Design of Limited Feedback for Robust MMSE Precoding in Multiuser MISO Systems

In this thesis, we consider a multiuser system with a transmitter equipped with multiple antennas and only one antenna at each receiver user. This system, which is termed MUMISO (Multi User Multiple Input/Single Output is of use to model the downlink of a wireless communication system, where multiple antennas at the base station transmit to several users with usually only one antenna at each receiving unit. This downlink channel is also called Broadcast Channel (BC). When considering this broadcast channel, the centralized transmitter clearly has more degrees of freedom than each of the receivers. Therefore, it is appropriate to separate the signals by applying precoding at the transmitter. To be able to design precoding, the transmitter needs knowledge about the channel states of the different receivers. In the case of Frequency Division Duplex (FDD) systems, this knowledge can be obtained by feedback (at least partially), where the Channel State Information (CSI) of the receivers is quantized to adapt to the limited rate conditions of the feedback channel. The standard assumption for feedback design is error free CSI at the receivers, but the receivers get their CSI by estimation. Thus, it contains errors. In order to properly design the limited feedback, it is necessary to obtain an adequate statistical characterization of the CSI errors. The following sources of error are considered throughout this work: channel estimation, truncation (rank reduction), quantization, and feedback channel delay. It is assumed, however, that the feedback channel does not suffer from errors during the transmission. As a first approach, we propose a design based on a CSI MSE metric, i.e. the feedback parameters are found by means of the minimization of the Mean Squared Error (MSE) between the true channel and the erroneous channel sent from the receiver side to the transmitter. The precoder filters, however, are obtained by means of a different minimum squared error optimization. In other words, we propose a joint optimization of the estimation, the rank reduction, and the codebook used for the feedback, available at both the transmitter and the receiver side. Interestingly, the estimator and the rank reduction resulting from this formulation are independent of the codebook used, which can be computed off line with the generalized Lloyd algorithm. The results in terms of Bit Error Rate (BER) can be improved by the algorithm proposed to dynamically allocate the bits associated to the quantization process by means of easily computing the obtained MSE. As a second approach, we jointly design the channel estimators and the quantizers at the receivers together with the precoder at the transmitter based on a single criterion oriented to the precoder instead of the CSI MSE criterion applied for the first approach. Therefore, this optimization consists of minimizing the MSE between the symbols transmitted and recovered by each user. The codebook entries are now the possible precoder filters so that each receiver feeds back the index corresponding to a set of precoders and the intersection of the sets gives the optimum precoder to be used while channel statistics remain unchanged. Several simulations carried out using MATLAB show that robust precoding based on fed back information clearly outperforms conventional precoding that does not take into account the errors in the CSI. Additionally, we observe that a robust design is especially crucial for systems employing nonlinear precoders with scarce feedback rate. Some comparisons between the abovementioned approaches show that a limited feedback design involving the precoder in the MSE optimization exhibits better performance compared to the isolated precoder optimization, although the computational complexity is much higher.