Application of basis selection algorithms to wireless communications systems

有效的信号表示需要有效的信号分解算法。信号分解的基选择问题包括从一个大的冗余向量集中选择一个小的向量子集来匹配给定的数据。基选择算法通常被视为它们所用于的特定应用的一部分。这些应用包括语音编码、频谱估计、视频编码和信道估计的时间/频率表示。使用穷举搜索找到最佳解是不可行的，已经提出了需要较低计算复杂度的次优方法。在这些次优技术中，我们集中在顺序基选择（SBS），特别是匹配追踪算法，具有较低的计算复杂度比传统的最小二乘法和工作，特别是在稀疏性的应用程序。 我们提出的研究的目的是提高这些SBS算法的性能，并将其应用范围扩展到更复杂的无线应用。我们正在优化相关的字典结构。这对应于用于信道估计的训练序列设计、用于到达角检测的阵列结构设计和用于多用户检测的码结构设计。通过对字典的优化，消除了SBS算法中对组合搜索的要求，进一步降低了算法的复杂度。扩展的无线应用，利用SBS算法将完成多输入多输出（MIMO）系统，和无线电定位系统。MIMO系统由于其在容量和质量方面提供实质性增益的能力而受到关注。类似地，精确地无线电定位终端对于现代无线系统的有效网络操作是必要的。由于SBS算法的低复杂度，将过完备信号展开应用于这类系统可以得到许多重要的结果。除了MIMO信道和地理位置的估计，其他潜在的应用，我们将调查更高的维度到达角估计，和信道编码系统中的解码器设计。

Efficient signal representations require efficient signal decomposition algorithms. The problem of basis selection for signal decomposition consists of determining a small subset of vectors chosen from a large redundant set of vectors to match a given data. The basis selection algorithms are generally treated as a part of the specific application for which they are used. These applications include time/frequency representations of speech coding, spectral estimation, video coding and channel estimation. Finding an optimal solution using an exhaustive search is infeasible, suboptimal methods that require lower computational complexity have been proposed. Among these suboptimum techniques we have focused on sequential basis selection (SBS) in particular matching pursuit algorithms which have lower levels of computational complexity than the conventional least squares methods and work well especially in applications with sparsity properties.   The objective of our proposed research is to improve the performance of these SBS algorithms and extent their applications to more complex wireless applications. We are working on optimizing the associated dictionary structures. This corresponds to a training sequence design for channel estimation, array structure design for angle of arrival detection and code structure design for multi-user detection. By optimizing the dictionary, the requirement of a combinatorial search in the SBS algorithm is eliminated and the  complexity can be further reduced. Extending the wireless applications which utilize SBS algorithms will be done for multiple input multiple output (MIMO) systems, and for radiolocalization systems. MIMO systems are of interest due to their ability to provide substantial gains in capacity and quality. Similarly, accurately radiolocating a terminal is essential for efficient network operation of modern wireless systems. Many important results can be obtained by applying the overcomplete signal expansions to such systems due to the low complexities of the SBS algorithms. In addition to estimation of MIMO channels and geolocation, other potential applications we will investigate are higher dimensional angle of arrival estimation, and decoder design in channel coding systems.