基于稀疏Kerdock矩阵的压缩邻居发现
Compressed Neighbour Discovery using Sparse Kerdock Matrices
摘要：
我们研究了无线网络中的网络范围内的邻居发现问题，其中网络中的每个节点都必须发现其邻居的网络接口地址（NIA）。我们在Guo和Zhang（2010）提出的快速开-关划分双工框架内工作，其中所有节点被分配不同的开-关签名，这允许它们在其关时隙期间监听相邻节点的传输，导致每个节点处的压缩感知问题，其中折叠码本由给定节点的传输签名确定。我们提出稀疏Kerdock矩阵作为邻居发现问题的码本。这些矩阵与基于Reed Muller码的某些Delsarte-Goethals帧共享相同的行空间，同时非常稀疏。我们目前的数值实验，使用两种不同的压缩感知恢复算法，一步重采样保持（OST）和归一化迭代硬重采样保持（NIHT）。对于这两种算法，与Zhang和Guo（2011）提出的基于具有随机擦除的Reed Muller码的码本相比，使用稀疏Kerdock矩阵成功识别出更高比例的邻居。我们认为，这种改进是由于稀疏Kerdock矩阵在根据给定节点的传输签名折叠时具有更好的干扰消除特性。我们通过显式计算表明，从稀疏Kerdock矩阵产生的折叠码本的相干性仍然接近最佳。
英文摘要：
We study the network-wide neighbour discovery problem in wireless networks in which each node in a network must discovery the network interface addresses (NIAs) of its neighbours. We work within the rapid on-off division duplex framework proposed by Guo and Zhang (2010) in which all nodes are assigned different on-off signatures which allow them listen to the transmissions of neighbouring nodes during their off slots, leading to a compressed sensing problem at each node with a collapsed codebook determined by a given node's transmission signature. We propose sparse Kerdock matrices as codebooks for the neighbour discovery problem. These matrices share the same row space as certain Delsarte-Goethals frames based upon Reed Muller codes, whilst at the same time being extremely sparse. We present numerical experiments using two different compressed sensing recovery algorithms, One Step Thresholding (OST) and Normalised Iterative Hard Thresholding (NIHT). For both algorithms, a higher proportion of neighbours are successfully identified using sparse Kerdock matrices compared to codebooks based on Reed Muller codes with random erasures as proposed by Zhang and Guo (2011). We argue that the improvement is due to the better interference cancellation properties of sparse Kerdock matrices when collapsed according to a given node's transmission signature. We show by explicit calculation that the coherence of the collapsed codebooks resulting from sparse Kerdock matrices remains near-optimal.
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