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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 fast 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. [ABSTRACT FROM AUTHOR]

The joint sparsity of uplink channels in massive multi‐input–multi‐output (MIMO) systems is explored and a block sparse model is proposed for joint channel estimation. The block coherence of this model is analysed. It is indicated that as the number of antennas at the base station grows to be infinity, the block coherence will be zero. Then a block optimised orthogonal matching pursuit (BOOMP) algorithm is proposed. Simulation results verify the analysis and show that the joint estimation using the BOOMP algorithm can significantly improve the channel estimation performance. [ABSTRACT FROM AUTHOR]