Pilot power allocation is investigated under the framework of physical layer secure communications in time-division duplex systems, where the secret keys are generated from the estimates of sparse wireless channels. The joint optimisation of secret key capacity and sparse channel estimation performance based on pilot power allocation is formulated as a convex optimisation problem. Considering the fairness between these two sides, a scaling factor is introduced. Then, a scheme is proposed to

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... solve the problem by looking up a table and using existing optimisation solvers. Simulation results show that a proper scaling factor can make a trade-off between the secret key capacity and sparse channel estimation performance.