Transmission strategies under imperfect instantaneous CSIT

We propose a simple solution based on Perron-Frobenius theorem and uplink-downlink duality to the longstanding problem of transmission strategies: maximize the minimum SINR or minimize the transmit power. In contrary of using perfect and instantaneous CSIT (requires higher overhead and backhauling), or using only average CSIT, e.g. channel covariance which suffers from quality fluctuations; we account for imperfect instantaneous CSIT. The solution emerges from the observation that the crux of the robustness problem is the construction of SINR estimates itself. We provide a MLE-based estimate which being sub-optimal and failing to incorporate the channel estimation error, we reinforce it by biasing the estimate, which not only achieves smaller error but is strictly conservative as well. We also consider both transmission strategy problems, and show that the biased estimates are not only robust compared to traditional unbiased estimates, but also substantially outperform the probabilistic method with Bernstein-type relaxation proposed in [1].