In many wireless communication systems, radios are subject to a duty cycleconstraint, that is, a radio only actively transmits signals over a fraction ofthe time. For example, it is desirable to have a small duty cycle in some lowpower systems; a half-duplex radio cannot keep transmitting if it wishes toreceive useful signals; and a cognitive radio needs to listen and detectprimary users frequently. This work studies the capacity of scalardiscrete-time Gaussian channels subject to duty cycle constraint as well asaverage transmit power constraint. An idealized duty cycle constraint is firststudied, which can be regarded as a requirement on the minimum fraction ofnontransmissions or zero symbols in each codeword. A unique discrete inputdistribution is shown to achieve the channel capacity. In many situations,numerically optimized on-off signaling can achieve much higher rate thanGaussian signaling over a deterministic transmission schedule. This is in partbecause the positions of nontransmissions in a codeword can convey information.Furthermore, a more realistic duty cycle constraint is studied, where the extracost of transitions between transmissions and nontransmissions due to pulseshaping is accounted for. The capacity-achieving input is no longer independentover time and is hard to compute. A lower bound of the achievable rate as afunction of the input distribution is shown to be maximized by a first-orderMarkov input process, the distribution of which is also discrete and can becomputed efficiently. The results in this paper suggest that, under variousduty cycle constraints, departing from the usual paradigm of intermittentpacket transmissions may yield substantial gain.
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