  This paper presents a tutorial for CS applications in communications
networks. The Shannon's sampling theorem states that to recover a signal, the
sampling rate must be as least the Nyquist rate. Compressed sensing (CS) is
based on the surprising fact that to recover a signal that is sparse in certain
representations, one can sample at the rate far below the Nyquist rate. Since
its inception in 2006, CS attracted much interest in the research community and
found wide-ranging applications from astronomy, biology, communications, image
and video processing, medicine, to radar. CS also found successful applications
in communications networks. CS was applied in the detection and estimation of
wireless signals, source coding, multi-access channels, data collection in
sensor networks, and network monitoring, etc. In many cases, CS was shown to
bring performance gains on the order of 10X. We believe this is just the
beginning of CS applications in communications networks, and the future will
see even more fruitful applications of CS in our field.
