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A range of efficient wireless processes and enabling techniques are put under a magnifier glass in the quest for exploring different manifestations of correlated processes, where sub-Nyquist sampling may be invoked as an explicit benefit of having a sparse transform-domain representation. For example, wide-band next-generation systems require a high Nyquist-sampling rate, but the channel impulse response (CIR) will be very sparse at the high Nyquist frequency, given the low number of reflected propagation paths. This motivates the employment of compressive sensing based processing techniques for frugally exploiting both the limited radio resources and the network infrastructure as efficiently as possible. A diverse range of sophisticated compressed sampling techniques is surveyed, and we conclude with a variety of promising research ideas related to large-scale antenna arrays, non-orthogonal multiple …