Net Filter Discrimination: The Interference Calculation Nobody Explains

The coordination software flagged the link as a fatal adjacent-channel conflict. The 11 GHz proposal showed clear line of sight, a link budget closing with better than 35 dB of fade margin, and a frequency offset of one full channel bandwidth from the nearest co-area station. The coordination team pulled the EMC report. The printed NFD was 8.4 dB against a required value of 30 dB. The deficit was 21.6 dB.

That number was wrong.

The adjacent station was operating at reduced power — well below the threshold at which the FCC Part 101.111(a) absolute emission floor becomes the binding constraint rather than the relative mask. The coordination database had applied the default regulatory envelope without correcting for the floor artifact, and the resulting TX power spectral density mask was wider than the actual radio would ever produce. The NFD calculation integrated over a phantom spectrum.

Most engineers who run coordination never see this. The software presents NFD as a black-box output — a number with a pass or fail attached. The derivation is absent from the report. The mask assumptions are absent from the report. The grounds for challenging the result are absent from the report unless you know to ask for them.

This article shows the derivation, the numerical implementation, and the two most common places where the inputs go wrong.

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I. From First Principles

§1 NFD is a ratio: total transmitter power to the fraction of that power that passes through a receiver’s IF filter when the transmitter and receiver are tuned to different frequencies. Formally, define the transmitter’s normalized power spectral density as $P_{TX}(f)$ in watts per hertz, normalized such that:

$${\int }_{-\infty }^{\infty }{P}_{TX}(f)df=P_{\text{total}}$$

Define the receiver IF selectivity as $H_{RX}(f)$, a dimensionless transfer function equal to unity at the passband center and falling toward zero in the stop band. Both functions are in general symmetric about their respective carrier frequencies.

When the transmitter carrier is at $f_0$ and the receiver is tuned to $f_0+\Delta f$, the receiver sees the transmitter’s PSD convolved against a filter shifted by $\Delta f$. The power that leaks through — the interference power — is the integral of the product:

$$P_{\text{leak}}(\Delta f)={\int }_{-\infty }^{\infty }{P}_{TX}(f)\cdot H_{RX}(f-\Delta f)df$$

NFD is defined as the ratio of total transmitter power to this leaked power, expressed in decibels:

$$\text{NFD}(\Delta f)=10{\log }_{10}\left[\frac{{\int }_{-\infty }^{\infty }{P}_{TX}(f)df}{{\int }_{-\infty }^{\infty }{P}_{TX}(f)\cdot H_{RX}(f-\Delta f)df}\right]$$

As $\Delta f$ increases, the receiver filter shifts further from the transmitter’s emission, the overlap between $P_{TX}(f)$ and $H_{RX}(f-\Delta f)$ decreases, and the denominator shrinks — meaning better discrimination. Coordination databases can err on both sides: overestimating the TX emission width, or underestimating the RX selectivity depth.

§2 A worked example illustrates the sensitivity. Consider a transmitter occupying a 28 MHz channel under FCC Part 101, with a mask that is flat within the authorized bandwidth and falls to −25 dBc at the channel edge. A receiver with an 8-pole Butterworth selectivity characteristic, 3 dB down at the passband edge, provides approximately 48 dB of stop-band attenuation at one channel separation. At $\Delta f=28$ MHz (adjacent channel), the transmitter’s −25 dBc shoulder sits directly on the receiver’s transition band. The leaked power integral is dominated by the overlap between the transmitter’s shoulder and the receiver’s transition region.

At $\Delta f=56$ MHz (two channels), the shoulder is past the stop-band edge and the integral is dominated by the transmitter’s deep out-of-band emissions. NFD rises above 50 dB. The question of whether the adjacent-channel case passes or fails hinges on the precise shape of both masks in the transition region — exactly where parametric approximations diverge from vendor-measured data.

