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...In this case, the system is optimized to achieve a given quality of service (QoS) for every possible CSI error if the problem is feasible, thereby, achieving absolute robustness. It was also shown in =-=[12]-=- that a bounded worstcase model is able to cope with quantization errors in CSI. In this letter, we shall employ the worst-case approach to address the robust beamforming design problem. Consider the ...

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...o the robust formulations will be described in the second and third subsections. A. Robust Secrecy-Rate Problem Formulations Our model assumption for imperfect CSI is based on the deterministic model =-=[38]-=-–[40]. We model the Alice-to-Bob channel and the Alice-to-Eve channels respectively by h = h̄+∆h, Gk = Ḡk +∆Gk, k = 1, . . . ,K. Here, h̄ and Ḡk are the channel means and they are known to Alice; ∆h...

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...er are particularly sensitive to these mismatches. For example, it has been shown [3], [4] that imperfect channel knowledge at the transmitter can result in the downlink becoming interference limited; i.e., the growth of the SINR of each user with the transmitted power saturates. One approach to incorporating robustness against channel uncertainty into the precoder design is to consider a bounded model for the error in the transmitter’s estimate of the channels and to constrain the design of the precoder so that the users’ QoS requirements are satisfied for all channels admitted by this model [5], [6], [1]. In this paper, we consider an alternative approach that assumes a stochastic model for the uncertainty in the transmitter’s estimate of the channel coefficients of each user, and we design the precoder so as to minimize the total transmitted power subject to the satisfaction of the SINR-based QoS constraints with a maximum allowed outage probability. We consider two stochastic models for the uncertainty in the the channel coefficients of each user. The first is a Gaussian model that is appropriate for uncertainty that results from estimation errors, such as those that arise in syst...

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...mputed efficiently. In [4], the authors provide a rank-relaxation method to transform the robust SINR-constrained problem to a convex semidefinite programming (SDP) problem. Similarly, the authors of =-=[5]-=- propose different levels of relaxation leading to SDP problems with different levels of complexity. The same authors also present robust formulations for MSE-constrained problem [6]. Finally, the aut...

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...ce-plus-noise ratio (SINR) among all users in the interference channel. In the literature, precoder-decorrelator optimization for worst-case SINR are proposed for broadcast and point-to-point systems =-=[10]-=-–[13]. Specifically, in [10], [13] the authors consider precoding design for the worst-case SINR in MISO broadcast channel, where it is shown that the precoder optimization problem is always convex. I...

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...which in addition to some theoretical justification also offers various computational benefits on account of its convexity. Traditionally, the uncertainty has been assumed to lie in a given ellipsoid =-=[20]-=-, [21].7 Nonetheless, such an assumption limits the possibilities of modeling uncertainty in several other cases of practical interest. For example, modeling the uncertainty set as a polyhedron is bet...

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...ncorporate other system uncertainty factors, e.g. estimation errors, in CSI as well. Robust designs based on similar uncertainty models for typical CoMP systems or relaying can also be found in [12], =-=[14]-=-–[17]. In contrast to the rich results in robust designs for typical AF relaying [16], [17] or downlink CoMP [12], few literatures discuss CoMP relaying [18] or CoMP AF relaying [19]. To the best of o...