Timing Advance With Calculation

A Timing Advance (TA) is used to compensate for the propagation delay as the signal travels between the Mobile Station (MS) and Base Transceiver Station (BTS). The Base Station System (BSS) assigns the TA to the MS based on how far away it perceives the MS to be. Determination of the TA is a normally a function of the Base Station Controller (BSC), bit this function can be handled anywhere in the BSS, depending on the manufacturer.

Time Division Multiple Access (TDMA) requires precise timing of both the MS and BTS systems. When a MS wants to gain access to the network, it sends an access burst on the RACH. The further away the MS is from the BTS, the longer it will take the access burst to arrive at the BTS, due to propagation delay. Eventually there comes a certain point where the access burst would arrive so late that it would occur outside its designated timeslot and would interfere with the next time slot.

Access Burst

As you recall from the TDMA Tutorial, an access burst has 68.25 guard bits at the end of it.

This guard time is to compensate for propagation delay due to the unknown distance of the MS from the BTS. It allows an access burst to arrive up to 68.25 bits later than it is supposed to without interfering with the next time slot.

68.25 bits doesnt mean much to us in the sense of time, so we must convert 68.25 bits into a frame of time. To do this, it is necessary to calculate the duration of a single bit, the duration is the amount of time it would take to transmit a single bit.

Duration of a Single Bit

As you recall, GSM uses Gaussian Minimum Shift Keying (GMSK) as its modulation method, which has a data throughput of 270.833 kilobits/second (kb/s).

Calculate duration of a bit.

So now we know that it takes 3.69µs to transmit a single bit.

Propagation Delay

Now, if an access burst has a guard period of 68.25 bits this results in a maximum delay time of approximately 252µs (3.69µs × 68.25 bits). This means that a signal from the MS could arrive up to 252µs after it is expected and it would not interfere with the next time slot.

The next step is to calculate how far away a mobile station would have to be for a radio wave to take 252µs to arrive at the BTS, this would be the theoretical maximum distance that a MS could transmit and still arrive within the correct time slot.

Using the speed of light, we can calculate the distance that a radio wave would travel in a given time frame. The speed of light (c) is 300,000 km/s.

So, we can determine that a MS could theoretically be up to 75.6km away from a BTS when it transmits its access burst and still not interfere with the next time slot.

However, we must take into account that the MS synchronizes with the signal it receives from the BTS. We must account for the time it takes for the synchronization signal to travel from the BTS to the MS. When the MS receives the synchronization signal from the BTS, it has no way of determining how far away it is from the BTS. So, when the MS receives the syncronization signal on the SCH, it synchronizes its time with the timing of the system. However, by the time the signal arrives at the MS, the timing of the BTS has already progressed some. Therefore, the timing of the MS will now be behind the timing of the BTS for an amount of time equal to the travel time from the BTS to the MS.

For example, if a MS were exactly 75.6km away from the BTS, then it would take 252µs for the signal to travel from the BTS to the MS.

The MS would then synchronize with this timing and send its access burst on the RACH. It would take 252µs for this signal to return to the BTS. The total round trip time would be 504µs. So, by the time the signal from the MS arrives at the BTS, it will be 504µs behind the timing of the BTS. 504µs equals about 136.5 bits.

The 68.25 bits of guard time would absorb some of the delay of 136.5 bits, but the access burst would still cut into the next time slot a whopping 68.25bits.

Maximum Size of a Cell

In order to compensate for the two-way trip of the radio link, we must divide the maximum delay distance in half. So, dividing 75.6km in half, we get approximately 37.8 km. If a MS is further out than 37.8km and transmits an access burst it will most likely interfere with the following time slot. Any distance less than 37.8km and the access burst should arrive within the guard time allowed for an access burst and it will not interfere with the next time slot.
In GSM, the maximum distance of a cell is standardized at 35km. This is due mainly to the number of timing advances allowed in GSM, which is explained below.

How a BSS Determines a Timing Advance

For each 3.69µs of propagation delay, the TA will be incremented by 1. If the delay is less than 3.69µs, no adjustment is used and this is known as TA0. For every TA, the MS will start its transmission 3.69µs (or one bit) early. Each TA really corresponds to a range of propagation delay. Each TA is essentially equal to a 1-bit delay detected in the synchronization sequence.

In order to determine the propagation delay between the MS and the BSS, the BSS uses the synchronization sequence within an access burst. The BSS examines the synchronization sequence and sees how long it arrived after the time that it expected it to arrive. As we learned from above, the duration of a single bit is approximately 3.69µs. So, if the BSS sees that the synchronization is late by a single bit, then it knows that the propagation delay is 3.69µs. This is how the BSS knows which TA to send to the MS.

The Distance of a Timing Advance

When calculating the distances involved for each TA, we must remember that the total propagation delay accounts for a two-way trip of the radio wave. The first leg is the synchronization signal traveling from the BTS to the MS, and the second leg is the access burst traveling from the MS to the BTS. If we want to know the true distance of the MS from the BTS, we must divide the total propagation delay in half.

For example, if the BSS determines the total propagation delay to be 3.69µs, we can determine the distance of the MS from the BTS.

We determined earlier that for each propagation delay of 3.69µs the TA is inceremented by one. We just learned that a propagation delay of 3.69µs equals a one-way distance of 553.5 meters. So, we see that each TA is equal to a distance of 553.5 meters from the tower. Starting from the BTS (0 meters) a new TA will start every 553.5m.

The TA becomes very important when the MS switches over to using a normal burst in order to transmit data. The normal burst does not have the 68.25 bits of guard time. The normal burst only has 8.25 bits of guard time, so the MS must transmit with more precise timing. With a guard time of 8.25 bits, the normal burst can only be received up to 30.44µs late and not interfere with the next time slot. Because of the two-way trip of the radio signal, if the MS transmits more than 15.22µs after it is supposed to then it will interfere with the next time slot.