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Application Notea) Baseband Generation2-Channel AWGQuadrature ModulatorIQIF/RF Outb) Direct RF Generation in the First Nyquist Band1-Channel AWGLPFIF/RF Outc) Direct RF Generation in the Second Nyquist Band1-Channel AWGBPFIF/RF OutFigure 6. AWGs can use diverse methods to generate modulated carriers. Baseband generation (a) requires a two-channel AWG and an external quadrature modulator. Samplingrate requirements depend only on the modulation bandwidth which is limited by the modulator itself. Direct RF generation (b) creates a ready-to-use modulated RF carrier. It requiresa single-channel AWG while sampling rate requirements depend on both the carrier frequency and the modulation bandwidth. As modulation bandwidth is always a fraction of thecarrier frequency, modulation bandwidth is virtually unlimited. A variant of direct RF generation uses the signal image located in the second Nyquist band (c) so the requirementsfor sampling rate are relaxed. However, the amplitude of the image, the steep roll-off of the AWG frequency response at these frequencies, and the limited modulation bandwidthsupported may dramatically reduce the usability of the generated signal.2.2 Radar Signal Generation ArchitecturesAWGs can generate RADAR signals through three basicmethods (Figure 6):Baseband generation: the AWG generates the time-domainsignal to be applied to an RF modulator. For simple signalswhere pulses are generated by controlling the envelopeof a carrier, a one-channel AWG output is applied to anamplitude modulator (AM). For more complex signalsrequiring complex digital modulation or fast frequencysweeps (chirp) both the amplitude and the phase of thecarrier must be instantaneously controlled. In this case, theeasiest and most flexible solution is a quadrature modulator.This requires two baseband signals: the In-Phase (or I), andthe Quadrature (or Q) components. These two basebandsignals can be generated by an AWG with two channels orby two synchronized single-channel AWGs.6www.tektronix.com/awg70000IF (Intermediate Frequency) generation: the AWG generatesa modulated signal at a relatively low carrier frequency.Often the signal can be applied directly to a signalprocessing block in the receiver or transmitter. In situationsinvolving the final RF/μW frequency it is necessary to use anup-converter block to reach the final carrier frequency.Direct RF generation: the AWG is able to generate themodulated carrier at the final RF/μW frequency. Noadditional signal-processing blocks aside from the normalfilters or amplifiers are required.

Radar Signal Generation with a High-Performance AWGEach of these methods has both advantages and drawbacks.Baseband and IF generation can be implemented withmoderate-performance AWGs. For most signals, a samplerate of a few GS/s is sufficient. But in both cases, themodulation bandwidth of the final RF/μW signal will be limitedby the characteristics of the modulator or up-converter. Forexample, commercially available instrument-grade quadraturemodulators can generate signals of up to 2GHz bandwidthbut this may be not sufficient for some RADAR applications.Worse yet, wideband quadrature modulation is extremelysensitive to I/Q imbalance or quadrature errors. Accuratealignment after careful calibration is required to producesignals of adequate quality. On the other hand, Direct signalgeneration requires an extremely fast AWG whose samplerate is at least 2.5 times higher than the maximum frequencycomponent of the signal. Traditionally, obtaining good-qualitysignals with respect to spurious-free dynamic range (SFDR)has been difficult with ultra-high speed AWGs, given theirlimited DAC resolution (6 bits). However, the latest generationof Tektronix high-speed AWGs, the AWG70000 Series, offers10-bit vertical resolution at speeds up to 50 GS/s, opening thedoor to quality signal generation beyond the Ku band(12-18GHz).2.3 Baseband Signal GenerationAt first glance, the generation of baseband signals appears tobe a relatively simple task, as modulation and up-conversionare performed by an external device. The modulation devicemay be a simple amplitude modulator (AM) for basic pulsedRF signal generation. However some baseband signals(i.e. the Barker Codes used in pulse compression) requirea suppressed carrier, which is not supported by most AMmodulators because the instantaneous phase can taketwo values--0 and 180 or BPSK. In addition, basebandgeneration of FM chirps, QPSK/QAM, and, in most cases,UWB OFDM signals, requires a quadrature modulator, asboth the instantaneous amplitude and phase of the carriermust be controlled. Emulation of realistic radar echoes thatincorporate the effects of the target characteristics, multi-path,Doppler shifts, noise, and jamming always requires quadraturemodulation because there are both I and Q components.Consequently a two channel AWG is mandatory for basebandgeneration (Figure 6a).Generating good-quality wideband modulated signals usingthis scheme is not an easy task. The frequency response ofboth baseband generators and RF modulators is not flat andgroup delay is not constant over the bands of interest whensignal bandwidths are high. Regarding AWGs, even a perfectinstrument incorporating ideal DACs will show a 0th (zeroth)order hold response:H(f) sinc(πf/Fs) sin(πf/Fs)/( πf/Fs),Fs Sampling FrequencyThis response will introduce linear distortions to the RF pulses,altering the shape of the transitions and modifying the riseand fall times. Additionally, the analog frequency response ofthe AWG, cabling, and the modulator frequency response willadd to the distortions. Unwanted images resulting from thesampled nature of signals generated by AWGs can also affectsignal quality, as they will show up as unwanted sidebands inthe RF domain. Lastly, the limited time resolution available inany AWG may result in unexpected levels of pulse-to-pulsejitter.The good news is that AWGs can generate either undistortedor distorted signals. Deliberate distortion mathematicallyapplied to waveforms stored in the generator’s memory cancompensate for external distortions. After careful calibrationof the overall frequency response it is possible to design acompensation filter that improves flatness and group delayresponse. Typically, the compensation filter takes the form ofa pre-emphasis filter as it will correct the generation system’soverall low-pass frequency response. As high frequencycomponents are boosted, the low-frequency components ofthe signal must be attenuated in order to maintain a peak-topeak value that fits within the available DAC dynamic range.www.tektronix.com/awg700007

