1 2+Peter+H%C3%A4ndel+Slides
Transcript of 1 2+Peter+H%C3%A4ndel+Slides
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INVESTIGATING THE USRP: I/Q IMBALANCE
Peter Hndel and Per Zetterberg
Signal Processing Lab
ACCESS Linnaeus Center
Royal Institute of Technology
Stockholm, Sweden
RFMTC09, October 6-7, 2009, Gvle, Sweden.
THE RESEARCH LEADING TO THESE RESULTS HAS RECEIVED FUNDING FROM THE EUROPEAN
RESEARCH COUNCIL UNDER THE EUROPEANCOMMUNITYSS EVENTH FRAMEWORKPROGRAMME
(FP7/2007-2013) / ERC GRANT AGREEMENT NO. 228044 (AMIMOS).
Available atwww.ee.kth.se Forskning Publikationer
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PURPOSE OF THE WORK
Design methodologies
buy hardware plug it in something does not work
buy hardware test it (and replace if needed) plug it insomething does not work, but at least the hardware is ok
Fast and simple test routines . . .
. . . are advantageous for development purposes
. . . needed in production testing every second is worth a million
Contributions in this work:
Test procedure for receiver IQ imbalance
Measurement of KTH USRPs (# 4)
New insights in seven-parameter sinewave fit (baseband model,
L-phenomena)
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1.7 GHZ TONE EXCITATION - BASEBAND OUTPUT
HP8656B
SIGNALGEN
RADIO FREQUENCY BASEBAND
1.7646 GHz
-60dBm
MINI-CIRCUITS
FK300
MINI-CIRCUITS
SHP-900
HP-FILTER
S P L I T T E R
Z A P D
- 3 0
USRP
I/Q CHANNEL 2
I/Q CHANNEL 1
MINI-CIRCUITS
ATTENUATORS
-40dB
2 1.5 1 0.5 0 0.5 1 1.5 290
80
70
60
50
40
30
20
10
0
FR
P
F
2F
3F 2F
C
F
1.5 1 0.5 0 0.5 1 1.51.5
1
0.5
0
0.5
1
1.5
INPHASE
QUADRATURE
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PERFECT I/Q DEMODULATOR
Baseband representation of theRF inputsin(2FRFt)
zn=xn+j yn = cos(on) +j sin(on) =ejon (1)
(relatively an arbitrary scaling, absolute time, or initial phase)
angular frequencyo = 2F/FS = 0.6/4 = 0.15
F =FRFFLO = 1764.61764.0 = 0.6MHz
FS,FRF andFLO are not required for the proposed test method
FLO 10-20 kHz for the USRP
BP-
FILTER
BP-
FILTER
LP-
FILTER
LP-
FILTER
LNAcos
sin LO
ADC
ADC
IN-PHASE
QUADRATURE
VGA
VGA
RF INPUT
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PRACTICAL I/Q DEMODULATOR
in-phase representation of the RF stimuli
xn =gI sinon+I+
2+cI+v
In (2)
quadrature
yn =gQ sin
on+Q
+cQ+vQn. (3)
gI, gQ are gains;I, Qinitial phases;cI, cQDC offsets;vIn andvQnare noise terms
Parameters of interest
gain imbalanceG = gIgQ
quadrature skewQ =IQ
LO leakageL = 2
c2I+c2
Q
g2I+g2Q
BP-FILTER
BP-FILTER
LP-
FILTER
LP-
FILTER
LNA
cossin
LO
ADC
ADC
IN-PHASE
QUADRATURE
VGA
VGA
RF INPUT
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REFORMULATION OF PROBLEM
Baseband datazn=xn+j yn can be written as
zn=a ein +b ein +c+vn. (4)
a,b care complex-valued constants
vn complex-valued zero mean noise
Parameters of interest
gain imbalanceG = |a+b|
|ab|
quadrature skewQ = a+b
ab LO leakageL =
|c|2
|a|2 +|b|2
Based on{zn}N1 find estimatesa,b,cand(7 parameters)
BP-
FILTER
BP-
FILTER
LP-
FILTER
LP-
FILTER
LNAcos
sin LO
ADC
ADC
IN-PHASE
QUADRATURE
VGA
VGA
RF INPUT
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NON-LINEAR LEAST-SQUARES ESTIMATION
1. found by a one-dimensional search (Periodogram-type of costfunction)
2.a,bclinear least-squares based on3.G,QandLfroma,bc Comments
Slight modification of a classical spectral estimation problem
Gaussian noise, but no need for maximum likelihood, because
the practical performance is independent on the noise variances in
I and Q channels.
