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In this letter, packet-by-packet vertical handover is investigated as a means to improve the performance of unlicensed spectrum access. The analysis focuses on the optimization of a channel access strategy for a cognitive multi-standard radio node that has the capability to switch between two orthogonal uplink radio interfaces, based on long-term channel state information. The radio interfaces differ for coverage and quality of service (QoS) requirements of primary users. The proposed strategy prescribes a cross-layer selection of physical-layer (transmitting powers) and medium access control layer (handover probability) parameters and is designed to maximize secondary throughput while guaranteeing the primary QoS constraints. Analysis and numerical results bring insight into the impact of network topology, measurement errors and primary QoS constraints on the optimal system design and corresponding performance.