Application NoteRadar Signal GenerationFig. 7Sinc(f)DAC Response-FDAC/2FDAC/2FDACfQuantization NoiseFD́AC FDACSinc(f)DAC ResponseReconstructionFilter-FmaxFmaxQuantization NoiseFD́ACfFigure 7. Generating a limited bandwidth signal at a much higher sampling rate than that required by the sampling theorem (Fs 2xBW) is known as oversampling. This techniqueimproves the quality and usability of the signal as it improves SNR (and effective bits) and flatness while relaxing the requirements for reconstruction filters.The maximum sampling rate greatly influences signal quality.Generally speaking, it is good practice to set the AWGsampling rate well over the minimum Nyquist requirementfor a given signal. This is known as oversampling (Figure 7).A higher sampling rate increases signal quality for variousreasons:Flatter frequency response: The influence of the sinc(πf/Fs) response is reduced as sampling rate increases. For a4 GHz BW signal generated at 12 GS/s by an ideal AWG,the impact onflatness will be 1.65dB, while the same signalgenerated at 25GS/s will result in flatness of 0.37dB.Image rejection: The first image will be located at a higherfrequency and, as a consequence, the gap between thewanted signal and the unwanted images will grow. Thisenables the use of lower-order reconstruction filters withgentler roll-offs and more linear phase response with goodimage rejection.Lower quantization noise: Although quantization noise isbasically a function of the DAC’s vertical resolution, thequantization noise power density will decrease as sampling8www.tektronix.com/awg70000rate increases, since the same power is spread over ahigher bandwidth. Oversampling is, in fact, equivalentto increasing the vertical resolution by a number of bitsΔn 10 x log10(Oversampling Factor)/6.02. As a point ofreference, the AWG70001B running at 50GS/s will beequivalent in terms of raw vertical resolution to a 12-bitAWG running at 12GS/s.Lower pulse-to-pulse jitter: Positioning of very fast edges(rise/fall times equal or lower than one sampling period) withpulses it depends completely on the sampling period, so afaster sampling rate yields a more accurate edge location.Unless the pulse repetition rate is an exact submultiple ofsampling rate, positioning errors will result in a pulse-topulse jitter with a peak-to-peak amplitude equivalent to thesample period. Accurate edge positioning, well below thesampling period, is only possible when rise/fall times of theedges are equal or larger than two (2) sampling periods(the signal frequency content must meet the Nyquistcriterion). This equates to 170ps rise/fall times for a 12GS/sgenerator, 80ps for a 25GS/s unit and a mere 40ps for a50GS/s AWG, such as the Tektronix AWG70000 series.

