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NSF, NSERC, MIT CICS
Fred Chen, Omid Abari, Fabian Lim (co-PI), Prof. Anantha Chandrakasan, Prof. Vladimir Stojanovic
Compressed sensing (CS) is a groundbreaking, technique for sub-Nyquist sampling (data compression) of sparse signals, and has many potential applications.
One of the such applications of CS is in wireless sensors, to reduce transmission energy by first compressing the data that needs to be transmitted.
Another potential application is in Analog Information Converters (AIC) for high-speed sampling. If the signal frequencies are high, but information rates are low, AICs have been proposed as a potential solution to overcome the resolution and performance limitations of traditional, Nyquist-rate high-speed analog-to-digital converters (ADC), whose performance and resolution are often limited by sampling jitter, aperture and other circuit impairments.
This project is aimed at advancing compressed sensing techniques on both hardware and theoretical fronts.
We look at key issues which determine the practicality of CS technologies for various applications.
Hardware design and circuit archictures for CS-based (wireless) sensors
The utility of a wireless sensor node is limited by its finite energy source and the replacement cost of the node once the source has been exhausted. We begin by examining the sensor node's energy consumption, and explore algorithms and circuit architectures that might significantly improve on the energy-efficiency of sensor nodes and hence extend their utility. Figure 1 shows the typical circuit blocks used in sensors for medical monitoring and their associated energy cost and power consumption at a given sample rate. As Fig. 1 shows, the radio power is typically dominant so any reduction in the amount of data transmitted essentially reduces the system power likewise. Therefore, the high energy cost to transmit a bit of information and the radio’s limited bandwidth, necessitate data compression/filtering at the sensor in order to reduce energy consumption and data throughput.
In , we present the design and implementation of a new sensor system architecture, based on the theory of compressed sensing (CS). This allows efficient reduction of the number of bits transmitted, while preserving the original signal information. This approach reduces the average radio power by exploiting signal sparseness to encode the data at a high compression factor . We also find that the reconstruction (decompression) enables power reduction in the frontend circuitry, via a relaxation of both noise and resolution requirements of the AFE and ADC. The universality of CS allows the same techniques to apply to a wide variety of signals, while only requiring these signals to be sparse. In conjunction with the compressed sensing work, a new DAC switching algorithm for SAR ADCs aimed at reducing area and enabling more parallel architectures has also been developed .
Fig 1. Energy and power costs for typical components in bio-sensor applications. It is assumed that the DSP performs some sort of data reducation and that the TX power scales with data rate.
Fig 2. Proposed compressed sensing based system architecture
- F. Chen, A.P. Chandrakasan, and V. Stojanovic, “Design and Analysis of a Hardware-Efficient Compressed Sensing Architecture for Data Compression in Wireless Sensors,” IEEE Journal of Solid-State Circuits, vol. 47, no. 3, pp. 744-756, March 2012.(paper)
- F. Chen, A. Chandrakasan, and V. Stojanovic, and E. Alon, "A Signal-agnostic Compressed Sensing Acquisition System for Wireless and Implantable Sensors," IEEE Custom Integrated Circuits Conference, September, 2010. (paper)
- F. Chen, A. Chandrakasan, and V. Stojanovic, "A Low-power Area-efficient Switching Scheme for Charge-sharing DACs in SAR ADCs," IEEE Custom Integrated Circuits Conference, September, 2010. (paper)
End-to-End evaluation framework for CS systems
A pratical CS system is limited by numerous factors, e.g. quantization and channel noise, operating energy costs, signal quality, etc. To make an informed decision on the practicality of such a system, we developed a methodology for performing end-to-end evaluations of CS systems. We applied this methodology framework to i) wireless sensors  and ii) analog-to-information convertors (AIC) . We encourage other research groups to also apply the methodology to their applications, where our code is freely available online (site).
Fig 1. Comparing a traditional ADC-based sensor with a CS-based one
Figure 1 above shows system diagrams for wireless sensors, on top is the traditional ADC-based system, and the bottom the newer CS-based sytem. The ADC-based system uses no compression. Figure 2 belows hows our energy cost comparisons, as found by applying our end-to-end framework evaluation. The plot is made as follows. For a given signal quality (this is measured by the percent root difference (PRD) metric, for both systems we optimize various parameters (i.e. no of quanitization bits, compression ratio, etc) to find the minimum operating point. We do this for both average-case and worst-case PRD. Here we are mainly interested in transmission energy (for CS we ignore energy burned in the reconstruction back-end). As we can see, the CS system achieves about 10X in energy savings, at higher distortions (for average-PRD the savings are also seen in the lower distortion regime).
We also apply the same framework while incorporating error control strategies. On the right of Figure 2, we describe an error control scheme where each transmitted (compressed) sample (represented in a bit sequence) is protected by an error detection code. If the sample is detected as corrupted, we simply throw it away and recover based on the other samples. We observe good gains using small error detection codes (cyclic redundency check CRC-1 and CRC-5 with small number of parity bits). Using simple codes eases implementation demands.
Fig 2. Evaluating tradeoffs between min. energy points and signal qualities of CS systems
In  we also apply the same framework for the AIC system for high-speed systems. While CS archiectures are speculated to relax sampling requirements, we found little advantages of AIC over high speed ADCs. This is because the signal encoding, typically realized with a mixer-like circuit, still needs to occur at the Nyquist frequency of the input to avoid aliasing. The jitter and aperture in the mixer stage of AICs is found to similarly limit the resolution of AICs.
- F. Chen, F. Lim, O. Abari, A.P. Chandrakasan, and V. Stojanovic, "Energy-Aware Design of Compressed Sensing Systems for Wireless Sensors under Performance and Reliability Constraints", accepted for publication in IEEE Transactions on Circuits and Systems I.
- O. Salehi-Abari, F. Chen, F. Lim, and V. Stojanovic, "Performance Trade-offs and Design Limitations of Analog-to-Information Converter Front-Ends," IEEE International Conference on Acoustics, Speech and Signal Processing, Kyoto, Japan, 4 pages, March 2012. (paper) (talk)
Re-affirming implementation design using non-asymptotic theoretical analysis.
For implementations we found small system sizes to be more energy efficient.
However does theory support such a design?
If we look to the standard restricted isometry analyses (RIP) type CS theory, the answer is no.
Figure 1 shows the probability of failure of theoretical CS guarantees, based on randomized sampling theory.
We see that even for 2-sparse signals at 50 compressed measurements, the probablity of failure is high.
RIP theory does not even support recovery of 2-sparse signals.
But in our experiments we recover 4-sparse signals with not much difficulty.
Thus there is potential to find a theory that better fits our empirical observations.
Fig 1. Issues with restricted isometry analyses at small system sizes
In our work , we propose to use U-statisical theory in place of RIP theory.
For our system sizes, we find better empirical agreement, even when compared to Donoho-Tanner recent large deviation bounds.
We show how U-statistical very naturally obtain "average-case" analyses.
The theoretical investigations are led by postdoctorial associate Fabian Lim.
Read more about this component on his personal website. (site).
F. Lim, and V. Stojanovic “Non-Asymptotic Analysis of Compressed Sensing Random Matrices : An U-Statistics Approach,” IEEE International Conference on Communication, Ottawa, Canada, 6 pages, June 2012. (paper), (poster)