We study the problem of frequency and power allocation and scheduling at a time-slotted cognitive ad-hoc wireless network, where cognitive nodes share a number of frequency bands and frequency reuse is allowed. In such a network the throughput maximization problem generally results in a mixed zero-one nonlinear non-convex problem. Interestingly, in the low-SINR regime, the power allocation policy that maximizes the total throughput follows an “on/off” strategy with maximum power usage in the “on” state. In this paper we show that the on/off strategy in the low-SINR regime is also optimal with respect to throughput when scheduling users over time and frequency subject to minimum SINR requirements. We show that these additional constraints will not change the optimum strategy, but may affect the set of “on” or “off” transmitters. Also we present an approach that transforms the mixed zero-one nonlinear problem to an equivalent mixed zero-one linear problem at the expense of extra variables.
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