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Multicorrelator

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ReceiversReceivers
Title Multicorrelator
Edited by GMV
Level Advanced
Year of Publication 2011
Logo GMV.png

It is commonly said that correlation is the key operation in GNSS receivers, in order to achieve synchronization with the incoming signals from each satellite. However, a single correlator is not enough to fulfill this purpose: in fact, even the simplest GNSS receiver supports multiple correlators to achieve synchronization and / or improve the accuracy of the generated observables.

Contents

Concept

The basic concept within the baseband processing of a GNSS receiver relies in correlating the incoming signal with a local replica of the PRN code (also called ranging code), in order to derive estimates of the Doppler frequency and the code delay from which to shift and adjust the local replica generation, guaranteeing that it is aligned with the incoming signal. The aligned replica is often called Prompt (P) correlator - also discussed here.

In reality, even the simplest GNSS receiver supports at least three correlators:

Figure 1: Example of the outputs of the E, P, L correlators when the prompt correlator is completely aligned with the incoming signal (right hand side), and when synchronization has not yet been achieved (left hand side), for BPSK modulation.

Figure 1 depicts an example of the outputs of these correlators when the prompt correlator is completely aligned with the incoming signal, which is the desired situation, and when synchronization has not yet been achieved.

The correlation results are points over the autocorrelation function – in this example, it is a triangular function accounting for BPSK modulation used, for example in GPS L1 C/A. From inspection of the figure, the following comments can be intuitively derived (these concepts are further explored here):

Block Diagram

Figure 2:Multicorrelators Block Diagram.

Figure 2 depicts the baseband processing block diagram for a single channel, with focus on the correlators. This representation shows how the correlators’ outputs (both the real and the imaginary part, i.e. using the In-phase (I) and Quadrature (Q) component of the incoming signal respectively) are computed. These outputs are then used by the tracking loops to compute new estimates of:

This is an iterative process that the receiver supports continuously. The Integrate and Dump (I&D) blocks are used to integrate the correlation outputs over time, either coherently or non-coherently, as discussed in baseband processing.

In parallel, lock detectors use these correlator outputs to assess whether or not the incoming signal is actually being tracked. This is justified by the fact that, in noisy conditions, the tracking loops may diverge from the real peak, or that a false acquisition may occur.

Mathematical Model

Neglecting noise and picking up from baseband processing, the Prompt correlator output can be written as:


I_P = Ad R_{x} (\tau_e) cos(\phi_e)\,

Q_P = -AdR_{x}(\tau_e)sin(\phi_e)\,


The expressions for the Early and Late replicas are given by:


I_E = Ad R_{x} (\tau_e-\frac{\delta}{2}) cos(\phi_e)\,

Q_E = -AdR_{x}(\tau_e-\frac{\delta}{2})sin(\phi_e)\,

I_L = Ad R_{x} (\tau_e+\frac{\delta}{2}) cos(\phi_e)\,

Q_L = -AdR_{x}(\tau_e+\frac{\delta}{2})sin(\phi_e)\,


where:

Please note that the phase error can also be written as:


\phi_e = 2\pi f_e t + \phi_0\,


where:


Further Applications

Although basic receivers use three correlators to track the incoming signal, one can imagine that the number of correlators could be increased (at the cost of power and resources consumption) in order to extract further information. These kind of techniques are actually used in advanced signal processing receivers to achieve higher performances. Two examples are:

Figure 3:Multipeaked Auto-Correlation Functions for two examples of BOC modulations.

Related articles

References

  1. ^ R. Van Nee, “The Multipath Estimating Delay Lock Loop”, IEEE ISSSTA 92, 1992, Japan, pp 39-42.
  2. ^ B. Townsend, P. Fenton, K. Van Dierondonck, R.Van Nee, “Performance Evaluation of the Multipath Estimating Lock Loop”, ION Navigation, VOL. 42, No. 3, fall 1995,pp 503-514.
  3. ^ P. Fine, W. Wilson, “Tracking Algorithm for GPS Offset Carrier Signals,” ION NTM 1999, San Diego, MA, pp. 671-676.
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