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Microwaves and RF
Peter DelosFri, 2014-09-12 13:52
With digital beamforming phased arrays continuing to grow in
popularity, Lockheed Martin's Peter Delos runsdown crucial concepts
for those designing receivers to keep in mind.
Introduction
Digital beamforming phased arrays are becoming an increasingly
common antenna product both for defenseand commercial applications.
The primary technological advancement making this possible is the
developmentof high performance miniaturized and highly integrated
receivers. Much literature exists on receiver design as asingle
entity. This tutorial is intended to summarize the collection of
receiver design considerations withemphasis on impact to the
digital beam-forming phased array application.
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The subject is approached by first describing distributed
receiver correlated versus uncorrelated errors thathistorically
have not been considered for systems with a single centralized
receiver. This is followed by adetailed evaluation of both a direct
conversion receiver and a super-heterodyne receiver. Channel
paircancellation is introduced and is directly related to the
ability to form nulls in the antenna pattern. Theconcluding section
contains some additional receiver terms for completeness.
Digital Beamforming Application Overview
The digital beam-forming concept is shown in Fig. 1. The
phased-array antenna is made up of many elementsand many receivers.
The number of receivers may be less than the number of elements. An
every elementsystem is defined as having a receiver for every
element. In many cases this becomes impractical due to size or
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power constraints. For these cases, an analog beam-former is
used before the receivers. The analogbeam-former could be power
combining of several elements or a weighted sum of overlapped
elements. Thereceivers convert the RF frequency to a digital
output. Processing is performed to compute the antenna patternand
numerous patterns can be processed simultaneously.
Many references exist on digital beam-forming methods and
antenna design. The scope of this discussion is tosummarize
considerations for the receiver design in this application.
Correlated Versus Uncorrelated Error Terms
A digital beam-forming system sums weighted versions of every
receiver output to form antenna patterns. Acalibration is performed
to ensure the desired signals add coherently. A system concern is
the effect of receivererrors through the digital beam-forming
process.
Consider the sum of two error voltage terms, written as:
Error terms that are uncorrelated (c = 0) reduce by l0logN,
where N is the number of receiver channels.Correlated errors (c =
1) add coherently across the array and do not reduce at the system
level. If an error termis perfectly matched across all the
receivers, the system error will be the same as the individual
receiver error.Thus, tracking of correlated and uncorrelated error
terms in the system is a primary concern.
As each error term is evaluated, it can be broken down into
correlated and uncorrelated components:
Mixer Spurious Components
A mixer is a form of analog multiplication. The intention is to
reduce the received RF frequency to a lowerfrequency by
multiplication with an LO. An ideal frequency translation would
be:
The upper sideband can be filtered and the difference frequency
is used. Unfortunately, during the mixingprocess with practical
components, harmonics of both the LO and the RF frequency are
created and also
multiplied together. The multiplication of harmonics creates
additional frequencies.18 The accumulation offrequencies created is
written as:
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In receiver design, great care is taken in frequency planning to
avoid in-bandspurious. For digital beamforming, the frequency
planning effort remains,however an additional consideration is
ensuring the spurious signals aredecorrelated across the array of
receivers. A proven method to ensure mixerspurious decorrelate is
to add a phase shifter in the LO path and provide a
digitally controlled random LO phase across the array.6 Consider
the cosinemultiplication of a particular harmonic as:
Filtering the harmonic leaves the in-band spur of:
The calibration is on the primary signal when n = m = 1, and the
phase shift is removed. For the mth harmonicthe spur is rotated an
additional amount m. The method requires phase shift control of a
complete 360-deg.range but does not require great phase shift
accuracy.
Distributed PLL Considerations
A method to distribute LO frequencies to all the receivers is
necessary. This could be a centrallized LO, adistributed LO
generated locally at every receiver, or an in-between approach with
an LO generated for somenumber of receivers.
A centralized LO distributed to all the receivers will provide a
common reference to all the receivers. Howeverthe LO noise will
also be a correlated noise source across the array. To achieve the
noise benefit of combinedreceivers the LO noise must be 10logN
better than a single receiver where N is the number of
elements.
