Capacity of Gaussian channels with duty cycle and power constraints
Proceedings of the IEEE International Symposium on Information Theory, St. Petersburg, Russia, July 2011

In many wireless communication systems, radios are subject to  duty   cycle   constraint , that is, a radio only actively transmits signals over a fraction of the time. For example, it is desirable to have a small duty   cycle  in some low  power  systems; a half-duplex radio cannot keep transmitting if it wishes to receive useful signals; and a cognitive radio needs to listen and detect primary users frequently. This work studies the  capacity  of scalar discrete-time  Gaussian   channels  subject to  duty   cycle   constraint as well as average transmit  power   constraint . The  duty   cycle   constraint  can be regarded as a requirement on the minimum fraction of nontransmission or zero symbols in each codeword. A unique discrete input distribution is shown to achieve the  channel   capacity . In many situations, numerical results demonstrate that using the optimal input can improve the  capacity  by a large margin compared to using  Gaussian  signaling over a deterministic transmission schedule, which is capacity -achieving in the absence of the  duty   cycle   constraint . This is in part because the positions of the nontransmission symbol in a codeword can convey information. The results suggest that, under the  duty   cycle   constraint , departing from the usual paradigm of intermittent packet transmissions may yield substantial gain.