最小错误率信道均衡与k-最近邻及神经网实现

On Minimum-Error-Probability Channel Equalization and Its Realizations Using k-Nearest Neighbor Rule and Neural Nets

本文论述一种在通信意义上最佳的信道均衡方法——最小错误概率(MEP)均衡法及其 k-最近邻法则和后向扩散(BP)神经网实现问题.主要结果包括:1)从理论上说明了在码间干扰最大值小于传输符号幅值时,信道均衡问题总是线性可分离的.2)引入了 MEP 均衡问题的基本概念和关系式.用具体数值结果说明了 MEP 均衡器优于线性均衡器的程度.3)提出了用 k-最近邻法则实现 MEP 均衡的方法,给出了渐近收敛定理和误差界.4)证明了基于最小均方误差的后向扩散神经网络能使错误概率(误码率)为最小,由此诱导出了又一种 MEP 均衡实现方法.

This paper addresses the minimum-error-probability(MEP) channel equlization problem and its realizations using the k-nearest neighbor rule and backpropagation(BP) neural nets.The main contributions of this paper include: (1)It shows that in the case of the intersymbol interference less than the magnitude of the desired symbol,the channel equalization problem is always linearly separable.(2) The basic concepts and relations of the MEP equaliza- tion are introduced.Based on these results,some numerical results are provided to indicate the performance advantage over the linear equalizer.(3) Subsequ- ently presented are the MEP adaptive equalizer implemented by the k-nearest neighbor rule and the theorems concerning the asymptotic convergence and error bounds.(4) Finally it shows that the backpropagation neural nets with appropriate layers and nodes,which take the minimum-mean-squared-error as its optimization goal,also minimize the error probability,thus leading to an- other realization of the MEP equalization.