Agilent RF Receiver Test

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Testing and TroubleshootingDigital RF Communications

Receiver DesignsApplication Note 1314

Wireless Test Solutions

I

Q



Page

1 Introduction

2 1. Digital Radio Communications Systems

3 1.1 Digital Radio Transmitter

3 1.2 Digital Radio Receiver

3 1.2.1 I/Q Demodulator Receiver

4 1.2.2 Sampled IF Receiver

4 1.2.3 Automatic Gain Control (AGC)

5 1.3 Filtering in Digital RF Communications Systems

6 2. Receiver Performance VerificationMeasurements

6 2.1 General Approach to Making Measurements7 2.2 Measuring Bit Error Rate (BER)

8 2.3 In-Channel Testing

8 2.3.1 Measuring Sensitivity at a Specified BER

9 2.3.2 Verifying Co-Channel Rejection

9 2.4 Out-of-Channel Testing

9 2.4.1 Verifying Spurious Immunity

10 2.4.2 Verifying Intermodulation Immunity

11 2.4.3 Measuring Adjacent and Alternate ChannelSelectivity

14 2.5 Fading Tests

14 2.6 Best Practices in Conducting Receiver PerformanceTests

Page

15 3. Troubleshooting Receiver Designs

15 3.1 Troubleshooting Steps

15 3.2 Signal Impairments and Ways to Detect Them

16 3.2.1 I/Q Impairments

17 3.2.2 Interfering Tone or Spur

17 3.2.3 Incorrect Symbol Rate

18 3.2.4 Baseband Filtering Problems

19 3.2.5 IF Filter Tilt or Ripple

19 3.3 Table of Impairments Versus Parameters Affected

20 4. Summary

20 5. Appendix: From Bit Error Rate (BER) toError Vector Magnitude (EVM)

22 6. Symbols and Acronyms

23 7. References

Table of Contents



This application note presents thefundamental measurement principlesinvolved in testing and troubleshootingdigital RF communications receivers—particularly those used in digital RFcellular systems. Measurementsetups are explained for the variousreceiver tests, and troubleshootingtips are given.

The demand for ubiquitous wirelesscommunications is challenging thephysical limitations of current wire-less communications systems.Wireless systems must operate in a

very limited area of the radio spectrumand not interfere with other systems.The maturing wireless markets arebecoming much more competitive,and product cycle times are nowmeasured in months instead of years.Consequently, network equipmentmanufacturers must produce wirelesssystems that can be quickly deployedand provide bandwidth-efficientcommunications.

Digital modulation has severaladvantages over analog modulation.These include bandwidth efficiency,superior immunity to noise, lowpower consumption, privacy, and

compatibility with digital data services.These advantages, coupled withadvances in digital signal processingand in analog-to-digital conversion,have spawned the current migrationto digital RF communications formats.

Digital RF communications systemsuse complex techniques to transmitand receive digitally modulated signalsthrough the radio channel. Thesecomplexities challenge designersin the isolation of system problems.Signal impairments can be traced

back to a component, device, orsubsystem of the digital RF communi-cations system. Successful receiverdesign depends on the ability tolocate sources of error.

The digital radio receiver mustextract highly variable RF signalsin the presence of interference andtransform these signals into closefacsimiles of the original basebandinformation. Several tests verifyreceiver performance in the presenceof interfering signals. Theseperformance verification tests arecategorized as either in-channel orout-of-channel measurements.

This application note includes:

• A block diagram of a digital radiocommunications system.

• Common receiver designs.

• In-channel tests, including sensitivityand co-channel immunity.

• Out-of-channel tests, includingspurious and intermodulationimmunity and adjacent and alternatechannel selectivity.

• Best practices in the receiverperformance tests.

• Troubleshooting techniques forreceiver designs.

• An appendix that relates Bit ErrorRate (BER) to Error VectorMagnitude (EVM).

The setups required to performthe receiver performance tests areincluded in this application notealong with descriptions of potentialerrors in the measurement process.Troubleshooting techniques applicableto the design of digital radio receiversare also provided.

1

Introduction



The digital radio signal experiencesmany transformations in its migrationfrom a baseband signal at the trans-mitter to its replication at the receiver.

A rudimentary block diagram of adigital radio communications system(Figure 1) reveals the transformationprocess the signal undergoes fromorigination to reception.

The system-level diagram in Figure 1displays the symmetry of the digitalradio. To a certain degree, the receiv-er can be considered a reverse imple-mentation of the transmitter.

Consequently, the measurementchallenges are similar for both partsof the digital radio system. However,unique problems exist at variouslocations in the system. For example,the receiver must detect weak signalsin the presence of noise and is there-fore tested with very low level signals.The transmitter must not interferewith other radio systems and isconsequently tested for the amountof interference it produces in thenearby frequency channels.

Certain parts of the digital radio maybe implemented in a Digital SignalProcessor (DSP), an Application-Specific Integrated Circuit (ASIC),or a Digital Down Converter (DDC).The DSP, ASIC, or DDC has differentlevels of involvement in the variousdigital radio designs. Sometimes it isdifficult to distinguish those problemsoriginating in the digital portion of the radio from those originating inthe analog portion. This applicationnote describes how to isolate andclarify sources of error in digitalradio receiver tests and designs.

2

1. Digital Radio Communications Systems

Transmitter

Receiver

SymbolEncoder

Input(Data or Voice)

Channel Coding/Interleaving/Processing

Amplifier

Power Control

RF LO

UpconverterBaseband

Filter IF FilterI

Q

I/QModulator

IF LO

I

Q

IF Filter

DemodulatorOutput

(Data orVoice)

Low-NoiseAmplifier with

AutomaticGain Control

PreselectingFilter

BitDecoder

BasebandFilter

I

Q

I

Q

IF LORF LO

Downconverter Downconverter

Channel

Figure 1. Block Diagram of a Digital Radio System



3

1.1 Digital Radio TransmitterThe digital radio transmitter (Figure 1)accepts a baseband waveform and

translates that signal into a waveformthat it can effectively transmitthrough the channel. Before thetransformation from baseband to aRadio Frequency (RF) channel, thewaveform is digitized to utilize theadvantages of digital modulation.Coding is applied to the signal tomore efficiently use the availablebandwidth and to minimize theeffects of noise and interference thatwill be introduced by the channel.The coded signal is filtered, modulated,and changed back to an analog wave-

form that is converted to the desiredfrequency of transmission. Finally,the RF signal is filtered and amplifiedbefore it is transmitted from theantenna. A more detailed descriptionof digital transmitters can be found inthe companion Agilent Technologiesapplication note, Testing andTroubleshooting Digital RF Communications Transmitter

Designs (Ref. 1, pg. 23) .

