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.

- Please note that the above capacity calculations are for eight users simultaneously connected over the 100 MHz channel. The data rate achieved by a single user, in the T-Mobile experiment, was 5600/8=700 Mbps.
- Also note that much higher bandwidths are available in the millitmeter wave band and this may increase the data rates 10 fold or even higher.

References:

https://www.t-mobile.com/news/network/t-mobile-achieves-mind-blowing-5g-speeds-with-mu-mimo

https://www.waveform.com/a/b/guides/5g-and-shannons-law

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