1The problem with sweeping a wide band

Spectrum monitoring used to end at detection. An operator saw an unknown carrier, wrote down a frequency, and went looking for someone who could say what it was. The systems being built now are asked to answer that question themselves, and they answer it with a trained model.

That changes what the receiver is for. It is no longer a display feeding a human; it is a sensor feeding a statistical estimator, and the estimator inherits every property of the data it is given. The question this paper asks is therefore not how fast an analyzer can sweep, but whether what it produces is fit to train on.

A faster sweep is the first remedy to consider, and its limit is set here because everything after depends on it. The fraction of each pass spent inside any one resolution cell is RBW divided by span, and that fraction does not depend on how fast the pass is. A receiver that sweeps twice as fast revisits sooner and hears less each time, in the proportion that leaves the product unchanged. The quantity that decides what a monitoring system sees is how much of the band is being listened to at once, and sweep speed does not move it.

Start with the sweep itself. A swept receiver moves a fixed intermediate-frequency filter across the span. That filter is a physical resonator with a settling time of roughly the reciprocal of its bandwidth, and the signal is inside it for only the fraction of the sweep given by the ratio of resolution bandwidth to span. Requiring the filter to settle gives the classical relation:

The resolution bandwidth appears squared for two reasons at once, and this is the structural fact to carry. Halving it doubles the number of resolution cells to visit, and it also doubles the settling time in each one. The two effects multiply.

Table 1 works that through for a full-span survey at five resolution bandwidths, with the cell count that drives each row.

2What a swept receiver intercepts

Sweep time is not the governing number. The governing number is how long the receiver waits before it sees a given emitter at all. For a periodic emitter of pulse duration τ and repetition interval T at a fixed frequency, observed by a receiver that revisits that frequency every T_r and dwells there for t_d, the per-revisit intercept probability is the overlap of the dwell and the pulse:

The substitution is done on the page rather than asserted. Expected time to first intercept is the revisit divided by the per-revisit probability, T_r / p. Where the pulse is short against the dwell, p → t_d / T, and substituting t_d = T_r · RBW / S gives T_r · T · S / (T_r · RBW). The revisit cancels, which is the algebra behind the sentence in section 1:

Two worked cases, both for a 40 GHz span. A radar with a 1 microsecond pulse at 1 kHz repetition, observed at 1 MHz resolution with a 100 ms revisit, gives a 2.5 microsecond dwell and a per-revisit probability of 0.0035: expected time to first intercept 28.6 seconds, and a 3.4 percent chance of seeing it in a one-second look. Narrow the resolution to 100 kHz for a better look and the revisit stretches to 8 seconds, so expected time to intercept becomes 381 seconds. Improving resolution by ten made time to first intercept thirteen times worse.

A second penalty follows. An intercept is not a measurement. A pulse shorter than the reciprocal of the filter's impulse bandwidth cannot develop full response, and the displayed amplitude is low by approximately:

That 1 microsecond pulse at 100 kHz resolution reads 16.5 dB low. At 100 nanoseconds it reads 36.5 dB low. So with a swept receiver the setting that makes an emitter findable and the setting that makes it measurable are different settings, and no single sweep provides both. Figure 1 draws the first case against the emitter.

Figure 1 draws the two timelines against each other. The strips are drawn wide enough to see: at true scale a dwell would be 25 micrometers on a timeline one meter long. Read it for the order of the two rates rather than their ratio. Pulses arrive a thousand times a second and the receiver returns to that frequency ten times a second.

3What gap-free capture guarantees instead

A real-time engine transforms a continuous stream rather than tuning across it. Where a vendor publishes the governing relation rather than a headline figure, the guarantee can be computed rather than trusted:

The factor of two is the arrival-phase penalty. A burst landing anywhere inside a single transform window is detected, but its amplitude is wrong, because only part of the window held energy. Spanning two consecutive frames guarantees that at least one saw it whole. The published operating points for the 9.5, 20 and 40 GHz models are 0.512 microseconds at a 32-point transform and 32.768 microseconds at 2048 points, at frame rates of 3,906,250 and 61,035 per second respectively.

The density capture of Figure 2 was taken at neither of those two points. Its display reports a 65.54 microsecond probability of intercept, and 2 × 4096 × 8 ns is 65.536, which is 65.54 to the four digits the display carries; the handheld datasheet publishes that point, N = 4096 with option 50, for the ICX-045, ICX-060 and ICX-090. Its 60.3 kHz resolution is 1.98 bins of the 30.518 kHz spacing a 4,096-point transform gives at 125 MSPS. Five readings off one screen agree with each other and with the relation above, which is what a published relation buys over a published figure: the reader can price any transform size, not only the typical points on the datasheet.

Figure 2 is the density surface with persistence set to accumulate rather than decay. Read the color as occupancy rather than as amplitude: a faint continuous band is an emitter present at low duty cycle, and a bright narrow line is one that is always there. That distinction is not available from a max-hold trace, which reports both as a line.

