Outage Constrained Robust Transmit Optimization for Multiuser MISO Downlinks: Tractable Approximations by Conic Optimization

In this paper, we study a probabilistically robust transmit optimization problem under imperfect channel state information (CSI) at the transmitter and under the multiuser multiple-input single-output (MISO) downlink scenario. The main issue is to keep the probability of each user's achievable...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 62; no. 21; pp. 5690 - 5705
Main Authors: Kun-Yu Wang, So, Anthony Man-Cho, Tsung-Hui Chang, Wing-Kin Ma, Chong-Yung Chi
Format: Journal Article
Language:English
Published: New York IEEE 01.11.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Approximation
Approximation methods
Array signal processing
Constrictions
Downlink
Heuristic
Imperfect channel state information
Mathematical analysis
Mathematical models
Methods
MIMO precoder designs
multiuser MIMO
Optimization
outage probability
Outages
Quadratic forms
robust optimization
Robustness
Silicon
Uncertainty
Vectors
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:In this paper, we study a probabilistically robust transmit optimization problem under imperfect channel state information (CSI) at the transmitter and under the multiuser multiple-input single-output (MISO) downlink scenario. The main issue is to keep the probability of each user's achievable rate outage as caused by CSI uncertainties below a given threshold. As is well known, such rate outage constraints present a significant analytical and computational challenge. Indeed, they do not admit simple closed-form expressions and are unlikely to be efficiently computable in general. Assuming Gaussian CSI uncertainties, we first review a traditional robust optimization-based method for approximating the rate outage constraints, and then develop two novel approximation methods using probabilistic techniques. Interestingly, these three methods can be viewed as implementing different tractable analytic upper bounds on the tail probability of a complex Gaussian quadratic form, and they provide convex restrictions, or safe tractable approximations, of the original rate outage constraints. In particular, a feasible solution from any one of these methods will automatically satisfy the rate outage constraints, and all three methods involve convex conic programs that can be solved efficiently using off-the-shelf solvers. We then proceed to study the performance-complexity tradeoffs of these methods through computational complexity and comparative approximation performance analyses. Finally, simulation results are provided to benchmark the three convex restriction methods against the state of the art in the literature. The results show that all three methods offer significantly improved solution quality and much lower complexity.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2014.2354312