A distributed LO relaxes the noise requirements for the LO
generation, but comes with some additionalconsiderations. A
reference is still needed and must be distributed to the LO
generation circuitalthough thereference is typically at a lower
frequency, which is easier to distribute. All the distributed LOs
maintain theirrelative phase across the array at the completion of
the antenna calibration. If this is not maintained, thecalibration
to align all the receivers is no longer valid. This requirement can
limit the options of implementationmethods for distributed LO
generation. In theory, a distributed integer N PLL can achieve
this, but absolutephase errors need to be specified for the
application; if the PLL output is used for any digital clocks, no
cycleslips can be tolerated from the PLL.
Direct conversion receivers, also known as Zero-IF or homodyne
receivers, offer significant advantages inimplementation for a
wideband receiver. Complications in direct conversion receivers are
well documented, andinclude LO leakage, in-band IF harmonics, and
the IQ image.
A block diagram of a direct conversion receiver is shown in Fig.
3. The input RF signal is mixed with two LOsignals that are
identical in frequency, but 90 deg. out of phase. This mixing
scheme is called a quadraturedemodulator and creates the I/Q
channels directly that are then sampled by two A/D converters.
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In-Band LO Concerns
In a direct conversion receiver the LO is in the center of the
received band. In any mixing system there arepractical isolation
limits. Mixers specify the isolation among their ports. There are
several conducted andradiated isolation paths of concern for a
direct conversion receiver. Each one will be systematically
evaluated.
The first concern is LO energy radiated out of the receive
antenna. The LO will conduct to the RF port at a levelbased on the
LO power level and the mixer LO to RF isolation. This unwanted
energy will continue toward theradiating element based on the S12
of each component. Since the LO is in the operating band, there is
noadditional filtering to help suppress this signal. In a phased
array, power will be radiated back into the air at asum of the LO
leakage from all the receivers. The energy likely will not
correlate due to provisions for spurdecorrelation; however, it will
non-coherently sum to a broad antenna pattern of radiated energy.
The concernfor this term depends on the system specifications for
radiated power during receive.
Some amount of LO energy can will be radiated to the front of
the LNA. The severity of this leakage pathdepends on the circuit
layout. This can also result in radiated LO power, but the primary
concern for this path isthat it can be amplified by the LNA,
increased in power and delivered to the mixer similar to any other
receivesignal. Once in the mixer, this will mix to a DC term at the
IF port.
An in-band LO can also degrade the noise figure contribution of
the mixer. The LO will have a sideband noiselevel that needs to be
considered. This noise will appear at the RF and IF ports on the
mixer attenuated by theLO to RF and IF isolation. This noise can be
above thermal noise in many cases and becomes an additional
termdegrading mixer noise figure.
The leakage paths above are discussed in many of the references.
An additional area for phased arrays not
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widely discussed is conducted leakage degrading channel to
channel isolation. Just as the LO can conductthrough reverse
isolation to the radiating element, the RF from one channel can
conduct to other channelsthrough the LO distribution. Filtering
available in heterodyne receivers can alleviate this problem but,
in adirect conversion phased array, reverse isolation of
distribution components should be compatible with channelto channel
isolation requirements.
IP2
IP2 can be a dominant concern in direct conversion receivers.
The second and third order distortion terms canbe modelled as:
The concern with second order distortion is any input signal
whether in band or out of band the gets into the
mixer will down-convert to DC. This can be seen observing a cos2
identity.
The IQ image is formed from amplitude and phase errors in the
quadrature demodulators and is also welldocumented. For a phased
array, distributed digital beam-forming architecture, the dominant
concern with theIQ image is to develop a method that will ensure
the image term decorrelates. Decorellation of the IQ image
willallow 10logN improvement through beamforming gain in a manner
similar to noise terms.
The ideal output of the quadrature demodulator is:
By including amplitude error, e, and a phase error, , the output
of the quadrature demodulator becomes:
Identities used in the next derivation include:
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The quadrature demodulator output can be rewritten as:
The term ejWIFt represents the primary signal and the term
e-jWIFt represents the image.
