Beyond Bandlimited Sampling

Yes, I know I should move on to a more rigorous papers but these IEEE magazines are sitting on my shelf and beg to be read.

IEEE SP MAG, May 2009- Yonina Eldar and Tomer Michaeli

Remember how you are suppose to sample a signal at twice it's bandwidth? Well there are classes of signals where due to a priori knowledge of the structure of the signal, Nyquist sampling isn't necessary. This paper views "sampling in a broader sense of projection onto appropriate subspaces and then choosing the subspaces to yield interesting new possibilities." The three fundamental assumptions made when applying the Nyquist sampling theorem are 1) the signal is bandlimited ("natural signals are almost never truly bandlimited," 2) the sampling device is ideal (an understanding of how an ADC works makes this point clear and 3) the sinc kernal is used for reconstruction, (in reality it is truncated early). The authors then explore several methods used to implement a more accurate sampling of imperfect signals.

IEEE SP MAG, Nov 2008

Cognitive Radio Technology, Swarm Theory Overview and Slope Filtering.

This issue of SP Mag detailed several view of cognitive radio which I thought were very interesting. A few quotes which I would like to remember:

"The general cognitive network exploits cognition at a subset of its nodes (users). We focus on cognition in the form of nodes having extra information, or side information, about the wireless environment in which they transmit."

An article discussed how "the wavelet transform provides higher sidelobe suppression [which is needed when secondary users are communicating in the primary user's space] when compared to the rectangular window [Fourier] sidelobes in regular Orthogonal frequency division multiplexing (OFDM).

Another article discusses antijamming coding techniques for cognitive radio. Since primary wireless users are not aware of the secondary users, the secondary users must be robust enough to recover if the primary transmits before the secondary can detect the primary and adapt.

The most fascinating of the CR articles was the one on game theory. In a distributed network where secondary users may be greedy of spectrum, the authors proposed rules of a spectrum sharing game where users are rewarded for honesty and punished for cheating. They define the Nash equilibrium (NE) as follows: "as a set of strategies for all the users such that no user can improve his/her utility by unilaterally deviating from the equilibrium strategy, given that the other users adopt the equilibrium strategies."

A lot of the articles I was partially interested in so I just read the intro, conclusion, figures and the first paragraph of each section. This seemed a good way of getting an idea of the article with out devoting a month to deriving all of their equations.

There was an excellent short article on swarm intelligence, detailing ant colony optimization (ACO) and particle swarm optimization (PSO).

ACO: "A colony of artificial ants constructs solutions for a given combinatorial optimization problem. The process of building up a solution corresponds to a series of probabilistic decisions that are made based on experience (reflected in the pheromone values) and external knowledge on the optimization problem (reflected in heuristic information for an individual decision of an ant). Ants that found good solutions are allowed to increase the pheromone values that correspond to the decisions they made during the constructive solution process. In this way better decisions are enforced to have a higher likelihood to be taken again. In an iterative process the colony of ants uses this principle of indirect communication, usually denoted as stigmergy, to improve the quality of the solutions.

ACO "utilizes an indirect memory for building solutions in a constructive manner."

In a PSO [think flock of birds] algorithm the velocity vectors of the particles are adjusted at each iteration of the algorithm. For the new velocity vector of a particle, its prior personal best position and also the global best position that is the overall best position found so far by the particles act as attractors. The influence of the prior personal best position is considered as the cognitive aspect of the particles behavior whereas the influence of the global best position is considered as the social aspect.

Lastly, there was a quick article on slope filtering. The author took the linear regression equations and manipulated them until they were simple to implement in DSP as a dot product. He made some assumptions which I am not sure of their validity but would need to be explored before one would attempt to implement this. He used the filter for pulse detection and signal transition detection.