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Monday, September 15, 2008

C/A code: Demodulation and decoding

Since all of the satellite signals are modulated onto the same L1 carrier frequency, there is a need to separate the signals after demodulation. This is done by assigning each satellite a unique pseudorandom sequence known as a Gold code, and the signals are decoded, after demodulation, using modulo 2 addition of the Gold codes corresponding to satellites n1 through nk, where k is the number of channels in the GPS receiver and n1 through nk are the pseudorandom numbers associated with the satellites. The result of these modulo 2 additions are the 50 bps navigation messages from satellites n1 through nk. The Gold codes used in GPS are a sequence of 1023 bits with a period of one millisecond. These Gold codes are highly mutually orthogonal, so that it is unlikely that one satellite signal will be misinterpreted as another. As well, the Gold codes have good auto-correlation properties.

There are 1025 different Gold codes of length 1023 bits, but only 32 are used. These Gold codes are quite often referred to as "pseudo-random noise" since they contain no data. However, this may be misleading since they are actually deterministic sequences.

If the almanac information has previously been acquired, the receiver picks which satellites to listen for by their PRN numbers. If the almanac information is not in memory, the receiver enters a search mode and cycles through the PRN numbers until a lock is obtained on one of the satellites. To obtain a lock, it is necessary that there be an unobstructed line of sight from the receiver to the satellite. The receiver can then acquire the almanac and determine the satellites it should listen for. As it detects each satellite's signal, it identifies it by its distinct C/A code pattern, then measures the received time for each satellite. To do this, the receiver produces an identical C/A sequence using the same PRN number as depicted in the diagram, referenced to its local clock, starting at the same time the satellite sent it. It then computes the offset to the local clock that generates the maximum correlation. This offset is the time delay from the satellite to the receiver, as told by the receiver's clock. Since the PRN repeats every millisecond, this offset is precise but ambiguous, and the ambiguity is resolved by looking at the data bits, which are sent at 50 Hz (20 ms/bit) and aligned with the PRN code.

Next, the orbital position data, or ephemeris, from the Navigation Message is then downloaded to calculate precisely where the satellite was at the start of the message. A more-sensitive receiver will potentially acquire the ephemeris data more quickly than a less-sensitive receiver, especially in a noisy environment.

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