The complete baseband signal can now be rewritten as:
The term e-j/2 can be ignored as a constant phase shift. The
primary signal terms can be assigned K1 and theimage signal K2, and
the magnitude of the image defined as an image reject
ratio(IRR).
Image Reject Ratio as a function of amplitude and phase are are
shown in Fig. 5. Practical limitations in theanalog circuitry
typically limit the image rejection ratio to ~40dB. Digital
corrections can be applied and someanalyses have claimed image
reject ratio improved toward 60 dB.
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The above image rejection analysis is not new. The advancement
will come in using the analysis to develop amethod to ensure IQ
image is not correlated across an array of receivers.
Equations 12 and 13 track the error terms of the primary signal
and the image in a form that allows coherentaddition. Through
beam-forming the terms can be coherently added to form a combined
image rejection ratioas:
To consider the effect in summing K1 and K2, consider breaking
the error terms further into terms that are
common (or correlated) across the receivers, and terms that are
random across the receivers:
K1 and K2 can now be expanded to:
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Through addition of K1 and K2 across many receivers, the random
terms will decorrelate and their contribution
will approach zero. However, the correlated amplitude or phase
error terms will remain and dominate theCombined Image Rejection
Ratio.
The error terms begin with analog errors in the quadrature
demodulator. If these errors can be made trulyrandom, then a 10logN
benefit should be realized through digital beam-forming gain.
Through mass productionof the RFICs, it seems highly likely the
analog errors will be consistent and thus correlated across the
receivers.If the assumption of consistency in the RFICs is correct,
efforts to improve analog circuitry may yield littlebenefit in a
distributed system.
A digital error correction appears as a viable method to remove
the correlated errors. In general a digitalcorrection will improve
the IQ image to within SNR limits of the measurements. The
calibration limitations arefrom noise and thus random. Therefore if
the output of the digital correction is truly random across
thereceivers, then a 10logN benefit could be realized in addition
to the improvement of a single receiver.
LO Quadrature Generation
A common method for generation of the LO frequencies (the 0- and
90-deg. LO signals to the mixers) is to use adigital frequency
divider and tap different nodes within the latch circuits. Digital
frequency dividers can bemade easily, with very low noise, very
broadband, and a high upper frequency limit. The quadrature
accuracy isalso very good because the nodes tapped are digital and
controlled by the clocks to the divider. The concern withthis
method of quadrature generation is that if the LO is interrupted
during the frequency transition, the dividerwill reset and come up
in one of two possible phase states.
This problem requires careful coordination with the LO
synthesizer design to ensure all dividers remain in sync,or
coordination with the system level calibration to provide a method
for a rapid calibration during thissituation. The frequency divider
method also requires an input at twice the LO frequency and is
anotherconsideration for impact in the synthesizer design.
An alternate method is to provide a quadrature phase shifter.
This method is analog and does not have anystartup concerns; the
input frequency is the LO frequency used by the mixers. The
compromise with thismethod could be additional noise and limited
broadband accuracy depending on the specific method chosen.
Many errors result in a DC term. The IP2 term any frequency into
the mixer results in DC. LO leakage into thereceive path self-mixes
with the LO and creates DC. One noise consideration is that flicker
noise in the IF chainfollows a 1/f curve, causing the overall noise
to be higher for any near DC reception. For these reasons
manydirect-conversion systems implement a DC null. This could be
with a capacitive coupled highpass filter, or acontrol loop to
remove the DC bias.
Another concern is any two signals closely spaced and separated
by f in frequency that get to the mixer willmix together to create
a baseband signal at f.
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The Super-Heterodyne Receiver
When the disadvantages described for the direct conversion
architecture cannot be overcome to meet thesystem specifications,
an alternate method is needed. The superheterodyne receiver
mitigates every problempreviously discussed with direct conversion.
The expense paid is added complexity. There are times, however,when
the added complexity is worth the price in order to achieve the
performance objectives.
The super-heterodyne receiver dates back to a 1918 invention by
Edwin Armstrong.14,15 The term"heterodyning" sounds impressive, but
is just the concept of mixing two signals together to create a
lower beatfrequency. In Armstrongs concept the incoming RF is mixed
with an LO to a lower intermediate frequency (IF).This intermediate
frequency is filtered and sent to a detection circuit to extract
the modulated informationsignal. Numerous variations and
improvements have been made over the years, and this architecture
becamethe standard for almost all radio and television receivers in
the 20th Century.
