Transcript
GNSS Technologies GNSS Acquisition 25.1.2016
Dr. Zahidul Bhuiyan Finnish Geospatial Research Institute, National Land Survey
Content GNSS signal background
Binary phase shift keying (BPSK) modulation Binary offset carrier (BOC) modulation Pseudo random noise codes
Brief receiver overview Searching for BPSK signals (acquisition) Software GPS acquisition
Slides based on: GNSS Applications and Methods, by S. Gleason and D. Gebre-Egziabher (Eds.), Artech House Inc., 2009 http://www.gnssapplications.org/
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GNSS Signal Background (1) GNSS is a spread spectrum (SS) system, where the spread signal occupies a bandwidth much greater than the rate of the data being transmitted Redundancy suppresses the effects of interfering signals and reduces the peak transmitted signal power levels to effectively hide the signal in background noise DS-SS: a carrier wave is
modulated by a data signal overlaid with a high frequency PRN spreading signal 3
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GNSS Signal Background (2)
A spread spectrum system, with the modulation onto the carrier omitted for simplicity 4
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GNSS Signal Background (3) The innovation of the GPS is to use the PRN code sequence as a ranging signal
path difference from transmitter to receiver to be recovered -> range/distance
The GPS satellite signals share the same carrier frequency and are separable in the receiver, because each respective transmission employs a unique PRN spreading code Each effective bit of the PRN code sequence is called a chip
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GNSS Signal Background (4) GPS uses binary phase shift keying (BPSK) modulation, where ideally the carrier phase changes instantaneously by 180°, depending on the datamodulated spreading sequence. A BPSK-modulated signal can be written as
P is the signal power, d(t) is the biphase data signal, a(t) is the biphase PRN code spreading signal, and w is the carrier frequency
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GNSS Signal Background (5) GPS L1 C/A code is a BPSK signal:
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GNSS Signal Background (6)
L-band GNSS frequency allocations:
Currently, GPS consists of 24-32 satellites broadcasting three navigational signals in the Lband: one signal available for civil use transmitted on the L1 and two military signals transmitted on L1&L2 The future 30-satellite Galileo constellation will introduce six data-modulated and four dataless signals into the L-band spectrum occupying four frequency bands
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GNSS Signal Background (7) BOC modulation is a rectangular subcarrier modulation (sine or cosine) of the PRN spreading code and is denoted BOC( fs , fc ), where fs is the subcarrier frequency, and fc is the PRN code chipping rate, and both are multiples of 1.023 × 106
For future Galileo and military GPS signals
The effect of BOC modulation is that the signal is amplitudemodulated, with its power spectrum shifted away from the carrier frequency in upper and lower sidebands with a null at the center frequency The null is the primary benefit of BOC modulation, allowing frequency reuse alongside existing PSK signals BOC modulation has greater resistance to short-range multipath and a small advantage in code tracking accuracy
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However, these advantages come at a price, namely the difficulties in acquiring and tracking signals with a subcarrier modulation GNSS Technologies
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GNSS Signal Background (8)
A BOC signal is created through modulation of a PRN sequence a(t) by a square wave subcarrier s(t) and can be represented as follows
where b(t) = a(t) × s(t) The GPS M-code signals are to be transmitted using a BOC(10, 5) modulation with a sine-phased subcarrier in the L1 and L2 bands The Galileo signals for the E5a and E5b bands are combined onto a single-center frequency though the use of alternate BOC(AltBOC) modulation For future L1 civil signals, a common multiplexed BOC (MBOC) structure has been designed 10
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GNSS Signal Background (9)
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GNSS Signal Background (10)
The GPS C/A code is generated using two 10-bit linear feedback shift registers (LFSR) The resulting PRN codes are maximal length sequences with N = 2n − 1 chips, where n is the length of the LFSR The periodic autocorrelation function for a PRN sequence a(t) of length n chips, with a chip period TC can be written as
The autocorrelation envelope can be approximated by a triangle function, the peak of which (amplitude A) corresponds to the perfect alignment (=correlation) between the received code and the locally generated replica 12
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GNSS Signal Background (11)
The ideal autocorrelation of a PRN sequence is as follows
Outside the correlation interval the ideal cross-correlation function is −A/N In practice the sequences identified by the codes exhibit a three-valued cross-correlation function with values
where
The code sequences employed for GPS C/A have crosscorrelation values of 13
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GNSS Signal Background (12)
Normalized autocorrelation of GPS C/A code (PRN 1)
Short 1023 chip code -> relatively poor correlation performance 14
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GNSS Signal Background (13)
Layered PRN codes are to be broadcast by both GPS modernized and Galileo signals to reduce cross-correlation effects
overlaying the fast changing PRN sequence (primary code) with a secondary code whose bit period is equal to one primary code epoch
The secondary code length is then chosen such that the secondary code period is equal to one symbol period of the navigational data stream
A code or channel with no data modulation is known as a pilot
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the pilot allows longer integration periods to be easily implemented in the receiver for weak-signal acquisition and tracking GNSS Technologies
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GNSS Signal Background (14)
Power spectral densities of GPS L1 signals 16
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GNSS Signal Background (15)
Power spectral densities of Galileo signals
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Signal Acquisition & Tracking: Introduction
Code shift and Doppler frequency acquisition are needed for reliable performance of any CDMA system The code synchronization task is typically split into:
coarse synchronization (or acquisition stage) and fine synchronization (or tracking stage).