1.2 Digital Radio ReceiverThe digital radio receiver (Figure 2)can be implemented several ways,but certain components exist in allreceivers. The receiver must extractthe RF signal in the presence of potential interference. Consequently,a preselecting filter is the first compo-nent of the receiver, and it attenuatesout-of-band signals received by theantenna. A Low-Noise Amplifier(LNA) boosts the desired signal levelwhile minimally adding to the noiseof the radio signal. A mixer down-converts the RF signal to a lower

Intermediate Frequency (IF) bymixing the RF signal with a LocalOscillator (LO) signal. The IF filterattenuates unwanted frequencycomponents generated by the mixerand signals from adjacent frequencychannels. After the IF filter, the

variations in receiver designmanifest themselves.

Of the many different ways to imple-ment a digital radio receiver, mostdesigns fall into two basic categories:I/Q demodulation and sampled IF.

1.2.1 I/Q Demodulator Receiver

I/Q demodulation implemented withanalog hardware is a commonly useddigital radio receiver design. Thefunction of the analog I/Q demodulator(Figure 3) is to recover the baseband Iand Q symbols.

After downconversion to the IF, thesignal is separated into two distinctpaths. To convert to baseband,each path is mixed with an LO whosefrequency equals the IF frequency.The upper-path signal (I) is simplymixed with the LO and then filtered.In the lower path, a 90° phase shift isintroduced in the mixing signal. Thislower-path signal (Q) is converted tobaseband by mixing with the phase-shifted LO signal, and then filtered.This process produces the in-phase(I) and out-of-phase (Q) basebandcomponents of the data stream.For a detailed explanation of I/Qmodulation, consult (Ref. 2, pg. 23) .

IF Filter

LO

Demodulatorand Decoder

Output(Data orVoice)

Low-NoiseAmplifier with

AutomaticGain Control

PreselectingFilter Downconverter

φ

IF Filter

LO

Low-NoiseAmplifier

PreselectingFilter

BasebandFilter

ADC I

Q

BasebandFilter

ADC

LO

90-Degree Phase Shifter

Mixer

Mixer

Downconverter

Figure 2. Receiver Block Diagram

Figure 3. I/Q Demodulator



Although the I/Q demodulator receiveris a popular design, it has potentialproblems. Unequal gain in the I andQ paths and/or a relative phase shiftother than 90° (quadrature error)will cause image suppression problemsin the baseband mixers. I/Q demodu-lators inherently produce a spuriousresponse at DC (that is, in the centerof the passband) regardless of theinput frequency. As a result, I/Qdemodulators are most commonlyused in single-channel base stationreceivers that have a separate receiverfor each frequency channel, ratherthan in multi-channel base stationreceivers that use a single, wide-bandwidth receiver for the entireband of frequencies.

The I and Q data streams are sampledby Analog-to-Digital Converters (ADCs).This allows filtering and signalcorrections to be performed withdigital signal processing. Basebandfiltering by a DSP, ASIC, or DDCremoves many of the problemsassociated with analog filter imple-mentations (for example, phase andgroup delay problems) and providesfilter characteristics closer to idealthan those of analog filters. Basebandfiltering, whether it is analog or digital,is better behaved than IF filtering.

1.2.2 Sampled IF Receiver

To decrease analog hardwarecomplexity, the digitally modulatedsignal can be sampled earlier in thesignal path, which increases thedigital or software complexity of the receiver design. The sampled IFreceiver converts the analog signal toa digital data stream earlier than theI/Q demodulator does (Figure 4) .

In this receiver, the IF signal isdigitized. The sampled data streamfrom the ADC is digitally demodulatedinto its I and Q components, and theoriginal signal is reconstructed.

This type of receiver is becomingmore popular because of advancesin ADCs and DSPs. The sampled IFreceiver design requires less analoghardware than the I/Q demodulatortype and does not split the analogsignal into two paths. The I/Qdemodulation is actually performedin a DSP, ASIC or DDC. Digital I/Qdemodulation avoids phase andamplitude imbalance between I andQ signals. The trade off is more digitalsignal processing and power-hungry

ADCs fast enough to capture all the

information in the analog signal(two factors that reduce battery lifein mobile phones). As with the I/Qdemodulator, the sampled IF receiverrequires a downconverter that doesnot degrade the incoming signal.

1.2.3 Automatic Gain Control (AGC)

AGC is used in digital radio receiversto handle the wide range of signal

levels encountered at the receivingantenna. AGC compresses the signalrange by reducing the gain of the IF,and sometimes the RF, stages as thesignal level increases. A strong RFsignal can overdrive the mixer andcause excessive signal distortion.The receiver must also process weakRF signals in the presence of noise.Therefore, the RF portion of thereceiver may incorporate AGC toprocess the full range of signal levelspresented to it. Used in the IF stage,

AGC can prevent overload and

maintain a reasonably constantsignal input to the demodulator stage.For all applications, the AGC circuitrymust maintain allowable levels of signal distortion over a broad rangeof power levels. Also, the AGC shouldrespond quickly to signal level changesas it processes signals over its entiredynamic range.

4

IF Filter

LO

Low-NoiseAmplifier

PreselectingFilter

ADC

Downconverter

Figure 4. Sampled IF Receiver



1.3 Filtering in Digital RFCommunications Systems

Distortion-free transmission of thedigital I and Q signals theoreticallyrequires infinite bandwidth. Aninfinite-bandwidth RF communicationssystem would interfere with othersystems and would not provideefficient use of radio spectrum.Filtering narrows the bandwidth of RF systems, but it also slows downsignal transitions.

Baseband filtering rounds off therapid transitions in the transmitteddata, but this can cause Inter-SymbolInterference (ISI). A Nyquist filter,

which is a type of raised-cosine filter,minimizes ISI by forcing the filter’simpulse response to zero at the symbolpoints (except at the center of thefilter). Thus, the time response of theNyquist filter (Figure 5) goes throughzero with a period that exactlycorresponds to the symbol spacing.

Adjacent symbols do not interferewith each other at the symbol timesbecause the response equals zero at allsymbol times except the desired one.

