Abstract
In many wireless communication systems, radios are subject toÌý duty Ìý cycle Ìý 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 Ìý cycle Ìýin some lowÌý power Ìýsystems; 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 theÌý capacity Ìýof scalar discrete-timeÌý Gaussian Ìý channels Ìýsubject toÌý duty Ìý cycle Ìý constraint as well as average transmitÌý power Ìý constraint . TheÌý duty Ìý cycle Ìý constraint Ìýcan 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 theÌý channel Ìý capacity . In many situations, numerical results demonstrate that using the optimal input can improve theÌý capacity Ìýby a large margin compared to usingÌý Gaussian Ìýsignaling over a deterministic transmission schedule, which is capacity -achieving in the absence of theÌý duty Ìý cycle Ìý constraint . This is in part because the positions of the nontransmission symbol in a codeword can convey information. The results suggest that, under theÌý duty Ìý cycle Ìý constraint , departing from the usual paradigm of intermittent packet transmissions may yield substantial gain.