USRP N210 quickstart

For various experiments I got an USRP N210. Here's how to get going with gnuradio.

By default it shows up at, so configure your PC eth-interface on 192.168.10.XXX. Now

$ uhd_find_devices

Should find the device:

-- UHD Device 0
Device Address:
type: usrp2

However uhd_usrp_probe suggest upgrading the firmware and FPGA image, so we do that by:

$ sudo /usr/lib/uhd/utils/

$ sudo /usr/bin/uhd_image_loader --args="type=usrp2,addr="

and after power-cycling the device we now get (in addition to a long description of the RX and TX interfaces or installed daughter-boards):

$ uhd_usrp_probe
FW Version: 12.4
FPGA Version: 11.1

To show that it works in gnuradio a simple USRP-source can be connected to a QT GUI Sink (or QT GUI Frequency Sink) that visualizes RX I/Q samples:
The source needs to be configured with "addr=" and it uses the samp_rate, freq, and gain variables.

The USRP now samples at 100 MS/s, digitally downconverts a bandwidth samp_rate around a center frequency freq, and streams the samples over Ethernet to the gnuradio source node. When setting freq=10e6 and samp_rate=200k (the minimum possible!?) and applying a 10.020 MHz sine-wave to the RF1-input we get this:

With a signal that seems close to maximum amplitude the dB-scale shows a peak at -16 dB, and without any signal applied the noise-floor close to the center frequency dips just below -140 dB rising to -135 dB at 20 kHz offset.

Awesome stuff! The 200 kS/s samples from one I/Q channel produce about 800 kB/s of Ethernet traffic.

Stay tuned for more SDR updates in the near future!

Espoorastit Ämmässuo

After a long walk to the start #1 went OK, a bit far north on #2, fairly safe route to #3. #5-#6 is probably the worst split as the open area was slow and my position was uncertain after the road. #7 was more nicer terrain for a change. At the end drifted too much south at #11 - this is an area that has been difficult before also...

Nice weather with a bit of wind. A lot of people preparing for Jukola in 1.5 weeks.


scipy.stats.chi2.ppf() without scipy

Allantools has a dependence on scipy because it uses scipy.stats.chi2.ppf() (inverse of the chi-squared cumulative distribution function) in the code for confidence intervals.

When testing scipy takes quite a long time to install and the whole package seems a bit overkill for just this one function.

So I tried implementing it using just numpy. It sort of works, but not for corner cases where p is very close to 1.0 or k is a big number. I get for example:

    top = pow(x, s)*math.exp(-x)*pow(x,k)
OverflowError: (34, 'Numerical result out of range')

Maybe there's something trick when numerically evaluating lower_gamma() using the series expansion that I am missing...

import scipy.stats
import math
import numpy
def bisection(function, k, p, a, b, tol):
	assert (function(a,k)-p)*(function(b,k)-p) < 0 # a, b must bracket root
	c = (a+b)/2.0
	while (b-a)/2.0 > tol:
		if (function(c, k)-p) == 0:
			return c
		elif (function(a,k)-p)*(function(c,k)-p) < 0:
			b = c
		else :
			a = c
		c = (a+b)/2.0
	return c
def lower_gamma(s,x):
	# lower incomplete gamma function
	g  = 0
	last_g = 1.0
	done = False
	tol = 1.0e-6
	while not done:
		top = pow(x, s)*math.exp(-x)*pow(x,k)
		bot = [float(s+j) for j in range(k+1) ] )
		dg = float(top)/float(bot)
		if dg == float("Inf"):
		g += dg
		k += 1
		if k>100: # get at least 100 terms in the sum
			if g==0:
			delta = abs(dg/g)
			if delta == float("Inf"):
			if delta < tol:
				done = True
		last_g = g
	return g
def chi2_cdf(x, k):
	# chi-squared cumulative density function
	# cdf(x; k) = lower_gamma(k/2, x/2) / gamma(k/2)
	return lower_gamma(k/2.0, x/2.0) / math.gamma(k/2.0)
def chi2_ppf(p, k):
	# chi-squared Percent point function (inverse of cdf percentiles).
	# look for x such that
	# p = chi2_cdf( x=chi2_ppf(p, k), k)
	tol = 1e-8
	lolim = 0
	hilim = k
	while (chi2_cdf(lolim,k)-p)*(chi2_cdf(hilim,k)-p) > 0: 
		hilim *= 1.5
	return bisection( chi2_cdf, k, p, lolim, hilim, tol)
print "scipy cdf: ",scipy.stats.chi2.cdf(55, 33)	
print "own   cdf: ",chi2_cdf(55, 33)
print "scipy ppf ", scipy.stats.chi2.ppf(0.4, 33)
print "  own ppf ", chi2_ppf(0.4, 33)
# test that we really found the inverse
print scipy.stats.chi2.cdf(scipy.stats.chi2.ppf(0.4, 33), 33)
print chi2_cdf( chi2_ppf(0.4, 33), 33 )
# try to check the scipy function against our own function
# for some random input of (p, k)
for n in range(100):
	k = numpy.random.randint(20, 200)
	p = numpy.random.random()
	print k, p,
	a=scipy.stats.chi2.ppf(p, k)
	b=chi2_ppf(p, k)
	ok = numpy.isclose(a, b)
	if ok:
		print  ok
		print  ok, a, b
	assert ok