252 |
Spread Spectrum and CDMA |
|
|
of the local clock in time and frequency against the received signal may appear rather large. Among the factors causing such a mismatch are autonomous operation of the transmitter and receiver clocks, the wide range of variations of path length between the transmitter and receiver, Doppler frequency shift due to their relative motion etc. In such circumstances direct implementation of the ML rule sometimes proves to be excessively demanding or even prohibitive in terms of resource consumption, as is demonstrated by the example below.
Example 8.1.1. The ranging C/A signal of the GPS (see Section 11.2) has period containing L ¼ 1023 chips or in real time LD ¼ 1 ms. To solve the navigation task, one should measure the time position of the signal with accuracy no worse than a split microsecond, for instance 0.1 of chip duration D. If the receiver is initialized with no prior knowledge of a local clock mismatch versus the signal, the uncertainty of the signal delay spans one period, i.e. LD. Turning to the correlator-bank receiver of Figure 2.18, one can see that its realization means implementing 10 230 parallel correlators. Switching to the matched filter structure (Figure 2.19) does not make the problem easier: such a filter with memory LD, digitally realized, would have to operate with at least 10 samples per chip, performing 1023 summations during one sampling interval (smaller than 100 ns). Involving such an enormous hardware or software resource for performing only one of many tasks of the receiver does not look commercially justified, at least considering current technological tendencies.
In order to avoid implementation difficulties, the practical procedures of time– frequency estimation in a wide uncertainty region are often performed in the form of two successive steps. The first, called acquisition (code acquisition, search), performs a coarse measuring of the necessary parameters and provides preliminary estimates used by the second step, called tracking. This second step, typically performed by special code tracking and frequency tracking loops, delivers fine time–frequency estimations used further immediately by a local reference generator to align the despreading signal with a received spreading code. But in order to capture synchronism (pull-in) and enter the tracking state, the tracking loops need an initial targetting, e.g. knowledge of a received signal timing within one chip duration or so. This, as was already pointed out, is the task of the acquisition stage, reducing the primary uncertainty of signal parameters to that demanded by a tracking loop. Comparatively soft requirements towards the accuracy of estimates at the acquisition step allow cutting down the amount of calculated statistics and simplifying the implementation. To come back to Example 8.1.1, slackening the demands on the necessary precision of time measurement to one chip duration means a ten times smaller number of correlators in the scheme of Figure 2.18 or ten times lower processing speed in the matched filter structure. Yet the main resource-saving technique exploited by acquisition is a partial or complete replacement of parallel computations of the decision statistics by a serial one.
To explain this let us treat unknown delay and frequency shift F of the signal as signal coordinates on the time–frequency plane. Suppose that the initial uncertainty ranges of and F are u and Fu, respectively, and that as a result of acquisition those ranges should be reduced to and F. Then, as Figure 8.1 shows, signal position is within one of M F rectangular cells, where M ¼ (Fu u)/( F ). The acquisition