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首页> 外文期刊>Information Theory, IEEE Transactions on >Asymptotically Equivalent Sequences of Matrices and Multivariate ARMA Processes
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Asymptotically Equivalent Sequences of Matrices and Multivariate ARMA Processes

机译：矩阵和多元ARMA过程的渐近等价序列

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摘要

The present paper considers a special class of vector random processes that we call multivariate asymptotically wide sense stationary (WSS) processes. A multivariate random process is said to be asymptotically WSS if it has constant mean and the sequence of its autocorrelation matrices is asymptotically equivalent (a.e.) to the sequence of autocorrelation matrices of some multivariate WSS process. It is shown that this class of processes contains meaningful processes other than multivariate WSS processes. In particular, we give sufficient conditions for multivariate moving average (MA) processes, multivariate autoregressive (AR) processes and multivariate autoregressive moving average (ARMA) processes to be asymptotically WSS. Furthermore, in order to solve multiple-input–multiple-output (MIMO) problems in communications and signal processing involving this kind of processes, we extend the Gray definition of a.e. sequences of matrices and his main results on these sequences to non-square matrices. As an example, the derived results on a.e. sequences of non-square matrices are applied to compute the differential entropy rate and the minimum mean square error (MMSE) for a linear predictor of a multivariate asymptotically WSS process.
机译：本文考虑了一类特殊的向量随机过程，我们称其为多元渐近广义感知平稳（WSS）过程。如果多元随机过程具有恒定的均值并且其自相关矩阵的序列与某些多元WSS过程的自相关矩阵的序列渐近等效（a.e.），则称其为渐近WSS。结果表明，此类流程包含除多元WSS流程以外的有意义的流程。特别是，我们为多元移动平均（MA）过程，多元自回归（AR）过程和多元自回归移动平均（ARMA）过程渐近WSS提供了充分的条件。此外，为了解决涉及此类过程的通信和信号处理中的多输入多输出（MIMO）问题，我们扩展了a.e.的Gray定义。矩阵的序列及其在这些序列上的主要结果为非平方矩阵。作为示例，得出的结果是应用非平方矩阵序列来计算多元渐近WSS过程的线性预测变量的差分熵率和最小均方误差（MMSE）。

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