MMSE analysis of certain large isometric random precoded systems
MMSE analysis of certain large isometric random precoded systems
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DOI：
10.1109/tit.2003.810641
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发表时间：
2003-05-01
影响因子：
2.5
通讯作者：
de Courville, M
中科院分区：
文献类型：
--
作者：
Debbah, M;Hachem, W;de Courville, M
线性预编码包括将通过对要发送的符号序列进行串并转换而获得的K维向量乘以N×K矩阵。本文借用自由概率理论中的新工具，分析了某些大随机等距预编码系统在衰落信道下的最小均方误差(MMSE)接收机的性能。等距条件表示具有正交列的预编码矩阵的情况。结果表明，当N~+无穷大且K/N~+α小于或等于1时，均衡器输出端的信干噪比(SINR)几乎必然收敛到一个确定值，这取决于信道系数的概率分布。这些渐近结果被用来分析正交扩频的影响以及在接收端保持简单的MMSE均衡方案的同时，最优地平衡线性预编码和经典卷积编码之间引入的冗余度。
Linear precoding consists in multiplying by an N x K matrix a K-dimensional vector obtained by serial-to-parallel conversion of a,symbol sequence to be transmitted. In this paper, new tools, borrowed from the so-called free probability theory, are introduced for the purpose of analyzing the performance of minimum mean-square error (MMSE) receivers for certain large random isometric precoded systems on fading channels. The isometric condition represents the case of precoding matrices with orthonormal columns. It is shown in this contribution that the signal-to-interference-plus-noise ratio (SINR) at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when N --> +infinity and K/N --> alpha less than or equal to 1. These asymptotic results are used to analyze the impact of orthogonal spreading as well as to optimally balance the redundancy introduced between linear precoding versus classical convolutional coding, while preserving a simple MMSE equalization scheme at the receiver.