CS: Channel Estimation for Opportunistic Spectrum Access: Uniform and Random Sensing

Channel Estimation for Opportunistic Spectrum Access: Uniform and Random Sensing by Quanquan Liang, Mingyan Liu. The abstract reads:

The knowledge of channel statistics can be very helpful in making sound opportunistic spectrum access decisions. It is therefore desirable to be able to efficiently and accurately estimate channel statistics. In this paper we study the problem of optimally placing sensing times over a time window so as to get the best estimate on the parameters of an on-off renewal channel. We are particularly interested in a sparse sensing regime with a small number of samples relative to the time window size. Using Fisher information as a measure, we analytically derive the best and worst sensing sequences under a sparsity condition. We also present a way to derive the best/worst sequences without this condition using a dynamic programming approach. In both cases the worst turns out to be the uniform sensing sequence, where sensing times are evenly spaced within the window. With these results we argue that without a priori knowledge, a robust sensing strategy should be a randomized strategy. We then compare different random schemes using a family of distributions generated by the circular $\beta$ ensemble, and propose an adaptive sensing scheme to effectively track time-varying channel parameters. We further discuss the applicability of compressive sensing for this problem.

A related conference paper can be found here.

I note the following:

"For the reconstruction to be successful, two conditions need to be satisfied: the signal needs be sparse in some domain (i.e., the existence of a \psi such that a is sufficiently sparse), and the two matrices \phi and \psi need to be incoherent. Due to the binary property of the channel state sequence, it’s difficult to find a basis matrix \psi that has dense entities. As a result we have two very sparse matrices and they are highly coherent. For these reasons we have not found compressive sensing to have an advantage in our channel estimation problem....The time window is set to 4096 time units. Overall compressive sensing based estimation dose not compare favorably with uniform sensing and random sensing, due to the coherence problem between the two matrices. It remains an interesting problem to find a good basis matrix that can both sparsify x and at the same time be sufficiently incoherent with the measurement matrix."

If sparsity is an issue in the measurement matrix, what about using the sparse matrices of Indyk et al for \phi and and \psi be the identity ?

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