Reorganize notes; measure effect of LNA gain, ADC calibration.
Python code to experiment with IF filtering.
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NOTES.txt
65
NOTES.txt
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@ -2,15 +2,23 @@
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This file contains random notitions
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-----------------------------------
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Valid sample rates
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------------------
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Sample rates between 300001 Hz and 900000 Hz (inclusive) are not supported.
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They cause an invalid configuration of the RTL chip.
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rsamp_ratio = 28.8 MHz * 2**22 / sample_rate
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If bit 27 and bit 28 of rsamp_ratio are different, the RTL chip malfunctions.
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The RTL chip has a configurable 32-tap FIR filter.
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Behaviour of RTL and Elonics tuner
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----------------------------------
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The RTL chip has a configurable 32-tap FIR filter running at 28.8 MS/s.
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RTL-SDR currently configures it for cutoff at 1.2 MHz (2.4 MS/s).
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Casual test of ADC errors:
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Casual test of ADC mismatch:
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* DC offset in order of 1 code step
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* I/Q gain mismatch in order of 4%
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* I/Q phase mismatch in order of 1% of sample interval
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@ -32,18 +40,54 @@ mode causes a brief level spike, while manually rewriting the same IF gain in
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AGC mode does not have any effect).
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It seems more likely that AGC is a digital gain in the downsampling filter.
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Default settings in librtlsdr:
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Elonics LNA gain: when auto tuner gain: autonomous control with slow update
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Default settings in librtlsdr
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-----------------------------
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Elonics LNA gain: when auto tuner gain: autonomous control with slow update
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otherwise gain as configured via rtlsdr_set_tuner_gain
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Elonics mixer gain: autonomous control disabled,
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Elonics mixer gain: autonomous control disabled,
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gain depending on rtlsdr_set_tuner_gain
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Elonics IF linearity: optimize sensitivity (default), auto switch disabled
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Elonics IF gain: +6, +0, +0, +0, +9, +9 (non-standard mode)
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Elonics IF filters: matched to sample rate (note this may not be optimal)
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RTL AGC mode off
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Elonics IF linearity: optimize sensitivity (default), auto switch disabled
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Elonics IF gain: +6, +0, +0, +0, +9, +9 (non-standard mode)
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Elonics IF filters: matched to sample rate (note this may not be optimal)
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RTL AGC mode off
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Local radio stations:
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Effect of settings on baseband SNR
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----------------------------------
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STATION SRATE LNA IF GAIN AGC SOFT BW IF LEVEL GUARD/PILOT
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radio3 1 MS/s 24 dB default off 150 kHz 0.19 -62.6 dB/Hz
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radio3 1.5 MS 24 dB default off 150 kHz 0.19 -62.7 dB/Hz
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radio3 2 MS/s 24 dB default off 150 kHz 0.18 -62.7 dB/Hz
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radio3 2 MS/s 34 dB default off 150 kHz 0.46 -64.0 dB/Hz
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radio3 2 MS/s 34 dB default off 80 kHz -64.0 dB/Hz
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radio3 2 MS/s 34 dB default off 150 kHz adccal -64.0 dB/Hz
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radio4 2 MS/s 24 dB default off 150 kHz 0.04 -41.1 dB/Hz
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radio4 1 MS/s 34 dB default off 150 kHz 0.06 -43.3 dB/Hz
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radio4 1 MS/s 34 dB default off 80 kHz -51.2 dB/Hz
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radio4 2 MS/s 34 dB default off 150 kHz 0.10 -42.4 dB/Hz
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radio4 2 MS/s 34 dB default off 80 kHz -48.2 dB/Hz
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radio4 2 MS/s 34 dB default off 150 kHz adccal -42.4 dB/Hz
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Note: all measurements 10 second duration
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Note: all measurements have LO frequency set to station + 250 kHz
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Conclusion: Sample rate (1 MS/s to 2 MS/s) has little effect on quality.
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Conclusion: LNA gain has little effect on quality.
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Conclusion: Narrow IF filter improves quality of weak station.
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Conclusion: ADC gain/offset calibration has no effect on quality.
