Compressive Detection and Estimation with Applications to Cognitive Radio and Radar
Bai, Linda Yunlu
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According to Nyquist Sampling theorem, a band-limited signal can be reconstructed accurately if the sampling rate exceeds twice the maximum frequency of the signal. In many scenarios, this Nyquist sampling rate cannot be achieved due to hardware limitations. Compressive sensing (CS) is a technique to reconstruct a signal from sub-Nyquist samples, given that the signal is sparse in a known domain. The CS technique has been applied to different areas in the field of communications and networking. Of fundamental importance to current research is the need to adapt CS according to different requirements and constraints in each area. In Chapter 2 and Chapter 3, the application of compressive sensing to spectrum sensing in cognitive radio is discussed. Fast and reliable detection of available channels (i.e. temporarily unoccupied by primary users) is a fundamental challenge in cognitive radio design. The (mean) time to detection of an idle channel is governed by the (increasing) front-end bandwidths to be searched for a given (channel) bandwidth resolution. Wideband RF front-ends followed by suitable channelization and digital signal processing algorithms are consistent with speedier detection, but they also imply the need for very high speed analog-to-digital converters (ADCs) that are currently impractical. On the other hand, traditional heterodyne receiver architectures that consist of analog bandpass filtering require much lower rate ADCs, but at the expense of significant scanning operation steps, that constitute a roadblock towards lowering of the scan duration. In Chapter 2, for detection of one idle channel, we propose a multi-resolution spectrum sensing scheme based on the principle of under-sampling (bandpass sampling) that provides a suitable middle ground between the above choices, i.e. our approach requires modest ADC sampling rate yet achieves fast scanning. A performance model for this architecture is developed based on an analysis for the mean time to detect an idle channel. The detection threshold and the sub-sampling factor are optimized jointly to minimize the mean detection time. In Chapter 3, we propose a new compressive spectrum sensing architecture based on bandpass sampling) to detect all the idle channels in the given spectrum. Compared to other compressive spectrum sensing architectures, the proposed method does not require a high-speed Nyquist rate analog component. Numerical results show that the proposed schemes in these two chapters provide significantly faster idle channel detection than the conventional serial search scheme with a heterodyne architecture. In Chapter 4, the application of compressive sensing to clutter subspace estimation in cognitive radar is discussed. Space-Time Adaptive Processing (STAP) based on matched filter processing in the presence of additive clutter (modeled as colored noise) requires knowledge of the clutter covariance matrix. In practice, this is estimated via the sample covariance matrix using samples from the neighboring range bins around the reference bin. By applying compressive sensing, the number of training samples needed to estimate the covariance matrix can be significantly reduced, provided that the basis mismatch problem, inherent to compressive sensing can be mitigated. This chapter presents an adaptive approach to choosing the best sparsifying basis, using dictionary learning to estimate the radar clutter subspace. Numerical results show that the proposed algorithm achieves the desired reduction in training samples, and is more accurate than previous reduced-rank algorithm baseline.
- Electrical engineering