We will talk about a variety of theoretical results from compressive sensing that should be of interest to researchers in RADAR. Topics will include: 1) Random convolution. We will discuss how compressive sampling can be implemented using random convolution followed by subsampling. The message of these results is that if we are sensing a scene by sending out random pulses, then we can sample the returns at a rate considerably lower than the bandwidth of these pulses; 2) Multichannel separation. We consider the basic problem of estimating the channels between all transmitters and all receivers in a multiple-input multiple-output (MIMO) system. We discuss how these channels can all be estimated with all transmitters activated simultaneously with random probes; 3) Analog-to-information receivers. We discuss a recently built broadband multichannel compressive sensing receiver for radio-frequency signals, and how it has been used for pulse descriptor word (PDW) extraction; 4) Parametric estimation. As in the PDW problem above, it is often the case that we are not so interested in reconstructing the signal itself, but rather in estimating some key parameters (i.e. time-of-arrival, modulation frequency, etc). We will discuss recently theoretical results that quantify how well this estimation can be done from compressed samples; 5) Multichannel sampling. We discuss how multiple signals coming off an array of sensors can be compressively sampled and then recovered using their latent correlation structure.
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