Radar Signal Generation with a High-Performance AWGThe only relevant drawback of oversampling is the memoryrequirement. The number of samples required to store a giventime window is proportional to the sampling rate. This is oneof the reasons why very long record lengths are so importantto very high-speed AWGs. Here, the AWG70000 with its32 GSample waveform memory can generate at 50 GS/salmost four times the time window that competing instrumentsrunning at 12 GS/s can create with their 2 GSamplewaveform memory.For quadrature-modulated radar signals such as FM-Chirps,two baseband signals, the I and Q components, must feedthe external modulator. These two components must begenerated independently and synchronously through a2-channel AWG or by using two synchronized one-channelAWGs . Ease-of-use and timing alignment for two-channelAWGs make them preferable to solutions based on two onechannel instruments, provided sampling rate is sufficient. TheTektronix AWG70002B (2 channels @ 25GS/s), with minimumchannel-to-channel jitter, offers an excellent combinationof bandwidth (10GHz RF Freq response leading to 20GHzmodulation bandwidth), convenience, and cost effectivenessfor generating IQ baseband signals. Quadrature modulationis very sensitive to channel-to-channel mismatches in alldomains. Differences between the I and the Q componentsmay come from mismatches in the amplitude/phasefrequency response for the two AWG channels, cabling andinterconnections, as well as imbalances and errors withinthe quadrature modulator itself. Even frequency-agile radarsystems may be simulated through quadrature modulationas baseband signals may be positioned anywhere within theexternal modulator modulation bandwidth with instantaneousfrequency switching and no PLL-induced transients. Again,the capability to generate such signals depends on theexternal modulator modulation bandwidth, which used to berather limited relative to radar signal requirements.Just as a good oversampling ratio and high analog bandwidthboth improve the overall signal quality in any AWG, they alsoimprove uniformity between channels. Operating the AWGto generate a relatively low-frequency signal results in betterflatness and phase linearity, so the consistency betweenchannels is also improved. Additionally, remaining amplitudeor delay differences can be removed by simply modifying theoverall signal amplitudes and carefully adjusting the channelto-channel delay. High oversampling ratios also ensurelower-amplitude images, located farther away from the signalof interest, so they can be easily filtered out before reachingthe modulator. Given the wideband nature of radar signals, thehigh oversampling ratio that can be reached with the Tektronixtwo-channel AWG70002B instrument, plus its excellent RFfrequency response ( 10GHz) and spurious performance,the external quadrature modulator may be the weak link.Wideband quadrature modulator response is far from flat andinternal I/Q imbalances may be much higher than those from aquality AWGs such as those in the AWG70000 series.www.tektronix.com/awg700009

Application NoteQuadrature imbalance and errors create unwanted imagesshowing up in the RF signal (Figure 8) and located atsymmetric frequency locations with respect to the carrier.Those unwanted images increase noise and reducemodulation quality. The amplitude of the image will dependon the phase and amplitude errors for a given modulationfrequency and will be a function of it. For example, a LFMChirp generated under conditions of quadrature error andimbalance will consist of the expected linear sweep in thefrequency domain plus an unwanted sweep in the oppositedirection in which amplitude and phase at a given frequencywill depend on the I/Q amplitude and phase mismatch forthat particular frequency. Again, AWGs can generate adifferentially corrected signal. Corrections must be basedon an extra calibration step of the overall generation systemwherein the quadrature error and imbalance as a function ofthe modulation frequency (positive and negative) is determinedand the resulting differential correction filter is selected. Afterachieving perfect balance and phase between the I and the Qcomponents, an additional overall amplitude/phase calibrationmust be performed. Actual calibration procedures can takecare of both calibration steps simultaneously and better resultsmay be obtained by iterating calibration to an already precorrected signal. Shifted SSB (Single Side Band) multi-tonesignals may be a good calibration signal as they allow forthe estimation of both the wanted carriers and the unwantedimage carriers over the whole modulation bandwidth. Thecalibration data will be valid for specific signal generationconditions and for a limited period of time. Typically, acomplete joint generator-modulator calibration will be valid fora period of up to 24 hours, mainly due to drifting parametersin the wideband quadrature modulator. Calibration is atime-consuming process that requires additional equipment;typically a high-end real-time oscilloscope, a wideband vectorsignal analyzer, and corresponding balanceIQIQQuadratureErrorIIQIRadar Signal GenerationFigure 8. Matching between the I and the Q signals is critical for modulation qualitywhen an external quadrature modulator is involved. Differences may come from theAWG, the interconnections, and the quadrature modulator itself. This is especially truefor wideband modulations as mismatches will be a function of the modulating frequency.Careful calibration and differential correction of the signals may reduce the level of theunwanted images caused by quadrature error or imbalance. Direct RF generation doesnot suffer of this problem as quadrature modulation is implemented numerically.

