Why 6 PRBs are Used for Sending RACH Messages in LTE

In LTE networks, when a UE needs to access the network for the first time or re-establish a connection, it sends a Random-Access Channel (RACH) message.

This message includes a preamble, which helps the network identify the UE. But why are specifically 6 Physical Resource Blocks (PRBs) used to transmit this preamble?

Understanding Preambles and PRBs:

• Preambles: These are special signal sequences used for identification purposes. In LTE, there are four preamble formats (0, 1, 2, and 3) defined in table 36.211 of the 3GPP specifications. Most operators utilize format 0 for its simplicity.
• PRBs: These are the basic resource units for data transmission in the LTE frequency domain. Each PRB consists of 12 subcarriers.

Reasoning Behind 6 PRBs:

While the actual RACH message might be small, the preamble itself requires a specific size for reliable detection in potentially noisy channels. Here's the breakdown:

• Zadoff-Chu Sequence: The preamble format 0 leverages a mathematical sequence called the Zadoff-Chu sequence, which has a length of 839 chips (symbols).
• Frequency Domain Representation: Each PRB carries 12 subcarriers. To accommodate the entire 839-chip sequence in the frequency domain, we need 6 PRBs (6 PRBs * 12 subcarriers/PRB = 72 subcarriers). This translates to a total occupied bandwidth of approximately 1.048 MHz (or roughly 1.4 MHz considering guard bands).
• Time Domain Representation: The transmission time for the preamble is roughly 1 millisecond (ms), calculated as T = 1 / (subcarrier spacing), where the subcarrier spacing for PRACH preambles is 1.25 kHz.

Additional Insights:

The difference between the subcarrier spacing used for PRACH preambles (1.25 kHz) and uplink subframes (typically 15 kHz) is likely due to historical reasons or specific design choices for the RACH process.

This narrower subcarrier spacing in PRACH might simplify the implementation and potentially improve robustness in noisy channels.

https://techlteworld.com/rach-random-access-control-channel-in-lte-2/

Feel free to discuss in the comments below!

• Have you encountered any challenges related to RACH procedures?
• What other aspects of LTE would you like to explore?

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