CIF: Small: Signal Processing for Multi-user Communications under Finite Alphabet Constraints

摘要NSF提案#0915846摘要：信道容量和互信息已被广泛研究的各种类型的有线和无线多用户通信信道。在大量的信息论文献中，大多数结果都是基于信道输入服从高斯分布的假设。然而，高斯输入在实际系统中永远无法实现。输入通常取自有限的字母表，这可能显著偏离高斯分布。理论容量和实际可达速率之间存在很大的非线性差距。这种非线性差距表明，高斯输入假设可能无法提供一个现实的设计指导实际系统。最大化有限字母输入信道上的互信息不仅有利于带宽效率，而且有利于误码率性能。然而，在这一重要议题上所做的工作要少得多。这主要是由于缺乏封闭形式的解决方案和高的计算复杂度。该项目研究了直接最大化的互信息和吞吐量的多用户信道与有限的字母输入。计算复杂性问题通过采用基于图的消息传递技术开发数学上易于处理且实际上准确的算法来解决。形状矩阵被引入到互信息的最大化。参数化的方法来解决最佳成形矩阵，导致全局最大的互信息。多址接入信道、广播信道和干扰信道是多用户通信的基本信道环境，是多用户通信研究的重点。使信道状态信息和/或信道协方差信息可用于发射机和接收机以最大化互信息。研究了频率平坦衰落信道和频率选择性衰落信道。

Abstract for NSF Proposal #0915846Abstract: Channel capacity and mutual information have been studied extensively for various types of wire-line and wireless multi-user communication channels. Among the vast information theoretic literature, most of the results are based on the assumption that the channel inputs are Gaussian distributed. However, Gaussian inputs can never be realized in practical systems. The inputs are usually taken from finite alphabets, which can significantly depart from Gaussian distribution. A large nonlinear gap exists between the theoretical capacity and practical achievable rate. This nonlinear gap indicates that Gaussian-input assumption may not provide a realistic design guideline to practical systems. Maximizing mutual information over channels with finite alphabet inputs will benefit not only bandwidth efficiency but also bit error rate performance. However, much less work has been done for this important topic. This is mainly due to lack of closed-form solution and high computational complexity.The project investigates the direct maximization of mutual information and throughput over multi-user channels with finite alphabet inputs. The computational complexity problem is tackled by developing mathematically tractable and practically accurate algorithms via employing graph-based message-passing techniques. Shaping matrices are introduced to the maximization of mutual information. Parameterized approaches are developed to solve optimal shaping matrices which lead to the global maxima of the mutual information. Research efforts focus on multiple access channels, broadcast channels and interference channels, which are the fundamental channel scenarios of multi-user communications. The channel state information and/or channel covariance information are made available to the transmitter and receiver for the maximization of mutual information. Both frequency-flat fading and frequency-selective fading channels are explored.