The X Loss: Band-Mix Selection with Uncertain Supply for Opportunistic Spectrum Accessing

Cognitive Radio technology releases the spectrum from shackles of authorized licenses and facilitates the trading of spectrum bands. In the spectrum market, primary service providers (PSPs) set prices for the vacant licensed bands of primary users (PUs) and sell/lease them for pecuniary gains, and the secondary service provider (SSP) can buy/rent the bands and support the secondary users (SUs) for their opportunistic spectrum accessing (OSA) when primary services are not active. However, due to the unpredictable activities of primary services, the SSP may suffer the monetary risk or failure to satisfy the traffic demands from the SUs. It is challenging for the SSP to measure the risk for OSA, to choose the bands to access, and to split the overall traffic on the band-mix, when there are multiple vacant bands and uncertain spectrum supply from PSPs. To address the concerns of the SSP, in this paper, we first introduce the X loss, an intuitive measurement to evaluate the risk for OSA at a given confidence level. Although the X loss is attractively simple, it theoretically underestimate the potential risk for OSA. Meanwhile, the X loss requires strong assumptions to support band-mix selection for traffic splitting, i.e., the primary services of different bands must satisfy normal distribution, which is not necessarily true in practice. To overcome the weakness of the X loss, we further propose a more suitable risk measurement, the expected X loss, which is theoretically subadditive and practically consistent with the SSP's perception of risk for OSA. Based on the proposed measurement, we formulate the band-mix selection problem for traffic splitting into an optimization problem and solve it by linear programming.