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This paper presents optimal power allocation strategies for a MIMO (Multiple Input Multiple Output) OFDM (Orthogonal Frequency Division Multiplexing) based Cognitive Radio (CR) system. The proposed power allocation schemes maximize the downlink transmission rate of the CR users under spatial interference constraints, considering both the availability and absence of the Primary User (PU) Channel State Information (CSI). It is demonstrated that the isotropic interference minimization in the absence of PU CSI can be formulated as a Semi-Definite Program (SDP) while it reduces to linear interference constraints based CR user sum-rate maximization in the presence of PU CSI. Closed form power allocation expressions are derived for the above scenarios under a sum-trace interference relaxation.
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