Abstract-This article describes a minimax regret approach to robust beamforming with an ellipsoidal uncertainty model for a steering vector, in which the objective is to minimize the worstcase regret over the uncertainty set, where 'worst' means largest. This problem can be solved efficiently by using an iterative method which uses an alternating sequence of optimization and worst-case analysis steps. Each of the two steps amounts to solving a convex optimization problem. The method typically converges to a solution within 5 iterations. The minimax regret beamforming is illustrated with numerical examples in planar random array antennas. The numerical results show that the minimax regret approach is less pessimistic (less conservative) and provides more robust performance than the worst-case SINR maximization (maximin) approach, where 'worst' means smallest.

In detecting a deterministic signal in the presence of Gaussian noise, the receiver operating characteristic (ROC) curve determined by a linear detector with slope maximizing the signal-to-noise ratio (SNR) and with varying threshold characterizes limits of detection performance. In this note, we consider the problem of detecting a signal in the presence of uncertainty in the signal itself and the noise covariance. We show that the classical result can be generalized to robust signal detection with a convex uncertainty model: the ROC curve determined by a linear detector with slope maximizing the worst-case SNR gives limits of detection performance in the worst-case sense. The worst-case SNR maximization problem can be solved using convex optimization, so robust ROC analysis is tractable.

With technology advances, the number of cores integrated on a chip and their speed of operation is increasing. This, in turn is leading to a significant increase in chip temperature. Temperature gradients and hot-spots not only affect the performance of the system, but also lead to unreliable circuit operation and affect the life-time of the chip. Meeting the temperature constraints and reducing the hot-spots are critical for achieving reliable and efficient operation of complex multi-core systems. In this work, we present Pro-Temp, a convex optimization based method that pro-actively controls the temperature of the cores, while minimizing the power consumption and satisfying application performance constraints. The method guarantees that the temperature of the cores are below a user- defined threshold at all instances of operation, while also reducing the hot-spots. We perform experiments on several realistic multi-core benchmarks, which show that the proposed method guarantees that the cores never exceed the maximum temperature limit, while matching the application performance requirements. We compare this to traditional methods, where we find several temperature violations during the operation of the system.

In Chebyshev finite-impulse response (FIR) equalization, we design an FIR filter that minimizes the Chebyshev equalization error,i.e., the maximum absolute deviation between the equalized and the desired frequency response functions, assuming the unequalized response function is known exactly. In robust Chebyshev FIR equalization, we take into account uncertainty in the unequalized response function, described as a set of possible values for the unequalized response at each frequency, by designing an FIR filter that minimizes worst-case Chebyshev equalization error over all possible unequalized response functions. When the uncertainty in unequalized response function is described by a complex uncertainty ellipsoid, at each frequency, we show that the robust Chebyshev FIR equalization design problem can be formulated as a semidefinite program (SDP), and therefore efficiently (and globally) solved. When the uncertainty is given by a complex disk, the design problem can be formulated as a second-order cone program (SOCP), which can be solved almost as fast as the nominal Chebyshev equalization problem (ignoring uncertainty). The robust equalizer design method is demonstrated with a numerical example.

We present a new inter-domain traffic engineering protocol based on the concepts of Nash bargaining and dual decomposition. Under this scheme, ISPs use an iterative procedure to jointly optimize a social cost function, referred to as the Nash product. We show that the global optimization problem can be separated into sub-problems by introducing appropriate shadow prices on the inter-domain flows. These sub-problems can then be solved independently and in a decentralized manner by the individual ISPs. Our approach does not require the ISPs to share any sensitive internal information (such as network topology or link weights). More importantly, our approach is provably Pareto-efficient and fair. Therefore, we believe that our approach is highly amenable to adoption by ISPs when compared to past naive approaches. We conduct simulation studies of our approach over several real ISP topologies. Our evaluation shows that the approach converges quickly, offers equitable performance improvements to ISPs, is significantly better than unilateral approaches (e.g. hot potato routing) and offers the same performance as a centralized solution with full knowledge.

In this letter, we show that worst-case robust beamforming, with uncertain weights subject to multiplicative variations, can be cast as a convex optimization problem. We interpret this problem as a weighted complex l1-regularization of the nominal beamforming problem, and show that it can be solved with the same computational complexity as nominal beamforming, ignoring the variations. We derive a simple lower bound on how much worse the robust beamformer will be compared to the nominal beamformer solution with no weight uncertainty. We demonstrate the robust approach with a simple narrowband beamformer