基于增量矩阵展开的大型随机矩阵和与积的特征值分布
Eigenvalue Distributions of Sums and Products of Large Random Matrices via Incremental Matrix Expansions
摘要：
本文采用增量矩阵展开法导出渐近特征值分布（a.e.d.）。的和与积的大随机矩阵。我们表明，结果可以直接推导出两个常见的假设的后果，并匹配从使用R-和S-变换在自由概率论中得到的结果。我们也给出了直接推导的a.e.d.。某些非自由随机矩阵之和的这是用来确定一个多用户CDMA系统的最小均方误差线性接收机的渐近信号干扰比。
英文摘要：
This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.'s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common assumptions, and matches the results obtained from using R- and S-transforms in free probability theory. We also give a direct derivation of the a.e.d. of the sum of certain random matrices which are not free. This is used to determine the asymptotic signal-to-interference-ratio of a multiuser CDMA system with a minimum mean-square error linear receiver.
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