# Shannon Bound

## Shannon Bound

### Maximum Physical Data Speed

Shannon Bound is an high threshold derived by the Shannon’s Law. Shannon’s Law is a statement in information theory that expresses the maximum possible data speed that can be obtained in a data channel. It has been formulated by Claude Shannon, a mathematician who helped build the foundations for the modern computer.

Shannon’s Law says that the highest attainable error-free data speed, expressed in bits per second (bps), is a function of the bandwidth and the signal-to-noise ratio.

Two major limitations in communications channels can be multi-path interference and the data throughput limitations, as a result of Shannon’s Law.

## MIMO

MIMO provides a way to use the multiple signal paths, that exist between a transmitter and receiver, to significantly improve the data throughput available on a given channel with its defined bandwidth.

By using multiple antennas, at the transmitter and receiver along with some complex digital signal processing, MIMO technology enables the system to set up multiple data streams on the same channel, thereby increasing the data capacity of a channel over the Shannon Bound. This means that data capacity is transmitted and received from multiple points and Shannon’s law is being repeated without cross the physical limits.

## Calculation Example

As LTE uses different channel bandwidths both for FDD and TDD (1.4, 3, 5, 10, 15 or 20 MHz), let’s take an example for LTE using FDD, where channel bandwidth can be 5 MHz, 10 MHz and 20 MHz.

In LTE release 8 there is no carrier aggregation, so let’s just consider this simple cases. Here we are calculating maximum data rate at the physical layer.

So, for example, in case of 5 MHz channel bandwidth, 300 subcarriers are used. For a perfect idle condition 64 QAM can be used.
That means that each symbol is now allowed to carry 6 bits.
So the total bits carried by 300 subcarriers for the duration of a symbol is 300 X 6 = 1800 bits.

Again, 1 symbol is 71.4 microseconds for LTE. So the data rate is 1800 / 71.4 = 25.2 Mbps

The data rate always depends on the channel bandwidth and the formula, to calculate the maximum data rate at physical layer is:

For 10 MHz using the same formula the maximum data rate in downlink is 50.4 Mbps and for 20 MHz it is 100.8 Mbps.

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