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大量冗余向量集中选择一个小子集来匹配给定的数据。基选择算法通常被视为使用它们的特定应用程序的一部分。这些应用包括语音编码的时间/频率表示、频谱估计、视频编码和信道估计。利用穷举搜索找到最优解是不可行的，因此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，我们重点研究了顺序基选择（SBS），特别是匹配追踪算法，它比传统的最小二乘方法具有更低的计算复杂度，并且在具有稀疏性的应用中工作得很好。我们提出的研究目标是提高这些SBS算法的性能，并将其应用范围扩展到更复杂的无线应用中。我们正在优化相关的字典结构。这对应于信道估计的训练序列设计、到达角检测的阵列结构设计和多用户检测的代码结构设计。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。扩展利用SBS算法的无线应用程序将用于多输入多输出（MIMO）系统和无线电定位系统。MIMO系统因其在容量和质量上的显著提升而备受关注。同样，对终端进行精确的无线电定位对于现代无线系统的有效网络运行至关重要。由于SBS算法的低复杂度，将过完备信号展开应用于此类系统可以获得许多重要的结果。除了MIMO信道估计和地理定位，我们将研究的其他潜在应用是高维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.