Digital quadrature demodulator with four phases mixing for digital radio receivers

Abstract

A digital quadrature demodulator is proposed that gives the complex components of the received signal. The adoption of a modulated local oscillator (LO) with four periodic phase states synchronized with the sampling avoids the use of two mixing paths, simplifying the radio-frequency (RF) circuits and allowing an effective VLSI integration. This receiver minimizes the in-phase/quadrature (I/Q) mismatch and, with an adequate choice of the periodic modulating sequence, avoids the direct current (dc) offset of the direct conversion receivers.

Full text

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 50, NO. 12, DECEMBER 2003 1011
Digital Quadrature Demodulator With Four Phases Mixing
for Digital Radio Receivers
Ángel Bravo and Fernando Cruz-Roldán
Abstract—A digital quadrature demodulator is proposed that gives the
complex components of the received signal. The adoption of a modulated
local oscillator (LO) with four periodic phase states synchronized with the
sampling avoids the use of two mixing paths, simplifying the radio-fre-
quency (RF) circuits and allowing an effective VLSI integration. This re-
ceiverminimizesthein-phase/quadrature(I/Q)mismatchand,withanade-
quate choice of the periodic modulating sequence, avoids the direct current
(dc) offset of the direct conversion receivers.
Index Terms—Digital quadrature demodulator, digital receiver, direct
conversion receiver, low IF receivers, mismatch cancellation, VLSI
integration.
I. INTRODUCTION
The implementation of digital receivers is facilitated when the
analog-to-digital conversion (ADC) is performed in the initial stages
of the receiver. The sampling of RF signals is a difficult and expensive
matter and several alternatives have been devised to circumvent it.
Direct conversion radio receivers that work with the local oscillator
operating at the nominal reception frequency [1] have several advan-
tages: they do not suffer from image frequency interference and they
do not have intermediate frequency (IF) stages. However, they do have
two important problems: the dc-offset [2] and the in-phase/quadrature
(I/Q) mismatch. Low IF receivers [3] solve the former problem, but
the circuit and process are more complex as they need sharper filters
and the sampling rate is higher if some kind of subharmonic sampling
is not adopted [4]. Quadrature IF radio receivers [5] are able to solve
the later by using two parallel IF stages and additional circuitry and
process. They use the digital quadrature demodulator technique [4] to
produce the baseband I and Q signals. This technique simplifies the
circuitry and process when the ADC is a sigma delta (??) modulator.
With the exception of the low IF receiver, the receivers mentioned
so far use two signal paths to recover the complex received signal. The
adoption of a single path is desirable for two reasons: the minimization
of theI/Q mismatchand thesimplification ofthe analogcircuitry inthe
signal path.
In this paper, we extend the digital quadrature demodulator tech-
nique by introducing a phase modulation in the local oscillator (LO),
and forcing it to periodically run four-phase states coincident with the
sampling instants. As a result, the spectrum of the received signal gets
translated to low-frequency bands. The complex components are re-
covered using a single signal path, therefore, minimizing the I/Q mis-
ManuscriptreceivedFebruary20,2003;revisedJune12,2003.Thisworkwas
supported in part by the Regional Government of Madrid under Project CAM
07T/0025/2001 and in part by the Ministry of Science and Technology under
Project MCYT TIC2001-0751-C04-02.
The authors are with the Department of Teoría de Señal y Comunicaciones,
Escuela Politécnica, Universidad de Alcalá, Alcalá de Henares, Madrid, Spain
(e-mail: angel.bravo@uah.es).
Digital Object Identifier 10.1109/TCSII.2003.820244
match [6] that appears in classical receivers with two mixers: one for
each component.
The receiver proposed here has, however, some disadvantages. It
does not provides image rejection. This function is performed by the
the RF front-end as in classical heterodyne receivers and the sampling
frequency may be relatively high to avoid a narrow RF filter. More im-
plementation problems may arise from the fact that the modulation of
LO and the sampling at the ADC must be synchronized.
II. CONVERSION AND SAMPLING
We consider a receiver whose LO is phase modulated by a periodic
signal that has definite phase states at the instants associated with the
sampling. Let ???? be the phase modulating signal built with a phase
modulator pulse ???? and a periodic sequence ??
???? ?
?
??? ?? ? ?????
(1)
Themodulatingpulse????iszerooutsidetherange??????,??isthedu-
rationofthepulseanditsvalueattheparticulartime????is??????? ?
?. The sequence ??has a period of ?? and the value it takes depend on
the index ?, the even ?-indexes come from the set ????? and the odd
ones from ??????????.
The constraints imposed on both, the sequence ?? and the function
????,allowustosplitthesignalmodulatingtheLOintwo:oneaffecting
the I component and the other the Q component
???? ?
?