Figure 6 shows a high end super-heterodyne architecture. The
variation shown is a dual down-conversion typewith many features
desirable in a high performance receiver. It is worth considering
this implementation, thefunctions of each component, and the
frequency plan impact. Once the approach is understood,
componentsunnecessary in particular receiver design and
requirements can be removed.
The RF path starts with a filter bank consisting of overlapped
filters covering the operating band. Thisfrequency is mixed to an
intermediate frequency and filtered. The intermediate frequency is
chosen high enoughthat image rejection can be provided by the front
end RF filters. When the intermediate frequency is too high
tosample in the A/D directly an additional down-conversion is added
to produce a 2nd intermediate frequency.An antialiasing filter is
provided prior to A/D sampling. Gain control is provided at every
frequency to allowprogrammable optimization of gain, noise figure
(NF), and the input third order intercept (ITOI).
Additional low pass filters are provided before every mixer to
ensure the amplifier harmonics do not dominatethe mixer spurious.
Low pass filters are provided after every mixer to filter the image
helping relax the ultimatebroadband rejection of the band-pass
filter. Limiting protection is provided prior to the LNA and
protection isalso provided before the A/D to prevent damage if the
final amplifier saturates.
Early in the receiver design the A/D operation is chosen.
Sampling in the 2nd Nyquist zone has become popular.The primary
benefits are that the 2nd IF harmonics produced either in the mixer
or in amplifier non-linearities
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are out of band and can be filtered. Sampling in a higher
Nyquist zone produces a digital downconversion andcan be quite
useful when frequency planning. The primary compromise of IF
sampling is the A/D performancedegrades as the input frequency
increases. This concern must be balanced with other tradeoffs in
the overallreceiver design.
Figure 8 shows an example frequency translation diagram. An
operating band filter is selected, the input mixeswith the 1st LO
to produce a signal in the IF filter range. The 1st IF mixes to
with the 2nd LO to create the 2ndIF which is sampled and creates
the digital output.
A single downconversion could also be considered. Considerations
for this option include sample rate requiredfrom the data
converters balanced with adequate image rejection in the
downconversion.
As a general statement, a properly designed superheterodyne
receiver will have far superior sensitivity andimmunity to
interference when compared to a direct conversion receiver. For a
phased array digitalbeam-forming the challenge becomes size, power,
and cost constraints when many receivers are needed acrossthe
array.
In modern digital beam-forming antennas, the ability to create
nulls in the antenna pattern has increasedimportance for operation
in high interference environments. The depth of the nulls in
limited by error terms inthe antenna receivers. Channel Pair
Cancellation Ratio (CPCR) has been established as the system
levelperformance metric in this area.
CPCR is a measure of how well a common input signal can be
cancelled between receivers. It represents howwell the receivers
can be matched after equalization. CPCR can be defined as an input
jamming-to-noise ratiodivided by an output jamming-to-noise
ratio.
CPCR can be conceptualized as shown in Fig. 9. In this example a
dual down conversion receiver is shown. Theequalizer is calculated
during the calibration process and is intended to match the two
receivers. A common RFinput signal is injected into both receivers.
The 2nd IF signal is digitized by the A/Ds and run through
anequalizer. One equalization output is subtracted from the other
and a residue remains. This residue left over isdue to mismatches
in the receivers. The residue relative to the input signal is in
effect the CPCR between the tworeceivers.
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It should be noted that until this point our goal was to ensure
all errors were uncorrelated across the array.CPCR has the opposite
objective. Correlated errors will cancel; uncorrelated errors will
not. Some of thehardware errors limiting CPCR performance are
referenced in ref. 8.
Additional Receiver Parameters
Sensitivity
Receiver sensitivity is a system metric given to any receiver.