The sharpness of a raised-cosine

filter is described by its alpha ( α )and quantifies the occupied band-width of the signal. An ideal (“brickwall”) filter would have an alpha of zero. Typical alpha values range from0.35 to 0.5. Filter alphas also affecttransmitted power. A low alpha

value results in low occupied band-width but requires high peak transmitpower. Consequently, the filter alphamust be carefully chosen to achieve abalance between spectral occupancyand required transmit power. Insome systems, a root-raised-cosine

filter is implemented at both ends of the digital radio, and the resultingoverall filter response is a raisedcosine.

Gaussian filters, such as those usedin GSM systems, do not provide thetheoretical zero ISI like the Nyquistfilters do. The Gaussian filter has aGaussian shape in the time andfrequency domains, and it does

not go to zero at the symbol spacing.This causes some ISI, but each symbolinteracts significantly with only thepreceding and succeeding symbols.The bandwidth-time product (BT) of the Gaussian filter corresponds to thealpha of the Nyquist filter, and typicalBT values range from 0.3 to 0.5.Unlike Nyquist filters, Gaussian filtersare not split into matched pairs in thetransmitter and receiver. They areonly used in the transmitter. GSMreceivers typically use Butterworthfilters that have a sharper roll-off thanthe Gaussian filters. Consequently,sensitivity is improved because lessout-of-channel noise and interferenceis allowed into the receiver’s pass-band.

A more thorough examination of filtering is provided in (Ref. 2, pg. 23) .

5

-10 -5 0 5 10ti

0

1

0.5hi

Symbol Period

Figure 5. Impulse Response of a Nyquist Filter



This section contains test setups andprocedures for performance tests ondigital radio receivers. Each receivermust meet strict performance criteriadefined by the various standards of the telecommunications industry’sgoverning bodies (the ITU, ETSI,TIA, and others). Design teamsmust develop performance criteriafor their receiver, or for a portion of that receiver, and conduct uniqueperformance tests to verify correctimplementation and modeling of components in the receiver. More-over, these performance tests verifyreceiver compliance prior to thedesign’s submission for typeapproval.

Performance verification tests aredivided into in-channel and out-of-channel measurements. In-channelmeasurements test the receiver’soperation within the frequenciesoccupied by the desired signal. Out-of-channel measurements verify thatthe receiver is not being adverselyaffected by (or affecting) other signalsoutside its specific frequency channel.

Although the performance tests pre-sented in this application note focuson digital RF cellular applications,many of the concepts and tests applyto other forms of digital RFcommunications.

2.1 General Approach toMaking MeasurementsThe most comprehensive receivertest is to evaluate the reconstructedbaseband signal that has beenprocessed by the receiver. In thistest, one piece of test equipmentstimulates the antenna port of thereceiver and is considered to be anideal transmitter. Another instrumentmonitors the demodulated digital bitstream. If desired, impairments can beintroduced by inserting interferencein the channel between the sourceand the receiver, or by alteringparameters in the source, to determinethe receiver’s ability to operate prop-erly under less-than-ideal conditions.

The following tests assume the receiveris complete. If the digital portion of the receiver is unavailable for testing(for example, if it’s still under devel-opment), then the analog RF designerneeds to establish performance goalsfor the analog portion of the receiver.Typical performance goals are theestimated optimum noise figure forthe receiver to pass the performance

verification tests and the estimatedoptimum Signal-to-Noise Ratio (SNR)for proper ADC operation (at thedigital conversion point).

2.2 Measuring Bit Error Rate(BER)BER is the fundamental measurementused when testing receiver performanceparameters such as sensitivity andselectivity. It is the percentage of erroneous bits received comparedto the total number of bits receivedduring an observation period.

Virtually all BER test instruments usea Pseudo-Random Binary Sequence(PRBS) as the test signal. PRBS signalsare usually labeled PNx, where x isthe number of bits being permutatedin the sequence (for example,PN9 = 2 9–1 or 511 bits). Since anentire PNx sequence can be recon-structed from any sequence of “x”bits, using a PRBS signal eliminatesthe need to synchronize the receivedand transmitted bits. Alternatively,the entire PRBS is reconstructed inthe BER tester (BERT) receiver fromthe first correct “x” bits received. Thereceived signal is then compared to thereconstructed correct bit sequence.For a thorough explanation of BERtesting, see (Ref. 3, pg. 23) .

Two popular methods exist for BERtesting of mobile phones: basebandBER and loopback BER. The featureset of the unit-under-test (UUT)dictates which test method to use.For the baseband BER test, thedemodulated PRBS signal at thereceiver remains at baseband and iscompared to the reconstructed PRBSby the BERT (Figure 6) . Typically,CDMA mobile phones and sub-assemblies use the baseband BERmeasurement method.

Conversely, for the loopback BER testthe received signal is retransmitted,

or looped back to a receiver (Figure 7) .In the loopback test, the UUTdemodulates the incoming RF signal,decodes it, then re-encodes the datastream (with possible errors), andretransmits the signal, often to theoriginal transceiver. To attain theBER, this received signal is compared

6

2. Receiver Performance Verification Measurements



to the expected PRBS that isreconstructed by the BERT (Ref. 3,

pg. 23) . GSM handsets are testedusing the loopback method.

The Agilent E4438C ESG signal gener-ator can be configured to provide theRF signal that carries the PRBS andperform the BER measurement.

Data is managed in telecommunicationssystems by a hierarchical system of bitgrouping. Speech frames are nearlythe lowest-level building blocks inthis hierarchical system. Not all bitsin a speech frame are equally impor-tant. Some bits are so important thatthe entire frame is erased if any of

them are bad. This leads to a newparameter for expressing receiverperformance—Frame Erasure Rate(FER). It is the percentage of erasedframes compared to the total numberof frames sent during an observationperiod. Frame erasure also leads to amodification of our BER measurement.When frames are erased, only theBER of the remaining frames ismeasured. This parameter is calledresidual BER (RBER).

