Implementation Of Real-Time Spectrum Analysis
Implementation of Real-TimeSpectrum AnalysisWhite PaperProducts:ıR&S FSWıR&S FSVRDr. Florian Ramian3.2015 - 1EF77 3eWhite PaperThis White Paper describes the implementation ofreal-time capabilities within the R&S FSW (withoption B160R) and the R&S FSVR. It shows fields ofapplication as well as the technical implementation.
Table of ContentsTable of Contents1 Real-Time Analysis . 31.1What “Real-Time” Stands for in R&S Real-Time Analyzers .31.2Real-Time Applications .42 Real-Time Implementation in the R&S Real-Time Analyzers . 62.1FFT Windowing .72.2FFT Length and Window Length .102.3FFT Update Rate .112.4FFT Overlapping .112.5Time Resolution of FFT Results .132.6Probability of Intercept (POI) .152.7Replay Zoom Mode .183 Triggering on Real-Time Spectra . 193.1Frequency Mask Trigger .193.1.1Setting up a Frequency Mask Trigger (FMT) .203.1.2Technical Background .224 Display Modes for Real-Time Signals . 234.1Spectrogram .234.1.1Parameters .244.2Spectrogram with Real-Time Spectrum .284.3Persistence Spectrum .294.3.1Parameters .315 Ordering Information . 341EF77 3eRohde & Schwarz Implementation of Real-Time Spectrum Analysis2
Real-Time Analysis1 Real-Time Analysis1.1 What “Real-Time” Stands for in R&S Real-Time AnalyzersThe measurement speed available in today's spectrum analyzers is the result of a longevolution. Traditional spectrum analyzers, like the R&S FSE, measured frequencyspectra by mixing the input signal to a fixed intermediate frequency (IF) using a sweptlocal oscillator. The signal was down converted in several mixing stages, and finally itpassed the analog resolution filter, which determined the frequency. The measurementtime was dependent on the settling time of the resolution filter and the time the firstlocal oscillator needed to return from its end frequency to its starting point, the socalled re-trace time.With increasing computing power, the next analyzer generation (R&S FSP, R&S FSU)was equipped with FFT filters for narrow bandwidths. Multiple narrowband FFTs wereconcatenated to a trace representing the selected frequency span. As the computingtime for the FFTs was small compared to the settling time for narrow RBW filters, theFFT method provided a great speed advantage over the traditional sweep method.The latest spectrum analyzer generation (R&S FSV, R&S FSW), makes excessive useof the FFT method for narrow resolution bandwidths. In addition, it introduces complexdigital RBW filters for swept measurements. These complex digital filters can be sweptup to 30 times faster than their analog counterparts.The measurement speed has increased dramatically from 20 sweeps/s on theR&S FSE to more than 1000 sweeps/s on the R&S FSV and R&S FSW platforms. Butone property has survived all evolution steps: even the R&S FSV does not detectsignals between the end of one sweep and the start of the next one. This gap in dataacquisition, the so-called "blind time", has decreased with each new spectrum analyzergeneration, but it is still present (see Fig. . 1-1: Sequential capture and analysis as used in e.g. FFT analyzersMeasuring signals in real time means: do not lose any signal. But how can we get rid ofthe blind times?1EF77 3eRohde & Schwarz Implementation of Real-Time Spectrum Analysis3
Real-Time AnalysisThe answer comes with today's wideband, high resolution analog to digital converters(ADCs). The 16 bit ADCs available today allow capturing wide frequency ranges (e.g.up to 160 MHz) in a single shot with sufficient dynamic range without having to movethe local oscillator (LO). Combining these wideband ADCs with fast FFT algorithmsimplemented in dedicated hardware (e.g. an FPGA) is the basis for the design of areal-time spectrum analyzer.The keys to a real-time spectrum analyzer are: Parallel sampling and FFT calculation: The data acquisition continues whilethe FFTs are performed. Fast processing of FFT algorithms: The computation speed must be highenough to avoid that “stacks” of unprocessed data are being built up. SlowFFT computation will result in an overflow of the capture memory and asubsequent data loss ( a new blind time).Fig. 1-2 shows the parallelized capture and analysis which avoids blind times. Clearly,nothing remains undetected with a real-time spectrum analyzer.Capture 1Capture 2.Capture nAnalysis 1.Analysis n-1Fig. 1-2: Parallel capture and analysis as used in real-time analyzers1.2 Real-Time ApplicationsWhat are typical applications for real-time measurements? All measurements on shortor seldom signals or signal variations, where you do not want to miss even one event.A typical application is the analysis of a given frequency band. Assume a DUT that hasa