Note what kind of claim this is. It is not a probability that improves with observation time. It is a boundary: below it, nothing is guaranteed; above it, everything is measured, whatever the arrival time. That difference in kind is what makes a specification meaningful, and Figure 3 draws both on one pair of axes: the step is a bound, the curve is an average, and only one of the two can be written into a requirement.

Figure 3 plots both on the same axes. The shapes matter more than the values: a step a specification can be written against, and a curve whose height depends on three settings the emitter knows nothing about.

4The pipeline, and where the data goes

A monitoring system is a sequence of volume reductions. Naming them in order, with their data rates, is the fastest way to see why the architecture is shaped as it is. The first two stages ship in SpectraCore; everything past the parameter record is the integrator's. Figure 4 sets out the stages.

The arithmetic behind the stages of Figure 4:

Table 2 turns that rate into storage per hour and per day, for the two published recording bandwidths and the whole span.

Figure 5 plots it. The difference between recording what was found and recording where it was found is the difference between a rack of disks and a shelf of them.

This is why the ICX-FieldHawk datasheets separate the two recording figures: on the 9.5, 20 and 40 GHz models burst recording covers the full 100 MHz into a 128 Mbyte buffer, which is about 0.26 seconds, while continuous recording to a host is specified at 25 MHz. The 4.5, 6 and 9 GHz handhelds publish 50 MHz of burst bandwidth (100 MHz with option 50) and 12.5 MHz continuous. Filling a buffer and sustaining a transfer are different constraints, and the datasheet states them separately. Figure 6 shows the parameterization stage of the pipeline on the instrument.

Figure 6 is the middle of the pipeline made concrete: each row is a few hundred bytes standing in for a burst that cost megabytes to record. One question remains about the last box in Figure 4, which is how the customer's classifier receives the samples. With the -SDR option, orderable on every current ICX model, the ICX-FieldHawk presents itself through SoapySDR, the vendor-neutral hardware abstraction layer, so it appears to GNU Radio and any other SoapySDR application as a standard software-defined radio device, and the instrument's calibration files install with the driver. The samples reaching the classifier are corrected before the first processing block sees them, and every standard measurement function stays installed. A system built this way inherits an existing ecosystem of detectors and demodulators instead of commissioning them, with the amplitude under every detection still traceable.

Where the classifier has to run at the sensor rather than in a data center, the ICX-FieldHawk-R IP68 tablets, the ICX-400R and ICX-095R, take an optional onboard NVIDIA Jetson Orin NX module, option 08, rated by its maker at up to 117 TOPS (sparse INT8) in a module power mode drawing up to 40 W. The tablet's published typical power is 10 to 16 W, so sustained throughput depends on the power mode the enclosure allows, and the model that runs on it is the user's own, loaded through the same API.

5Derived requirements

Sections 2 to 4 were an argument about architecture. Collapsed into requirements they are six things a reader can score any vendor against, this one included. The reasoning is in those sections; Table 3 indexes it.

6Why the capture sets the ceiling

The classifier never sees the emitter. It sees it after the channel and after the instrument. Class, signal and observation form a Markov chain, so the mutual information between the class and what the model sees can never exceed that between the class and the signal. The data processing inequality states it as a theorem: no architecture, no quantity of training data and no amount of compute recovers information the capture destroyed.

Four capture properties feed directly into that risk.

• Gaps. A capture with gaps is not a shorter capture, it is a different signal. A burst straddling a gap has the wrong duration, and periodic gating convolves the spectrum with a comb set by the instrument, which a cyclostationary feature extractor cannot tell from an emitter's own framing.
• Amplitude flatness. If the front end is 1.5 dB hotter at 2.4 GHz than at 5.8 GHz, and one class lives in each band, the model can score well by reading the front-end response, and a random train-test split does not reveal it.
• Phase noise. Integrating a flat −100 dBc/Hz from 1 kHz to 1 MHz gives 0.81 degrees of residual phase error, or 1.41 percent of error vector magnitude before the signal arrives, against the 3.5 percent that 3GPP TS 38.104 allows a base station transmitting 256-QAM. The local oscillator has spent two fifths of the budget, and classification errors concentrate between adjacent QAM orders. The receiver caps modulation-order accuracy before the model is trained. Figure 7 plots the contribution against the phase-noise level.
• Quadrature imbalance. One tenth of a decibel of gain error and one degree of phase error give about 40 dB of image rejection. The resulting mirror is spectral asymmetry manufactured by the receiver, and spectral asymmetry is a genuine modulation feature. The artifact has the same form as the feature.

7Measurement practice

None of this depends on which analyzer is used, and all of it determines whether the resulting dataset is worth training on.