7

Decoder

Comparator

Encoder

PatternGenerator

BasebandModulator

Option300

PRBS

RF Signal

Demodulator

RF SignalReceiver

IF Signal

Agilent E4440A PSASpectrum Analyzer

Agilent E4438C ESGSignal Generator

RF Signal

Figure 7. Loopback BER Test Configuration (this test set-up applies only to GSM/EDGE)

Comparator

Encoder

PatternGenerator

RF SignalSource

RF Signal

Baseband Signal00110110110001

BasebandModulator

Bit ErrorRate Tester

(Option UN7)

Agilent E4438C ESGSignal Generator

Figure 6. Baseband BER Test Configuration



8

2.3 In-Channel TestingThe most significant in-channel testmeasures the sensitivity of the receiver.

Sensitivity specifies the minimumsignal level for a specified percentageof errors in the demodulated informa-tion. As the separation betweentransmitter and receiver increases, oras fading occurs in the radio channel,the signal will drop into the noisefloor from the perspective of thereceiver. Information will be lostwhen the signal approaches the noisefloor. The ability of the receiver tocapture the information in a signalas it drops to very low levels is afunction of the receiver’s sensitivity.

The go/no-go method for sensitivitytesting is to stimulate the receiver

with a very accurate signal set to arelatively low power level and see if the receiver output is acceptable.

Alternatively, the signal level isadjusted for a specified SNR or otherperformance metric. For analog FMreceivers, the performance metric isknown as SINAD (12 dB is typical).SINAD is the ratio of signal-plus-noise-plus-distortion to the noise-plus-distortion at the same output.Similarly, for digital receivers thespecified performance metric is theBER or FER (Figure 8).

Co-channel immunity testing is similarto sensitivity testing. The level of signal distortion is monitored with aninterfering signal present in the sameRF channel. The interfering signal

may be Continuous Wave (CW),narrowband, or of the same type asthe desired signal. The ability of thereceiver to remain sensitive to thedesired signal while subjected to theinterfering signal is a measure of itsco-channel immunity.

2.3.1 Measuring Sensitivity at aSpecified BER

Sensitivity is one of the key specifica-tions for a digital radio receiver andis specified at a particular BER (orFER). Sensitivity is the minimumreceived signal level that producesa specified BER when the signal is

modulated with a bit sequence of data.

Because sensitivity is oftenexpressed in voltage units, such asµV, the following equation will beused to convert to dBm:

dBm = 10 * log (V rms2 /Z o) + 30

where V rms = receiver sensitivityin volts rms

Zo = receiver impedance(typically 50 Ω).

For example, if a receiver has a sensi-tivity expressed as 1 µV, the sensitivitycan be converted to –107 dBm for asystem with a 50 Ω impedance.

To perform the sensitivity test,connect a signal source to the anten-na port of the receiver with a cable of known loss. Then connect the outputof the receiver to the BERT (Figure 9).

If the approximate sensitivity isunknown, the signal level should beset to a nominal level (such as –90dBm) and decreased until thespecified BER occurs. The sensitivityis the power level of the signal minusthe loss in the cable. For example, if the signal generator is transmitting a–106 dBm signal when the specifiedBER is reached and the cable loss is4 dB, then the sensitivity is –110 dBmfor the receiver.

RF Input to Receiver (µV)

A u

d i o O u t p u t o

f R e c e

i v e r

( d B ) Desired Audio Signal

Residual Hum & Noise

12 dB SINAD

Figure 8. Understanding SINAD

The top curve in Figure 8 is the desired audio output of the receiver. As the RF input to the receiver isreduced, this curve falls off. The bottom curve is the residual hum and noise of the receiver. As the RFinput is reduced, the AGC of the receiver adds gain, which increases the residual hum and noise.SINAD is the difference between these two curves. The level of RF input required to maintain a SINADof 12 dB is generally defined as the sensitivity of an FM receiver.

Signal Generator

BERT

Data

DUT

Modulated RF Signal

Agilent E4438C ESG

Figure 9. Sensitivity Measurement Setup



9

2.3.2 Verifying Co-Channel Rejection

Most receivers are required to maintaina specified BER in the presence of aninterfering signal within the channel.Frequently, this co-channel interferingsignal will be a CW signal. Figure 10illustrates the test setup for the co-channel rejection measurement. Thissetup includes a power combiner thathas some power loss associated withit. Maximum insertion loss of most2-way resistive combiners is near6 dB when combining two noncoher-ent signals such as in this test. Forall measurements using a powercombiner, the combiner loss shouldbe characterized and offset by anincrease in signal power from thesignal generators.

The frequency of the desired signal, adigitally modulated test signal, is setto the center of the passband of thereceiver. The power of this signal istypically set to a level relative to themeasured sensitivity of the receiver(for example, 3 dB above). Thefrequency of the interfering signalis set within the passband of thereceiver. The power level of theinterfering signal is set to a nominallevel at which the BER of the receivermust not exceed the specified level.The required BER level is usually thesame level specified for the receiversensitivity measurement. The differ-ence in power levels between the twosignals is the interference ratio.

For example, suppose a 931.4375MHz pager has a sensitivity of –105dBm with a BER of 3%. The desiredsignal is set to 931.4375 with a powerlevel of –102 dBm. At this powerlevel the BER is less than 3%. The

channel width for the pager is25 kHz. The interfering signal is setto 931.4380 MHz. The power levelof the interfering signal is first setto –105 dBm and gradually increaseduntil the BER is again 3%. If a levelof –97 dBm is required to return theBER to 3%, then the co-channelrejection is 5 dB.

2.4 Out-of-Channel testingOut-of-channel, or blocking, tests

verify correct receiver operation in

the presence of out-of-channel signalsand monitor the receiver’s susceptibilityto internally generated spuriousresponses. Three prominent out-of-channel tests verify receiver perfor-mance: spurious immunity, intermod-ulation immunity, and adjacent/alternate channel selectivity. Forcertain digital formats, the single-tone blocking test verifies receiverperformance with a large signal ina nearby frequency channel. A largesingle tone slightly offset from thecarrier frequency could desensitize

a receiver to the desired signal. Thesingle-tone blocking test is straight-forward and will not be covered inthis application note.

Spurious immunity is the abilityof the receiver to prevent single,unwanted signals from causing anundesired response at the output of the receiver. Spurious immunity issimilar to co-channel immunity, butthe interfering signals occur across abroad range of frequencies instead of in-channel.

Intermodulation immunity tests fordistortion products that are generatedwhen more than one tone is presentat the input of the receiver. In thistest, two interfering signals arecombined with the desired signalat the input of the receiver. Thefrequencies of the interfering signalsare set such that one of the third-orderintermodulation products lies withinthe passband of the receiver. Thepower of these interferers is raiseduntil the sensitivity of the receiveris compromised.

Adjacent channel selectivity measuresthe ability of the receiver to processthe desired signal with a strong signalin the adjacent channel. Alternatechannel selectivity is a similar test inwhich the interfering signal is two RFchannels away from the passband of the receiver.