frequency hopping algorithm implemented. To analyze whether the DUT switchesover the frequencies in the desired order, not a single step must be lost.A transient event, such as the tuning of a VCO to its target frequency is another typicalapplication for a real-time analyzer. The analyzer captures the entire tuning processwithout any gaps and records even the shortest glitches in frequency and level.No matter what signals you are looking for, in most cases it is important to have atrigger possibility that allows triggering on the specific signal change of interest. A socalled frequency mask trigger (FMT) in the R&S FSVR and R&S FSW-B160R allowstriggering on any spectral shape that can be displayed by the analyzer. A typicalapplication is the analysis of a 2.4 GHz receiver. Besides the wanted signal of thesystem under investigation, many other (interfering) signals can be found in this ISMband. To analyze the influence of these interferers on the system under investigation,1EF77 3eRohde & Schwarz Implementation of Real-Time Spectrum Analysis4
Real-Time Analysisthe FMT can be placed around the wanted signal to start or stop capturing data assoon as an interferer violates the frequency mask. Without going into details, itbecomes clear from Fig. 1-3 that the persistence spectrum plot on the right hand sideshows details about how a signal changes over time, whereas the Max Hold trace of aspectrum analyzer does not. Clearly by not losing any information, theRohde & Schwarz real-time analyzers are able to give precise information of a timevariant signal, such as e.g. signal probability.Fig. 1-3: Comparison of a Max Hold spectrum analyzer trace and a persistence spectrum traceThe following chapters will explain the mechanisms behind data capturing without blindtimes and triggering on frequency masks in more detail.1EF77 3eRohde & Schwarz Implementation of Real-Time Spectrum Analysis5
Real-Time Implementation in the R&S Real-Time Analyzers2 Real-Time Implementation in the R&S RealTime AnalyzersThe high-end signal and spectrum analyzer R&S FSW can be upgraded to a real-timeanalyzer by adding option FSW-B160R, whereas the R&S FSVR is a dedicated realtime analyzer that provides the functionality of a traditional signal and spectrumanalyzer on top of the real-time functionality.In terms of RF performance, the R&S FSW-B160R inherits the high end performanceof the basic instrument. The R&S FSVR is based on the R&S FSV RF design, whichdetermines its RF performance.The core of the real-time analysis is the digital backend. As already stated earlier, thecritical point behind real-time analysis is to run data acquisition and data processing inparallel. To achieve this, the digital backends of the R&S FSW and R&S FSVR areequipped with a chain of powerful ASICs and FPGAs in combination with a largememory for captured data. This combination allows the instrument to process the datain several stages in a pipeline architecture. The last stage of the pipeline is the CPU,which reads the pre-processed data, applies the necessary scaling information anddisplays the results on the screen.All available real-time display modes and the frequency mask trigger run in parallel onthe Rohde & Schwarz real-time analyzers. This means that all available real-timeresults can be displayed in multiple diagrams at a time and the frequency mask triggercan be used in addition to capture rare events. This flexibility is a unique feature of theR&S real-time analyzers.IQ memoryAnalog-DigitalConverter (ADC)Resampler /Digital DownConverter (DDC)N bin FFTPointreductionN MUp to 598,938 FFTsper SpectrumFMT MaskEvaluationTriggerControlFig. 2-1: Signal flow chart of the digital real-time part of the Rohde & Schwarz real-time analyzersFig. 2-1 shows the signal flow diagram from the A/D converter (ADC) to the display unitfor the frequency domain displays. The ADC is operated at a constant sampling rate(128 MHz on the R&S FSVR, 1 GHz on the R&S FSW). The ADC streams raw datainto the resampler and digital downconverter, which converts the input signal into thedigital baseband, with a bandwidth equal to the selected frequency span and a1EF77 3eRohde & Schwarz Implementation of Real-Time Spectrum Analysis6
