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理论原理对于未来通信系统的优化设计具有重要意义。许多新提出的系统结构都需要对维数呈指数增长的参数集进行操作，例如：多天线协作发射机、大带宽认知无线电系统、非正交多用户通信系统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--对于蜂窝无线电网络越来越重要的--骨干网中的路由。就在发送任何用户数据比特之前，这种传统过程需要网络中的大量通信和信号处理资源--在终端处，在反馈信道上，另一方面，在越来越多的应用中，典型的用户业务仅由像状态更新这样的短消息组成。因此，存在这样一种矛盾的情况，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阶数。由于智能手机的使用越来越多，移动的机器对机器通信和无线传感器网络的相关性，一个解决这个问题的办法可能是使用不连贯的战略和新的不连贯的战略，用于反馈信道的自适应压缩方法，两者都具有可能的随机特性。虽然这些方法在信号和信息理论中已经公知很长时间，一个新的组合理论是必要的，它明确地说明了参数集的复杂性降低，但在大尺寸和短消息类型该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，在该项目中应建立用于通信参数的总体集合基本上是稀疏的和低秩类型的情况的缩放结果和算法方法，即在大维度中通常具有低维可压缩结构。

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.