2.4.1 Verifying Spurious Immunity

Spurious responses, also called spurs,manifest themselves in radio receiversin two ways: they are generatedinternally by the receiver, or theyresult from the interaction of thereceiver with external signals.

Σ

Demodulated,Decoded Data

In-band CW orModulated RF Signal

(Interfering)

DUT

Combiner

Modulated RF Signal (Desired)

Agilent E4438C ESG with BERT

Signal Generator

Signal Generator

Agilent E4438C ESG

Figure 10. Co-Channel Rejection Measurement Setup



Both types of spurs should be identified.Replacing the antenna of the receiverwith a load will ensure that thereceiver is not picking up any straysignals. Connect the final analogoutput of the receiver to a spectrumanalyzer. Any spur viewed on thespectrum analyzer is internallygenerated by the receiver and maybe a harmonic of the power supply,a harmonic of the system clock, or aspur from an LO.

Spurious response immunity is ameasure of the receiver’s ability toprevent single, unwanted signalsfrom causing an undesired responseat the output of the receiver. Priorto making this measurement, the

internally generated spurs must beidentified (as described above) andshould be below the specified level.To perform the spurious immunitymeasurement, one signal generatorsupplies a modulated test signal inthe desired RF channel at a levelabove the sensitivity of the receiver(usually 3 dB above). The secondsignal generator supplies an interferingsignal. This interfering signal isadjusted to several frequencies to

verify the receiver’s immunity tospurs (Figure 11).

The interfering signal may bemodulated or unmodulated, dependingupon the frequency range and thecommunications standard. The

output amplitude of the interferingsignal is set at a specific level at whichthe BER of the receiver under testmust be less than a specified level(usually the BER specified in thesensitivity test). The amplitudedifference between the test signal andthe interfering signal is the spuriousimmunity (SI) of the receiver:

SI = P int – P test (dB)

Spurs from the signal generator usedto provide the interfering signal cancause a good receiver to appear bad.

Any spurs created by the interferingsignal generator should be less thanthe receiver’s spurious immunity.

2.4.2 Verifying IntermodulationImmunity

Intermodulation products may begenerated within the receiver whenmore than one signal is present at theinput of the receiver. Intermodulationproducts are caused by receiver non-linearities. Two-tone intermodulationis a common method of testing areceiver. The test signal is the samesignal used in other measurements(for example, spurious immunity).The frequencies of the interferingsignals are set such that one of thethird-order intermodulation products(f rx1 = 2f 1 – f 2 and f rx2 = 2f 2 – f 1) fallswithin the passband of the receiver(Figure 12).

The power levels of the interferingsignals are set equal to each other ata specified level, and the BER of thedesired signal is checked. As withother receiver tests, the required BERlevel is usually the BER at which thesensitivity is measured.

10

Σ DUT

Combiner


Signal Generator

Signal Generator

Agilent E4438C ESG

Out-of-band CW orModulated RF Signal

(Interfering)



Figure 11. Spurious Immunity Measurement Setup

f1

f2

frx1=2f 1 – f2frx2=2f 2 – f1

frx1 frx2

f1 f2

Low-NoiseAmplifier

PreselectingFilter

Antenna

IF Filter

LO

f1 f2

Figure 12. Intermodulation Products



Whenever two signals are input toa combiner, the nonlinearities of the signal generators may createintermodulation products (Figure 13).There are several techniques forreducing signal generatorintermodulation products:

1) maintain a frequency separationbetween the interfering signals thatis greater than the bandwidth of the

Automatic Level Control (ALC) of thesources; 2) add attenuators to theoutputs of the signal generators; 3)use hybrid combiners; 4) use isolators;and 5) turn off the ALC of the sources.

All these techniques may be applied

simultaneously to reduce intermodu-lation products. Maintaining a largefrequency separation is usually themost effective means to combat thisproblem. For example, if the ALCbandwidth is 1 kHz, the signalseparation should be at least 10 kHz.If this cannot be done, adding attenu-ation at the signal generator outputstheoretically reduces the intermodu-lation products 3 dB for every 1 dBof attenuation.

2.4.3 Measuring Adjacent andAlternate Channel Selectivity

Adjacent and alternate channelselectivity measure the receiver’sability to process a desired signalwhile rejecting a strong signal in anadjacent channel (one channel away)or alternate channel (usually twochannels away). The selectivitytests are very important for commu-nications receivers in which channelspacings are narrow and adjacentand alternate channel power is hardto control (for example, SpecializedMobile Radio, or SMR). An adjacentand alternate channel selectivity testsetup is shown in Figure 14 . One signalgenerator inputs a test signal at thedesired channel frequency at a levelrelative to the sensitivity of thereceiver (usually 3 dB above).

The second signal generator inputseither the adjacent channel signal,offset by one channel spacing, or thealternate channel signal, offset by twochannel spacings. The out-of-channelsignal is set to a specified level atwhich the BER of the test signal isbelow a certain rate (usually the samelevel specified in the sensitivity test).

For example, the sensitivity of an NADC base station receiver isspecified at –110 dBm with a BERof 10-3, or 0.1%. The adjacent channelspecification requires that the BER beno worse than 10-3 with the in-channelsignal set to –107 dBm, a 3 dBincrease, and the adjacent channelsignal set to –94 dBm, or 13 dB abovethe in-channel signal level. This

11

Σ DUT

Combiner


Signal Generator

Signal Generator

Agilent E4438C ESG

Modulated RF Signalin Adjacent or

Alternate Channel(Interfering)



Figure 14. Adjacent and Alternate Channel Selectivity Test Setup

Σ


Out-of-band CW orModulated RF Signals

(Interfering)

DUT

Combiner



Signal Generator

Signal Generator

Agilent E4438C ESG

Signal Generator

Agilent E4438C ESG

Figure 13. Intermodulation Immunity Measurement Setup



implies that the adjacent channel signalcannot increase the receiver noise floorby more than 3 dB. For alternatechannel selectivity, the alternatechannel signal is set to –65 dBm,or 42 dB above the in-channel signallevel. Figure 17 displays the specifiedNADC adjacent and alternate channelselectivity spectrum.

In addition to level accuracy, thespectral characteristics of the testand interfering signals are important.For many receivers, the single sideband(SSB) phase noise of the signalgenerator used to produce theinterfering signal is a critical spectralcharacteristic. If the phase noiseenergy inside the passband of the IFfilter is excessive, the receiver mayappear to fail the test (Figure 15).