NLS equals MLE when the channels have same noise power.
NLS solves the same problem as seven-parameter fit (P.M. Ramos),
but in a different way
Asymptotic Cramr-Rao bounds available for the estimates.
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Theorem 1: Consider any unbiased estimator producing the estimatesG,Q,andLbased on the receiver outputz. If
noise is Gaussian
number of samples large
then the asymptotic variances are bounded from below by:
2G
= 1 +G2
NSNRQ(5)
2Q= 1 +G2
NSNRI(6)
2L = 2L(1 +L)
NSNR(7)
whereSNRdenotes the average SNR, that isSNR= (SNRI+SNRQ)/2.
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MATLAB: NON-LINEAR LEAST-SQUARES
function []=iqmain(y);
y=y/sqrt(cov(y)); N = length(y); T =(1:N)';
%Frequency estimate - requires IQparest.m and myfun2.m
west = IQparest(y,4);
%LS-fit of linear parameters
zhat = exp(i*west*T);
Zhat = [zhat conj(zhat) ones(N,1)];
hateta = Zhat\y;%Extract a, b, c
hata = hateta(1);
hatb = conj(hateta(2));
hatc = hateta(end);
%% Calculate quantities of interest
G = abs(hata+hatb)/abs(hata-hatb);
Q = angle((hata+hatb)/(hata-hatb));
L = abs(hatc)^2/(abs(hata)^2 + abs(hatb)^2);
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MATLAB: EXAMPLE OF RESULTS
>> iqmain(z)
---
data sequence length N: 50000
gain imbalance G: -0.1319 dB
quadrature skew Q: -1.8305 deg
LO leakage: -27.134 dB
>>
Results presented in dB and deegrees
Elapsed time (Intel [email protected] - old laptop)
N= 1024: Elapsed time is 0.023951 seconds
N= 50000: Elapsed time is 0.579940 seconds
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DATASHEET VALUES FOR AD8347 AT 1.905 GHZ
The FLEXRF family of daughter-boards, which are widely used with the
USRP platform, is designed around the AD8347 direct conversion
quadrature demodulator.
Typ (Min/Max)
GdB +0.3 dB
Qo 1 (3) degreeLdBm 60 dBm (at RFIP)
LdBm 42 dBm (At IMXO/QMXO)
(Practitioner) Collect large number of data and run, but . . .
. . . (Rapid testing) is it sufficient with a handful of periods?
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GAIN IMBALANCE AND QUADRATURE SKEW
0 0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
8 7 6 5 4 3 2
0.1
0.2
0.3
0.4
GdB (dB)
Qo (deg)
norm
norm
USRP results based on non-overlapping segments (N= 64). USRP #1:
Channel 1 (), Channel 2 (), USRP #2: Channel 1 (), Channel 2 ().
GandQ can be estimated from short sample records (hereN= 64)
1 out of 4 receives with outlier performance
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LO LEAKAGE
Datashet:LdBm =60dBm (at AD8347 RFIP) RFIP:PRFIP=PRF+ 13 dBm (MGA-82563)LdBm =60 + 13 +LdB
LdBm
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CONCLUSIONS
Tone test for IQ imbalance
Low-complexity and (almost statistically) efficient
Same LS-problem solved as by seven-parameter fit (P.M. Ramos)
KTH USRPs
3 out 4 USRPs have performance according to the data-sheet
Outlier performance isolated to one FLEXRF1800
Efficient LO leakage compensation (enabled as default)
Estimator properties
N= 64sufficient forG (0.1dB) andQ (0.5deg)
N= 64L spread40 dB and bias15 dB!
N= 16k needed forL within a couple of dBs
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