Real-Time Implementation in the R&S Real-Time Analyzerssampling rate fulfilling the Nyquist criterion. The ratio between complex basebandsample rate and selected frequency span is 1.2, meaning that e.g. a 40 MHz span issampled with 50 (complex) MSamples per second, a 160 MHz span with200 MSamples/s. For smaller bandwidths, the sampling rate is automatically reduced.The sampling rate determines the number of samples which are available for analysis.After resampling, the data stream is transformed into the frequency domain by meansof an FFT.On the R&S FSVR, each FFT consists of 1024 so called bins or data points. TheFPGA running the FFT algorithms delivers up to 250,000 FFTs per second. With theR&S FSW-B160R option, the FFT length is flexible, from 16,384 bins down to 1024bins. Depending on the FFT length and operating mode, the R&S FSW reaches anFFT update rate of up to 585,938 FFTs per second.In parallel to the FFT processing, the resampled baseband data is written into theanalyzer’s I/Q memory for additional offline (non real-time) post-processing, like e.g.zooming into a captured region or reading out I/Q samples via LAN or GPIB. Note thatthe I/Q memory is implemented as a circular buffer which means that once the memoryis full, the oldest samples will be overwritten.All Rohde & Schwarz real-time analyzers support time domain displays in real-timeoperation mode. Time domain displays are Power-versus-Time and Power-versusTime Waterfall.The R&S FSW real-time application operates in two different modes: High Resolutionand Multi Domain. In High Resolution mode, the entire FPGA space is dedicated toFFT computation. In Multi Domain mode, a part of the FPGA is programmed for timedomain displays. Thus, the maximum bandwidth in Multi Domain mode is limited to100 MHz and the frequency resolution for a given span is limited compared to HighResolution mode.2.1 FFT WindowingMany engineers remember the frequency domain counterparts of common timedomain signals and vice versa, without even thinking of it. A sine wave corresponds totwo Dirac pulses in frequency domain, a pulsed signal to an Si-function and so on.These correspondences are true for the infinite continuous Fourier transform.However, all digital signal processing is time discrete and relies on a finite amount ofsampled signal. Therefore a Discrete Fourier Transform (DFT) is utilized to transformtime domain signals into the frequency domain. The best known DFT algorithm is theFast Fourier Transform (FFT). DFTs deliver the same results as continuoustransforms, if the finite sampled signal contains the same information as the continuousinfinite signal. A sine wave for example, sampled at least with twice its frequency andfor exactly an integer multiple of one period will result in a Dirac pulse when processedby an FFT algorithm. For all other cases, the resulting frequency domain signal willexhibit phenomena called spectral leakage, scalloping loss, and processing loss.Applying a window function to the signal in time domain prior to FFT computationsignificantly reduces these effects, as the window forces the signal to be periodic withexactly the window length. Generally, the window length NWindow is equal to the FFT1EF77 3eRohde & Schwarz Implementation of Real-Time Spectrum Analysis7
Real-Time Implementation in the R&S Real-Time Analyzerslength NFFT, but in some special cases, shorter windows may be used (see section 2.2for an example).Various different window functions with different properties exist. In general, theproperties spectral leakage, amplitude accuracy, and frequency resolution influencethe decision for a specific window. A so called rectangular window is automaticallyapplied whenever the sampled signal is limited to a finite acquisition length. In thiscase the window length equals the acquisition length.110.80.80.60.60.40.4Normalized AmplitudeNormalized AmplitudeDifferent window functions not only influence the spectral representation of thewindowed signal, but also the time domain representation. Fig. 2-2 shows theattenuating (weighting) effect of a Blackman window in time domain compared to arectangular 100.20.40.60.8100.20.4Normalized Time0.60.81Normalized TimeFig. 2-2:Sine wave signal in time domain. Different window functions are applied to the same signal:left - rectangular, right - Blackman110.80.8Normalized AmplitudeNormalized AmplitudeFor rare events, such as pulses, the location within the window function makes asignificant difference in terms of level accuracy. Pulses located in the central part of thewindow function will be displayed with their correct power. Pulses located towards theedges are significantly attenuated. This dependency is minimized on a real-timeanalyzer with sufficient overlapping (see section 2.4).0.60.40.20.60.40.20000.20.40.6Normalized Time0.8100.20.40.60.81Normalized TimeFig. 2-3: Pulse signal in time domain. Different window functions are applied to the same signal: left rectangular - no weighting, right - Blackman - pulses on the right and left are highly attenuatedAs mentioned in the beginning, a window function is usually chosen for itscharacteristics in the frequency domain. Fig. 2-4 shows the spectral representation ofthe sine wave signal from Fig. 2-2. The figure shows the difference between aBlackman window and a rectangular window. The Blackman window clearly reduces1EF77 3eRohde & Schwarz Implementation of Real-Time Spectrum Analysis8