The required signal generator SSBphase noise may be calculated from:

Φn = P ac – 10 * log(1/B e) + P mar

whereΦn = signal generator SSB phase

noise (dBc/Hz) at the channelspacing offset

P ac = adjacent or alternate channelselectivity specification (dB)

Be = receiver noise-equivalentbandwidth (Hz)

P mar = test margin (dB)

Since Pac and B e are fixed by thespecifications or design, the testmargin determines the power thatthe signal generator phase noise willbe allowed to contribute to the IFpassband of the receiver. A large testmargin increases the confidence thatthe receiver operates properly in thepresence of SNR degradation due tofading in the channel or due toimperfections in receiver components.For a system using a new technologyor new operating frequencies, a largetest margin should be used tocompensate for uncertainties.

For a receiver with a noise-equivalentbandwidth of 14 kHz, a Pac at theadjacent channel of 70 dB, a marginof 10 dB, and a channel spacing of 25 kHz, the required SSB phase noiseis –122 dBc/Hz at a 25 kHz offset.This is typical for an analog FMreceiver. Unlike the FM receiver inthis example, most digital communi-cations receivers have adjacentchannel selectivity values less than15 dB. For a GSM receiver with anoise-equivalent bandwidth of 200kHz, a P ac at the adjacent channel of 9 dB, a margin of 10 dB, and a channelspacing of 200 kHz, the required SSBphase noise is –72 dBc/Hz at a 200 kHzoffset. The required SSB phase noiseis driven primarily by P ac .

Table 1 lists the values of adjacentand alternate channel selectivity for

various communications systems aswell as the required signal generatorSSB phase noise. A 10 dB test marginwas used. Clearly, for the digital RFcommunications formats, the signalgenerator SSB phase noise is not asimportant as for analog FM systems.

For selectivity tests the spectralshape of the signal is the special

characteristic that is of primaryimportance. The digital modulationformats used by GSM, CDMA, NADC,and PDC characteristically leak asmall amount of power into theadjacent channels. Figures 16–18 plotamplitude versus frequency for theselectivity values specified in Table 1 .The impact of the spectral shape onthe adjacent and alternate channelsof the receiver is evident. To properlytest your digital radio receiver, the

Adjacent Channel Power (ACP) of your signal generator must be belowthe required system specificationplus the desired test margin.

12

Channel Spacing

Frequency

SSB Phase Noise

IF Rejection Curve L e v e

l ( d B m

)

Figure 15. Phase Noise in Adjacent Channel Selectivity



13

Table 1. Maximum Tolerable SSB Phase Noise

System Channel Approximate Adjacent Maximum SSB Alternate Maximum SSBType Spacing Receiver Noise Channel Phase Noise Channel Phase Noise

Bandwidth Selectivity @ Offset Selectivity @ OffsetAnalog FM 25 kHz 14 kHz 70 dB –122 dBc/Hz @ 25 kHz

GSM 200 kHz 200 kHz 9 dB –72 dBc/Hz @ 200 kHz 41 dB –104 dBc/Hz @ 400 kHzNADC 30 kHz 35 kHz 13 dB –68 dBc/Hz @ 30 kHz 42 dB –97 dBc/Hz @ 60 kHz

PDC 25 kHz 33 kHz 1 dB –56 dBc/Hz @ 25 kHz 42 dB –97 dBc/Hz @ 50 kHz

– 44

– 76

– 85

fc +200 +400

Offset from Nominal Center Frequency (kHz)

A m p

l i t u d e

( d B m

) 41 dB

9 dB

Figure 16. GSM Adjacent and Alternate Channel Selectivity Spectrum

+30

– 65

– 94

– 107

fc +60


A m p

l i t u d e

( d B m

) 42 dB

13 dB

Figure 17. NADC Adjacent and Alternate Channel Selectivity Spectrum

– 58

– 99 – 100

fc +25 +50

1 dB


A m p

l i t u d e

( d B m

) 42 dB

Figure 18. PDC Adjacent and Alternate Channel Selectivity Spectrum





Digital RF communications systemsrequire complex digital radiotransmitters and receivers. Complexdesigns challenge engineers in theisolation of system problems. Mostphysical impairments can be tracedback to a component, device, or sub-system. Successful receiver designoften depends upon the ability tofind the source of error. This sectionsuggests some basic techniques fortroubleshooting a receiver that doesnot pass a certain test. Also, a tablethat links measurement characteristicsto possible causes of error in thedifferent sections of the receiver isprovided.

3.1 Troubleshooting StepsIf the receiver under test fails anyof the performance tests, you shouldattempt to isolate the source of theerror in the receiver. The following isa suggested troubleshooting procedureto follow if your receiver does notmeet the expected performancecriteria.

Test Failed:

1. Sensitivity. Measure the BER versus

the input power. If the BER is highat high input powers, check for I/Qimpairments (see section 3.2.1),excessive group delay in analogcomponents, or phase noise from anLO. If the BER is high at low inputpowers, measure the noise figureof the analog front end (from theantenna port to the ADC). If thenoise figure is higher than expected,measure the noise figure and gain(or loss) of each stage of the receiver.If no noise figure problems aredetected, the gain of the front endmay be low, there could be a detectionalgorithm problem in the digitalportion of the receiver, or a spurmay be desensitizing the receiver(see section 3.2.2).

2. Co-channel Immunity. Check forcompression occurring in theanalog components or check for analgorithm implementation problemin the digital realm.

3. Spurious Immunity . Look for anyinterfering tone (see section 3.2.2).If no interfering tone is found,perform a Fast Fourier Transform(FFT) on the data from the ADC toconvert to the frequency domain.Then check for spurs generated bythe ADC.

4. Intermodulation Immunity. Measurethe third-order intercept (TOI) of the RF front end. If it meets the

expected value, measure the TOIand gain of each analog stage.

5. Selectivity. Look at the shape of the IF filter (see section 3.2.5), andcheck for excessive LO phase noiseor sidebands.

Specific guidelines should be followedwhen connecting to the receiver duringtroubleshooting. When connecting toanalog nodes of the receiver, the testprobe alters signal characteristics toa certain degree, which increasesuncertainty in the test results. In a

conventional analog receiver thereare many accessible test points, suchas the outputs of the LNA, the LO,the mixers, and the various filters.

