Combating Strong–Weak Spatial–Temporal Resonances in Time-Reversal Uplinks

In a time-reversal (TR) communication system, the signal-to-noise ratio (SNR) is boosted and the inter-user interference (IUI) is suppressed due to the spatial-temporal resonances, commonly known as the focusing effects, of the TR technique when implemented in a rich scattering environment. However, since the spatial-temporal resonances highly depend on the location-specific multipath profile, there exists a strong-weak spatial-temporal resonances effect. In the TR uplink system, different users at different locations enjoy different strengths of spatial-temporal resonances, i.e., the received signal-to-interference-noise ratios (SINRs) for different users vary, and the weak ones can be blocked from correct detection in the presence of strong ones. In this paper, we formulate the strong-weak spatial-temporal resonances in the multiuser TR uplink system as a max-min weighted SINR balancing problem by joint power control and signature design. Then, a novel two-stage adaptive algorithm that can guarantee the convergence is proposed. In stage I, the original nonconvex problem is relaxed into a Perron Frobenius eigenvalue optimization problem and an iterative algorithm is proposed to obtain the optimum efficiently. In stage II, the gradient search method is applied to update the relaxed feasible set until the global optimum for the original optimization problem is obtained. Numerical results show that our algorithm converges quickly, achieves a high energy-efficiency, and provides a performance guarantee to all users.