Acquisition is used to get a rough timing estimate, say within +/- 0.5 chips in case of GPS L1 C/A signal Tracking means finding and maintaining fine synchronization Signal tracking is much easier given the initial acquisition Signal acquisition, however, is usually considered as one of the most challenging tasks in any spread spectrum system Signal acquisition is usually a one-shot estimate. On the contrary, signal tracking is performed in a continuous fashion 18
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Signal Uncertainty Regions
Timing uncertainty: determined by the transmission time of the transmitter and the propagation delay (and clock uncertainties)
a larger timing uncertainty means a larger search area (due to a search through all possible delays)
Frequency uncertainty: determined by the Doppler shift and mismatch between the transmitter and receiver oscillators Moreover, initial code acquisition must be accomplished in low Signal-to-Noise Ratio (SNR) environments and in the presence of various interferers The possibility of channel fading and multipath propagation can make initial acquisition even harder to accomplish 19
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Time-frequency uncertainty
One correlation output forms a time-frequency bin. Several bins form a time-frequency window. The whole search space = time-frequency unertainty window.
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Acquisition
Signal Acquisition
Typically performed in 2 stages: Searching stage: build the time-frequency window with various delay and frequency candidates (via correlations). Detection stage - form a decision variable and compare it with a threshold in order to detect whether the signal is present or absent. Threshold choice is an important step in designing a good acquisition stage. Either constant or variable (e.g., according to SNR) thresholds can be used, as it will be discussed later on. The larger the time or frequency uncertainty is ⇒ the greater time it will take to achieve acquisition, or the greater receiver complexity is required for a given acquisition time requirement 22
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Acquisition: Searching Stage
The search strategy can be:
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serial: there is only one bin per window ⇒ low complexity (only one complex correlator needed), high acquisition time (many bins to be searched; acquisition time is proportional with the code epoch length, i.e. 1023 chips for standard GPS, up to 10230 for Galileo and modernized GPS). hybrid: there are several bins per window and there are several windows in the whole search space ⇒ tradeoff between complexity and acquisition time; general case. parallel: there are more than one bin per window and there is only one window in the whole search space⇒ high complexity (need many correlators), low acquisition time. GNSS Technologies
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Acquisition: notes about correlation
Correlation is done between the received signal and a reference (local) code at the receiver (e.g., C/A code) In time domain:
Rx signal
Rx signal
Discrete (I&D= Integrate and Dump)
Analog Ref. signal
In frequency domain: Rx signal
FFT
X
IFFT *
FFT Ref. signal 24
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Example of FFT vs time correlation
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Acquisition: Detection Stage (I)
The detection strategy can be classified into:
Variable dwell time detector (also called sequential detector) and Fixed dwell time detector.
Examples of detector structures for GPS: Sequential detector:
1.
Fixed dwell detector:
2.
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Tong search detector - it uses a counter variable KTong and a confirmation threshold U. If KTong = U ⇒ acquisition. At each cell, the counter is initialized to B > 0 value. Tong detector is sub-optimum, but more efficient than a fixed dwell time detector. M of N search detector - N correlation envelopes are compared with a threshold; if at least M of them exceed the threshold ⇒ acquisition. GNSS Technologies
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Example: Tong Search Detector
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Acquisition: Detection stage (II)
The detection strategy can also be classified into:
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Coherent: phase information available; limitations due to navigation data and channel effects Non-coherent: no phase information; taking absolute value or squared absolute value of the correlation outputs.