Accessibility of components in thedigital radio receiver depends on thelevel of circuit integration. Many of the components of receiver subsystemsare embedded in Integrated Circuits(ICs). For receivers containing ICs,tests are normally conducted at thesubsystem levels of the receiver. Totest embedded components, strategictest points must be designed into

the IC.

A noise figure measurement on theRF front end, or any analog componentor subsystem of the receiver, is atwo-port measurement (from inputto output). For more informationon noise figure measurements, see(Ref. 6, pg. 23) . The TOI measurementis also a two-port measurement see(Ref. 7, pg. 23) . ADC measurementsprocess the digital output of the ADCand are unaffected by probe placement.

3.2 Signal Impairments andWays to Detect ThemCertain signal impairments appearin specific measurements. In thesemeasurements, variations from the

expected results can help locateproblems in different parts of thereceiver. The following sectionsexplain some common impairmentsand how to recognize them throughtheir effects on the different measure-ments. With the exception of the IFfilter measurement, Agilent 89400 or89600 series vector signal analyzers(VSA) are used to troubleshootreceiver designs in this applicationnote. The IF filter measurement isperformed with the Agilent 8753E

vector network analyzer (VNA).

15

3. Troubleshooting Receiver Designs







recovering the carrier frequency, orthe receiver is not achieving symbollock. To recover the proper carrierfrequency, the receiver must lockonto the phase of the carrier. Toaccurately extract the symbols fromthe carrier, the receiver must alsodetermine when symbol transitionsoccur. A timing recovery loop providesthe mechanism for the receiver toachieve the necessary symbol lock.When the receiver does not achieveproper phase lock and/or propersymbol lock, symbol rate errors occur.If you suspect an incorrect symbolrate and no problem exists with thecrystal, verify proper operation of thecarrier and timing recovery circuitryof the receiver.

3.2.4 Baseband Filtering Problems

Baseband filtering must be correctlyimplemented to provide the desiredbaseband frequency response and toavoid ISI as well as overshoot of thebaseband signal in time. The alphaparameter in a raised-cosine filter

defines the shape of the filter in thefrequency domain. A low alpha createsa sharp filter shape in the frequencydomain, but also creates high over-shoot in the time domain, which canbe recognized on a vector diagram.It is important to verify that thereceiver has the appropriate base-band frequency response and timecharacteristics for the specified alpha.

In cases where baseband filtering isshared between the transmitter andthe receiver, the filters must becompatible and correctly implementedin each. The type of filter and thecorresponding roll-off factor (alpha)are the key parameters that must beconsidered. For raised-cosine filters,an error in the selection of alpha mayresult in undesirable amplitude over-shoot in the signal. It may also resultin ISI. Incorrect filtering due to awrong roll-off factor may affect theamount of interference from anadjacent channel signal. This couldcause an otherwise good receiver tofail many of the performance

verification tests.

To verify baseband filter performance,examine the vector constellationdiagram for excessive overshoot of the signal trajectory between symbolstates. The magnitude of the error

vector versus time would be a goodindicator of roll-off factor discrepancies.If the wrong roll-off factor is used, themagnitude of the error vector will behigh between symbol points and lowat the symbol points (Figure 26) .

The correct roll-off factor can befound by using different roll-off factors in the VSA while viewing theerror vector time display. When thecorrect value is used, the magnitudeof the error vector between symboldecision points will be approximatelyequal to the magnitude of the error

vector at the decision points (Figure 27) .Furthermore, equalization can beapplied to decrease the errors causedby baseband filtering problems.

18

Figure 26. Vector Diagram and Magnitude of the Error Vector

Versus Time for Wrong Roll-off Factor

Figure 27. Vector Diagram and Magnitude of the Error Vector

Versus Time for Correct Roll-off Factor



3.2.5 IF Filter Tilt or Ripple

The IF filter attenuates out-of-channelinterference. Errors in the design of this filter can affect the overall signal.IF filter problems include filter tilt orripple in the frequency response and

variations in group delay. Ideally,the filter should be flat across thefrequency band of interest, and itsgroup delay should be constantacross the same frequency band.Filter tilt or ripple in the frequencyresponse causes linear distortion inthe signal. Improper matching of anycomponent between the antenna andthe IF filter also causes tilt or ripple.For example, mismatch between thepreselecting filter and the LNA causesreflections that result in distortion of the overall frequency response of thereceiver.

Filter tilt or ripple causes distortionon the demodulated baseband signal.This distortion is discernible in theconstellation diagram. Also, themagnitude of the error vector will behigher than expected at the symbolpoints as well as during symbol tran-sitions. Since the IF filter is the maincontributor to the frequency responseof the receiver, IF filter shape distortionis observed and analyzed by performinga frequency response measurement onthe filter alone, as shown in Figure 28 .

3.3 Table of ImpairmentsVersus Parameters AffectedTable 2 shows the physical impairmentsencountered with digitally demodulatedsignals, and the parameters that theseimpairments affect.

The key to troubleshooting is toidentify the impairments that couldbe causing signal degradation. Eachof the different impairments uniquelyaffects the quality of a digitallydemodulated signal. As the tableindicates, the I/Q constellation istypically affected by physical impair-ments. Although the constellationdiagram is a good indicator of problems,

further analysis may be necessary to

isolate the source of the error. EVMis a powerful signal analysis toolthat can be scrutinized to pinpointsources of interference in receivertests. Frequency response and groupdelay measurements prove effectivein the detection of filtering problems.Phase error analysis can detectsources of unwanted phase noise.

Strategic use of these analysis toolswill enhance your ability to trackdown sources of error in your digitalradio receiver designs. The ability toquickly locate design problems cangreatly reduce product developmentand test verification times, and facilitatethe type approval of receiver designs.

