1Why the environment has to become a file

A receiver fault that appears once an hour at one intersection cannot be bisected against a radio environment that never recurs. The scene at any antenna is the superposition of every emitter in view, each with its own traffic, power control and mobility, and two successive observations of the same place differ in interferer timing, channel occupancy and fading state.

A standards-compliant generated waveform repeats exactly, and it is the right stimulus for conformance. It contains only what was synthesized: no co-channel clutter, no adjacent-channel leakage, no unplanned transients. A receiver that passes it can still fail in the field on the content the synthesis did not include.

Record and playback is real and repeatable at a chosen point in space. Capture the environment once as complex samples; replay it on the bench as often as needed, identically. The recording becomes a portable, versionable test asset: a scene that can be shared between teams, replayed against every firmware candidate, and attached to a fault report as the reproduction recipe. Figure 1 draws the chain this paper works through.

2Complex baseband, and why bandwidth B needs sample rate B

A real band-limited signal at carrier frequency f_c can be written as an in-phase term on a cosine and a quadrature term on a negative sine. Those two real streams, taken together, carry both the amplitude and the phase of the modulation, and the generator reverses the operation exactly:

A real signal has a conjugate-symmetric spectrum, so each real sample carries one degree of freedom and unambiguous representation up to bandwidth B needs a sample rate of twice B. A complex sample carries two degrees of freedom, and a complex sequence at rate f_s represents a full span of width f_s about the tuned center without any symmetry requirement. So bandwidth B needs complex sample rate B rather than 2B. No information is gained: B complex samples per second is 2B real numbers per second either way. Figure 2 draws the two representations.

Figure 3 shows that pair on an instrument display: the two traces are the same signal a quarter cycle apart, and the rate field under them is the sample rate, shown on a screen as a setting rather than in an equation.

3What limits fidelity

Every impairment appears twice in a two-instrument chain, once in the analyzer and once in the generator, and where the two are uncorrelated they combine as a root sum of squares in error-vector terms. Images and spurs at related offsets do not obey that and can add coherently at the worst frequency in the scene. The two ends are not symmetric, and which end to specify more tightly follows from that.

Quantization, and the bits a converter delivers

Ideal quantization of a full-scale sine into b bits gives a signal to noise ratio of 6.02b plus 1.76 decibels. Real converters fall short, and the figure to use is the effective number of bits derived from measured signal to noise and distortion:

Two consequences follow. Headroom costs bits: every decibel of unused input range below full scale is a decibel of signal to noise forfeited, so reference level at capture is a fidelity decision rather than a convenience, and a multi-emitter scene with a high peak to average ratio sets that headroom. And decimation buys it back, at ten times the log of the ratio between the original and final bandwidths: recording a 5 MHz emission out of a 100 MHz span is a factor of twenty, or 13.0 dB, which is more than two bits returned for the cost of a filter setting.

Quadrature imbalance, and why it is the term to check

Gain imbalance and quadrature phase error between the I and Q paths produce an image of the signal mirrored about the center frequency, with a rejection ratio of approximately:

Table 1 shows how little imbalance it takes to cap image rejection, and Figure 4 plots the relation across the range that matters in practice.

Spectral asymmetry about a carrier is a genuine modulation feature: it is how single sideband differs from double, and it appears in asymmetric channel allocations. An imbalance image is spectral asymmetry manufactured by the instrument. In a replayed scene, the image of a strong emitter can land on a weak wanted signal mirrored about the center, and nothing downstream can tell the two apart. That corruption is specific to record and playback, and section 7 gives the test for it.

Reference offset and phase noise

A reference offset of x parts per million displaces the carrier by x × 10⁻⁶ times the carrier frequency, and it does so twice, in different ways. An offset at capture is frozen into the file as an apparent frequency error common to every emitter in the scene. An offset at replay shifts the reconstructed scene. Locking both instruments to a shared 10 MHz reference removes the second and cannot remove the first. The same offset also stretches time: one part per million lengthens a sixty second recording by sixty microseconds and scales every modulation rate by the same factor.

