Secure Degrees of Freedom in Cooperative MIMO Cognitive Radio Systems

We study the achievable secure degrees of freedom (DoF) in a cooperative MIMO cognitive radio system consisting of one primary source-destination pair, one or two secondary sourcedestination pairs, and one eavesdropper who is interested only in primary user´s data. The cognitive radio users help to secure primary user´s transmission against the eavesdropper and in return, the primary user allows the secondary users to access its licensed spectrum. All users are equipped with multiple antennas. We investigate the secure DoF using the interference alignment concept coupled with a zero inter-user interference constraint. We propose a beamforming design based only on the channel state information (CSI) between the primary and secondary user pairs which the legitimate users exchange among each other; no information data are exchanged and no eavesdropper CSI is needed. In the case of a single secondary user pair, we show that if all users have M antennas, secure DoF d_p and DoF d_s of primary and secondary users, respectively, are achievable if they satisfy 2d_p ≤ M and d_s ≤ M - 2d_p. In the case of two secondary user pairs, secure DoF d_p and DoFs d_s1, d_s2 of primary user and two secondary users, respectively, are achievable if they satisfy 2d_p <; M, d_p + d_i ≤ M, d_s1 + d_s2 ≤ M, i ∈ {s₁,s₂}, or 2d_p = M, d_p + d_i ≤ M, d_s1 + d_s2 <; M, i ∈ {s₁, s₂}. Simulation examples corroborating the theoretical results are presented.