Robust Precoding with Limited Feedback Design based on Precoding MSE for MU-MISO Systems

The final publication is available http://dx.doi.org/10.1109/TSP.2012.2186446[Abstract] For the separation of the signals in the vector broadcast channel (BC), some information about the channel state is necessary at the transmitter. In many cases, this channel state information (CSI) must be fed back from the receivers to the transmitter. We jointly design the channel estimators and the quantizers at the receivers together with the precoder at the transmitter based on a precoder-centric criterion, i.e., the minimization of a mean square error (MSE) metric appropriate for the precoder design. This is in contrast to our previous works, where the quantizer design was based on a CSI MSE metric, i.e., based on the minimization of the MSE between the true channel and the channel recovered by the transmitter using a feedback channel. Interestingly, the estimators resulting from this joint formulation are independent of the used codebook. The codebook entries are the employed precoders. Therefore, each receiver feeds back the index of a set of precoders and the intersection of the sets gives the appropriate precoder. Since the quantizers of the different receivers have to work separately, the metric for the computation of the partition cells cannot be expressed as a simple squared error depending on the quantizer output. The proposed system based on a joint optimization clearly outperforms previous designs with separate optimization of feedback and precoding.Ministerio de Ciencia e Innovación; TEC2010-19545-C04-01Ministerio de Ciencia e Innovación; CSD2008-00010Galicia. Consellería de Economía e Industria; 09TIC008105P

Robust Precoding with Bayesian Error Modeling for Limited Feedback MU-MISO Systems

The final publication is available http://dx.doi.org/10.1109/TSP.2010.2052046[Abstract] We consider the robust precoder design for multiuser multiple-input single-output (MU-MISO) systems where the channel state information (CSI) is fed back from the single antenna receivers to the centralized transmitter equipped with multiple antennas. We propose to compress the feedback data by projecting the channel estimates onto a vector basis, known at the receivers and the transmitter, and quantizing the resulting coefficients. The channel estimator and the basis for the rank reduction are jointly optimized by minimizing the mean-square error (MSE) between the true and the rank-reduced CSI. Expressions for the conditional mean and the conditional covariance of the channel are derived which are necessary for the robust precoder design. These expressions take into account the following sources of error: channel estimation, truncation for rank reduction, quantization, and feedback channel delay. As an example for the robust problem formulation, vector precoding (VP) is designed based on the expectation of the MSE conditioned on the fed-back CSI. Our results show that robust precoding based on fed-back CSI clearly outperforms conventional precoding designs which do not take into account the errors in the CSI.Galicia, Consellería de Innovación, Industria e Comercio; PGIDT06TIC10501PRMinisterio de Educacion y Ciencia; TEC2007-68020-C04-01Ministerio de Educacion y Ciencia; CSD2008-00010.Ministerio de Educacion y Ciencia; HA2006-0112Alemania. Deutscher Akademischer Austauschdienst; D/06/1280

Sum-Rate Maximization for Linearly Precoded Downlink Multiuser MISO Systems with Partial CSIT: A Rate-Splitting Approach

This paper considers the Sum-Rate (SR) maximization problem in downlink MU-MISO systems under imperfect Channel State Information at the Transmitter (CSIT). Contrary to existing works, we consider a rather unorthodox transmission scheme. In particular, the message intended to one of the users is split into two parts: a common part which can be recovered by all users, and a private part recovered by the corresponding user. On the other hand, the rest of users receive their information through private messages. This Rate-Splitting (RS) approach was shown to boost the achievable Degrees of Freedom (DoF) when CSIT errors decay with increased SNR. In this work, the RS strategy is married with linear precoder design and optimization techniques to achieve a maximized Ergodic SR (ESR) performance over the entire range of SNRs. Precoders are designed based on partial CSIT knowledge by solving a stochastic rate optimization problem using means of Sample Average Approximation (SAA) coupled with the Weighted Minimum Mean Square Error (WMMSE) approach. Numerical results show that in addition to the ESR gains, the benefits of RS also include relaxed CSIT quality requirements and enhanced achievable rate regions compared to conventional transmission with NoRS.Comment: accepted to IEEE Transactions on Communication

A Rate-Splitting Approach To Robust Multiuser MISO Transmission

For multiuser MISO systems with bounded uncertainties in the Channel State Information (CSI), we consider two classical robust design problems: maximizing the minimum rate subject to a transmit power constraint, and power minimization under a rate constraint. Contrary to conventional strategies, we propose a Rate-Splitting (RS) strategy where each message is divided into two parts, a common part and a private part. All common parts are packed into one super common message encoded using a shared codebook and decoded by all users, while private parts are independently encoded and retrieved by their corresponding users. We prove that RS-based designs achieve higher max-min Degrees of Freedom (DoF) compared to conventional designs (NoRS) for uncertainty regions that scale with SNR. For the special case of non-scaling uncertainty regions, RS contrasts with NoRS and achieves a non-saturating max-min rate. In the power minimization problem, RS is shown to combat the feasibility problem arising from multiuser interference in NoRS. A robust design of precoders for RS is proposed, and performance gains over NoRS are demonstrated through simulations.Comment: To appear in ICASSP 201

AMMSE Optimization for Multiuser MISO Systems with Imperfect CSIT and Perfect CSIR

In this paper, we consider the design of robust linear precoders for MU-MISO systems where users have perfect Channel State Information (CSI) while the BS has partial CSI. In particular, the BS has access to imperfect estimates of the channel vectors, in addition to the covariance matrices of the estimation error vectors. A closed-form expression for the Average Minimum Mean Square Error (AMMSE) is obtained using the second order Taylor Expansion. This approximation is used to formulate two fairness-based robust design problems: a maximum AMMSE-constrained problem and a power-constrained problem. We propose an algorithm based on convex optimization techniques to address the first problem, while the second problem is tackled by exploiting the close relationship between the two problems, in addition to their monotonic natures.Comment: IEEE Global Communications Conference (GLOBECOM) 201