The X Loss: Band-Mix Selection for Opportunistic Spectrum Accessing with Uncertain Spectrum Supply from Primary Service Providers

In a cognitive radio network, primary service providers (PSPs) set prices for the vacant licensed bands and sell/lease them for pecuniary gains while the secondary service provider (SSP) can buy/rent the bands and support opportunistic spectrum accessing (OSA). However, due to the unpredictable activities of primary services, the SSP may suffer the monetary risk or failure to meet the traffic demands from the secondary users (SUs). It is challenging for the SSP to measure the risk for OSA, to choose the bands to use, and to split the traffic on the band-mix, when there are multiple vacant bands from PSPs. In this paper, we first introduce the X loss, an intuitive measurement for the risk for OSA. Although the X loss is attractively simple, it underestimates the potential risk for OSA and is mathematically not subadditive, which makes it difficult to support the band-mix selection for traffic splitting. To overcome this problem, we propose a more suitable risk measurement, which is subadditive and consistent with the SSP's perception of the risk. Based on the proposed risk metric, we formulate the band-mix selection problem as an optimization problem and solve it by linear programming.