面向无线传感器网络的源-信道-网络联合无线传输理论研究

In modern signal processing techniques, there are three techniques with good performance, which are compressed sensor (CS), low-density parity-check (LDPC), and network coding (NC). By using CS and NC techniques, the energy efficiency and spectral efficiency of the systems can be greatly improved, respectively. At the same time, LPDC technique has the capacity to approach theoretical capacity limits. The common characteristic of the three techniques are that the signals are transformed from a space to another by using transform matrixes. It is an open issue how to perfectly integrate the three techniques, though the relationship among CS, LDPC, and NC has been explored in literatures. This requires not only the uniform transform matrix among the three techniques, but also the uniform decoding (or signal recovery) algorithms and the measurement criterions for good performance. By using the sparsity of the sensing signals of the wireless sensor networks (WSN), the relationship between the CS and LDPC techniques will be investigated firstly. Secondly, with the consideration of high diversity gain and the using of LDPC, the network coding schemes will be presented as well as the corresponding decoding algorithms. Finally, with LDPC technique as a link, a joint source-channel-network coding scheme will be presented as well as the corresponding performance analysis for wireless sensor networks, which is referred to as CS-LDPC-NC scheme, in which the three techniques are integrated together perfectly. The scheme not only combines the merits of the three techniques, but also makes it possible to implement in engineering. The study will provide the science basis for the development of wireless sensor network and the exploration of the relationship between CS, LDPC, and NC.

压缩感知(CS)、LDPC码和网络编码(NC)技术是三个性能优良的现代信号处理技术，它们的共同特点是通过一个转换矩阵实现了从一个空间到另一个空间的几何映射。虽然有文献初步研究了CS与LDPC之间的关系和基于LDPC技术的网络编码，但是就如何将这三种技术有机地融合在一起，则是一个全新的课题，其不仅要求要有统一的转换矩阵，而且要有统一的译码算法和性能度量准则。课题通过探索无线传感器网络的稀疏特性，充分利用WSN感知信号的空、时相关特性，研究CS和LDPC技术之间的相互转换关系和基于LDPC技术的高分集增益网络编码方案，建立以LDPC技术为纽带、面向无线传感器网络的联合源-信道-网络无线传输方案，即CS-LDPC-NC方案，并对其性能进行分析。该方案不仅具有较高的能量效率、较高的频谱效率和接近香浓容限的特征，而且易于实现。为探索CS、LDPC和NC技术之间的本质联系及其在WSN中的应用奠定理论基

课题充分利用无线传感器网络（WSN）感知信号的空、时相关特性，研究了CS和LDPC技术之间的相互转换关系和基于LDPC技术的高分集增益网络编码方案，建立了以LDPC技术为纽带、面向无线传感器网络的联合源-信道-网络无线传输方案，即CS-LDPC-NC方案，并研究了其在中继协作、认知无线电无线传感器网络的实现。课题的主要工作和结论有：.1. LDPC信道编码与压缩感知之间的相互关系.项目根据无线传感器网络感知信号的稀疏性、LDPC信道编码原理和CS技术的稀疏性要求，通过阐明CS理论和LDPC信道编码理论的物理概念、数学模型和译码算法（或信号重建算法），揭示了它们之间的内在联系，进一步定义、改进和规范了它们的数学模型，给出了LDPC编码矩阵和压缩感知测量矩阵之间的关系，设计出了满足约束等容条件的LDPC生成矩阵。.2. LDPC码度量准则与压缩感知度量准则之间的相互关系.在CS理论中，测量矩阵的设计要求满足约束等容属性(restricted isometry property：RIP)；而在LDPC码中，最有效的度量准则是Tanner图的围长。对此两个属性，我们证明了它们的相互转换关系和等效性。我们证明可以用LDPC码的0-1奇偶校验矩阵作为CS的测量矩阵，并且当该矩阵所对应的LDPC码具有良好性能时，其作为测量矩阵所对应的CS系统也具有良好的性能。从而就保证了基于编码矩阵构建得到的测量矩阵的有效性（良好性能），也保证了我们可以用统一的矩阵（或适当地等效变换）进行联合压缩感知与源-信道编码设计。.3. 基于LDPC技术的网络编码方案和译码算法.项目选取M-N-1上行多接入信道模型，即M个节点源信号通过N个中继节点转发到一个信宿节点，在中继节点处采用LDPC网络编码技术。对此模型，我们采用Tanner图方法提出了LDPC结构，基于传统的LDPC码LLR-BP译码算法（对数似然比置信传递译码算法），提出了联合LDPC-NC解码算法，给出了联合迭代译码结构(JICD)，并与传统的线性网络编码译码算法做了比较分析，分析结果表明，其性能要优于基于异或运算的XOR-NC结构。.该课题所给出的方案不仅具有较高的能量效率、较高的频谱效率和接近香浓容限的特征，而且易于实现。为探索CS、LDPC和NC技术之间的本质联系及其在WSN中的应用奠定理论基。

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