19

Table 2. Impairments Versus Parameters AffectedPhysical Impairments Parameters AffectedI/Q Gain Imbalance I/Q Constellation (Figure 20)I/Q Quadrature Errors I/Q Constellation (Figure 21), Average EVM, Magnitude of the Error

Vector versus Time, Error Vector SpectrumI/Q Offsets I/Q Constellation (Figure 22)

Interfering Tone or Spur I/Q Constellation (Figure 23), Average EVM, Error Vector Spectrum(Figure 24)

Incorrect Symbol Rate I/Q Constellation, Phase Error

Baseband Filtering Problems I/Q Constellation, Average EVM, Magnitude of the Error Vector versusTime (Figures 26 and 27)

IF Filter Tilt or Ripple I/Q Constellation, Magnitude of the Error Vector versus Time,Frequency Response (Figure 28), Group Delay

1: – 10.172 dB 190.050 000 MHzCH1 S21 LOG 1 dB/REF – 7 dB

PRm

Cor

Center 190.000 000 MHz Span 10.000 000 MHz

1

Figure 28. Undesired Tilt and Ripple in the IF Filter



Digital RF communications receiversare challenging to design, test, andtroubleshoot. Two digital radioreceiver designs were discussed in thisapplication note: I/Q demodulatorand sampled IF. Receivers mustmeet strict conformance standards.Common in-channel and out-of-channel tests verify that receiverdesigns meet these standards. Toreduce measurement errors, bestpractices should be followed, with anawareness of measurement caveats.

A basic troubleshooting procedurehelps to isolate design problems.

Application of these testing andtroubleshooting techniques canreduce product cycle times andincrease confidence in properoperation after the receiver ismanufactured and put into use.

20

5. Appendix: From Bit Error Rate (BER) toError Vector Magnitude (EVM)

4. Summary

BER is the best measurement to verifyreceiver performance, but BER testingis not always possible in the subsystemsof a digital radio receiver. Also, BERcan indicate a problem exists, but itmay not help identify the source of the problem. An alternative to BERtesting is to examine the quality of ademodulated signal. The most widelyused modulation quality metric indigital RF communications systemsis the EVM. EVM provides a way toquantify the errors in digital demodu-lation and is sensitive to any signalimpairment that affects the magnitudeand phase trajectory of a demodulatedsignal.

As shown in Figure 29 , the error vectoris the vector difference between thereference signal and the measuredsignal. The error vector is a complexquantity that contains a magnitudeand phase component. Expressedanother way, the error vector is theresidual noise and distortion remainingafter an ideal version of the signal

has been stripped away. EVM is theroot-mean-square (rms) value of theerror vector over time at the instantsof the symbol clock transitions. Byconvention, EVM is usually normalizedto the outermost symbol magnitudeat the symbol times and expressedas a percentage:

EVM = (rms error vector / outermostsymbol magnitude) x 100%

The error vector information of the trajectory between the points(viewable in the magnitude of theerror vector versus time display of the Agilent 89441A VSA) helps youtroubleshoot baseband filtering

problems in your receiver design (seesection 3.2.4). Also, the spectrum of the error vector can help you locatesources of interference (see section3.2.2). The magnitude error andphase error between the two vectorsprovide a way to view unwantedphase and amplitude modulationthat may occur in your receiver.

θ

φ

Q

I

Magnitude Error

Phase of Error Vector

Measured Signal

Ideal Signal(Reference)

Phase Error

Error Vector

Magnitude of Error Vector

Figure 29. EVM and Related Quantities



EVM may also be normalized to thesquare root of the average symbolpower. In this way, EVM can berelated to the SNR:

SNR = –20 * log (EVM / 100%)

The importance of the above equationis that it relates EVM to BER throughthe SNR.

Many textbooks have standardcurves that relate BER to SNR, as inFigure 30 (Ref. 8, pg. 23) . Generally,these curves assume that the noise is

Additive White Gaussian Noise (AWGN)with a finite peak-to-average ratio, orcrest factor. The assumptions made

in generating textbook plots of BER versus SNR will not necessarily applyto a particular receiver. The noise ina receiver under test, for example,may not be AWGN but may insteadhave a strong spectral component.In addition, the steep slope of BERcurves makes BER estimations frommeasured SNR (or EVM) more proneto error. However, EVM provides an

easily measured figure-of-merit thatcan be used to monitor design changes,locate design problems and, whenbaselined against a BER measurement,indicate the likelihood that a designwill meet the required specifications.Hence, the connection of BER to EVMis through the SNR, the more generalindicator of likely signal quality(Figure 31) .

Measurements of EVM and relatedquantities can provide powerfulinsight into the performance of adigital radio receiver. When properlyapplied, these signal quality measure-ments can pinpoint sources of errorby identifying the exact type of degradation in a signal. For moredetail on using EVM measurementsto analyze and troubleshoot vector-modulated signals see (Ref. 4 and

Ref. 5, pg. 23) .

21

Peak-to-Average Ratio of 1.4

2.5 2.7 2.9 3.1 3.3 3.5

30

28

26

24

S N R ( d B )

Figure 31. SNR Versus EVM for Crest Factor of 1.4

16-PSK

16-APKor 16 QAM

8-PSK8-APK

BPSK

4-PSK(QAM)

Class IQPR

10 – 10

10 – 9

10 – 8

10 – 7

10 – 6

10 – 5

10 – 4

10 – 3

6 8 10 12 14 16 18 20 22 24 26

SNR (dB)

P(e)

Figure 30. Probability of Error Versus SNR



22

α Alpha (roll-off factor) of aNyquist filter

ACP Adjacent Channel Power

ADC Analog-to-Digital Converter

AGC Automatic Gain Control

ALC Automatic Level Control

ASIC Application-SpecificIntegrated Circuit

AWGN Additive White GaussianNoise

BER Bit Error Rate

BERT Bit Error Rate Tester

BT Bandwidth-Time product(roll-off factor) of a Gaussianfilter

CDMA Code Division Multiple Access

CW Continuous Wave

DDC Digital Down Converter

DSP Digital Signal Processor

DUT Device Under Test

ETSI EuropeanTelecommunicationsStandard Institute

EVM Error Vector Magnitude

FER Frame Erasure Rate

FFT Fast Fourier Transform

GSM Global System for MobileCommunications

I In-phase

IC Integrated Circuit

IF Intermediate Frequency

ISI Inter-Symbol Interference

ITU InternationalTelecommunications Union

LNA Low-Noise Amplifier

LO Local Oscillator

NADC North American DigitalCellular

PDC Pacific Digital Cellular

PHS Personal HandyphoneSystem

PRBS Pseudo-Random BinarySequence

Q Quadrature-phase

RBER Residual Bit Error Rate

RF Radio Frequency

SMR Specialized Mobile Radio

SAW Surface Acoustic Wave

SNR Signal-to-Noise Ratio

TDMA Time Division Multiple Access

TIA TelecommunicationsIndustry Association

TOI Third-Order Intercept

UUT Unit Under Test

VNA Vector Network Analyzer

VSA Vector Signal Analyzer

6. Symbols and Acronyms





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