Radar Signal Generation with a High-Performance AWGRSA5126B1-Channel AWGIF/RF OutDUTRF InFigure 9. Using a generator to simulate the RF environment while analyzing the response of the Device Under Test (DUT) with a Real-Time Signal Analyzer.Figure 10. Wide-band environment generated by a one-channel AWG70001B.Figure 11. This test result evaluates the pulse repetition interval (PRI) is beingmeasured on a set of 953 pulses constructed as a staggered PRI CW pulse waveformon the AWG70001B.2.4 De-embedding Radar Subsystems usingHigh-Performance Test Equipmentthe RSA5126B. Several communication signals and otherinterferers can also be seen in the same frequency bands asthe radar signals.When a Radar subsystem is being designed the rest of thesystem is not always available. By using off-the-shelf, generalpurpose test equipment to simulate other subsystems thedevice under test can be tested to exact specifications undercontrolled signal conditions.Radars operate in a very cluttered open-air environment. Thisenvironment can be simulated using a wide-band AWG tohelp test a radar receiver’s ability to deal with the real-lifeenvironment. Figure 10 shows a wide-band environmentgenerated by a one-channel AWG70001B. Various signalssuch as wide- and narrow-band chirp (LFM), narrowband,CW and frequency-hopped d radar signals are seen here onRadar transmitter testing includes extensive evaluation ofa wide variety of test signals. In many cases the evaluationincludes 100’s or 1000’s of pulses, which are then evaluatedusing statistical techniques. The test result shown in Figure 11evaluates the pulse repetition interval (PRI) is being measuredon a set of 953 pulses constructed as a staggered PRI CWpulse waveform on the AWG70001B. The histogram providesa statistical view of the distribution of the PRI measurements,while the pulse table and pulse waveform can be used to viewmeasurements for each individual pulse.www.tektronix.com/awg7000011

Application NoteNo additional equipment is required. Given the cost ofwideband modulators, this translates into important costsavings especially when multiple synchronous signals arerequired (i.e. for MIMO Radar or Phase Array emulation).Direct, virtually unlimited, agile frequency radar signalemulation.A single AWG can generate multiple dissimilar carriers orwideband noise so more realistic test scenarios can beobtained with a single instrument.Simplified calibration procedure; only the inherently stableAWG amplitude/phase frequency must be established andno external modulators are involved.Figure 12. AWG70001B frequency response after removing the influence of the DAC’sSinc(f) response. The low attenuation of frequencies as high as 20 GHz permits thedirect generation of modulated carriers at those frequencies.2.5 Direct Carrier GenerationIdeal AWGs can produce any signal from DC up to half thesampling rate (Fmax Fs/2). With a high enough samplingrate it is possible to directly generate a modulated RF signal(Figure 12). Previously, relatively low sampling rate and poorspurious-free dynamic range (SFDR) limited high-speedAWGs to generating carriers of only a few GHz. The TektronixAWG70000 series, with its 50 GS/s and improved SFDRperformance, breaks the limitations, allowing the directgeneration of wideband signals with carriers up to 20 GHz andvirtually unlimited modulation bandwidth. Direct generationoffers important advantages over the traditional baseband/external modulator combination:Baseband generation and quadrature modulation areperformed mathematically. As a result, there are nounwanted quadrature imbalances or errors. This approachresults in higher-quality, more repeatable test signals.Only one channel is required.12www.tektronix.com/awg70000Although advantages are overwhelming, actualimplementations of this architecture can show somedrawbacks as well. One important issue is record lengthrequirements. For a given record length (RL), the maximumtime window (TW RL/Fs) that can be implemented isinversely proportional to sampling rate (Fs). As samplingrates for direct RF generation tend to be higher than thosefor baseband signal generation, the same record lengthtranslates to shorter achievable time-windows. This is whymaximum record length is an especially important dimensionfor high-speed AWGs. The AWG70000 series with its up to32 GSample waveform memory is capable of storing muchlonger time-windows than the closest competitor running atless than 1/6th the sampling rate. Record length is crucial fora realistic emulation of complex radar systems incorporatingstaggered pulse sequences, frequency hopping patterns ortime varying echo characteristics caused by target movementor antenna vibration. The Tektronix AWG70001B

Radar Signal Generation Fig. 3 Ft vs. Time f1 f2 f2 f4 f3 f3 f4 f1 Radar Signal Generation Fig. 4 Figure 3. Staggered PRF changes the timing between pulses over time. By doing that, blind speeds can be removed and targets beyond the radar's nominal range can be detected while obtaining a signal more resilient to countermeasures or jamming.