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Local radio stations
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--------------------
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radio2 92600000 (good)
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radio3 96800000 (good)
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radio4 94300000 (bad)
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@ -52,3 +96,4 @@ radio538 102100000 (medium)
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radio10 103800000 (bad)
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radio west 89300000 (medium)
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--
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7
TODO.txt
7
TODO.txt
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@ -1,19 +1,16 @@
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* (experiment) make nice plot of baseband distortion due to IF filtering
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* (experiment) consider downsampling IF signal before FM detection
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* (experiment) measure effect of IF gain on baseband SNR
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* (experiment) measure effect of IF gain linearity on baseband SNR
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* (experiment) measure effect of RTL AGC mode on baseband SNR
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* (experiment) measure effect of ADC calibration on baseband SNR
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* (experiment) measure effect of IF bandwidth on baseband SNR
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* (experiment) measure effect of IF sample rate on baseband SNR
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* (experiment) try if RTL AGC mode improves FM decoding
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* (feature) support 'M' 'k' suffixes for sample rates and tuning frequency
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* (feature) implement off-line FM decoder in Python for experimentation
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* (feature) implement stereo pilot pulse-per-second
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* (quality) consider DC offset calibration
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* (speedup) maybe replace high-order FIR downsampling filter with 2nd order butterworth followed by lower order FIR filter
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* figure out why we sometimes lose stereo lock
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* it looks like IF level sometimes varies so much that it saturates the receiver; perhaps this can be solved by dynamically managing the hardware gain in response to level measurements
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* (quality) figure out if I/Q balance can improve weak stations
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* (quality) figure out if hardware gain settings can improve weak stations
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* (feature) implement RDS decoding
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* (quality) consider FM demodulation with PLL instead of phase discriminator
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103
pyfm.py
103
pyfm.py
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@ -6,6 +6,8 @@ import sys
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import types
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import numpy
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import numpy.fft
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import numpy.linalg
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import numpy.random
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import scipy.signal
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@ -78,24 +80,37 @@ def firFilter(d, coeff):
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return scipy.signal.lfilter(coeff, 1, d)
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def quadratureDetector(d):
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"""FM frequency detector based on quadrature demodulation."""
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def quadratureDetector(d, fs):
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"""FM frequency detector based on quadrature demodulation.
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Return an array of real-valued numbers, representing frequencies in Hz."""
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k = fs / (2 * numpy.pi)
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# lazy version
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def g(d):
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prev = None
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for b in d:
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if prev is None:
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yield numpy.angle(b[1:] * b[:-1].conj())
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else:
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x = numpy.concatenate((prev[-1:], b[:-1]))
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yield numpy.angle(b * x.conj())
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if prev is not None:
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x = numpy.concatenate((prev[1:], b[:1]))
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yield numpy.angle(x * prev.conj()) * k
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prev = b
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yield numpy.angle(prev[1:] * prev[:-1].conj()) * k
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if isinstance(d, types.GeneratorType):
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return g(d)
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else:
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return numpy.angle(d[1:] * d[:-1].conj())
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return numpy.angle(d[1:] * d[:-1].conj()) * k
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def modulateFm(sig, fs, fcenter=0):
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"""Create an FM modulated IQ signal.
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sig :: modulation signal, values in Hz
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fs :: sample rate in Hz
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fcenter :: center frequency in Hz
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"""
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return numpy.exp(2j * numpy.pi * (sig + fcenter).cumsum() / fs)
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def spectrum(d, fs=1, nfft=None, sortfreq=False):
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@ -232,11 +247,12 @@ def pll(d, centerfreq, bandwidth):
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return y, phasei, phaseq, phaseerr, freq, phase
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def pilotLevel(d, fs, freqshift, bw=150.0e3):
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def pilotLevel(d, fs, freqshift, nfft=None, bw=150.0e3):
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"""Calculate level of the 19 kHz pilot vs noise floor in the guard band.
