2013 Understanding Probability of Intercept for Intermittent Signals Richard Overdorf & Rob Bordow Agilent Technologies
Agenda Use Cases and Signals Time domain vs. Frequency Domain Probability of Intercept Real-Time Spectrum Analysis Windowing and Amplitude Windowing vs. Sample Rate Display and Analyze Agilent RTSA Review 2
Finding Dynamic and/or Transient Events Where this is becoming more important: Intermittent spurious emissions (restrictions, SIGINT ) Agile communications Modern radar Jamming Switching Modes Components or subsystems 3
Time vs. Frequency Domain Time Domain: When Simple to understand Relationship to other events Peak power Repetition Instrumentation Widest bandwidth (higher SR) Triggering Capture Phase and amplitude Frequency Domain What Decompose crowded spectrum Understand the type of signals Frequency relationships Dynamic frequencies Instrumentation Higher frequency Better dynamic range Scalar or vector analysis Vector is narrow band (analysis) 4
Probability of Intercept GOAL: Find an event that is of a specified duration (or longer) The next level: Detection Accuracy Power Every event? 5
The Swept Analysis Mode A swept LO w/ an assigned RBW. Covers much wider span. Good for events that are stable in the freq domain. Magnitude ONLY, no phase information (scalar info). Captures only events that occur at right time and right frequency point. Data (info) loss when LO is not there. Lost Information Lost Information Lost Information Swept LO Freq Time 6
IQ Analyzer (Basic) Mode Complex Spectrum and Waveform Measurements A parked LO w/ a given IF BW Collects IQ data over an interval of time. Performs FFT for timefreq-domain conversion Captures both magnitude and phase information (vector info). Data is collected in bursts with data loss between acquisitions. Lost Information Analysis BW Parked LO Freq Meas Time or FFT Window Length Meas Time or FFT Window Length Time 7
What is Real-Time Analysis? In this context it means the following things: Gap free no dead time between acquisitions; all sampled data is processed; process is continuous Consistent speed all hardware implementation of FFT spectrum generation not subject to Windows task interruptions High speed measurements many thousands of FFT generated spectrums per second, vastly exceeding software FFT speed High speed displays - combine large numbers of measurements to form responsive, insight-producing displays 8
Real Time Spectrum Analysis A parked LO w/ a given IF BW Collects IQ data over an interval of time. Data is corrected and FFT d in parallel Vector information is lost Advanced displays for large amounts of FFT s Parked LO Freq Acquisition or slice time Acquisition or slice time Real-time BW Time 9
Simplified block diagram of a real-time system ADC Real-time corrections and decimation Time Domain Processor Overlap Memory FFT Engine Power vs Time trace memory Display trace memory Display trace memory Frequency Mask Trigger Display processor 10
The FFT At first glance Window Window Samples 11
Specifications for POI Target: Never miss a signal get it 100% of the time Amplitude reading equivalent to CW signal Trigger on the event using frequency mask trigger (FMT) 12
Windowing Basics Off bin vs. on-bin On-bin: even number of wavelengths in FFT Off-bin: uneven number of wavelengths in the FFT Degraded SNR, Inaccurate representation of the signal, Poor visual representation FFT size Larger the FFT the narrower RBW Lower noise floor Better Resolution 13
Windowing Variations Rectangular Does not attenuate signal Poor representation of off-bin signals SNR degradation Other windows Kaiser, Blackmann-Harris, Hanning Much more forgiving for where signal lands in FFT More attenuation of the signals as you get further away from the center 14
Windowing Understanding Choices Rectangular Blackmann-Harris Hanning Kaiser Flat-top 15
