Awesome

SUMMARY

Kalibrate, or kal, can scan for GSM base stations in a given frequency band and can use those GSM base stations to calculate the local oscillator frequency offset.

The description below is for original kal - this version has been modified for RTL-SDR dongles.

This project can work only correct the a small offset of ppm. You need to either get a rough initial estimate yourself, or use a project which can correct larger offsets automatically. For example https://github.com/viraptor/fm_tune or https://github.com/JiaoXianjun/LTE-Cell-Scanner

WHAT

On Clocks

The USRP1, similar to a number of devices, has a built-in oscillator which is only guaranteed accurate to within 20 parts per million (ppm). (Although in practice the USRP oscillator is normally closer to 3ppm.) This is sufficient for a number of purposes, but not for others. Fortunately, the USRP also supports an external oscillator. For example, the Clock Tamer, the KSP 52MHz and the FA-SY 1 are all accurate clocks that work well with the USRP.

Normally, these external clocks must be calibrated to ensure they are set as accurately as possible. An oscilloscope is probably the best way to determine the accuracy of these clocks. However a good oscilloscope is expensive and not everyone has access to one. There are other ways to calibrate these devices -- the FA-SY 1 documentation discusses using the WWV time signals. Similarly, GSM base stations are required to be accurate to within 0.05ppm and so they can also provide an accurate reference clock.

If you own a USRP daughterboard that covers the GSM frequencies in your area, using a GSM base station is a particularly convenient.

Description

A base station transmits a frequency correction burst on the Frequency Correction CHannel (FCCH) in regular positions. The FCCH repeats every 51 TDMA frames and the frequency correction burst is located in timeslot 0 of frames 0, 10, 20, 30, and 40.

A frequency correction burst consists of a certain bit pattern which, after modulation, is a sine wave with frequency one quarter that of the GSM bit rate. I.e., (1625000 / 6) / 4 = 67708.3 Hz. By searching a channel for this pure tone, a mobile station can determine its clock offset by determining how far away from 67708.3Hz the received frequency is.

There are many ways which a pure tone can be identified. For example, one can capture a burst of data and then examine it with a Fourier transformation to determine if most of the power in the signal is at a certain frequency. Alternatively, one can define a band-pass filter at 67708.3 Hz and then compare the power of the signal before and after it passes through the filter. However, both of these methods have drawbacks. The FFT method requires significant resources and cannot easily detect the frequency correction burst edge. The filter method either isn't accurate or cannot detect larger offsets. Multiple filters can be used, but that requires significant resources.

kal uses a hybrid of the FFT and filter methods. The filter kal uses is an adaptive filter as described in the paper:

G. Narendra Varma, Usha Sahu, G. Prabhu Charan, Robust Frequency Burst Detection Algorithm for GSM/GPRS.

An Adaptive Line Equalizer (ALE) attempts to predict the input signal by adapting its filter coefficients. The prediction is compared with the actual signal and the coefficients are adapted so that the error is minimized. If the input contains a strong narrow-band signal embedded in wide-band noise, the filter output will be a pure sine at the same frequency and almost free of the wide-band noise.

kal applies the ALE to the buffer and calculates the error between the ALE prediction and the input signal at each point in the signal. kal then calculates the average of all the errors. When the error drops below the average for the length of a frequency correction burst, this indicates a detected burst.

Once we have the location of the frequency correction burst, we must determine what frequency it is at so we can calculate the offset from 67708.3 Hz. We take the input signal corresponding to the low error levels and run that through a FFT. The largest peak in the FFT output corresponds to the detected frequency of the frequency correction burst. This peak is then used to determine the frequency offset.

Any noise in the system affects the measurements and so kal averages the results a number of times before displaying the offset. The range of values as well as the standard deviation is displayed so that an estimate of the measurement accuracy can be made.

HOW

kal uses the GNU Autoconf system and should be easily built on most *nix platforms.

Debian example:

$ git clone https://github.com/steve-m/kalibrate-rtl.git
$ sudo apt-get install libtool libfftw3-dev

jl@thinkfoo:~/src$ cd kal-v0.4.1
jl@thinkfoo:~/src/kal-v0.4.1$ ./bootstrap && CXXFLAGS='-W -Wall -O3' ./configure && make
[...]
jl@thinkfoo:~/src/kal-v0.4.1$ src/kal -h
kalibrate v0.4.1, Copyright (c) 2010, Joshua Lackey

Usage:
	GSM Base Station Scan:
		kal <-s band indicator> [options]

	Clock Offset Calculation:
		kal <-f frequency | -c channel> [options]

Where options are:
	-s	band to scan (GSM850, GSM900, EGSM, DCS, PCS)
	-f	frequency of nearby GSM base station
	-c	channel of nearby GSM base station
	-b	band indicator (GSM850, GSM900, EGSM, DCS, PCS)
	-R	side A (0) or B (1), defaults to B
	-A	antenna TX/RX (0) or RX2 (1), defaults to RX2
	-g	gain as % of range, defaults to 45%
	-F	FPGA master clock frequency, defaults to 52MHz
	-v	verbose
	-D	enable debug messages
	-h	help
jl@thinkfoo:~/src/kal-v0.4.1$ src/kal -s 850
kal: Scanning for GSM-850 base stations.
GSM-850:
	chan: 128 (869.2MHz -  13Hz)	power: 9400.80
	chan: 131 (869.8MHz +   7Hz)	power: 4081.75
	chan: 139 (871.4MHz +  10Hz)	power: 2936.20
	chan: 145 (872.6MHz -   7Hz)	power: 33605.48
jl@thinkfoo:~/src/kal-v0.4.1$ src/kal -c 145
kal: Calculating clock frequency offset.
Using GSM-850 channel 145 (872.6MHz)
average		[min, max]	(range, stddev)
-   1Hz		[-8, 7]	(14, 3.948722)
overruns: 0
not found: 0

WHO

I'd like to thank Alexander Chemeris for his valuable input, ideas, and his testing of a large number of alpha versions. I'd also like to thank Mark J. Blair for his help getting kal to work with Mac OS X.

I'd also like to thank Mark J. Blair for his help getting kal to work with Mac OS X. (And also for helping me realize that I never actually used the -F parameter...)

Temporary maintenance: Stan Pitucha (viraptor@gmail.com)