Robust Downlink Beamforming Based on Outage Probability Specifications

Robust precoding design for multibeam downlink satellite channel with phase uncertainty

“…We denote the availability of the ith user in the first constraint by fi(W), where W = {Wi} Tr (RiZi) is a random variable and using (9), it can be simplified to…”

“…The robust precoding design paradigms have been considered in literature towards mitigating the sensitivity of the precoding techniques on CSIT [8][9][10][11]. In general, there are several different strategies to obtain robustness against channel uncertainty [12]: (a) Worstcase design using a deterministic uncertainty model, where the true value is known to be within a certain interval, and optimizing the performance of the worst case situation.…”

“…(b) Expectation-based design using a stochastic uncertainty model but optimizing the average performance. (c) Probabilistic design using a stochastic uncertainty model and optimizing the performance at a certain outage level [9][10][11].…”

“…In particular, the probabilistic approach will be used for the robust design since it can guarantee a certain level of user availability (1− outage probability×100%) which is a very important QoS measure for satellite operators. While literature focuses on additive uncertainty model for robust designs [8][9][10][11][12][13], the current study employs a multiplicative model for phase induced channel uncertainty. The use of such an uncertainty model and the ensuing analysis are novel, especially in the satellite communication literature.…”

Optimal Resource Allocation in Coordinated Multi-Cell Systems

“…The system cannot account for any error; the stochastic error vector˜ k could potentially cancel out the nominal vector as˜ k = − h k or be very large (the distribution is even unbounded for Rayleigh fading channels). This is often handled by only considering a subset of error vectors, the uncertainty set, that has high probability of containing the error [9,17,26,50,239,241,242,257,286,289,328]. If the design of these sets is explicitly included in the resource allocation (e.g., optimization with acceptable outage probabilities), it seems that conservative approximations 1 of each user's performance are required to achieve tractable problem formulations [50,241,289].…”