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

色散和非相干条件下通信的信号和信息论原理对未来通信系统的优化设计具有重要意义。许多新提出的系统设置必须在维度呈指数增长的参数集上运行。其中有示例性：具有多天线的合作发射机，在大带宽下操作的认知无线电系统，非正交多用户场景和传感器网络中的信号聚合。传统的通信通常使用复杂的方法来估计和协调大量的系统参数。这包括同步、信道估计和预测、资源分配以及主干网中的路由（对蜂窝无线网络来说越来越重要）。在传输任何一位用户数据之前，这一传统程序需要在网络中——在终端、在反馈信道上、在几个控制和发送单元之间的中间通信中以及在骨干网络中——使用大量的通信和信号处理资源。另一方面，在越来越多的应用程序中，典型的用户流量仅由状态更新等短消息组成。因此，出现了矛盾的情况，即这些复杂通信系统的控制开销与原始信息的预期交换具有相同且更高的顺序。由于智能手机的使用越来越多，移动机器对机器通信和无线传感器网络的相关性，预计未来会更加恶化。解决这个问题的方法可能是使用非相干策略和新的非自适应压缩方法，这两种方法都可能具有随机性质。尽管这些方法在信号和信息理论中已经存在了很长时间，但这里需要一种新的组合理论，该理论明确地解释了复杂性降低但维度大的参数集和用户数据的短消息类型。本研究项目的目标是在估计和检测理论以及信号处理方面做出贡献。对于整体通信参数集本质上是稀疏的低秩型，即在大维度上一般是低维可压缩结构的情况，本项目需要建立标度结果和算法方法。

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.