sign-alternating periodic waveforms, which are derived from a single shift-register chain.

More details on the theory and algorithms behind this sub-Nyquist system can be found here
Testing and verification setup	Testing and verification setup	A demonstration setup of the MWC hardware (newline) National instruments cards + LabView environment	The experiment setup

Periodic Mixing of Mutliband Wideband Communication

The Modulated Wideband Converter (MWC) treats multiple narrowband transmissions, without prior knowledge on their carrier frequencies. To accomplish this goal, mixing with a set of periodic waveforms aliases the entire wideband spectrum to low rate frequencies. The following experiment demonstrates the effect of periodic mixing. Several transmissions are concurrently aliased to the origin.

The video presents a set of experiments that were conducted at lab in order to verify the design of the modulated wideband converter.

Spectrum-Blind Reconstruction from Sub-Nyquist Sampling

The crown glory experiment -- reconstruction from sub-Nyquist sampling. Three signal generators that were combined at the input terminal of the MWC prototype: an amplitude-modulated (AM) signal at 807.8 MHz with 100 kHz envelope, a frequency-modulation (FM) source at 631.2 MHz with 1.5 MHz frequency deviation and 10 kHz modulation rate, and a pure sine waveform at 981.9 MHz. The carrier positions were chosen so that their aliases overlay at baseband, as the photos below demonstrate. The digital recovery algorithm (CTF) was executed and detected the correct support set . The unknown carrier frequencies were estimated up to 10 kHz accuracy. In addition, correct reconstruction of the AM and FM signal contents is validated.

Wideband Spectrum Sensing for Cognitive Radio

Based on the paper:
M. Mishali and Y. C. Eldar, "Wideband Spectrum Sensing at sub-Nyquist Rates," submitted, May 2010.

Mobile cognitive radio (CR) aims at utilizing unused frequency regions on an opportunistic basis. Commercialization of CR technology necessitates a spectrum sensing mechanism that reacts in real time to cognitive decisions.

The Modulated Wideband Converter (MWC) provides a mixed analog-digital spectrum sensing method that is especially suited to the typical wideband setting of CRs. The advantages of the MWC system with respect to previous spectrum sensing methods are threefold. First, the analog front-end is fixed and does not involve scanning hardware. Second, both the analog-to-digital conversion (ADC) and the digital signal processing (DSP) rates are substantially below Nyquist. Finally, the sensing resources are shared with the reception path of the CR, so that the lowrate streaming samples can be used for communication purposes of the device, besides the sensing functionality they provide. Combining these advantages leads to a real time map of the spectrum with minimal use of mobile resources.

To verify the sensing potential of the MWC in a wideband environment, we use the following setup. An HP-E4432B signal generator inputs a sinusoid to the MWC hardware. The four output channels were recorded using an Agilent Infiniium 54855A four-channel scope. All digital computations were carried out in Matlab. The pure sinusoid represents a challenging scenario of a legacy user with extremely narrow bandwidth. We varied the sinusoid frequency from 100 MHz to 1100 MHz in steps of 5 MHz. The CTF outputs the spectral support at resolution 20 MHz. The DSP estimates the carroer position. The results demonstrate that out of these 200 experiments, there are only 2 outliers, which means 99% correct support and carrier estimation. The outliers stem from solving an MMV system with polynomial-time sub-optimal, rather than optimal exponential-time algorithms (see text for a detailed discussion).

ICASSP Hardware Demo: Joint Collaboration with National Instruments

The Modulated Wideband Converter (MWC) was presented in the Show&Tell event of ICASSP'10. With the generous support of National Instruments (NI), a PXI-based chassis was introduced. The PXI solution provides the MWC with a multiband signal and allowed to control the spectral support during the live demonstration.

In addition, the PXI-based system received the outputs from the system and visualized their spectrum, proving that high-rate frequencies are aliased to baseband.

The Modulated Wideband Converter (MWC)

Hardware Demo: The Modulated Wideband Converter (MWC)

The Modulated Wideband Converter (MWC) was presented in the Show&Tell event of ICASSP'10.
In the picture: Yonina Eldar presenting the ICASSP demonstration. To her left stands Dr. James Truchard, CEO, president and co-founder of National Instruments corp. Prof. Al Oppenheim from MIT stands to the right.

To view the poster from the event: High Quality (3.7 MB) or Low Quality (150 kB).

The MWC hardware and related work were presented in the following conferences:

M. Mishali, Y. C. Eldar and J. A. Tropp "Efficient Sampling and Stable Reconstruction of Wide Band Sparse Analog Signals", Proc. of IEEEI, 25th convention, pp. 290-294 (Talk). Best Student Paper Award.
M. Mishali and Y. C. Eldar, "Low-rate Wideband Receiver", Proceedings of the 2009 Workshop on Sampling Theory and Applications (SampTA'09), May 2009.
M. Mishali, A. Elron and Y. C. Eldar, "Sub-Nyquist Processing with the Modulated Wideband Converter," IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP 2010), pp. 3626--3629, March 2010.
Y. Chen, M. Mishali, Y. C. Eldar, and A. O. Hero III, "Modulated wideband converter with non-ideal lowpass filters," IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP 201008), pp. 3630--3633, March 2010.
M. Mishali and Y. C. Eldar, "Xampling: Analog Data Compression", DCC 2010, pp. 366--375, June 2010.
M. Mishali, Y. C. Eldar, O. Dounaevsky and E. Shoshan "Sub-Nyquist Acquisition Hardware for Wideband Communication", IEEE Workshop on Signal Processing Systems (SiPS), pp. 156 -161, October 2010 (Poster).

Moshe Mishali --- Homepage

Xampling: Analog to Digital at Sub-Nyquist Rates