§3 The ETSI EN 302 217-2 Class 4 mask translates the roll-off requirement into specific attenuation values at four breakpoints referenced to the carrier. For a 28 MHz channel:

Offset from carrier	Offset in BW	Min. attenuation
±14 MHz	0.5 BW (band edge)	0 dBc
±21 MHz	0.75 BW	−30 dBc
±28 MHz	1.0 BW (one channel)	−33.5 dBc
±56 MHz	2.0 BW (two channels)	−41.9 dBc

Beyond ±21 MHz, attenuation increases logarithmically:

$$A(f)=-30-28{\log }_{10}\left(\frac{|f|}{21}\right)\text{dBc, }|f|>21\text{ MHz}$$

The 28 dB/decade slope is shallower than FCC Part 101’s 23 dB/decade beyond the shoulder, but ETSI Class 4 starts 5 dB deeper at the initial breakpoint: −30 dBc at 0.75 BW vs. −25 dBc at 0.5 BW for FCC. In practice, both masks reach comparable stop-band depths by two channel spacings. Equipment routinely exceeds these regulatory envelopes by 10–15 dB in the transition region, which is why measured NFD consistently exceeds the coordinated value.

§4 The receiver IF selectivity is the second operand in the convolution. The 8-pole Butterworth model has a closed-form magnitude response:

$$|H(f)|={\left[1+{\left(\frac{f}{f_c}\right)}^{16}\right]}^{-1/2}$$

where $f_c=B/2$ is half the authorized channel bandwidth — 14 MHz for a 28 MHz channel. At key offsets from the filter center:

Offset from RX center	Normalized $f/f_c$	Attenuation
±14 MHz	1.0	−3.0 dB
±21 MHz	1.5	−28.2 dB
±28 MHz	2.0	−48.2 dB
±42 MHz	3.0	−64.3 dB

The 45 dB transition from −3 dB to −48 dB occurs over a single octave (14 to 28 MHz offset). This octave coincides with the TX mask’s own transition region — so errors in either curve concentrate their effect on the overlap integral at exactly the offset where conflicts are most likely to occur.

Physical IF filters in fixed microwave equipment use crystal or SAW resonators to achieve selectivity comparable to a Butterworth model, but with steeper actual roll-off in the 1.5–2.0 $f_c$ region due to higher effective filter order at the resonator level. This gap between the Butterworth model and measured hardware selectivity is systematic, and it always favors the equipment: real radios are harder to interfere with than the coordination model predicts.

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II. The TN-360 Numerical Implementation

§5 Coordination databases do not perform continuous integration. They discretize both spectral masks into frequency bins — typically 100 kHz or 1 MHz wide, depending on the applicable channel plan — and sum the products across bins. For a bin width $\delta f$ and bin centers $f_k$:

$$\text{NFD}(\Delta f)\approx 10{\log }_{10}\left[\frac{\sum _k{P}_{TX}(f_k)\delta f}{\sum _k{P}_{TX}(f_k)\cdot H_{RX}(f_k-\Delta f)\delta f}\right]$$

The $\delta f$ terms cancel in the ratio, so the result is independent of bin width provided the masks are well-sampled. ISED TN-360 specifies the filter width parameter as ten times the effective TN-360 bandwidth, spanning five effective bandwidths on each side of center. For a 28 MHz channel, this yields a computational window of roughly ±140 MHz.

§6 When the transmitter’s emission designator is present in the TN-360 mask table, the database uses the TN-360 mask directly. This is the intended case. When the emission designator is absent or unrecognized, the database falls back to the generic regulatory envelope specified in FCC 47 CFR Part 101.111(a) for the licensed fixed service. This envelope is defined by the rule, not by the equipment, and represents a worst-case bound rather than a typical emission characteristic. When even that fails — when the modulation type cannot be matched to any mask in the fallback chain — some implementations fall back to a Gaussian approximation, which has no physical basis for digital modulation and can be significantly wrong in the transition region.

Each step down the fallback chain widens the effective TX mask used in the denominator integral. A wider TX mask creates more spectral overlap with the receiver filter at any given $\Delta f$, reduces the denominator, and decreases the computed NFD. The software does not flag which mask was used.

The correct diagnostic is to pull the raw EMC report data, identify the emission designator against the TN-360 table, and confirm that the mask used matches the designator. If the database has fallen back to a generic envelope, the coordination is using an upper-bound TX mask that the actual equipment cannot produce.

