Digital beam forming

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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.

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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.

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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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