?? ?
???
???????????????????????????????????????
(2)
where ?? ? ????? and ?? ? ???????????
Let????and????be thelow-pass componentsofthe received signal
and ????? the low-pass signal at the output of the mixer
????? ??
???????? ???? ??
???????? ???? ?
(3)
Using the fact that the functions ??? ? ???? and ??? ? ???? are
nonoverlapping for ? ?? ?, the function ??? ???? is as seen in (4),
at the bottom of the page, where ???? is a rectangular pulse with a
height of one in the range ??????. A similar expression is obtained for
??? ???? .
It is not necessary to impose any condition on the shape of the pulse
????, other than its value at the particular argument ????. However, the
rectangular shape has two advantages: 1) the sampling window, i.e.,
the time period where the signal is viewed for sampling, is the biggest
possibleand2)itiseasytoimplementwithaphasemodulator.Thelow
pass signal with a rectangular pulse is
????? ??
?????
?
???
???
????? ? ????? ??????
??
?????
?
???
???
????? ? ??? ? ????? ??????
(5)
??? ???? ?
?
? ? ?
???
??????????????? ??? ????????????????? ?? ????????????????
??? ??? ????????????????
(4)
1057-7130/03$17.00 © 2003 IEEE
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1012IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 50, NO. 12, DECEMBER 2003
Fig. 1.4-phase rectangular modulating pulse. Shape and spectrum.
where ??? ???????, ??? ??????? and ?????? ???????.
By sampling ????? at times ?? ? ??????, ? ?
component from the even samples and the Q component from the odd
ones
, we obtain the I
?????? ???
???????
?
? ????????
?
???????
?? ??????
????? ? ?? ???
????????
?
? ?????????
?
???????
????? ? ?????
(6)
Therefore, the real part of the low-pass component of the received
signal is obtained from the even samples of ?????, after multiplying
these by the values of the sequence ??, i.e.,; ????? ? ?????? ??.
Similarly, ???? ? ?? ? ????? ? ?? ??. The properties of the se-
quences ???? and ???? are important as they influence the low-pass
signals ?????. If they do not have the zero-frequency component, or if
it is small, the low-pass signal will not have it either. In that case, dc
problems are avoided. In our simulations we use the sequences ?? ?
?????????????????? and ?? ? ??????????????????. The corre-
sponding modulating shape and its Fourier series coefficients are pre-
sented in Fig. 1. Note that ???? and ???? are not time aligned. They can
be aligned using interpolation.
Weuse rectangularmodulating pulses, but other shapes arealso pos-
sible. If the pulses have a linear slope and there are no discontinu-
ities in the transition between adjacent pulses, i.e., the phase varies lin-
early with the time, then the LO carrier will have a constant frequency
added to it. In this case, the LO is not modulated and its frequency
??? is related to the sampling rate ????by the following expression:
??? ? ??? ???????, with ??being the nominal reception frequency.
In this case, the sequences ??and ??are the same as those previously
described. A related result appears in [4] where the IF signal is sam-
pled at ????, with ??? being the angular value of the IF. The sign
inversion and time alignment of the samples of the I and Q compo-
nents are carried out as described above. The value of the IF can cause
a high-sampling rate and subharmonic sampling is used in order to re-
duce the sampling rate. These limitations do not appear in the receiver
that we present.
III. IMPLEMENTATION AND SIMULATION OF THE RECEIVER
The general block diagram of the receiver is shown in Fig. 2, where
we have included the RF source and the power meter used to test it.
We have simulated it using custom C++ code. The image frequencies
closest to the central one, caused by the sampling, appear at ?? ? ???
?????, ? ?
. This is due to the effective sampling of ???? and ????
with a period ???. The main function of the RF filter is to attenuate
them and, if ???? is high enough, the RF filter is not narrowband. If,
for instance, ????? ??? MHz, the attenuation at ?????? MHz must
be larger than the specified value for the image rejection.
The mixer is considered ideal, with no noise, and the post mixer
filter (PMF) transforms the spectrum of the modulated LO in order to
avoid interferences between adjacent or close samples. The combined
spectrumofthepulse????in(5)andthePMFmusthaveaNyquistfilter
shape [7], for instance, a raised cosine (RS) filter. The specifications of
this filter are known as the period ?? is fixed, assuming a particular
value of the filter parameter ?. The maximum bandwidth of the PMF
filter is a significant fraction of ????, i.e., the filter is not narrowband.
For ???? ? ??? MHz the bandwidth is about 100 MHz. The delay of
the PMF has to be taken into account in order to perform the sampling
at the appropriate instants. The actual implementation of the filter is
affordable as its frequency response shape is not sharp.
