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...quadratic program. While the polyhedron approach is less conservative, the size of the description and, hence, the complexity of solving the problem grows with the number of vertices. Vorobyov et al. =-=[9]-=-, [10] have described the use of second-order cone programming for robust beamforming in the case where the uncertainty in the array response is isotropic. In this paper, we consider the case in which...

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...rtial CSIT, e.g., [76]. Another different philosophy is to start with a signal processing approach, for which typically perfect CSIT is assumed, and make it robust to imperfections in the CSIT, e.g., =-=[10, 101, 123, 159, 165]-=-. 1.3 A First Glimpse at Linear Transceivers: Beamforming Beamforming is a term traditionally associated with array processing or smart antennas in wireless communications where an array of antennas e...

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...alistic situations. Hence, it is reasonable to assume perfect CSIR and imperfect CSIT, as is considered in this paper. There are different ways to design a system that is robust to imperfect CSIT. In =-=[3, 4]-=-, worst-case designs are considered. This guarantees a certain system performance for any possible channel sufficiently close to the estimated one. This approach leads to conservative designs, which m...

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...and describing several applications in signal processing. This approach has been recently used in the classical problem of designing a receive beamformer under mismatches in the presumed model, as in =-=[29]-=-, where the errors were assumed to be in the estimated steering vector and to belong to a spherical uncertainty region. This was afterwards generalized in [30] to embrace uncertainties both in the arr...

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...ssion. based on optimizing the average or outage performance [8], [9]. Alternatively, the deterministic model assumes that the CSI uncertainty, though not exactly known, is bounded by possible values =-=[10]-=-, [11]. 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 s...

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...propagation channels and the mobility of the users. Therefore, we propose an approach to robust beamforming design in the case of erroneous CSI which uses the concept of worst-case design (see, e.g., =-=[23]-=- and references therein). Specifically, we assume that all channel vectors are known with certain errors and that these errors are all norm-bounded, that is, where the parameter is assumed to be known...

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... quantization cells in the interior of the quantization region can be approximated by balls of size δk. A similar bounded uncertainty model has been used in the context of generic beamforming systems =-=[17]-=-, [18], where it is the error in the estimate of the steering vector that is being bounded, and in CDMA systems [19]. By using the vector e k = [Re{ek},Im{ek}], the uncertainty set of each channel can...

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... that perfect CSI for the links to the legitimate user is available at both transmitters, while for the eavesdropper links there exist channel mismatches that are norm-bounded by some known constants =-=[31]-=-, [32]. Following [9], [11], and [15], Gaussian inputs are assumed in the paper. We focus on obtaining robust transmit covariance matrices for both the source and the helper, based on maximizing the w...