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

Abstract

We consider the robust precoder design for Multi-User 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).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. Three well-known precoder types, namely Linear Precoding (LP), Vector Precoding (VP), and Tomlinson-Harashima Precoding (THP), are designed based on the expectation of the MSE conditioned on the fed-back CSI. Our results show that robust precoding based on fedback CSI clearly outperforms conventional precoding designs which do not take into account the errors in the CSI.Additionally, we observe that a robust design is especially crucial for systems employing non-linear precoding with scarce feedback rate. Index TermsFeedback channel, Bayesian approach, imperfect CSI, robust precoding. I. INTRODUCTIONWe consider a MU-MISO system, i.e. a multiple antennas transmitter and several single-antenna receivers, since the centralized access point in a cellular system admits more complexity and cost than the mobiles. A MU-MISO system is a prominent example of a vector broadcast channel [1]. Recently, it has been shown that the Dirty Paper

Performance of MIMO systems in measured indoor channels with transmitter noise

“…Figure 9 plots the BER performance in terms of SRxNR for MIMO systems with both MMSE and ZF TH precoding. Note the high sensitivity of the performance of MIMO systems with THP with respect to Txnoise, which produces that the curves go up again for high scenarios [31]. The performance of both MMSE and ZF TH precoding is considerably degraded due to the Tx-noise and an error floor arises at the significant value of 2 × 10 -3 (at 40dB of SRxNR).…”

Robust Precoding With Limited Feedback Design Based on Precoding MSE for MU-MISO Systems

“…The obtained results for and can be substituted into (9). Thus, the MSE for the given codebook entries and partition cells is expressed as MSE (15) As mentioned before, thanks to introducing the alternative representation of the channel estimator in (11), we can obtain the optimum channel estimator by finding the basis that minimizes the above MSE expression for a fixed , i.e., MSE subject to:…”

“…For simplicity reasons, the feedback channel is assumed to be error-free and without delay. The delay effect is relatively easy to correct (see [14] and [15]) but at the cost of unnecessarily complicating our notation.…”

“…Contrary to the quantizers used in [14] and [15], where the codebook entries were white channel coefficients, the codebook entries of the quantizers proposed in this work are the precoders of Fig. 1, i.e., the quantized information eventually represents a precoder and not a CSI.…”

The Sign-Definiteness Lemma and Its Applications to Robust Transceiver Optimization for Multiuser MIMO Systems

“…Although this mechanism may reduce the overall spectral efficiency of the system when taking into account the overhead, it appears to be indispensable. Since usually the receivers quantize the CSI before sending it to the central station, the linear equalizers designed in the central station have more uncertainty relative to the ones that could be designed by the receivers themselves [53].…”