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Acquisition: Detection stage (III)
The detection strategy can aditionally be classified into:
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Single-dwell: detection is taken in one step Multiple-dwell: detection is taken in several steps (see next slide for an example of two-dwell structure). Multiple-dwell structures are typically used to decrease Mean Acquisition Times (MAT) (tradeoff with increased complexity)
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Example of a double-dwell detector
First stage threshold chosen for low false alarm (and low detection probability). Second stage threshold: higher detection probability (at higher false alarm, but overall false alarm is low, due to first dwell stage) -> achieved via a higher integration level. 30
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Acquisition: Threshold Choice (I)
Acquisition problem is in fact a detection problem: detect signal in noise, or, equivalently, separate between hypothesis H1 (signal plus noise are present) and hypothesis H0 (noise only is present).
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Acquisition: Threshold Choice (II) Threshold can be chosen as a tradeoff between a good detection probability and a sufficiently low false alarm (detection probability increases when false alarm probability increases) The Probability Distribution Functions (PDFs) under each hypothesis are derived according to the decision statistic (see previous slide), which can be, for example, the maximum in a certain correlation window 32
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Acquisition: performance measures (I)
Detection probability and false alarm probability: Classical detection problem of signal in noise (e.g., Kay’s book on Detection Theory)
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Acquisition: performance measures (II)
Mean Acquisition Time (MAT)
Example:
Assume that the time uncertainty corresponds to N pseudorandom chips (or NTc = ΔT seconds, where Tc = chip duration. Assume that there is no carrier frequency uncertainty (e.g., assisted acquisition) Assume also that detection probability at the correct hypotheses is Pd = 1 and the false alarm probability at incorrect hypotheses is Pfa = 0 (ideal case). What is the MAT time for a dwell time τD if the timing search update is in half-chip increments (0.5Tc)? Answer: there are Q = 2N timing positions (hypotheses, bins) to be searched and the time to search one time bin is τD ⇒Tacq = 2N τD If all hypotheses are equally probable ⇒ the mean acquisition time can be approximated by half of Tacq => MAT ≈ N τD 34
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Acquisition: performance measures (III)
Time to First Fix (TTFF): The time from receiver turn on until the first navigation solution is obtained. The complete navigation solution (min 4 satellites in view) is needed to compute TTFF Typical values of TTFF: 30-40s without assistance; 1s with network assistance (e.g., A-GPS) The TTFF is commonly broken down into three more specific scenarios:
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Cold (or factory): The receiver is missing, or has inaccurate estimates of, its position, velocity, the time, or the visibility of any of the GNSS satellites. Warm or normal: The receiver has estimates of the current time within 20 seconds, the current position within 100 kilometers, and its velocity within 25 m/s, and it has valid almanac data (i.e., coarse orbital information of satellites). Hot or standby: The receiver has valid time, position, almanac, and ephemeris data (i.e., accurate orbital data of satellites), enabling a rapid acquisition of satellite signals. GNSS Technologies
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Receiver overview (1)
Basic GNSS receiver channel
GNSS signals are normally received through the use of a right-hand circularly polarized (RHCP) antenna and amplified using a low-noise amplifier (LNA), which essentially determines the receiver’s noise figure The RF signals are down-converted, typically in a number of stages, to an intermediate frequency (IF), sufficiently high in frequency to support the signal bandwidth
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Receiver overview (2)
After down-conversion, the signal is digitized by an analog-to-digital converter (ADC), with automatic gain control (AGC), and the digital IF is then passed to the receiver’s correlator channels In the correlator channels, the carrier signal and code sequence are removed from the signal by correlating the received signal with locally generated replicas
The processor then extracts the raw navigational data by monitoring the changes in phase angle
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This data can be used in combination with phase information derived from the carrier and code tracking loops to form pseudorange and Doppler estimates, ultimately resulting in position, velocity, and time information for the user GNSS Technologies
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Software receiver acquisition (1)
Software receiver (fastgps) acquisition algorithm
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Software receiver acquisition (2)
Gathering a reasonable amount of data for use in the FFT acquisition processing
When enough data has been collected, the acquire is started, specifying the satellite to search for
The default value is currently 4 ms of data samples
Scan over coarse Doppler bins; Perform FFT on input sample buffer; Multiply sample FFT and precalculated PRN code FFT; Perform inverse FFT; Search for peaks exceeding the detection threshold; If a signal is found perform fine Doppler search and store results; Perform debug searches if specified
If a signal is found, allocate it to a tracking channel 39
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Software receiver acquisition (3)
Example of the inverse FFT result performed by the fastgps software receiver acquisition process
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The four peaks represent the GPS PRN code repeating at 1-ms intervals The largest peak is used to initialize the signal-tracking loops The four peaks show the signal repeating across the four milliseconds of input data A data buffer longer than the one millisecond GPS PRN code length is often used to ensure a more reliable signal detection GNSS Technologies
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