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On the Correlation Space of the Biproduct Coefficient Matrix Structure

机译：双积系数矩阵结构的相关空间

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摘要

The biproduct correlation coefficient matrix structure has gained acceptance and application in wireless communications. Yet, the set of correlation matrices that has this structure has not been fully identified. It is known that the positive equicorrelated matrix satisfies the biproduct condition, but little else is known. The set of admissible correlation matrices having the special biproduct structure is investigated. Constraints on the signs of the correlation coefficients that define the admissible set are revealed. Additional constraints on the magnitudes of the correlation coefficients for admissibilty are also identified. The set of matrices satisfying the required structure is much more restricted than previously thought. The constraints are shown to become increasingly restrictive as the dimension of the correlation matrix increases. The constraints also become more restrictive as the values of the correlation coefficients increase to approach 1. Previously, only the equicorrelated matrix has been identified as having the biproduct structure. Two additional correlation matrix structures satisfying the biproduct structure are identified. Tests that exclude a correlation matrix from having the biproduct structure are derived.
机译：双积相关系数矩阵结构已经在无线通信中得到认可和应用。但是，尚未完全确定具有这种结构的一组相关矩阵。已知正等相关矩阵满足双积条件，但鲜为人知。研究了具有特殊双​​积结构的可允许相关矩阵集。揭示了定义可允许集合的相关系数符号的约束。还确定了关于可接纳性的相关系数的大小的其他约束。满足所需结构的矩阵集比以前认为的要受限制得多。随着相关矩阵的维数增加，约束变得越来越严格。随着相关系数的值增加到接近1，约束也变得更加严格。以前，只有等相关矩阵被确定为具有双积结构。确定满足双乘结构的两个附加相关矩阵结构。推导排除了具有双乘结构的相关矩阵的检验。

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