Signals that are shorter than the FFT Signal shorter than 1 FFT Signal amplitude will not be accurate Function of what percentage the signal is on for FFT length Amplitude reported is a function of the area under the curve (window) Signal On 16
Signals that are shorter than the FFT Use cases Examples Sample rate 200 MHz, 1024 pt. FFT Full amplitude accuracy (5.12 us) Example 1 Assume ¼ of the window and right in the middle Middle of window (blue) Example 2 Assume ¼ of the window and starting at the very right side Example 1: -4.125 db Example 2: -29.129 db 17
Effect of Sample Rate Sample rate changes time scale t Same number of points in FFT but they come faster Same signal (t is the same) Top signal represents a slow sample rate Bottom signal represents a faster sample rate samples t Time samples 18
Effect of Overlap FFT clock running faster than the sample rate The larger the difference the more the overlap P = (1024*(Fclk Fs)/Fclk). Samp Rate (MHz) Span (MHz) Overlap (points) Duration for 1024 Window (usec) Duration for 512 Window (usec) Duration for 256 Window (usec) Duration for 128 Window (usec) Duration for 64 Window (usec) Duration for 32 Window (usec) 200 160 341 8.53 * 5.97 4.69 4.05 3.73 3.57 150 120 512 10.23 * 6.82 * 5.11 4.26 3.83 3.62 100 80 682 13.65 * 8.53 * 5.97 4.69 4.05 3.73 50 40 853 23.88 * 13.6 * 8.52 * 5.96 4.68 4.04 25 20 938 44.40 * 23.9 * 13.6 * 8.52 * 5.96 4.68 19
Effect of Overlap For full amplitude accuracy the signal must stay on for almost 2 FFT s 1024 point window Center of window is spaced 1024 samples apart Signal must last 1024 + 1023 32 point window Signal must last 1024 + 31 FFT size is still 1024 20
Effect of Overlap The number of samples (N) the signal must last for amplitude accuracy equal to a CW signal is: N = (Window Size + 1024 - P - 1) To calculate the minimum duration a signal would need to be for full amplitude accuracy: Tmin = N / Fs Example (32 pt window 341 pt FFT overlap): N = (32 + 1024-341 - 1) = 714 ; Tmin = 714 / 200 (MHz) = 3.57 us Example (1024 pt window 341 pt FFT/window overlap): N = (1024 + 1024 341 1) = 1706 ; Tmin = 1706 / 200 (MHz) = 8.53 us 21
Detection Using FMT 22
Signals with Amplitudes Greater than the Threshold Goal: Calculate what duration is required if the signal is 40 db above the mask (using 200 MHz SR) Worst case: signal at 854 (683 +171) The sum of the coefficients must reach 0.01 times the sum of all the coefficients must total; (20log(0.01)) = -40 db Window Rectangular: 11 samples Blackman Harris: 65 samples 23
Overlap Lowering the sample rate Lowering the sample rate from 200 MHz to 100 MHz yields twice as many points (682 total) Summing the coefficients to reach 0.01 times the sum of all the coefficients. Blackman Harris window: 100 MHz: 8 samples 200 MHz: 65 samples It takes twice as long to take the samples (5 ns vs. 10 ns) but takes the required signals down from 325 ns to 80 ns. 24
Overlap and SR 100% POI Spec vs. Offset for 1024 pt. Blackman-Harris Window Samp Rate (MHz) Span (MHz) Overlap (points) Duration 0 db offset (usec) Duration 6 db offset (usec) Duration for 12 db offset (usec) Duration for 20 db offset (usec) Duration for 40 db offset (usec) Duration for 60 db offset (usec) 200 160 341 8.53 * 3.42 * 2.44 * 1.58 * 0.325* 0.035* 150 120 512 10.23 * 3.42 * 2.12 * 1.04 * 0.120* 0.013* 100 80 682 13.65 * 3.48 * 1.76 * 0.71 * 0.080* 0.010* 50 40 853 23.88 * 4.66 * 2.22 * 0.88 * 0.100* 0.020* 25 20 938 44.36 * 8.36 * 4.00 * 1.64 * 0.240* 0.040* 25
When Detection is All That is Needed 100% POI Spec vs. Offset for 1024 pt. Rectangular Window Samp Rate (MHz) Span (MHz) Overlap (points) Duration 0 db offset (usec) Duration 6 db offset (usec) Duration for 12 db offset (usec) Duration for 20 db offset (usec) Duration for 40 db offset (usec) Duration for 60 db offset (usec) 200 160 341 8.53 * 3.42 * 1.29 * 0.515* 0.055* 0.010* 150 120 512 10.23 * 3.42 * 1.71 * 0.69 * 0.073* 0.013* 100 80 682 13.65 * 5.13 * 2.57 * 1.03 * 0.110* 0.020* 50 40 853 23.88 * 10.26 * 5.14 * 2.06 * 0.220* 0.040* 25 20 938 44.36 * 20.52 * 10.28 * 4.12 * 0.440* 0.080* 26
