Ex4 - Acquisition

01LPXBP – Satellite Navigation Systems

Exercises 4 Acquisition & Tracking Exercise 4.1 Acquisition performances A GPS signal is received by a commercial receiver with the following parameters: •

C/N0 = 45 dBHz

•

Received power of -156 dBW at the output of the antenna

•

IF frequency fIF = 4 MHz

•

An IF filter that can be approximated as an ideal pass-band with a bandwidth B=2MHz and unitary amplitude; the filter cuts the 10% of the power of the signal

•

Serial acquisition scheme

•

Integration time Tint= 1 code period

•

Sampling frequency fs= 16 Msamples/s

•

No quantization

Ex4 - Acquisition

1

01LPXBP – Satellite Navigation Systems Evaluate the variance of the noise at the output of the correlators, and the probability of miss-detection in case of a threshold Vt equal to 70% of the maximum of the correlation. (Note: suppose the noise after the sampler is still white)

Exercise 4.2 Acquisition schemes For the acquisition stage of a given GNSS receiver, the following parameters are known: • Tint = 2 code periods • C/N0 = 45 dB-Hz • Front-end bandwidth: B = 4 MHz • Sampling frequency: fS = 16 MHz Determine, in case of both GPS C/A and Galileo E1 (hyp: dataless) signals: 1. the detection threshold to be applied in case of a serial search in order to obtain a false alarm probability pfa =10-3 2. the improvement in terms of detection/false-alarm probabilities obtained with a “M/N” statistical algorithm with M = 3 and N = 5 3. the frequency bin width given by the “empirical” rule, in case of serial-search correlation scheme 4. the frequency bin width in case of the frequency-domain parallel correlation scheme.

Exercise 4.3 Tracking: Coherent E-L discriminator Consider a GPS receiver with a narrow correlator architecture with spacing d = 0.5. Draw the open-loop discrimination function (S-curve) supposing to have non-selective filters within the front-end (infinite pre-correlation bandwidth). Evaluate the slope of the S-curve in the tracking point.

Ex4 - Acquisition

2