Phase noise enters the same way, once at each end, and what a demodulator sees is its integral between the carrier-recovery bandwidth and the symbol-rate edge. A phase-noise figure at one offset therefore does not score the term; the figure is needed across the offsets the modulation occupies, which is how requirement R4 of section 6 is written.

4How long a scene can be

Figure 5 draws the two recording figures a datasheet carries on one timeline, and the arithmetic behind both is one line:

Table 2 turns that rate into scene duration, and Figure 6 plots the two regimes against bandwidth.

This is why a datasheet quotes two different bandwidths. Burst capture writes into instrument memory at fabric speed and is bounded by capacity: the ICX-FieldHawk 9.5, 20 and 40 GHz models publish a 128 Mbyte buffer and a 100 MHz burst bandwidth, which at 125 MSPS and 16-bit components is about 0.26 seconds. Continuous capture has to sustain the slowest link in the chain indefinitely, and is published at 25 MHz for those models. The 4.5, 6 and 9 GHz handhelds publish 50 MHz burst (100 MHz with option 50) and 12.5 MHz continuous. Filling a buffer and sustaining a transfer are different constraints, and a scene specification names which one it needs.

Three levers manage the arithmetic. Decimate at capture and record the emission's bandwidth rather than the survey's, which is where the 13 dB of section 3 is spent. Trigger rather than stream, with enough pre-trigger depth to hold the leading edge, since the turn-on transient is where emitter signatures are. Choose the format deliberately: 32-bit float doubles the file for no information gained over 16-bit integers, and lossless compression on near-noise IQ achieves little.

5Two channels, and what synchronized means

Multi-antenna receivers, wanted-plus-interferer scenarios and receiver blocking tests all need two generator outputs at once. The word synchronized covers three different requirements, and a specification that does not say which one it needs cannot be scored. Table 3 separates the three rungs, in ascending cost and ascending capability.

The wanted-plus-interferer case of Figure 7 solves a problem a single channel cannot. In a single recorded scene the ratio between the wanted signal and the interference is frozen at capture. Splitting them across two channels lets the operator sweep interferer power while the wanted carrier stays put, which is what a blocking or desensitization test requires. Using a recorded real aggressor rather than a clean modulated blocker also reproduces the mechanisms an idealized blocker understates: reciprocal mixing, converter overload and gain-control pumping. Figure 8 shows what a single recorded scene holds.

Figure 8 read against the fidelity budget: each panel is a different projection of one array of complex samples, so an impairment introduced at capture appears in all four and can be removed from none. That is the asymmetry of section 3, seen from the operator's side of the display.

6Derived requirements

Sections 3 to 5 were a fidelity budget. Turned into requirements, they are what to put on a purchase specification for a record and playback bench, and Table 4 states each one with the term it comes from. Note which half of the chain each requirement lands on: that split is the reason this paper keeps the two instruments apart. R2 and R3 are the ones a datasheet does not answer directly, which is why section 7 measures them rather than reading them.

Scoring the capture half

A requirements table that is not scored is a rubric rather than an argument, so here is the capture half against the requirements a datasheet can answer. The ICX-FieldHawk 9.5, 20 and 40 GHz models, driven by SpectraCore or by the published interfaces beneath it, publish IQ sample rates to 125 MSPS with decimation from 1 to 4096, which satisfies R1 for any scene up to 100 MHz with the 1.25 factor in hand and gives the R5 lever directly. R5 itself is published as two separate figures rather than one: burst recording to 100 MHz into 128 Mbyte, and continuous recording to a host at 25 MHz, which is the form the requirement was written to find.