The output of the PMF feeds the sampler that operates at a rate of
????, synchronously with the modulation of the LO. The ADC works
with a number of bits/samples high enough to allow a large dynamic
range; 8 b sample renders a dynamic range of about 50 dB [7], that is
lower than that of the signals at the input of the receiver: 90–100 dB.
Increasing the number of bits/samples at the ADC is expensive and
oversampling can reduce this figure by 1 b per 4 oversampling factors.
Oversamplingisneededinordertoincreasethegapbetweenthecentral
frequencyofthereceivedsignalandtheimagefrequencies.Thisavoids
the need to use narrow RF filters.
Therestoftheelementsofthereceivercarryouttheinterpolationand
time alignment mentioned earlier. The LPF1 filter works at the high-
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 50, NO. 12, DECEMBER 20031013
Fig. 2.Block diagram of the receiver.
Fig. 3. Interference results with 4-phase rectangular modulating pulse.
sampling rate. However, its specifications are not very strict as the sub-
sequentfilter,atalowrate,cangivethesharpestattenuationprofile.This
situationisparalleltothatofanalogreceiverswithtwoIFs.
A frequency sweep has been performed using the diagram in Fig. 2
inorder toseek possibleinterfering sinusoidal signals. Thesimulations
have been performed with the 4-phase LO modulation previously men-
tioned and without LO modulation. In the latter case, the PMF was im-
plemented with a bandpass IF filter. The ADC bits/sample was set with
the computer float representation in order to register very low-signal
levels.TheresultsareshowninFigs.3and4,respectively.TheRFfilter
wasdesignedtoattenuate60-dBimagefrequenciesat??? ????????.
The main difference between the two alternatives is that the LO mod-
ulation generates image frequencies below the central reception fre-
quency. After RF filtering, both alternatives have image components
below a prescribed level.
The use of an LO without modulation is advantageous when the
transmitter and receiver operate in an uncoordinated way. However, it
is possible to share the same modulated carrier with the transmitter and
in this case the circuits are simpler.
In order to test the noise behavior, a noise source has been used as
an RF generator together with an RF sinusoidal source in the receiver
band.Thesignal-to-noiseratio(SNR)overthenominalreceptionband-
widthwasadjustedtoavalueof27dB.ThemeasuredSNRattheoutput
of the receiver was 25.12 dB, a value very similar to the input SNR.
The dominant internal source of SNR degradation of this receiver is
the quantization distortion and this perturbation has little impact if the
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1014IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 50, NO. 12, DECEMBER 2003
Fig. 4.Interference results with unmodulated LO.
Fig. 5.Receiver response to a GMSK modulated carrier.
external noise is high enough. The input signal and noise levels were
chosen with this purpose and the small reduction of the output SNR
shows that the above assumption is correct.
An RF carrier modulated by a GMSK signal with ?? ? ??? has
been used to test the whole receiver. We adopted a quantization value
of 8-b/sample. The output of the receiver is shown in Fig. 5 where we
present the RF, I and Q signals. The output and the RF modulating
signals are very similar.
With the aim of testing the signal plus quantization distortion and
the dynamic range, two sinusoidal signals are applied, in the recep-
tion frequency band, to the input of the receiver. One of the signals has
themaximum undistortedlevel,inourcase,???? relativepower. The
otherhasalowlevel.Thenumberofbits/sampleoftheADCwas8.The
spectrumoftheIandQsignalsisregistered.InFig.6wepresentthere-
sults obtained when the low level signal is 70-dB below the high–level
signal. The x axis is labeled with frequencies normalized to the max-
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 50, NO. 12, DECEMBER 20031015
Fig. 6.Signals and quantization noise at the receiver output with two sinusoidal signals at the input.
mum aliasing free frequency. In this case, this frequency is determined
by the low sampling rate. The ratio of strong signal to weak signal is
dependent on frequency offset due to shaped quantization noise floor.
A rough estimation of the quantization distortion value obtained from
Fig. 6 is ??? dB relative power over bandwidth 0.1 Hz. This figure
can be considered as the minimum distinguishable signal value. The
dynamic range is the difference between the value of the levels of the
high and low signals: ? ?? dB in the present case. Fig. 6 shows that
although the low-level signal is below the minimum signal level, it is
distinguishable.
Receiver blocking is determined by the saturation of some of its
stages. Dynamic range influences this characteristic but, with no
knowledge of the RF amplifier gain, it is not possible to give a precise
indication of its value.
IV. CONCLUSION
A digital receiver with the LO linked to the sampling circuit is pre-
sented. The converted signal does not have dc components and the
low-passcomplexcomponentsofthereceivedsignalsareobtainedwith
a simple sampling process. The receiver uses a single-mixing path,
minimizing the I/Q mismatch and, if the sampling rate is high enough,
the RF front-end does not need sharp filters, allowing for an effective
integration.
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