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In this paper, we consider precoding matrices optimization for a new two-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system, where in addition to forwarding the source signals, the relay node concurrently transmits its own signals to the destination node. Compared with conventional AF MIMO relay systems where the relay node only forwards the source signals, the transceiver optimization problem in the new system is more challenging to solve. We prove that for all Schur-concave objective functions, the optimal source and relay matrices jointly diagonalize the source-relay-destination and relay-destination channels, which simplifies the matrices optimization problem to a joint subchannel and power allocation problem with scalar variables. It is shown that to achieve a maximal sum mutual information (MI) of both the source and relay links, the strongest subchannels of the second-hop channel should be allocated for transmitting signals from the relay node. With additional quality-of-service constraints in terms of the lower bounds of the MI of both links, the optimal subchannel allocation problem is NP-hard. In this case, we propose a suboptimal channel allocation algorithm with a low computational complexity. For a given subchannel allocation, we develop a primal decomposition based algorithm to efficiently solve the power allocation problem. Simulation results show that compared with the exhaustive search based channel allocation approach and the general nonlinear programming based power allocation algorithm, the proposed subchannel and power allocation algorithms have a much lower computational complexity with only a small performance loss.

This paper proposes a new source number estimator with improved degrees of freedom for blind source separation, where the mixing matrix does not have the parameterized structure. In order to enhance the degrees of freedom, we exploit the sample dependence of each source and construct a new matrix by vectorizing some delayed covariance matrices based on Khatri–Rao product. Then, an improved Gerschgorin disk estimator for source number is presented based on the new matrix. This estimator can detect the number of sources up to $2M - 1$ using only $M$ sensors, while the traditional source number estimators can merely estimate the number of sources less than $M$ employing the same number of sensors. Simulation results verify the superiority of the proposed method by comparing with the existing source enumeration methods in scenario of spatially non-uniform noise when the sensor number is more than the source number and validate the reliability of the proposed method in the case with fewer sensors than sources.