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Conclusion

Module by: Graham de Wit, Nicholas Newton, Grant Cathcart. E-mail the authors

Summary: The Conclusion module of the Sparse Signal Recovery in the Presence of Noise collection.

Conclusion

With priming, the regression line correlating number of samples and standard deviation is roughly (sd^2)/6.5 + 1, which amounts to O(N^2) complexity. However, although this may seem slow, our method permits perfect recovery of complicated (albeit sparse) signals with arbitrary levels of AWGN. Thus, for reasonable data set sizes and values of standard deviation, the algorithm functions quite nicely for accurate signal reconstruction. Although if given infinite samples and time, it can recover any signal that is relatively sparse given infinite time.

Without priming the noise, and taking 50 samples, we can achieve O(1) complexity – extremely desirable, but the recovery percentage falls off rapidly with increase in noise standard deviation starting at standard deviation values around 3.5. Thus, this version of the algorithm could be desirable in non-critical applications where the strength of the noise is known to be low relative to that of the signal. We certainly would not recommend using the non-primed algorithm in data sensitive digital applications.

Further Avenues of Inquiry

Colored Noise

It would be interesting to extend the algorithm to accept different types of noise – pink, brown, purple, etc. Logically the exact same algorithm would work on these, but it would be nice to verify this experimentally.

Physical Prototype

A physical prototype of this system would allow a far better testing of the theory than simple simulation. Unfortunately, due to the cost of even moderate quality receivers and FPGAs, this was not feasible.

Dynamic Noise

One major benefit of a noise resistant system is ECCM, Electronic Counter Countermeasures (counter-jamming). It would be interesting to test whether a system using the described algorithm could resist noise from a transmitter moving towards the system (without simply taking a conservative estimate of worst-case noise during the signal reconstruction period).

Dynamic Priming

A useful addition to this algorithm, would be to be able to pick the optimal bound for priming to minimize the number of samples rather than simply choosing the best of two options.

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

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