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

Abstract

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 monetary 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 the primary services are not active. However, due to the unpredictable activities of the primary services, the SSP may suffer the pecuniary loss or failure to satisfy the traffic demands from the SUs. It is challenging for the SSP to measure the loss 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 supply of spectrum from PSPs. To address the concerns of the SSP, in this paper, we first introduce the X loss, an intuitive measurement of evaluating the uncertain loss for OSA at a given confidence level. Although the X loss is attractively simple, it theoretically underestimate the potential loss for OSA. Meanwhile, the X loss requires strong assumptions to support traffic splitting, i.e., the primary services of different bands must be multivariate normally distributed, which is not necessarily true in practical. To overcome the weakness of the X loss, we further propose a more suitable loss measurement, the expected X loss, which is theoretically subadditive and convex, and practically consistent with the SSP's perception of loss 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 technique.