R4 is answered at four offsets. The reference input is published (external 10 MHz, MMCX), the standard TCXO and the option 01 OCXO both publish frequency accuracy under 1 ppm, with the OCXO's temperature stability under 0.15 ppm, and single-sideband phase noise is published at 1 kHz, 10 kHz, 100 kHz and 1 MHz offsets at two carriers per model, as Table 5 lists. For a modulation whose carrier-recovery bandwidth and symbol-rate edge fall between 1 kHz and 1 MHz, those four points bracket the integral of section 3; outside that range, and at carriers between the two published ones, the figure is not published, so R4 is met for offsets to 1 MHz and is a measurement beyond it.

Two of the six cannot be scored from the datasheet, and saying so is the point of the exercise. R2 is not published as SINAD at the record bandwidth, so the effective bits behind a capture are a measurement the buyer makes. R3 has two parts, and only one is published. RF image rejection, the superheterodyne front end's response at the image frequency, is published: above 90 dBc typical with spur rejection standard from 90 MHz to 9.5 GHz on the 9.5, 20 and 40 GHz models, and above 58 dBc from 33 to 40 GHz on the 40 GHz model. The in-band image of equation (3), the mirror within the analysis bandwidth that quadrature imbalance produces, is not published, so the gain and quadrature imbalance that set it are measured with a single-sideband tone. Both are the terms section 3 showed cannot be corrected out afterward, and both are an afternoon on a bench that already exists.

Scoring the playback half

The playback half is a Vector Signal Generator with an arbitrary I/Q generator that plays a loaded file at the file's sample rate on the capture's center frequency, and Berkeley Nucleonics publishes one: the Model 875 vector-modulated Signal Generator, in models to 4, 6, 12, 20 and 40 GHz and with up to four channels per device. Table 6 scores it against the three requirements that fall on playback.

One application, carried through

Take a single job and run it down the table. A consumer wireless device fails intermittently at one city intersection and nowhere else, and the team cannot reproduce the failure. The scene is the 2.4 GHz band at that intersection: an access point, a microwave oven, several handsets and a Bluetooth headset, all of them moving. R1 fixes the sample rate at 1.25 times the 83.5 MHz that holds the whole band, so 104 MSPS. Decimation runs in powers of two, so 104 is not a selectable rate: the choice is 125 MSPS or 62.5, and 62.5 carries 50 MHz usable, so the whole band forces the full 125 and the file is a fifth larger than R1 alone implies. That is the ordinary way a requirement meets hardware. R5 then fixes the duration: at 500 MB/s a one-minute scene is 30 Gbyte, which the burst buffer cannot hold and the sustained path cannot reach at that bandwidth, so either the scene is decimated to the 25 MHz that carries the suspect emitters, which is the sustained figure R5 publishes and therefore has no duration limit, or it is cut to the seconds around the failure that the burst buffer holds. That is a decision about the experiment, forced by the R5 row of Table 4, and it is made before the site visit. Decimation has one exception and this scene contains it: the headset hops across the whole 79 MHz, so a 25 MHz window keeps the access point and loses the hopper. For a frequency-hopping emitter the emission bandwidth is the survey bandwidth, and the only lever left is duration.

R6 decides the rest. Reproducing the failure shows only that it reproduces; finding the threshold means sweeping the interferer while the wanted signal stays put, which a single recorded scene cannot do because the ratio was frozen at capture. Two channels, a common reference and a hardware trigger turn the recording into an experiment with a variable in it: the scene answers what happened, and the second channel answers how much margin was missing. R2 and R3 apply to both, because an image or a lifted noise floor introduced at capture is replayed as though the intersection had produced it.

7Demonstrating that the replay is faithful

Fidelity is demonstrated, not assumed. Close the loop, as Figure 9 draws it: replay the file into the same analyzer under SpectraCore, capture it again, and compare against the original. Because the same instrument bounds both captures, this measures what the generation and recapture chain added, which is a slightly pessimistic bound on the generator alone.

