满足列相关约束的互补集矩阵
Complementary Set Matrices Satisfying a Column Correlation Constraint
摘要：
为了降低发射信号的峰均功率比（PAPR），我们考虑了一种列序列满足相关约束的互补集矩阵的设计。该设计算法从一对伴随序列开始递归地建立$2^{t+1}$相互正交（MO）互补集矩阵的集合。我们列序列的相关性的同伴对，并说明如何选择一个合适的同伴对，以确保一个给定的列相关性约束得到满足。对于$t=0$，伴随对性质直接决定矩阵列相关性质。对于$t\geq 1$，降低同伴对的相关性优点可以导致改进的列相关性属性。然而，一旦同伴对相关性价值小于由$t$确定的阈值，则列序列的最大离相非周期自相关的进一步减小是不可能的。我们还揭示了设计的同伴对，导致互补集矩阵Golay列序列。对于中长序列，穷举搜索满足列相关约束的配对是不可行的。相反，我们搜索两个较短的长度序列，通过最小化的成本函数在其自相关和互相关的优点。此外，一个改进的成本函数，这有助于减少最大的异相列相关的基础上的同伴对的属性。利用著名的Welch界，给出了满足列相关约束的伴随对存在的充分条件。
英文摘要：
Motivated by the problem of reducing the peak to average power ratio (PAPR) of transmitted signals, we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint. The design algorithm recursively builds a collection of $2^{t+1}$ mutually orthogonal (MO) complementary set matrices starting from a companion pair of sequences. We relate correlation properties of column sequences to that of the companion pair and illustrate how to select an appropriate companion pair to ensure that a given column correlation constraint is satisfied. For $t=0$, companion pair properties directly determine matrix column correlation properties. For $t\geq 1$, reducing correlation merits of the companion pair may lead to improved column correlation properties. However, further decrease of the maximum out-off-phase aperiodic autocorrelation of column sequences is not possible once the companion pair correlation merit is less than a threshold determined by $t$. We also reveal a design of the companion pair which leads to complementary set matrices with Golay column sequences. Exhaustive search for companion pairs satisfying a column correlation constraint is infeasible for medium and long sequences. We instead search for two shorter length sequences by minimizing a cost function in terms of their autocorrelation and crosscorrelation merits. Furthermore, an improved cost function which helps in reducing the maximum out-off-phase column correlation is derived based on the properties of the companion pair. By exploiting the well-known Welch bound, sufficient conditions for the existence of companion pairs which satisfy a set of column correlation constraints are also given.
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