Efficient data acquisition is key in diverse fields such as bio-medical applications, radar, communications, image processing and more. We develop efficient sensing approaches based on either rethinking the hardware components, improving the dynamic range, optimizing for a relevant task, or taking the signal structure into account. Several examples of our new sensing devices are given below.
Time Encoding Machine (TEM)
The time encoding machine (TEM) is an asynchronous event-driven method that samples and quantizes timings rather than amplitudes. Since TEM is not dependent on a global clock, it consumes less power. Furthermore, in contrast to traditional ADCs, increasing the signal's amplitude reduces the timing quantization dynamic range, cutting the number of bits per sample required. Thus, we can reduce power and bits while leveraging low-cost and simple hardware by combining TEM sampling with our robust recovery algorithms for a variety of signals.
Unlimited Dynamic Range ADC
Transmission medium or processing devices have limited dynamic range, meaning that signals beyond a certain dynamic range are clipped. A modulo operation can be used to limit the dynamic range prior to transmission. We suggest a robust modulo operation and recovery method with high accuracy, which enables sampling and processing signals of wide dynamic range using a small number of bits.
Analog Precoder 16X4
Another aspect we address in the lab is taking the specific task into account in order to reduce both sampling and quantization rates. Conventional ADCs are designed to facilitate recovery of the received signals by sampling at the Nyquist rate and using high resolution quantizers. However, to meet the ever-increasing demand for higher data rates nowadays, the dimensionality and bandwidth of the received signals can be extremely high. To address this issue, we propose efficient task-based quantization using the fact that, in practice, signals are often acquired in order to extract some underlying information, i.e., for a specific task. Our task-based approach first introduces an analog combiner which reduces the dimensionality of the input and then scalar quantizers are employed considering practical hardware limitations, followed by a digital domain processing module. This allows the acquisition of many classes of signals using low bit systems.
Finally, by exploiting structure in a wide class of analog signals, we can reduce sampling and processing rates to far below the Nyquist rate. Our approach relies on modeling the structure as a union of subspaces, and then designing preprocessing that aliases the signal prior to sampling. The aliased signal has lower dimension and can therefore be sampled at a low sub-Nyquist rate. Compressed sensing methods are then used to recover the underlying signal. Examples of this approach include low-rate sampling of pulse streams for radar and ultrasound and low-rate sampling of multiband signals for cognitive radio.
Sub-Nyquist Radar Prototype
We designed a Xampling-based hardware prototype that allows sampling of radar signals at rates much lower than Nyquist. We demonstrate by real-time analog experiments that our system is able to maintain reasonable detection capabilities, while sampling radar signals that require sampling at a rate of about 30MHz at a total rate of 1Mhz, namely, at 1/30 of the Nyquist rate even in the presence of strong noise and clutter.
Sub-Nyquist Radar with Distorted Pulse Shape
The radar prototype below can be extended to the blind setting where the pulse shape is not known by adding an additional receiver. The performance with two sub-Nyquist receivers is the same as that of a single sub-Nyquist system with a known pulse.
Multiple-Input Multiple-Output (MIMO) radar
Extending the ideas to a collocated multiple-input multiple-output (MIMO) radar. The setup allows reduced rate sampling in both the spatial and spectral domains at rates much lower than dictated by the Nyquist sampling theorem. We use frequency division multiplexing (FDM) to achieve the orthogonality of MIMO waveforms and apply the Xampling framework for signal recovery.
- H. Naaman, et al. "Time-Based Quantization for FRI and Bandlimited Signals", arXiv preprint arXiv:2110.01928 (2021).
- H. Naaman, S. Mulleti and Y. C. Eldar, "FRI-TEM: Time Encoding Sampling of Finite-Rate-of-Innovation Signals", Submitted to Transactions on Signal Processing, June 2021.
- Azar, Eyar, Satish Mulleti, and Yonina C. Eldar. "Residual Recovery Algorithm For Modulo Sampling" arXiv preprint arXiv:2110.03335 (2021).
- N. Shlezinger, Y. C. Eldar and M. R. D. Rodrigues, "Hardware-Limited Task-Based Quantization", IEEE Transactions on Signal Processing, vol. 67, issue 20, pp. 5223-5238, October 2019.
- N. Shlezinger, Y. C. Eldar and M. R. D. Rodrigues, "Asymptotic Task-Based Quantization with Application to Massive MIMO", IEEE Transactions on Signal Processing, vol. 67, issue 15, pp. 3995-4012, August 2019.
- N. Shlezinger and Y. C. Eldar, "Task-Based Quantization with Application to MIMO Receivers", Communications in Information and Systems, vol. 20, issue 2, pp. 131-162, 2020.
- F. Xi, N. Shlezinger, and Y. C. Eldar, "BiLiMO: Bit-Limited MIMO Radar via Task-Based Quantization", Transactions on Signal Processing, vol. 69, pp. 6267-6282, September 2021.
- Y. C. Eldar, "Recovering Lost Information in The Digital World", SIAM News, vol. 51, issue 9, pp. 1,3, November 2018.
- D. Cohen, S. Tsiper and Y. C. Eldar, "Analog to Digital Cognitive Radio: Sampling, Detection and Hardware", IEEE Signal Processing Magazine, vol. 35, issue 1, pp. 137-166, January 2018.
- D. Cohen and Y. C. Eldar, "Sub-Nyquist Radar Systems: Temporal, Spectral and Spatial Compression", IEEE Signal Processing Magazine, vol. 35, issue 6, pp. 35-58, November 2018.
- A. Kipnis, A. Goldsmith and Y. C. Eldar, "Analog-to-Digital Compression: A New Paradigm for Converting Signals to Bits", IEEE Signal Processing Magazine, vol. 35, issue 3, pp. 16-39, May 2018.