A robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization

This paper considers a wireless communication system with multiple transmit and receive antennas, i.e., a multiple-input-multiple-output (MIMO) channel. The objective is to design the transmitter according to an imperfect channel estimate, where the errors are explicitly taken into account to obtain a robust design under the maximin or worst case philosophy. The robust transmission scheme is composed of an orthogonal space–time block code (OSTBC), whose outputs are transmitted through the eigenmodes of the channel estimate with an appropriate power allocation among them. At the receiver, the signal is detected assuming a perfect channel knowledge. The optimization problem corresponding to the design of the power allocation among the estimated eigenmodes, whose goal is the maximization of the signal-to-noise ratio (SNR), is transformed to a simple convex problem that can be easily solved. Different sources of errors are considered in the channel estimate, such as the Gaussian noise from the estimation process and the errors from the quantization of the channel estimate, among others. For the case of Gaussian noise, the robust power allocation admits a closed-form expression. Finally, the benefits of the proposed design are evaluated and compared with the pure OSTBC and nonrobust approaches.Postprint (published version

Robust Secure Transmission in MISO Channels Based on Worst-Case Optimization

This paper studies robust transmission schemes for multiple-input single-output (MISO) wiretap channels. Both the cases of direct transmission and cooperative jamming with a helper are investigated with imperfect channel state information (CSI) for the eavesdropper links. Robust transmit covariance matrices are obtained based on worst-case secrecy rate maximization, under both individual and global power constraints. For the case of an individual power constraint, we show that the non-convex maximin optimization problem can be transformed into a quasiconvex problem that can be efficiently solved with existing methods. For a global power constraint, the joint optimization of the transmit covariance matrices and power allocation between the source and the helper is studied via geometric programming. We also study the robust wiretap transmission problem for the case with a quality-of-service constraint at the legitimate receiver. Numerical results show the advantage of the proposed robust design. In particular, for the global power constraint scenario, although cooperative jamming is not necessary for optimal transmission with perfect eavesdropper's CSI, we show that robust jamming support can increase the worst-case secrecy rate and lower the signal to interference-plus-noise ratio at Eve in the presence of channel mismatches between the transmitters and the eavesdropper.Comment: 28 pages, 5 figure

Robust MIMO Precoding for the Schatten Norm Based Channel Uncertainty Set

The full potential of multi-input multi-output (MIMO) communication systems relies on exploiting channel state information at the transmitter (CSIT), which is, however, often subject to some uncertainty. In this paper, following the worst-case robust philosophy, we consider a robust MIMO precoding design with deterministic imperfect CSIT, formulated as a maximin problem, to maximize the worst-case received signal-to-noise ratio or minimize the worst-case error probability. Given different types of imperfect CSIT in practice, a unified framework is lacking in the literature to tackle various channel uncertainty. In this paper, we address this open problem by considering several classes of uncertainty sets that include most deterministic imperfect CSIT as special cases. We show that, for general convex uncertainty sets, the robust precoder, as the solution to the maximin problem, can be efficiently computed by solving a single convex optimization problem. Furthermore, when it comes to unitarily-invariant convex uncertainty sets, we prove the optimality of a channel-diagonalizing structure and simplify the complex-matrix problem to a real-vector power allocation problem, which is then analytically solved in a waterfilling manner. Finally, for uncertainty sets defined by a generic matrix norm, called the Schatten norm, we provide a fully closed-form solution to the robust precoding design, based on which the robustness of beamforming and uniform-power transmission is investigated

Optimal Beamforming for Physical Layer Security in MISO Wireless Networks

A wireless network of multiple transmitter-user pairs overheard by an eavesdropper, where the transmitters are equipped with multiple antennas while the users and eavesdropper are equipped with a single antenna, is considered. At different levels of wireless channel knowledge, the problem of interest is beamforming to optimize the users' quality-of-service (QoS) in terms of their secrecy throughputs or maximize the network's energy efficiency under users' QoS. All these problems are seen as very difficult optimization problems with many nonconvex constraints and nonlinear equality constraints in beamforming vectors. The paper develops path-following computational procedures of low-complexity and rapid convergence for the optimal beamforming solution. Their practicability is demonstrated through numerical examples

Flexible MIMO architectures: guidelines in the design of MIMO parameters

One of the multiple advantages of communicating through MIMO systems is their inherent ability to provide flexible configurations. Following this line of thought, in this paper we present a generic framework to study the degrees of freedom in the design of MIMQ communication systems (e.g.: code length, number of multiplexed streams, or receiver structure). Precisely, we focus our efforts to bridge the gap between the design of MIMO systems with full and no channel state information at the transmitter side and also with different complexiry degrees at ihe receiver side. For instance, we can establish a trade-off, not only between the achievable rates and the diversity or beamforming gains, but also between the rate and the robustness to uncertainties in the channel state information.Postprint (published version

Robust Lattice Alignment for K-user MIMO Interference Channels with Imperfect Channel Knowledge

In this paper, we consider a robust lattice alignment design for K-user quasi-static MIMO interference channels with imperfect channel knowledge. With random Gaussian inputs, the conventional interference alignment (IA) method has the feasibility problem when the channel is quasi-static. On the other hand, structured lattices can create structured interference as opposed to the random interference caused by random Gaussian symbols. The structured interference space can be exploited to transmit the desired signals over the gaps. However, the existing alignment methods on the lattice codes for quasi-static channels either require infinite SNR or symmetric interference channel coefficients. Furthermore, perfect channel state information (CSI) is required for these alignment methods, which is difficult to achieve in practice. In this paper, we propose a robust lattice alignment method for quasi-static MIMO interference channels with imperfect CSI at all SNR regimes, and a two-stage decoding algorithm to decode the desired signal from the structured interference space. We derive the achievable data rate based on the proposed robust lattice alignment method, where the design of the precoders, decorrelators, scaling coefficients and interference quantization coefficients is jointly formulated as a mixed integer and continuous optimization problem. The effect of imperfect CSI is also accommodated in the optimization formulation, and hence the derived solution is robust to imperfect CSI. We also design a low complex iterative optimization algorithm for our robust lattice alignment method by using the existing iterative IA algorithm that was designed for the conventional IA method. Numerical results verify the advantages of the proposed robust lattice alignment method