Distribution results for a multi-rank version of the Reed-Yu detector
Distribution results for a multi-rank version of the Reed-Yu detector
复制标题
Reed-Yu 检测器的多秩版本的分布结果
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
R. W. Butler
中科院分区：
文献类型：
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作者：
Pooria Pakrooh;L. Scharf;R. W. Butler
在本文中，我们重新审视了一个检测器，它首先由Reed和Yu [1]导出，由布利斯和帕克[2]推广，最近由Hiltunen，Loubaton和Chevalier [3]，[4]研究。问题是检测在未知复增益和未知加性噪声协方差的未知MIMO信道上传输的已知信号。在文献[1]中，首先推导了SIMO信道下恒虚警检测器的概率分布。我们推广这种分布的情况下的MIMO信道，并表明CFAR检测器统计分布的产品的独立标量β随机变量下的空。我们的研究结果，β分布的随机矩阵的理论的基础上，持有M个符号从p个发射机发送，并在L个接收机接收。文[3]、[4]的渐近结果是建立在大随机矩阵理论的基础上的，其中假定L和M是无界的。
In this paper we revisit a detector first derived by Reed and Yu [1], generalized by Bliss and Parker [2], and recently studied by Hiltunen, Loubaton, and Chevalier [3], [4]. The problem is to detect a known signal transmitted over an unknown MIMO channel of unknown complex gains and unknown additive noise covariance. The probability distribution of a CFAR detector for this problem was first derived for the SIMO channel in [1]. We generalize this distribution for the case of a MIMO channel, and show that the CFAR detector statistic is distributed as the product of independent scalar beta random variables under the null. Our results, based on the theory of beta distributed random matrices, hold for M symbols transmitted from p transmitters and received at L receivers. The asymptotic results of [3], [4] are based on large random matrix theory, which assumes L and M to be unbounded.