In this paper, we design downlink (DL) beamforming vectors for a multiuser multicell network when only imperfect knowledge of the channel covariance is available at base stations. Specifically, we consider two different models for covariance errors: a) deterministic error bounded in a spherical region and b) stochastic error with known probability distribution. Our objective is to minimize the total DL transmit power subject to quality of service (QoS) constraint of every user. It is shown that for both uncertainty models, the optimization can be formulated as a convex semidefinite programming (SDP) problem using the standard rank relaxation approach. Interestingly, numerical results show that the obtained solutions fulfill the rank constraint and are therefore exact.Index Terms-Multicell beamforming, robust design, outage probability, semidefinite programming.
In this paper, we consider the problem of precoding design for amplify-and-forward (AF) relay network with imperfect channel state information (CSI). We find a general rank precoding matrix at the relay such that the relay transmit power is minimized subject to quality of service (QoS) constraint as the worst case signal-to-noise ratio (SNR) at the destination. Since the direct optimization is nonconvex, we apply conservative methods to reformulate it as a semi-definite programming (SDP) problem which provides the upperbound of the original objective. Specifically, we suggest two SDP formulations that can be solved efficiently via convex optimization tools. We numerically compare the proposed suboptimal methods with the existing method, i.e., collaborative robust relay beamforming (CRBF), and show that the proposed schemes achieve a significant performance gain for a majority of feasible uncertainty sizes.
In this paper, we design downlink (DL) beamforming vectors for a multiuser multicell cognitive radio (CR) network with imperfect channel state information (CSI) at base stations (BS). Specifically, we model channel estimation error as a random vector with known statistical distribution. Our objective is to minimize the total DL transmit power subject to probabilistic quality of service (QoS) constraints of every secondary user (SU) and primary user (PU). Utilizing Bernsteintype inequalities [12], we replace the probabilistic constraints with conservative deterministic constraints. By applying rank relaxation, the original problem is reformulated as semidefinite programming (SDP). Interestingly, numerical results show that the obtained solutions fulfill the rank constraint.
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