1. Lock both instruments to a common reference before comparing, so frequency offset does not contaminate the result.
2. Align coarsely by cross-correlation, then finely by estimating and removing residual delay, phase offset and carrier frequency offset. Normalize power.
3. Report a spectral comparison: Welch-averaged power spectral densities overlaid, with maximum and root-mean-square deviation in decibels across the band. This catches passband tilt, images, added spurs and a lifted noise floor in one plot, and it is the test for the manufactured asymmetry of section 3.
4. Report error vector magnitude against the original file, not against an ideal constellation. For record and playback the first is the metric that answers the question, because the question is replay fidelity rather than signal quality; Figure 10 shows the difference.

Every step above is arithmetic on a complex array, which decides who can do it. With the -SDR option, orderable on every current ICX model, the ICX-FieldHawk presents itself through SoapySDR, the vendor-neutral hardware abstraction layer, with a GNU Radio source block and the unit's calibration carried by the driver, so the capture side of this loop can be driven from GNU Radio or from any other SoapySDR application and the samples arrive corrected. The cross-correlation, the residual-offset estimator and the Welch comparison are then existing blocks rather than a development project, and the amplitude reference underneath the fidelity number remains traceable to the instrument's calibration.

Field evidence

One requirement recurs in record and playback purchases: two or more generator channels under a single control port and a single trigger, rather than separately addressed instruments. It reads as a packaging preference and it is not. Two channels commanded separately are two instruments with two time bases, and section 5 is the reason a buyer who has run the loop above asks for one port. The synchronization rung a test needs is decided at purchase, not at setup, and it is the hardest thing to add afterward.

8Limitations

• Playback reproduces one point in space, not a channel. The recording is the scene as seen by one antenna at one location, orientation and polarization. Replayed conducted into a device, the multipath geometry is frozen and moving the device under test changes nothing.
• A single-antenna capture cannot reproduce a spatial channel. One channel records one linear combination of the wavefield. A multi-antenna receiver fed copies of it sees a fully correlated channel, which is the condition it is designed to exploit least.
• Dynamic range is capped at capture. A scene containing a strong blocker and a signal a hundred and forty decibels below it cannot be captured in one pass by any practical converter. That case needs the two-channel construction or separate captures.
• Nothing outside the captured bandwidth exists. The scene is brick-walled at the capture filter, so out-of-band blockers and image-frequency responses are untested by in-band replay.
• Playback does not respond. It cannot take part in closed loops: retransmission, power control, handover signaling, two-way ranging and transponder interrogation all meet a stimulus that never reacts. Record and playback tests receivers; it does not emulate networks.
• Where other tools are the right ones. A channel emulator when the need is parametric, statistically controlled propagation; an over-the-air chamber when spatial behavior is under test; a scenario simulator when the trajectory has to be authored rather than experienced. They are complements, not rivals.

9Summary, definitions and further reading

Table 7 is the block to lift into an evaluation matrix.

Complex envelope

The in-phase and quadrature pair that together represent a modulated carrier at baseband, carrying both amplitude and phase.

Effective number of bits

The resolution a converter delivers, derived from measured signal to noise and distortion rather than from its nominal width.

Image rejection ratio

The ratio between a wanted signal and the mirror of it produced by quadrature imbalance. Distinct from RF image rejection, which is the front end's response at the image frequency of its mixer.

Further reading

• The Signal Metadata Format Specification, the open standard for pairing an IQ file with the center frequency, sample rate, datatype and timestamp it needs to remain usable.
• ANSI/VITA 49.0 and 49.2, the packetized transport that carries IQ between instruments in real time with per-packet timing and context.
• IEEE Std 1241, terminology and test methods for analog to digital converters, which defines the SINAD, ENOB and spurious-free dynamic range used here.
• B. Razavi, "Design considerations for direct-conversion receivers," IEEE Transactions on Circuits and Systems II, vol. 44, no. 6, 1997, for the imbalance and image relation.
• Berkeley Nucleonics, the ICX-FieldHawk and Model 875 datasheets at berkeleynucleonics.com.

If you are building a scenario library and want the fidelity budget worked against your own device under test, our application engineers would be glad to go through it with you, including the cases where a channel emulator rather than a replay is the right answer.