Repetitive Pulses Consistently viewing smaller signals Input signal: Constant successive pulse stream Device Analyzers FFT: Smallest window 1024 pts 32 pt window Zero padding 27
Repetitive Pulses Understanding the use case Overlaying input with analyzer FFT. Can not be synchronized! Must be long enough string to eventually line-up! 28
Real-Time Displays Video Example Video Example Video Example Video Example 29
Frequency Mask Trigger (FMT) Build Mask from trace and add offsets if required Edit table or use mouse to drag the mask points to the desired location Various criteria for Trigger: Enter, Leave, Inside, Outside, Enter Leave, Leave Enter Upper, Lower or Both masks available Import or Export masks as required FMT Combined with 89600B VSA software for further analysis Video Example 30
Using Post Processing for Deeper Analysis Advantages Mix and match FFT size and window size Use 99.99% overlap (view signal sample by sample) Correlation techniques are easier to accomplish Visualize data in multiple domains Typically more measurements Cataloged for reference Trade-offs: Acquisition limited Longer analysis time Using FMT More efficient capture Easier implementation 31
Performance X-Series Signal Analyzer Portfolio Oct 09 89600B VSA software Premier signal analysis & troubleshooting Sep 06 PXA X-Series Drive your Evolution 3 Hz to 50 GHz Oct 09 CXA X-Series Master the Essentials 9 khz to 26.5 GHz Sep 07 EXA X-Series Balance the Challenges 10 Hz to 44 GHz Price MXA X-Series Accelerate in Wireless 10 Hz to 26.5 GHz MXE CISPR 16-1-1 2010 Compliant EMI Receiver 32
PXA with Real-Time Specifications Feature Frequency Range Sweep Real Time Analysis Bandwidth Gap Free FFT Processing rate ADC Resolution A/D Converter Sample Rate Min signal duration for 100% Probability of intercept (with full Amp Accy) Min detectable signal duration (StM > 60dB) 3Hz to 3.6/8.4/13.6/26.5/44/50GHz Swept & FFT 85MHz / 160MHz 292,968.75 FFT/s 14 bit 400 Msa/s (200MHz complex) 3.57ms >5ns (nominal) Window Length 32-1024 RBW range Filter Type 6 RBW selections per span Gaussian, Flattop, Blackman-Harris, Rectangular, Hanning, Kaiser 33
Dynamic Range Lowest noise floor -157dBm/Hz at 10 GHz (radar & EW) PXA offers up to 75dB SFDR across 160 MHz bandwidth PXA s performance and low-noise path (LNP) provide the lowest noise floor, delivering significantly better performance 34
Using Software for Post Analysis 89600 VSA software, MATLAB, and SystemVue Using FMT to identify & immediately capture I/Q data for deeper analysis in 89600 VSA software Multiple displays such as phase or frequency vs. time Demodulation of >70 modulation types 35
Use FMT on PXA with 89600B VSA for Deeper Analysis Analysis Feature PXA +Real + Time + VSA Spectrum (Magnitude - Lin/Log) Power vs. Time (Lin/Log) Spectrogram, density, persistence (spectrum only) Spectrum (Complex - Lin/Log/Phase/Re/Im/Polar) Waveform (Complex - Lin/Log/Phase/Re/Im/Polar) AM / FM / PM demod (vs. time or vs. freq) Flexible Vector demod (2FSK thru 1024QAM) Standards-based demod: 2G, 3G, 4G, WLAN, etc. Time-Gating PDF, CCDF, PSD, AutoCorr, User Math, etc. Spectrogram, density, persistence (for any result) Waveform capture, playback, download, export. 36
Drive your Evolution with PXA Signal Analyzer Real-time Spectrum Analysis with the N9030A PXA Widest BW and Dynamic Range Scan 160MHz Real Time BW and up to 75dB Spur Free Dynamic Range Frequency Mask Trigger Combine FMT and low noise floor to detect signals as short as 3.57ms with 100% POI Analysis of Complex signals Seamless integration with 89600 VSA software Retain Full Swept-Tuned Performance Eliminate the need for dedicated instrument and upgrade existing PXA s 37
2013 Thank you! Know you ve got it