線性檢波系統如下:

從接收信號y估計發送信號x, x=Gy, y已知, 就是估計矩陣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原理與MMSE不同, ZF是最小化誤差, 用最小二乘法, 也因此, 沒有考慮進噪音的影響

如下:
公式(5)(6)是ZF對線性矩陣G和發送信號的估計, (7)(8)是MMSE的估計, 明顯MMSE中有SNR, 即噪音被考慮在內, 故MMSE一般更精確

總結

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