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III. Procedural Trap 1 — The Low-Power Correction Floor

§7 FCC 47 CFR Part 101.111(a) specifies both a relative emission mask (in decibels relative to the mean transmitter output power, dBc) and an absolute emission floor of −13 dBm/MHz for any out-of-band emission. The relative mask defines how steeply emissions must fall outside the authorized bandwidth. The absolute floor sets the minimum measurable emission limit regardless of transmitter output power.

At high transmitter power levels, the relative mask is always the binding constraint. The absolute floor is far below what the relative mask permits, and has no effect on the calculated NFD. As transmitter output power decreases, the in-band power spectral density drops, and the out-of-band emissions expressed in dBm/MHz drop with it — until they reach the −13 dBm/MHz floor. Below that power level, the floor becomes the binding constraint.

The problem for NFD arises from how the floor translates back into dBc. When the absolute floor binds, the apparent out-of-band emission is not a fixed number of dB below the carrier — it is a fixed number of dBm/MHz, which translates to a progressively smaller dBc value as the carrier power decreases. At a transmitter output of $P_{TX}$ dBm spread across bandwidth $B$ MHz:

$$\text{In-band PSD}=P_{TX}-10{\log }_{10}(B)\text{[dBm/MHz]}$$

The floor binds at the emission mask shoulder when:

$$P_{TX}-10{\log }_{10}(B)-\text{mask attenuation (dBc)}<-13\text{ dBm/MHz}$$

For a 28 MHz channel with a −25 dBc shoulder:

$$P_{TX}<-13+25+10{\log }_{10}(28)\approx +26.5\text{ dBm}\approx 450\text{ mW}$$

§8 A pair of cases makes the magnitude of the error concrete. Both use the 28 MHz FCC mask, adjacent channel ($\Delta f=1$ BW).

Case A — $P_{TX}=+23$ dBm (200 mW):

$$P_{\text{PSD}}=23-10{\log }_{10}(28)=+8.5\text{ dBm/MHz}$$

Shoulder emission from relative mask: $8.5-25=-16.5$ dBm/MHz. The floor is at $-13$ dBm/MHz — 3.5 dB higher. The floor binds. Effective shoulder:

$$A_{\text{eff}}=-13-8.5=-21.5\text{ dBc}\text{(vs. −25 dBc)}$$

The database uses a shoulder 3.5 dB shallower than the mask specifies, inflating the denominator integral by a corresponding factor.

Case B — $P_{TX}=+5$ dBm (3.2 mW):

$$P_{\text{PSD}}=5-10{\log }_{10}(28)=-9.5\text{ dBm/MHz}$$

Shoulder from relative mask: $-9.5-25=-34.5$ dBm/MHz. The floor at $-13$ dBm/MHz is 21.5 dB higher. Effective shoulder:

$$A_{\text{eff}}=-13-(-9.5)=-3.5\text{ dBc}\text{(vs. −25 dBc)}$$

At +5 dBm, the database treats the shoulder as only 3.5 dB below the carrier. The phantom emission is 21.5 dB stronger than the radio actually produces. The resulting NFD discrepancy — the gap between what the database computes and what the physical system achieves — is on the order of 15–20 dB.

LOW-POWER FLOOR TRAP

NFD actual: 15.5 dBNFD database: 15.1 dB

TX OUTPUT POWER+23 dBm (200 W)

0 dBm (1 mW)↓ floor binds at shoulder below +27 dBm ↓+30 dBm (1 W)

Gold: actual TX PSD in dBm/MHz (relative mask, scales with power). Orange fill: phantom emission — the gap between the floor and the relative mask that the database adds when the floor binds. Blue: RX selectivity at +1 BW offset. Below +27 dBm, the phantom emission lifts the denominator integral and the database NFD diverges downward.

§9 Coordination databases handle the floor correction inconsistently. Some implementations apply it automatically when the TX power field is below threshold. Others apply the generic regulatory mask unconditionally, without checking whether the absolute floor is the binding constraint for the stated power level.

The fix is manual recalculation. Determine the actual TX output power, compute the in-band PSD, identify whether the absolute floor binds at the shoulder, and if so, substitute the correct floor-limited attenuation value into the NFD integral. Write the recalculation into the technical justification. ISED’s technical analysis procedure identifies low-power mask correction as one of the enumerated grounds for conflict write-off; a well-documented recalculation is sufficient to resolve the flag provided the corrected NFD meets the applicable threshold.

