In the literature it is given that capacity is proportional to Min( Nt,Nr). Nt is the number of transmitting antennas, Nr is the number of users. I have seen that if the Nt >Nr, the capacity or throughput increases. But according to relation Min(Nt,Nr) capacity should be proportional to Nr if Nt>Nr. Please explain..
Hi, Jagstar,
It is true under the assumption that the pilot contamation is eliminated completely. And with perfect CSI assumtion. Thus the SINR can be achieved by arbitrary great values just by increasing the number of antennas. you can refer to the T. L. Marzetta's work titled by "Noncooperative cellular wireless with unlimited numbers of base station antennas"
In single-user MIMO and single-cell multi-user MIMO, one can say that the capacity is roughly proportional to Min( Nt,Nr). This occurs at high SNR when having perfect CSI.
If you fix Nr and increase Nt (so Nt>Nr) then the capacity will still be roughly proportional to Min(Nt,Nr)=Nr but the capacity will still improve with Nt, but only logarithmically and not linearly.
Thanks Emil Sir for your answer.. But in Massive MIMO we have seen that increasing the number of BS antennas, sum rate as well as EE will improve.I would like to ask in that in such case, how sumrate increases with increase in no. of BS antennas.
Thanks...
It is basically the same thing in massive MIMO, where there are always more antennas than users. Adding more users give a linear increase on the sum rate, while adding more antennas improves the user rates logarithmically.
Thanks Again Emil Sir..Is there is mathematical relationship or expression for these linear or log increase?
Yes, there are many different formulas that show this behaviors for different scenarios and processing schemes. One example is (1) in my paper "Massive MIMO: 10 Myths and One Grand Question". THe number of antennas is inside the log and the number of users is primarily in front of the logarithm (it also appears at other places in the expression).