# 5G Data Rates and Shannon Capacity

Recently I came across a post from T-Mobile in which they claim to have achieved a download speed of 5.6 Gbps over a 100 MHz channel resulting in a Spectral Efficiency of more than 50 bps/Hz. This was achieved in an MU-MIMO configuration with eight connected devices having an aggregate of 16 parallel streams i.e. two parallel streams per device. The channel used for this experiment was the mid-band frequency of 2.5 GHz.

Now let us revisit the Shannon Capacity theorem and see what data rate it predicts with the above parameters. Shannon Capacity theorem is given as:

C = N x BW x log2(1+SNR)

where

N=16 is the number of parallel streams enabled by multiple antennas at Tx and Rx

BW=100 MHz is the total bandwidth available to the carrier in the 2.5 GHz band

SNR=10 is the Signal to Noise Ratio (a moderately good SNR is assumed)

Plugging these numbers in, we get a capacity limit of 5.54 Gbps, approximately the same number obtained in the experiment. But it all depends upon the Signal to Noise Ratio, that has not been mentioned by T-Mobile in the reference post. With an SNR=20 dB, a very good channel condition, the capacity increases to about 10.65 Gbps but with an SNR=0 dB, a likely scenario at the cell edge, the capacity drops to 1.6 Gbps. The details for the capacity at different SNRs are given in the table and figure below.