1. Set the false-alarm budget first. Forty gigahertz at 100 kHz resolution is 400,000 cells. At one revisit per second, holding false alarms to one per hour needs a per-cell threshold about 6.1 standard deviations above the noise for a single look. Requiring three detections in five looks reaches the same rate at about 3.3 standard deviations, buying back most of the sensitivity at the cost of five times the latency and every emitter that appears fewer than three times. Figure 8 plots both.
2. Randomize everything that is not the label. Gain state, band, antenna, cable, site, day and temperature. Where a variable cannot be randomized, record it so its contribution can be tested afterward.
3. Record the SpectraCore state with every capture. Center frequency, sample rate, reference level, attenuation, decimation, transform size, temperature and a disciplined timestamp. An IQ file without its sidecar cannot be interpreted.
4. Decimate at the point of capture. Record the emission's bandwidth, not the survey's. Keeping 200 kHz of an emission found in a 100 MHz window is a 500 to 1 reduction before any other measure is applied, and the decimation filter returns the matching processing gain.
5. Never transform across a recorded gap. Mark overflows in the record and skip those frames rather than letting the seam manufacture wideband energy.
6. Calibrate the classifier's confidence. Neural network classifiers are systematically overconfident (Guo and others, 2017), and in a monitoring system the confidence number drives operator workload, so an uncalibrated score is an operational defect rather than a statistical footnote.

Field evidence

Monitoring programs built on this architecture, with the capture guarantee and the documented interface bought and every layer above the IQ line written by the integrator, which is the arrangement Figure 4 draws, report one decision as load-bearing, and it is not the classifier. A system that changes its detector can reprocess its archive and arrive at a comparable answer; a system that changes its receiver cannot compare across the change at all, so the capture is the only part of the pipeline that has to be right the first time.

8Limitations

• Sweeping is still the right tool for some jobs. Against a stationary carrier a swept receiver at a narrow resolution bandwidth reaches a lower noise floor and resolves closer-spaced tones than a real-time engine of the same cost, because it spends its entire dwell in one cell instead of dividing it across a band. If every emitter of interest is always on, the intercept arithmetic in section 2 never binds and the real-time engine adds nothing.
• A classifier cannot name what it was never trained on. A closed-set model assigns every input to a known class, confidently. Open-set methods reduce this; they do not remove it.
• Reported accuracy is conditional. Figures around 95 percent are reported on synthetic data with a known class set and a fixed record length; the same model over the air loses a substantial part of it (O'Shea, Roy and Clancy, 2018). An accuracy quoted without record length, class set and collection conditions is not a specification.
• The operator stays in the loop. The output that matters most operationally is the admission that the system has never seen something before, and that admission is by construction one the system cannot resolve. The metric that matters is not accuracy but operator-hours per confirmed identification.
• Externals and content are different activities, legally as well as technically. Frequency, bandwidth, timing, modulation and bearing are monitoring. Recovering content is not, and the architecture should reflect that: classify externals by default and gate demodulation behind an explicit, logged, authorized action. That is the same architecture the storage arithmetic already forced.

9Summary, definitions and further reading

Table 4 collects the governing relations and published values with their conditions.

CFAR

Constant false alarm rate. A detection threshold estimated from surrounding cells so that the false alarm rate stays fixed as the noise floor varies.

Cyclostationarity

Periodicity in a signal's second-order statistics, tied to symbol rate, carrier or frame structure. Stationary noise has none, which is why cyclostationary detection works below the energy detection floor.

Probability of intercept

The minimum duration a signal must be present for the analyzer to measure its amplitude correctly. A stronger claim than the duration required merely to detect it.

Revisit interval

The time between successive observations of the same frequency by a swept receiver. The quantity that governs what it misses.

Further reading

• Recommendation ITU-R SM.1600, Technical identification of digital signals. The anchor standard for identifying digital emissions from signal externals and IQ recordings.
• Recommendation ITU-R SM.1880, Spectrum occupancy measurement and evaluation.
• ITU Radiocommunication Bureau, Handbook: Spectrum Monitoring.
• T. J. O'Shea, T. Roy and T. C. Clancy, "Over-the-air deep learning based radio signal classification," IEEE Journal of Selected Topics in Signal Processing, vol. 12, no. 1, 2018. The source of the synthetic-versus-over-the-air accuracy gap.
• C. Guo, G. Pleiss, Y. Sun and K. Q. Weinberger, "On calibration of modern neural networks," Proceedings of the 34th International Conference on Machine Learning, 2017.
• T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed., Wiley, 2006, section 2.8, for the data processing inequality.
• 3GPP TS 38.104, NR; Base Station (BS) radio transmission and reception, table 6.5.2.2-1, for the EVM limits by modulation order.
• Berkeley Nucleonics, the ICX -SDR option datasheet and the SDR Integration Handbook (ICX-FieldHawk), berkeleynucleonics.com.

If you are specifying a monitoring sensor and want to work through the intercept and storage arithmetic against your own emitters of interest, our application engineers would be glad to do that with you.