Constellation Design under Channel Uncertainty

Abstract: The topic of this thesis is signaling design for data transmission through wireless channels between a transmitter and a receiver that can both be equipped with one or more antennas. In particular, the focus is on channels where the propagation coefficients between each transmitter--receiver antenna pair are only partially known or completetly unknown to the receiver and unknown to the transmitter.A standard signal design approach for this scenario is based on separate training for the acquisition of channel knowledge at the receiver and subsequent error-control coding for data detection over channels that are known or at least approximately known at the receiver. If the number of parameters to estimate in the acquisition phase is high as, e.g., in a frequency-selective multiple-input multiple-output channel, the required amount of training symbols can be substantial. It is therefore of interest to study signaling schemes that minimize the overhead of training or avoid a training sequence altogether.Several approaches for the design of such schemes are considered in this thesis. Two different design methods are investigated based on a signal representation in the time domain. In the first approach, the symbol alphabet is preselected, the design problem is formulated as an integer optimization problem and solutions are found using simulated annealing. The second design method is targeted towards general complex-valued signaling and applies a constrained gradient-search algorithm. Both approaches result in signaling schemes with excellent detection performance, albeit at the cost of significant complexity requirements.A third approach is based on a signal representation in the frequency domain. A low-complexity signaling scheme performing differential space--frequency modulation and detection is described, analyzed in detail and evaluated by simulation examples.The mentioned design approaches assumed that the receiver has no knowledge about the value of the channel coefficients. However, we also investigate a scenario where the receiver has access to an estimate of the channel coefficients with known error statistics. In the case of a frequency-flat fading channel, a design criterion allowing for a smooth transition between the corresponding criteria for known and unknown channel is derived and used to design signaling schemes matched to the quality of the channel estimate. In particular, a constellation design is proposed that offers a high level of flexibility to accomodate various levels of channel knowledge at the receiver.