Following is based on Scaling up MIMO : Opportunities and Challenges with Very Large Arrays, this is based on TDD system.

It is assumed that a BTS has large number of Antenna and they are communicating with multiple UEs and each UE has only one antenna.  We assume that the number of BTS antenna is very large comparing the number of UEs. Also we are assuming this is TDD system.

The channel matrix can be represented as follows.  In TDD in which it is assumed that channel reciprocality holds true. If you have channel matrix for uplink, you can get the downlink channel model just by transposing it and vice versa.

Reverse Link (Uplink)

The communication model for reverse path (from UE to BTS) is represented as shown below.

BTS can process the received data as following equation.

Capacity for this channel can be described as follows.

Forward Link (Downlink)

Communication model for Forward Link (from BTS to UE) can be described as follows.

The reciever (UE) can process the received data according to following equation.

The capacity for this link can be described as follows.

Reference

[1] Scaling up MIMO : Opportunities and Challenges with Very Large Arrays

Fredrik Rusek, Dept. of Electrical and Information Technology, Lund University, Lund, Sweden

Daniel Persson, Dept. of Electrical Engineering (ISY), Linkoping University, Sweden

Buon Kiong Lau, Dept. of Electrical and Information Technology, Lund University, Lund, Sweden

Erik G. Larsson, Dept. of Electrical Engineering (ISY), Linkoping University, Sweden

Thomas L. Marzetta, Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ

Ove Edfors, Dept. of Electrical and Information Technology, Lund University, Lund, Sweden

Fredrik Tufvesson, Dept. of Electrical and Information Technology, Lund University, Lund, Sweden