Real-Time Implementation in the R&S Real-Time Analyzersthe spectral leakage, i.e. the distribution of signal power over the entire spectral range;however, the rectangular window has the best frequency resolution, i.e. the narrowestmain lobe. So given that you are looking for a very weak signal in the presence of astrong signal, the Blackman window is a good choice, since it has low spectralleakage. For many closely spaced carriers with similar power, the rectangular windowis better suited to resolve all the involved carriers.0RectangleBlackman-10Normalized Power / dB-20-30-40-50-60-70-80-20-15-10-505Normalized Frequency101520Fig. 2-4: Frequency domain view of the signal from Fig. 2-2. The Blackman window showssignificantly lower spectral leakage than the rectangular window, but a wider main lobe. The inlaycompares the amplitude accuracy.Table 2-1 gives an overview of common window functions and their spectral leakageand frequency resolution capabilities. In addition, the table lists the amplitudeaccuracy, also called scalloping loss. Whenever a frequency component of a signal isnot located on exactly an FFT bin, but somewhere in between two bins, scalloping lossoccurs. The inlay of Fig. 2-4 shows the difference in amplitude accuracy for arectangular and a Blackman window, which can be as high as 1 dB for this example.Many FFT spectrum analyzers (including real-time analyzers) offer several differentwindow functions to maximize their performance. Table 2-1 assists you in selecting thebest window function for a specific application.1EF77 3eRohde & Schwarz Implementation of Real-Time Spectrum Analysis9
Real-Time Implementation in the R&S Real-Time AnalyzersWindowSpectral irRectangle FairGoodKaiserGoodGoodFairTable 2-1: Overview of window function characteristics2.2 FFT Length and Window LengthThe length of an FFT as introduced above is defined by the number of samples thatare fed into a single FFT. Most implementations of the FFT are based on an algorithmthat takes only power of 2 lengths. A very common length therefore is 1024 bins.Assuming a given bandwidth (or span) under investigation, the FFT length determinesthe minimum achievable resolution bandwidth (RBW) or frequency separation. Clearly,a longer FFT length is equivalent to more samples and therefore a longer capture time(assuming a constant sampling rate). A longer observation (capture) time allows betterfrequency resolution, i.e. smaller RBW. Therefore, it is equivalent to a lower displayednoise and thus a higher sensitivity. Shorter FFTs benefit from less computational effortand therefore higher FFT update rates.The window length in turn describes the length of a window function that can beapplied to the time domain signal, before FFT computation. The window length cantherefore be equal to or less than the FFT length. Window functions can effectivelyshorten the FFT length, enabling the user to minimize the duration of a capture. Thisapproach can provide 100% probability of intercept (POI), even when measuringextremely narrow pulses. Section 2.6 covers this topic in detail. The R&S FSVR uses aconstant FFT (and window) length of 1024 bins. The R&S FSW provides moreflexibility, allowing a selectable span-to-RBW ratio. As mentioned above, longer FFTsare equivalent to lower RBW for a given span, i.e. a higher span-to-RBW ratio. Sincespan and RBW are common parameters for spectral measurements, these parameterscan be changed within the real-time option of the R&S FSW instead of FFT length.
Real-Time Analysis 1EF77_3e Rohde & Schwarz Implementation of Real -Time Spectrum Analysis 3 1 Real-Time Analysis 1.1 What “Real-Time” Stands for in R&S Real-Time Analyzers The measurement speed available in today's spectrum analyzers is the result of a long
Real-Time Analysis 1EF77_0e Rohde & Schwarz Implementation of Real-Time Spectrum Analysis 3 1 Real-Time Analysis 1.1 What Real-Time stands for in the R&S FSVR The measurement speed available in today's spectrum analyzers is the result of a long
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4 Rohde & Schwarz R&S FSVR Real-Time Spectrum Analyzer Specifications Operating modes signal and spectrum analyzer real-time spectrum analyzer Specifications for all operating modes Frequency Frequency range R&S FSVR7 DC-coupled 10 Hz to 7 GHz AC-coupled 1 MHz to 7 GHz R&S FSVR13 DC-coupled 10 Hz to 13.6 GHz AC-coupled 10 MHz to 13.6 GHz
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