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d :: block of raw I/Q samples or lazy I/Q sample stream
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fs :: sample frequency in Hz
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nfft :: FFT length
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freqshift :: frequency offset in Hz
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bw :: half-bandwidth of IF signal in Hz
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@ -255,10 +271,10 @@ def pilotLevel(d, fs, freqshift, bw=150.0e3):
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d = firFilter(d, b)
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# Demodulate FM.
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d = quadratureDetector(d)
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d = quadratureDetector(d, fs)
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# Power spectral density.
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f, q = spectrum(d, fs=fs, sortfreq=False)
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f, q = spectrum(d, fs=fs, nfft=nfft, sortfreq=False)
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# Locate 19 kHz bin.
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k19 = int(19.0e3 * len(q) / fs)
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@ -266,7 +282,7 @@ def pilotLevel(d, fs, freqshift, bw=150.0e3):
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k19 = k19 - kw + numpy.argmax(q[k19-kw:k19+kw])
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# Calculate pilot power.
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p19 = numpy.sum(q[k19-1:k19+2]) * fs * 0.75 / len(q)
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p19 = numpy.sum(q[k19-1:k19+2]) * fs * 1.5 / len(q)
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# Calculate noise floor in guard band.
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k17 = int(17.0e3 * len(q) / fs)
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@ -278,3 +294,66 @@ def pilotLevel(d, fs, freqshift, bw=150.0e3):
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return (p19db, guarddb, guarddb - p19db)
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def modulateAndReconstruct(sigfreq, sigampl, nsampl, fs, noisebw=None, ifbw=None, ifnoise=0):
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"""Create a pure sine wave, modulate to FM, add noise, filter, demodulate.
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sigfreq :: frequency of sine wave in Hz
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sigampl :: amplitude of sine wave in Hz (carrier swing)
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nsampl :: number of samples
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fs :: sample rate in Hz
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noisebw :: calculate noise after demodulation over this bandwidth
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ifbw :: IF filter bandwidth in Hz, or None for no filtering
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ifnoise :: IF noise level
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Return (ampl, phase, noise)
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where ampl is the amplitude of the reconstructed sine wave (~ sigampl)
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phase is the phase shift after reconstruction
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noise is the standard deviation of noise in the reconstructed signal
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"""
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# Make sine wave.
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sig0 = sigampl * numpy.sin(2*numpy.pi*sigfreq/fs * numpy.arange(nsampl))
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# Modulate to IF.
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fm = modulateFm(sig0, fs=fs, fcenter=0)
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# Add noise.
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if ifnoise:
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fm += numpy.sqrt(0.5) * numpy.random.normal(0, ifnoise, nsampl)
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fm += 1j * numpy.sqrt(0.5) * numpy.random.normal(0, ifnoise, nsampl)
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# Filter IF.
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if ifbw is not None:
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b = scipy.signal.firwin(61, 2.0 * ifbw / fs, window='nuttall')
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fm = scipy.signal.lfilter(b, 1, fm)
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fm = fm[61:]
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# Demodulate.
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sig1 = quadratureDetector(fm, fs=fs)
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# Fit original sine wave.
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k = len(sig1)
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m = numpy.zeros((k, 3))
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m[:,0] = numpy.sin(2*numpy.pi*sigfreq/fs * (numpy.arange(k) + nsampl - k))
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m[:,1] = numpy.cos(2*numpy.pi*sigfreq/fs * (numpy.arange(k) + nsampl - k))
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m[:,2] = 1
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fit = numpy.linalg.lstsq(m, sig1)
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csin, ccos, coffset = fit[0]
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del fit
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# Calculate amplitude, phase.
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ampl1 = numpy.sqrt(csin**2 + ccos**2)
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phase1 = numpy.arctan2(-ccos, csin)
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# Calculate residual noise.
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res1 = sig1 - m[:,0] * csin - m[:,1] * ccos
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if noisebw is not None:
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b = scipy.signal.firwin(61, 2.0 * noisebw / fs, window='nuttall')
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res1 = scipy.signal.lfilter(b, 1, res1)
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noise1 = numpy.sqrt(numpy.mean(res1 ** 2))
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return ampl1, phase1, noise1
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