Multiantenna Secure Cognitive Radio Networks With Finite-Alphabet Inputs: A Global Optimization Approach for Precoder Design

This paper considers the precoder design for multiantenna secure cognitive radio networks. We use finite-alphabet inputs as the signaling and exploit statistical channel state information (CSI) at the transmitter. We maximize the secrecy rate of the secondary user and control the transmit power and the power leakage to the primary receivers that share the same frequency spectrum. The secrecy rate maximization is important for practical systems, but challenging to solve, mainly due to two reasons. First, the secrecy rate with statistical CSI is computationally prohibitive to evaluate. Second, the optimization over the precoder is a nondeterministic polynomial-time hard (NP-hard) problem. We utilize an accurate approximation of the secrecy rate to reduce the computational effort and then propose a global optimization approach based on branch-and-bound method. The idea is to define a simplex and transform the secrecy rate into a concave function. The derived concave function converges to the secrecy rate when the defined simplex shrinks down. Using this feature, we solve a sequence of concave maximization problems over iteratively shrinking simplices and eventually attain the globally optimal solution that maximizes the approximation of the secrecy rate. When the complexity is concerned, a low-complexity variant with limited number of iterations can be used in practice. We demonstrate the performance gains when compared with others through numerical examples.