Design Guidelines for Training-based MIMO Systems with Feedback

In this paper, we study the optimal training and data transmission strategies for block fading multiple-input multiple-output (MIMO) systems with feedback. We consider both the channel gain feedback (CGF) system and the channel covariance feedback (CCF) system. Using an accurate capacity lower bound as a figure of merit, we investigate the optimization problems on the temporal power allocation to training and data transmission as well as the training length. For CGF systems without feedback delay, we prove that the optimal solutions coincide with those for non-feedback systems. Moreover, we show that these solutions stay nearly optimal even in the presence of feedback delay. This finding is important for practical MIMO training design. For CCF systems, the optimal training length can be less than the number of transmit antennas, which is verified through numerical analysis. Taking this fact into account, we propose a simple yet near optimal transmission strategy for CCF systems, and derive the optimal temporal power allocation over pilot and data transmission.Comment: Submitted to IEEE Trans. Signal Processin

A robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization

This paper considers a wireless communication system with multiple transmit and receive antennas, i.e., a multiple-input-multiple-output (MIMO) channel. The objective is to design the transmitter according to an imperfect channel estimate, where the errors are explicitly taken into account to obtain a robust design under the maximin or worst case philosophy. The robust transmission scheme is composed of an orthogonal space–time block code (OSTBC), whose outputs are transmitted through the eigenmodes of the channel estimate with an appropriate power allocation among them. At the receiver, the signal is detected assuming a perfect channel knowledge. The optimization problem corresponding to the design of the power allocation among the estimated eigenmodes, whose goal is the maximization of the signal-to-noise ratio (SNR), is transformed to a simple convex problem that can be easily solved. Different sources of errors are considered in the channel estimate, such as the Gaussian noise from the estimation process and the errors from the quantization of the channel estimate, among others. For the case of Gaussian noise, the robust power allocation admits a closed-form expression. Finally, the benefits of the proposed design are evaluated and compared with the pure OSTBC and nonrobust approaches.Postprint (published version

Robust transmit beamforming design using outage probability specification

Transmit beamforming (precoding) is a powerful technique for enhancing the channel capacity and reliability of multiple-input and multiple-output (MIMO) wireless systems. The optimum exploitation of the benefits provided by MIMO systems can be achieved when a perfect channel state information at transmitter (CSIT) is available. In practices, however, the channel knowledge is generally imperfect at transmitter because of the inevitable errors induced by finite feedback channel capacity, quantization and other physical constraints. Such errors degrade the system performance severely. Hence, robustness has become a crucial issue. Current robust designs address the channel imperfections with the worst-case and stochastic approaches. In worst-case analysis, the channel uncertainties are considered as deterministic and norm-bounded, and the resulting design is a conservative optimization that guarantees a certain quality of service (QoS) for every allowable perturbation. The latter approach focuses on the average performance under the assumption of channel statistics, such as mean and covariance. The system performance could break down when persistent extreme errors occur. Thus, an outage probability-based approach is developed by keeping a low probability that channel condition falls below an acceptable level. Compared to the aforementioned methods, this approach can optimize the average performance as well as consider the extreme scenarios proportionally. This thesis implements the outage-probability specification into transmit beamforming design for three scenarios: the single-user MIMO system and the corresponding adaptive modulation scheme as well as the multi-user MIMO system. In a single-user MIMO system, the transmit beamformer provides the maximum average received SNR and ensures the robustness to the CSIT errors by introducing probabilistic constraint on the instantaneous SNR. Beside the robustness against channel imperfections, the outage probability-based approach also provides a tight BER bound for adaptive modulation scheme, so that the maximum transmission rate can be achieved by taking advantage of transmit beamforming. Moreover, in multi-user MIMO (MU-MIMO) systems, the leakage power is accounted by probability measurement. The resulting transmit beamformer is designed based on signal-to-leakage-plus-noise ratio (SLNR) criteria, which maximizes the average received SNR and guarantees the least leakage energy from the desired user. In such a setting, an outstanding BER performance can be achieved as well as high reliability of signal-to-interference-plus-noise ratio (SINR). Given the superior overall performances and significantly improved robustness, the probabilistic approach provides an attractive alternative to existing robust techniques under imperfect channel information at transmitter

Novel transmission and beamforming strategies for multiuser MIMO with various CSIT types

In multiuser multi-antenna wireless systems, the transmission and beamforming strategies that achieve the sum rate capacity depend critically on the acquisition of perfect Channel State Information at the Transmitter (CSIT). Accordingly, a high-rate low-latency feedback link between the receiver and the transmitter is required to keep the latter accurately and instantaneously informed about the CSI. In realistic wireless systems, however, only imperfect CSIT is achievable due to pilot contamination, estimation error, limited feedback and delay, etc. As an intermediate solution, this thesis investigates novel transmission strategies suitable for various imperfect CSIT scenarios and the associated beamforming techniques to optimise the rate performance. First, we consider a two-user Multiple-Input-Single-Output (MISO) Broadcast Channel (BC) under statistical and delayed CSIT. We mainly focus on linear beamforming and power allocation designs for ergodic sum rate maximisation. The proposed designs enable higher sum rate than the conventional designs. Interestingly, we propose a novel transmission framework which makes better use of statistical and delayed CSIT and smoothly bridges between statistical CSIT-based strategies and delayed CSIT-based strategies. Second, we consider a multiuser massive MIMO system under partial and statistical CSIT. In order to tackle multiuser interference incurred by partial CSIT, a Rate-Splitting (RS) transmission strategy has been proposed recently. We generalise the idea of RS into the large-scale array. By further exploiting statistical CSIT, we propose a novel framework Hierarchical-Rate-Splitting that is particularly suited to massive MIMO systems. Third, we consider a multiuser Millimetre Wave (mmWave) system with hybrid analog/digital precoding under statistical and quantised CSIT. We leverage statistical CSIT to design digital precoder for interference mitigation while all feedback overhead is reserved for precise analog beamforming. For very limited feedback and/or very sparse channels, the proposed precoding scheme yields higher sum rate than the conventional precoding schemes under a fixed total feedback constraint. Moreover, a RS transmission strategy is introduced to further tackle the multiuser interference, enabling remarkable saving in feedback overhead compared with conventional transmission strategies. Finally, we investigate the downlink hybrid precoding for physical layer multicasting with a limited number of RF chains. We propose a low complexity algorithm to compute the analog precoder that achieves near-optimal max-min performance. Moreover, we derive a simple condition under which the hybrid precoding driven by a limited number of RF chains incurs no loss of optimality with respect to the fully digital precoding case.Open Acces

Robust beamforming for collaborative MIMO-OFDM wireless systems

Collaborative beamforming is a powerful technique to increase communication energy efficiency and range in an energy-constrained network. To achieve high performance, collaborative beamforming requires accurate knowledge of channel state information (CSI) at the transmitters (collaborative nodes). In practice, however, such exact knowledge of CSI is not available. A robust transmitter design based on partial CSI is required to mitigate the effects of CSI mismatches.This thesis focuses on the design and evaluation of a beamforming scheme that is robust to CSI mismatches for collaborative multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) wireless systems. Using a max-min robust design approach, the robust beamformer is designed to maximize the minimum (worst-case) received signal-to-noise ratio (SNR) within a predefined uncertainty region at each OFDM subcarrier. In addition, several subcarrier power allocation strategies are investigated to further improve the robustness of collaborative systems. Numerical simulation results show that the robust beamformer offers improved performance over the nonrobust beamformers and the use of power allocation strategies among subcarriers further improves the system performance