We consider the downlink of a cellular system in which the base station employs multiple transmit antennas, each receiver has a single antenna, and the users specify certain quality of service (QoS) requirements. We study the design of robust broadcasting schemes that minimize the transmission power necessary to guarantee that the QoS requirements are satisfied for all channels within bounded uncertainty regions around the transmitter's estimate of each user's channel. Each user's QoS requirement is formulated as a constraint on the mean square error (MSE) in its received signal, and we show that these MSE constraints imply constraints on the received signal-to-interference-plus-noise ratio. Using the MSE constraints, we present a unified approach to the design of linear and nonlinear transceivers with QoS requirements that must be satisfied in the presence of bounded channel uncertainty. The proposed designs overcome the limitations of existing approaches that provide conservative designs or are only applicable to the case of linear precoding. Furthermore, we provide computationally efficient design formulations for a rather general model of bounded channel uncertainty that subsumes many natural choices for the uncertainty region. We also consider the problem of the robust counterpart to precoding schemes that maximize the fidelity of the weakest user's signal subject to a power constraint. For this problem, we provide quasi-convex formulations, for both linear and nonlinear transceivers, that can be efficiently solved using a one-dimensional bisection search. Our numerical results demonstrate that in the presence of bounded uncertainty in the transmitter's knowledge of users' channels, the proposed designs provide guarantees for a larger range of QoS requirements than the existing approaches that are based on bounded channel uncertainty models and require less transmission power to provide these guarantees.Index Terms-Broadcast channel, channel uncertainty, minimax design, linear transceivers, Tomlinson-Harashima transceivers, quality of service constraints, robust transceiver design.

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We consider joint transceiver design for general Multiple-Input Multiple-Output communication systems that implement interference (pre-)subtraction, such as those based on Decision Feedback Equalization (DFE) or Tomlinson-Harashima precoding (THP). We develop a unified framework for joint transceiver design by considering design criteria that are expressed as functions of the Mean Square Error (MSE) of the individual data streams. By deriving two inequalities that involve the logarithms of the individual MSEs, we obtain optimal designs for two classes of communication objectives, namely those that are Schur-convex and Schur-concave functions of these logarithms. For Schur-convex objectives, the optimal design results in data streams with equal MSEs. This design simultaneously minimizes the total MSE and maximizes the mutual information for the DFE-based model. For Schur-concave objectives, the optimal DFE design results in linear equalization and the optimal THP design results in linear precoding. The proposed framework embraces a wide range of design objectives and can be regarded as a counterpart of the existing framework of linear transceiver design.

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