Theses: Wideband Cognitive Radio: Monitoring, Detection and Sparse Noise Subspace Communication
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We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by a fixed assignment of spectrum resources by regulatory agencies. This has resulted into a blind alley, as current wireless spectrum has become an expensive and a scarce resource. However, recent measurements in dense areas paint a very different picture: there is an actual underutilization of the spectrum by legacy systems.

Cognitive radio exhibits a tremendous promise for increasing the spectral efficiency for future wireless systems. Ideally, new secondary users would have a perfect panorama of the spectrum usage, and would opportunistically communicate over the available resources without degrading the primary systems. Yet in practice, monitoring the spectrum resources, detecting available resources for opportunistic communication, and transmitting over the resources are hard tasks. This thesis addresses the tasks of monitoring, detecting and transmitting, in challenging scenarios including wideband signals, nonuniform sampling, inaccurate side information, and frequency-selective fading channels.

In the first task of monitoring the spectrum resources, this thesis derives the periodogram and Capon spectral estimates in nonuniform sampling exploiting a correlation-matching fitting from linearly projected data. It is shown that nonuniform sampling incurs the phenomenon of noise enhancement, which is circumvented by the proposed spectral estimates by implementing a denoising process, and further theoretically characterized in Bernoulli nonuniform sampling by establishing equivalence between nonuniform sampling and signal-to-noise ratio (SNR).

In the second task of detecting the available resources, this thesis considers the problems of multi-frequency signal detection, asymptotic performance, and cyclostationary signal detection. In multi-frequency signal detection, a unified framework based on the generalized likelihood ratio test (GLRT) is derived by considering different degrees of side information and performing maximum likelihood (ML) and correlation-matching estimation over the unknown parameters in uniform and nonuniform sampling, respectively. The asymptotic performance of signal detection is considered from two perspectives: the Stein's lemma, which allows discovering the influence of the main parameters on the error exponents in the error probabilities; and the asymptotic statistical characterization of the GLRT in Bernoulli nonuniform sampling, which allows the derivation of sampling walls in noise uncertainty, i.e., sampling densities below which the target detection probabilities cannot be guaranteed. Finally, this thesis exploits the cyclostationarity properties of primary signals by deriving the quadratic sphericity test (QST), which is the ratio between the squared mean and the arithmetic mean of the eigenvalues of the autocorrelation matrix of the observations; and the optimal GLRT in a parameterized model of the frequency-selective channel, which exploits the low rank structure of small spectral covariance matrices.

In the last task of transmitting over the available resources, a cyclostationary secondary waveform scheme is first proposed to mitigate the interference that an active cognitive radio may cause to an inactive cognitive radio that performs spectrum sensing, by projecting the oversampled observations into a reduced subspace. Second, this thesis derives and statistically characterizes the sphericity minimum description length (MDL) for estimating the primary signal subspace. And third, this thesis finally considers the minimum norm waveform optimization problem with imperfect side information, whose benefits are those of linear predictors: flat frequency response and rotationally invariance.

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