It is generally the minimum signal level detectablewith some
probability of detection. The value is a function of the receiver
noise figure and gain, the modulationbandwidth (and thus the noise
bandwidth), the processing gain of the waveform, and the
integration gain (ifmultiple pulses are integrated). During the
specification and component parameter allocation stage of
thereceiver design, the parameters for receiver sensitivity in
system should be clearly defined.
Out-of-Band Blocking
Immunity to out of band interference is a critical performance
metric for any receiver. Typically one may thinkof measurable
frequencies ending up in band somewhere in the receive chain. An
alternate metric proposed inref. 20 is a measure of compression in
the front end of the receiver. Even if the filters reject the
interferencesomewhere in the receive chain, a large interference
signal can saturate the receiver front end and alter thereceive
gain in small amounts of a percentage of a dB. This could seem
harmless, but with a pulsed interferer,gain changes in the receiver
can result in a measurable modulation on the carrier.
Cascaded Analysis
As specifications are flowed to the receiver, cascaded gain,
noise figure, ITOI budgets are tracked to thecomponents in the
receiver chain. The cascaded noise figure and ITOI equations are
included for the sake ofcompletion.
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Conclusion
Receiver design in the form of individual receivers is well
documented, and has become an established art. Thearea for further
growth and maturity is the effect of numerous receivers summed in
an array. This tutorial hascompiled a summary of considerations for
receiver design and presented considerations when used in a
digitalbeam-forming phased array application.
Peter Delos is lead RF/RFIC engineer for Lockheed Martin
Corp.
1. Abidi, Direct-Conversion Radio Transceivers for Digital
Communications, IEEE, 1995.
2. Razavi, Design Considerations for Direct-Conversion
Receivers, IEEE, 1997.
3. Rudell, Frequency Translation Techniques for High-Integration
High Selectivity Multi-Standard WirelessCommunication Systems,
Ph.D. thesis, University of California, Berkeley, 2000.
4. G. Vallant, et al., Analog IQ Impairments in Zero-IF Radar
Receivers: Analysis, Measurements and DigitalCompensation, IEEE,
2012.
5. L.C. Howard, N.K. Simon, and D.J. Rabideau, Mitigation of
Correlated Non-Linearities in Digital PhasedArrays Using
Channel-Dependent Phase Shifts, IEEE Int. Microwave Symp.,
2003.
6. L.C. Howard, D.J. Rabideau, Correlation of Nonlinear
Distortion in Digital Phased Arrays: Measurementand Mitigation,
IEEE Int. Microwave Symp., 2002.
7. K.C. Lauritzen, et al. Impact of Decorrelation Techniques on
Sampling Noise in Radio-FrequencyApplications, IEEE Trans. on Inst.
and Meas., Vol. 59, No. 9, Sep. 2010.
8. Lauritzen, Krichene, and Talisa, Hardware Limitations of
Receiver Channel Pair Cancellation Ratio, IEEETransactions of
Aerospace and Electronic Systems, Jan 2012.
9. McClaning, Vito, Radio Receiver Design, New York, Noble
Publishing, 2000.
10. Cook and Bernfeld, Radar Signals, An Introductory to Theory
and Application, New York, Academic Press,1967.
11. Skolnick, Radar Handbook, New York, McGraw Hill, 1978.
12. Stimson, Introduction to Airborne Radar, SciTech Publishing,
1998.
13. Barton, Modern Radar System Analysis, Norwood, MA, Artech
House, 1988
14. L. Lessing, Man of High Fidelity: Edwin Howard Armstrong, A
Biography, New York: Banton Books, 1969.
15. Microwaves101.com, Superheterodyne Receivers, 2012.
16. Microwaves101.com, Receiver Sensitivity.
17. K.C. Lauritzen, et al. High Dynamic Range Receivers for
Digital Beamforming Radar Systems, IEEE, 2007.
18. Henderson, Mixers in Microwave Systems, WJ Tech-Note,
1990.
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19. Stuetzle, Understanding IP2 and IP3 Issues in Direct
Conversion Receivers for WCDMA Wide AreaBasestations, Linear
Technology Application Note, 2008
20. V. Gregers-Hansen, Radar Dynamic Range Specification
Measurement, Radar Conference - Surveillancefor a Safer World,
2009. RADAR. International, October 2009
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