MIMO Settings Research Articles

Channel Hardening of IRS-Aided Multi-Antenna Systems: How Should IRSs Scale?

It is widely believed that large IRS-aided MIMO settings maintain the fundamental features of massive MIMO systems. This work gives a rigorous proof that confirms this belief. We show that using a large passive IRS, the end-to-end MIMO channel between the transmitter and the receiver always hardens, even if the IRS elements are strongly correlated. For fading direct and reflection links between the transmitter and the receiver, our derivations demonstrate that for a large number of reflecting elements on the IRS, the capacity of the end-to-end channel is accurately approximated by a real-valued Gaussian random variable whose variance goes to zero as the number of IRS elements grows unboundedly large. The order of this drop depends on how the physical dimensions of the IRS grow. We derive this order explicitly. Numerical experiments show that the closed-form approximation very closely matches the histogram of the capacity term, even in practical scenarios. As a sample application of the results, we characterize the dimensional trade-off between the transmitter and the IRS. The result is intuitive: For a target performance, the larger the IRS is, the fewer transmit antennas are required.

The Capacity and Optimal Signaling for Gaussian MIMO Channels Under Interference Constraints

Gaussian MIMO channel under the joint transmit (Tx) and interference power constraints (TPC and IPC) is studied. A closed-form solution for the optimal Tx covariance matrix in the general case is obtained using the KKT-based approach, up to dual variables. A number of more explicit closed-form solutions are given with optimal dual variables, including full-rank and rank-1 (beamforming) cases as well as the case of identical eigenvectors (typical for massive MIMO settings), which differer significantly from the standard water-filling solution. A “whitening” filter is shown to be an important part of optimal precoding under interference constraints. Sufficient and necessary conditions for each constraint to be redundant are given. Capacity scaling with the SNR is shown to be determined by a natural linear-algebraic structure of sub-spaces induced by channel matrices of multiple users. A number of unusual properties of optimal Tx covariance matrix under the joint TPC and IPC are pointed out and a bound on its rank is established. An interplay between the TPC and IPC is studied, including the transition from power-limited to interference-limited regimes as the Tx power increases. While closed-from solutions for optimal dual variables are given in some special cases, an iterative bisection algorithm (IBA) is proposed to find optimal dual variables in the general case and its convergence is proved for some special cases. Numerical experiments illustrate its efficient performance. Bounds for the optimal dual variables are given.

Fast Algorithms for Joint Multicast Beamforming and Antenna Selection in Massive MIMO

Massive MIMO is currently a leading physical layer technology candidate that can dramatically enhance throughput in 5G systems, for both unicast and multicast transmission modalities. As antenna elements are becoming smaller and cheaper in the mmW range compared to radio frequency (RF) chains, it is crucial to perform antenna selection at the transmitter, such that the available RF chains are switched to an appropriate subset of antennas. This paper considers the joint problem of multicast beamforming and antenna selection for a single multicast group in massive MIMO systems. The prior state-of-art for this problem relies on semi-definite relaxation (SDR), which cannot scale up to the massive MIMO regime. A successive convex approximation (SCA) based approach is proposed to tackle max-min fair joint multicast beamforming and antenna selection. The key idea of SCA is to successively approximate the non-convex problem by a class of non-smooth, convex optimization problems. Two fast and memory efficient first-order methods are proposed to solve each SCA subproblem. Simulations demonstrate that the proposed algorithms outperform the existing state-of-art approach in terms of solution quality and run time, in both traditional and especially in massive MIMO settings.

Optimal Transmit Antenna Selection for Massive MIMO Wiretap Channels

In this paper, we study the impacts of transmit antenna selection on the secrecy performance of massive MIMO systems. We consider a wiretap setting in which a fixed number of transmit antennas are selected and then confidential messages are transmitted over them to a multi-antenna legitimate receiver while being overheard by a multi-antenna eavesdropper. For this setup, we derive an accurate approximation of the instantaneous secrecy rate. Using this approximation, it is shown that in some wiretap settings under antenna selection the growth in the number of active antennas enhances the secrecy performance of the system up to some optimal number and degrades it when this optimal number is surpassed. This observation demonstrates that antenna selection in some massive MIMO settings not only reduces the RF-complexity, but also enhances the secrecy performance. We then consider various scenarios and derive the optimal number of active antennas analytically using our large-system approximation. Numerical investigations show an accurate match between simulations and the analytic results.

Near-optimal frequency-weighted interpolatory model reduction

This paper develops an interpolatory framework for weighted-H2 model reduction of MIMO dynamical systems. A new representation of the weighted-H2 inner products in MIMO settings is introduced and used to derive associated first-order necessary conditions satisfied by optimal weighted-H2 reduced-order models. Equivalence of these new interpolatory conditions with earlier Riccati-based conditions given by Halevi is also shown. An examination of realizations for equivalent weighted-H2 systems leads then to an algorithm that remains tractable for large state-space dimension. Several numerical examples illustrate the effectiveness of this approach and its competitiveness with Frequency Weighted Balanced Truncation and an earlier interpolatory approach, the Weighted Iterative Rational Krylov Algorithm.