Assume I have a system with one mobile station and multiple Transceivers (similar as in a "multi-static" RADAR system), in this example 4 transceivers:

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The bit error rate from RTX $i$ to the mobile startion to RTX $j$ depends on the SNR which depends on the channel. Assume we model any of these quantities with a simple number $a_{ij}$. Then we can write a matrix:

$$ A = \begin{bmatrix} a_{11} & a_{12} & a_{13} & a_{14}\\ a_{21} & a_{22} & a_{23} & a_{24}\\ a_{31} & a_{32} & a_{33} & a_{34}\\ a_{41} & a_{42} & a_{43} & a_{44}\\ \end{bmatrix} $$

I am trying to find any scenario in which the off diagonals would be stronger than the diagonal elements. That means, I get a better error rate when transmitting from any a RTC $i$ but receiving with a different RTX $j\neq i$ for all $i,j$.

This is equivalent to say: Does such a multi-static configuration (where all RTX can receive) have any advantage compared to a setup where each RTX would just communicate with the mobile station individually?

I am just not able to find such a scenario. Note that I have added a chunk of metal into the picture which can cause direct line-of-sight paths to disappear or reflect signals (multipath). But even then, by a simple geometric argument I can always find a $a_{ii}$ which is necessarily better than $a_{ij}$.

Can anyone come up with such a scenario (maybe using multipath arrangement or placing the mobile station arbitrarily)?


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