The Shannon capacity formula is different for different setups. I'm unsure what your setup is, but I don't think the expression that you are presenting is correct.

You can find capacity expressions for both point-to-point MIMO and multi-user MIMO in "Fundamentals of Wireless Communication" https://web.stanford.edu/~dntse/wireless_book.html

The MIMO capacity is seldomly linearly increasing upon increasing the number of antennas. The achievable capacity depends on how to use the multiple antennas, as Emil Björnson said the "setup". For example, the capacity of exploiting diversity gain scheme is totally different with exploiting multiplexing gain scheme.

Thanks dear prof.dr.Emil and prof.dr.jiakang for your cooperation and valuable comments

Dear Mothana,

Adding to the above colleagues, it seems that you speak about a single user MIMO system for space multiplexing. If this is the case then you can calculate the maximum channel capacity C bits per second of a specific user.

C= min( Nt, Nr) Wch log2 (1 + S/ min( Nt, Nr) (I+N)),

where the Bandwidth Wch is that of the single user, Nt is the number of transmit antennas, I interference power, N is the noise power and S is the total signal power radiated from all antennas and reached to the receiver antennas.

In case of a Nt=Nr=Na the above relation can be reduced to the expression:

C= Na Wch log2(1+ S/( Na (I+N)),

Best wishes

Thanks dear dr Abdelhalim abdelnaby Zekry for your cooperation and always valuable comments