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System Time

CDMA requires accurate time synchronization among all base stations and mobile stations. The accuracy must be within a few microseconds among base stations because the pilot code phase is used to distinguish them. When a mobile station is communicating with a base station they must be synchronized to within a fraction of a chip (814 ns). And the "clocks" (the PN generators) that must be synchronized have a period of 37 centuries. How does all this happen?

The "Clock"

All stations keep a conventional time-of-day, but this is not directly relevant to code synchronization. The code "clock" is really the combined state of the Short Code and Long Code generators. The short code has period 215 chips and the long code has period 242 - 1 chips. As these are relatively prime numbers, the overall period is the product, or about 257 chips. This is the 37 century clock.

How does a clock with this long a period get set? It isn't as hard as it might seem. The 257 period 257 clock is really two clocks with incommensurate periods. If they are separately set correctly, system time is correct. The Short Code must be set to system time, measured in chips, modulo 215; the long code must be set to system time modulo 242 -1. The former is 80/3 = 26.666... ms, and the latter is about 41 days.

Setting the clock consists of two steps. First, calculate the remainders after dividing the time by the two periods, 215 and 242 -1. These are the number of states that each generator must be offset from its zero reference state. Second, determine the generator state that corresponds to that number of states. It might seem that this is a hard thing to do. It is not. It is not quite obvious, but there are straightforward, easy-to-program algorithms that will offset an LFSR to any state, given the binary representation of its offset (see our LFSR page). The fact that the short code is a modified LFSR sequence only slightly complicates the process.

What is the system time scale?

System time is referenced to Global Positioning System (GPS) time. GPS time is synchronous with Universal Coordinated Time (UTC) except for leap second corrections added to UTC. GPS does not incorporate the leap second corrections. The origin of GPS time is January 6, 1980 00:00:00 UTC.

What is the reference state of the system clock relative to system time?

At system time zero the state of the Long Code generator is such that the current output is one, preceded by 41 zeros.

At system time zero the state of the each of the two Short Code generators is such that the current output is one, preceded by 15 zeros. This is the state immediately following the stuff bit.

OK, so I know how to set a clock.

How do I find out what time it is?If you are a base station: GPS.

System time typically is maintained in the base stations by means of a GPS receiver. GPS-derived time is normally accurate to a fraction of one CDMA chip (833 ns).

Even in the absence of a GPS reference, readily available atomic frequency standards permit stations to "flywheel" for many hours, perhaps days, and remain within spec. This gives plenty of margin for repair or replacement of failed or damaged equipment.

Direct use of GPS is not absolutely required, but timing must be synchronized with GPS.

If you are a mobile, listen to a base station.

Mobile stations derive system time from the pilot signals that they receiving. The system is specially designed to not require accurate timekeeping by the mobile stations while not active. Because the mobile stations do not have any simple means of determining the propagation delay, their derived system time will lag by that delay.

Mobile stations synchronize to system time by a multi-step process.

First, the mobile station synchronizes its short code generator with a pilot signal from a candidate serving base station. That code will be offset from system time according to the pilot offset used by that base station to distinguish itself from other base stations.

Second, the mobile demodulates and decodes the sync message. Once the mobile station has acquired the pilot, the sync channel interleaving synchronization is known because the interleaver block size is equal to the short code period, or 80/3 ms. Sync channel messages always start at an 80 ms "superframe" boundary, and are marked by a start-of-message indication. One superframe is three short code periods. Once the message has been successfully decoded the alignment of the superframes is known.

Third, using the pilot offset of that particular base station that is contained in the sync message, the mobile station adjusts its transmitter short code phase back to system time.

Fourth, the sync message also contains both the time of day and the long code state as of the next 80 ms boundary, adjusted for the pilot offset. The 80 ms boundaries are already known because the interleaver must have been synchronized in order to have correctly decoded the message. The long code state is loaded into the long code generator at the appropriate time.

When the mobile station has successfully performed all these steps, its "clock" set to system time, with a lag due to the base-to-mobile propagation delay. Transmissions from the mobile to the base will be aligned within two propagation delays when they arrive at the base. This accurate mobile transmit timing reduces the synchronization search window needed in the base.

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Copyright © 1996-1999 Arthur H. M. Ross, Ph.D., Limited