Receive diversity, multiple-single, simple scene model as follows.
Using mathematical expressions, a matrix is represented as follows.
Each of the different receiver using the weight w, the received last can be expressed as follows.
Starts from the last mathematical expression analysis, the SNR is defined as the noise energy in signal energy, the signal energy can be estimated by the portion of the channel or the processing of the pilot signal is obtained, but noise can not be measured, it is necessary to obtain statistical average method.
For noise, assuming that the following two conditions are met. First, the noise between the different receive antennas are independent of each other. Second, the Gaussian noise. The following derivation will use two characteristics of the noise, some of the processing items can be deleted.
Finally, signal to noise ratio can be expressed as
So how do you achieve maximum signal to noise ratio it?
After the weighting coefficients are normalized, the maximum signal to noise ratio can be seen to make, depending on the weighting factor, because for H , for a channel at a given time is determined.
For vectors w and h is a maximum inner product, the vectors w and h angle is 0, i.e., along the same line.
Finally, on behalf of the maximum signal to noise ratio of the expression can be obtained.
reference:
http://www.sharetechnote.com/html/Communication_ChannelModel_Diversity_Rx.html
