Non-adaptive methods in dimension reduction for dispersive and non-coherent communication channels

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The signal- and information-theoretic principles of communication underdispersive and non-coherent conditions is of great importance for the optimal design of future communication systems. Many newly proposedsystem setups have to operate on parameter sets with exponentially increasing dimension.Therein are exemplary: cooperating transmitters with multiple antennas, cognitive radio systems operating at large bandwidth, signal aggregiation in non--orthogonal multiuser scenarious and sensor networks. Conventional communication usually uses complex methods for estimation and coordination of this large number ofsystem parameters. This includes synchronization, channel estimation and prediction, resource allocation and - increasingly important for cellular radio networks - routing in the backbone network.Just before transmitting any bit of user data this conventional procedure requires a substantial amount of communication and signal processing resources in a network - at the terminals, on the feedback channel, in intermediate communication between the several controlling and transmitter units and in the backbone network.On the other hand, in an increasing number of applications the typical user traffic consists only of short messages like status updates. Thus, there is the paradox situation, that the control overhead for these complex communication systems is of the same and higer order as the intended exchange of the original information.Due to the increasing use of smartphones, the relevance of mobile machine to machine communication and wireless sensor networks, an even more exacerbation has to be expected in future.A solution to this problem could be the use of non--coherent strategies and new non-adaptive compression methods for the feedback channel with both having possibly random nature.Although these approaches are known for a long time in signal- and information theory, a new combined theoryis necessary here which explicitely accounts for parameter sets of reduced complexity but in large dimension and the short message type of user data.The goal of this research project is to contribute here in estimation and detection theory and signal processing.Scaling results and algorithmic methods should be established in the project for situations where the overall set of communication parameters is essentially sparse and of low rank type, i.e.has in general a low-dimensional compressible structure in large dimension.