An overview of recent results on the identification of sparse channels using random probes

In this paper, we collect and discuss some of the recent theoretical results on channel identification using a random probe sequence. These results are part of the body of work known as compressive sampling, a rapidly developing field whose central message is that sparse vectors can be recovered from a set of “random” underdetermined measurements. In the context of channel estimation, if the channel´s impulse response is sparse, then it can be estimated by exciting the channel with a random probing sequence and then taking a relatively small number of samples of the output. We also overview recent results in multiple channel estimation that show the channel responses in a multiple-input multiple-output (MIMO) system can be efficiently estimated by exciting all of the inputs with independent random probing signals simultaneously.