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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 β 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.

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Cognitive radio (CR) is considered one of the prominent techniques for improving the utilization of the radio spectrum. A CR network (i.e., secondary network) opportunistically shares the radio resources with a licensed network (i.e., primary network). In this work, the spectral-energy efficiency trade-off for CR networks is analyzed at both link and system levels against varying signal-to-noise ratio (SNR) values. At the link level, we analyze the required energy to achieve a specific spectral efficiency for a CR channel under two different types of power constraint in different fading environments. In this aspect, besides the transmit power constraint, interference constraint at the primary receiver (PR) is also considered to protect the PR from a harmful interference. Whereas at the system level, we study the spectral and energy efficiency for a CR network that shares the spectrum with an indoor network. Adopting the extreme-value theory, we are able to derive the average spectral and energy efficiency of the CR network. It is shown that the spectral efficiency depends upon the number of the PRs, the interference threshold, and how far the secondary receivers (SRs) are located. We characterize the impact of the multi-user diversity gain of both kinds of users on the spectral and energy efficiency of the CR network. Our analysis also proves that the interference channels (i.e., channels