Robust transmit beamforming based on probabilistic constraint (original) (raw)
Related papers
2009 17th European Signal Processing Conference, 2009
Transmit beamforming is a powerful technique for enhancing performance of wireless communication systems. Most existing transmit beamforming techniques require perfect channel state information at the transmitter (CSIT), which is typically not available in practice. In such situations, the design should take errors in CSIT into account to avoid performance degradation. Among two popular robust designs, the stochastic approach exploits channel statistics and optimizes the average system performance.
A Probabilistic Constraint Approach for Robust Beamforming with Imperfect Channel Information
2008
Transmit beamforming is a powerful technique for enhancing performance of wireless communication systems. Most exist ing transmit beamforming techniques require perfect channel s tate information at the transmitter (CSIT), which is typically not available in practice. In such situations, the design should take erro rs in CSIT into account to avoid performance degradation. Among t wo popular robust designs, the stochastic approach exploits c hannel statistics and optimizes the average system performance. T h maximin approach considers the errors as deterministic and opt imizes the worst-case performance. The latter usually leads to con servative results as the extreme (but rare) conditions may occur at a ve ry low probability. In this work, we propose a more flexible approac h that maximizes the average signal-to-noise ratio (SNR) and take s th extreme conditions into account proportionally. Simulati on results show that the proposed beamformer offers higher robustness against channe...
Transmit Beamforming with Imperfect Channel Information
2009
Transmit beamforming (or percoding) is a powerful technique for enhancing performance of wireless multiantenna communication systems. Standard transmit beamformers require perfect channel state information at the transmitter (CSIT) and are sensitive to errors in channel estimation. In practice, such errors are inevitable due to finite feedback resources, quantization errors and other physical constraints. Hence, robustness has become a crucial issue recently. Among two popular robust designs, the stochastic approach exploits channel statistics and optimizes the average system performance while the maximin approach considers errors as deterministic and optimizes the worst-case performance. The latter usually leads to a very conservative design against extreme (but rare) conditions which may occur at a very low probability. In this work, we propose a more flexible approach that maximizes the average signal-to-noise ratio (SNR) and takes the extreme conditions into account using the probability with which they may occur. Simulation results show that the proposed beamformer offers higher robustness against channel estimation errors than several popular transmit beamformers.
On the Robustness of Transmit Beamforming
IEEE Transactions on Signal Processing, 2000
Beamforming is a simple transmit strategy that uses only one eigen-direction in multiple-input multiple-output channels. This simplicity makes beamforming a competitive strategy in practice, but at the same time poses a doubt on the sensitivity of beamforming to the imperfectness of the channel state information at the transmitter (CSIT). This paper studies beamforming from the perspective of worst-case robustness. We show that beamforming can achieve the maximum received signal-to-noise ratio (SNR) or guarantees a given received SNR with the minimum transmit power, in the worst channel within an elliptical uncertainty region defined by the weighted spectral norm. This result further implies that beamforming has the ability to combat against the imperfectness of CSIT, especially for small channel dimensions or small channel uncertainty.
Robust receive beamforming with interference and channel uncertainty
IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC, 2012
In this paper, we introduce a general convex framework for robust beamforming, which is valid for both deterministic and stochastic uncertainty models, and provides robustness against errors both in the channel and in the interference covariance matrix estimations. Furthermore, we extend our design to a multiple-state interference model [12] and show the performance gains obtained by exploiting the interference structure.
Robust adaptive beamforming using probability-constrained optimization
IEEE/SP 13th Workshop on Statistical Signal Processing, 2005, 2005
Recently, robust minimum variance (MV) beamforming which optimizes the worst-case performance has been proposed in [1], . The worst-case approach, however, might be overly conservative in practical applications. In this paper, we propose a more flexible approach that formulates the robust adaptive beamforming problem as a probability-constrained optimization problem with homogeneous quadratic cost function. Unlike the general probability-constrained problem which can be nonconvex and NP-hard, our problem can be reformulated as a convex nonlinear programming (NLP) problem, and efficiently solved using interiorpoint methods. Simulation results show an improved robustness of the proposed beamformer as compared to the existing state-of-the-art robust adaptive beamforming techniques.
Robust Downlink Beamforming Based on Outage Probability Specifications
IEEE Transactions on Wireless Communications, 2000
A new approach to multi-antenna downlink beamforming is proposed that provides an improved robustness against uncertainty in the downlink channel covariance matrices caused by errors between the actual and estimated channel values. The proposed method uses the knowledge of the statistical distribution of such a covariance uncertainty to minimize the total downlink transmit power under the constraint that the outage probability does not exceed a certain threshold value. Although our approach initially leads to a non-convex optimization problem, it can be reformulated in a convex form using the semidefinite relaxation technique. The resulting convex optimization problem can be solved efficiently using the well-established interior point methods. Computer simulations verify performance improvements of the proposed technique as compared to the robust transmit beamforming method based on the worst-case performance optimization with judicious selection of the upper bounds on channel covariance errors.
IEEE Transactions on Signal Processing, 2008
An interesting relationship between the probability-constrained and worst-case optimization based robust minimum variance (MV) beamformers has been discovered. It is shown that both in the cases of circularly symmetric Gaussian and worst-case distributions of the steering vector mismatch, the probability-constrained robust MV beamforming problem can be tightly approximated as a convex second-order cone programming (SOCP) problem. The latter problem is mathematically equivalent to that resulting from the deterministic worst-case approach and, therefore, probability-constrained beamformers can be interpreted and implemented using their deterministic worst-case counterparts. However, an important advantage of the developed probability-constrained MV beamformers with respect to their standard worst-case counterparts is that the former approaches enable to explicitly quantify the parameters of the uncertainty region in terms of the beamformer outage probability.
Tight Probabilistic SINR Constrained Beamforming Under Channel Uncertainties
In downlink multi-user beamforming, a single basestation is serving a number of users simultaneously. However, energy intended for one user may leak to other unintended users, causing interference.With signal-to-interference-plus-noise ratio (SINR) being one of the most crucial quality metrics to users, beamforming design with SINR guarantee has always been an important research topic. However, when the channel state information is not accurate, the SINR requirements become probabilistic constraints, which unfortunately are not tractable analytically for general uncertainty distribution. Therefore existing probabilistic beamforming methods focus on the relatively simple Gaussian and uniform channel uncertainties, and mainly rely on probability inequality based approximated solutions, resulting in conservative SINR outage realizations. In this paper, based on the local structure of the feasible set in the probabilistic beamforming problem, a systematic method is proposed to realize tight SINR outage control for a large class of channel uncertainty distributions. With channel estimation and quantization errors as examples, simulation results show that the SINR outage can be realized tightly, which results in reduced transmit power compared to the existing inequality based probabilistic beamformers.