线性MMSE检波和ZF检波

线性检波系统如下:

从接收信号y估计发送信号x, x=Gy, y已知, 就是估计矩阵G.
Linear MMSE Detector
MMSE原理: 最小化MSE.

The main idea of the MMSE detector is to minimize the mean-square error (MSE) between the transmitted x and the estimated signal HHy as given by

where E is the expectation operator. MMSE detector takes the noise effect into consideration as

where I is the identity matrix. The output of the MMSE detector can be obtained by


ZF Detector
ZF原理与MMSE不同, ZF是最小化误差, 用最小二乘法, 也因此, 没有考虑进噪音的影响

如下:
公式(5)(6)是ZF对线性矩阵G和发送信号的估计, (7)(8)是MMSE的估计, 明显MMSE中有SNR, 即噪音被考虑在内, 故MMSE一般更精确