Understanding Signal Acquisition in GNSS receivers part – 1

Ganesh L G

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Part – 2 discusses the search algorithms for GNSS signal acquisition
Part – 3 discusses the Introduction to signal tracking loops GNSS receiver
Part – 4 discusses the functioning of GNSS tracking loops and discriminators used.

Signal acquisition is the first step performed by the GNSS receiver in digital domain. The two main
purposes of acquisition are the following.

Step – 1
Remove the Doppler component from chosen carrier frequency1.

Step – 2
Estimate the code phase of chosen signal for Pseudorange computations.

The third optional implementation in GNSS signal acquisition is to find the error2 in carrier phase3
depending on which the acquisition is regarded as Coherent or Non-coherent.

Since acquisition is the first step in demodulation process, it will decide the following critical specifications
of the receiver.
· Time to first fix
· Complexity (and hence the cost) of the receiver (in terms of number of correlators needed)
· Position or Navigation accuracy (The resolution4 of carrier frequency and code phase in search
technique5 will decide the accuracy of subsequent stages6)
The first part of this article discusses the first step of Doppler removal from the incoming signalKey players in Doppler removal step of Signal Acquisition process

fIF – Intermediate frequency of the carrier signal
fd – Actual Doppler offset present in carrier signal
δθ - Actual carrier phase of the incoming signal
θ_est – receiver’s estimate of carrier phase in internally generated signal
f_estd – receiver’s estimate of Doppler offset in internally generated signal

Coded in green (Navigation Data, Code phase) are not processed in Doppler removal step of Signal
Acquisition process and hence appear at the output of LPF as they were before acquisition started. It should
however be noted that both Navigation data and code phase are still unknown parameters which will be
taken care in next step of acquisition process called “Code wipe off”
Parameters processed in this step, coded in red, are the Doppler offset added to Carrier IF frequency
(fIF + fd) and Carrier phase δθ
Signal from ADC contains Navigation data, unknown code phase, known carrier frequency offset by a
Doppler frequency and unknown carrier phase
Mathematically it can be represented as
Cos(2π(fIF + fd) t + δθ)
Internally generated Signal 1 is such that which when multiplied with Signal from ADC removes the IF
component and results in a component with only Doppler error and carrier phase error after LPF.
Mathematically Internally generated Signal 1 can be represented as –
2 * Cos (2π(fIF + f_estd) t + θ_est)
The output signal from LPF 1 is Cos(2π(fd - f_estd) t + (δθ - θ_est )) – These are called In-phase samples
(because they are still cosine phased like the signal before the acquisition process started)
Internally generated Signal 2 is also such that which when multiplied with Signal from ADC removes the
IF component and results in a component with only Doppler error and carrier phase error after LPF but
with a phase 90 degree shifted from original signal (because Internally generated Signal 2 was Sine phased).
Mathematically Internally generated Signal 2 can be represented as –
2 * Sin(2π(fIF + f_estd) t + θ_est)
The output signal from LPF 2 is Sin(2π(fd - f_estd) t + (δθ - θ_est )) – These are called Quadrature-phase
samples (because they are Sine phased unlike the signal before the acquisition process started)
From the above discussion it is clear that following carrier IF wipe off, only the Doppler error and carrier
phase error remain in the signal.
The Doppler error is the difference between actual Doppler offset in the incoming signal and receiver’s
estimate in the internally generated signal. The Doppler error can be totally removed from incoming signal
if the receiver is able to internally generate a signal with an estimate which is close to actual Doppler offset.

1. The chosen carrier frequency corresponds to the centre frequency of chosen band for acquisition like L1, L2 or L5 for GPS
and E5a/b, E1 or E6 for GALILEO
2. Error refers to the difference between two values of same parameters which can be self corrected by receivers based on
implementation.
3. If Carrier phase is considered for acquisition, then the process is termed coherent acquisition.
4. Resolution refers to the step size in both the code phase and frequency bin axes in the search algorithm
5. Search algorithms are explained in detail in later parts of this article
6. Subsequent processes in receive involve transitioning into tracking loops.