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IV. Procedural Trap 2 — The CCDP Double-Bandwidth Artifact

§10 Co-channel dual-polarization (CCDP) entries present a different class of error. In CCDP operation, a single radio link occupies a single center frequency using orthogonal polarizations to carry two independent traffic streams. The two polarizations are in the same channel. The emission bandwidth of each polarization is the channel bandwidth — not twice the channel bandwidth.

During batch database uploads — particularly when converting from legacy formats or when CCDP entries are generated by network planning tools that treat each polarization as a separate station record — the emission bandwidth field is frequently set to twice the authorized channel bandwidth. The upload script interprets the dual-polarization pair as two co-located transmitters occupying a combined spectrum, rather than one transmitter occupying a single channel with two polarizations. The emission designator may be written correctly, but the bandwidth parameter is wrong by a factor of two.

The TX PSD mask is defined relative to the authorized emission bandwidth. If the bandwidth field is doubled, the mask is applied to a phantom spectrum that is twice as wide as the actual emission. At any given frequency offset $\Delta f$, the widened mask has non-negligible power spectral density at frequencies where the actual transmitter is far into its stop band. The overlap integral between this phantom TX mask and the receiver selectivity is dramatically larger than the physical overlap, the denominator of the NFD equation inflates, and the computed NFD collapses.

§11 The artifact is identifiable in the raw database record. CCDP entries carry a polarization code — typically “D” in North American coordination databases — in the entry’s antenna field or emission designator extension. The emission designator itself follows ITU-R format: a CCDP 28 MHz digital link would carry the designator 28M0G7W (or equivalent) with a “D” polarization code. A batch upload error producing a bandwidth of 56 MHz would present as a record with designator prefix 56M0 — twice the authorized channel width — sometimes with polarization codes “V” and “H” on two separate records rather than “D” on one.

The audit procedure:

1. Retrieve the emission designator and bandwidth field from the raw database record (ISED TAFL or equivalent). The designator prefix encodes necessary bandwidth in ITU notation — 28M0 means 28.0 MHz; 56M0 means 56.0 MHz.

2. Cross-reference against the licensed channel plan. For ETSI 11 GHz links on the standard 28 MHz channel plan, the necessary bandwidth is 28 MHz. A record showing 56 MHz is wrong.

3. Check the polarization code. A CCDP pair on a single carrier should have one record with polarization “D” and the single-polarization channel width. Two separate records with “V” and “H” at 28 MHz each is also correct. Two records at 56 MHz, or one record at 56 MHz, is the artifact.

4. Pull the adjacent station’s frequency and confirm the conflict frequency is the CCDP carrier itself, not a harmonic.

5. Recompute NFD using the correct 28 MHz bandwidth. The conflict will typically resolve with substantial margin.

CCDP ARTIFACT

TX BW field: 28 MHzNFD: 13.3 dB

NORMALCCDP ARTIFACT

Normal: TX mask at correct 28 MHz (1 BW). ETSI Class 4 stop-band attenuation of −33 dBc at the RX center frequency. NFD threshold 30 dB — passes by -16.7 dB.

The fix requires a database correction and a manual NFD rerun with the corrected bandwidth. This falls within the enumerated write-off grounds in ISED’s technical analysis procedure. Document the original database record, the identified discrepancy, and the corrected calculation. The write-off is a data quality issue, not a propagation or equipment issue.

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V. Worked Example — Full NFD Calculation

§12 Two 11 GHz links share a coordination area under ETSI EN 302 217-2. Both use Class 4 equipment with 28 MHz channels.

• Link A (proposed TX): CH-3 at 11,025.0 MHz, $P_{TX}=+23$ dBm, ETSI Class 4 mask
• Link B (existing RX): CH-4 at 11,053.0 MHz, 8-pole Butterworth, BW = 28 MHz
• Frequency offset: $\Delta f=28.0$ MHz = 1.000 BW

Step 1 — Computation window. TN-360 specifies ±5 BW, placing the window from −5 BW to +5 BW from the TX carrier. With 1 MHz bins, this is 280 bins. Bin width $\delta f$ cancels in the ratio.

Step 2 — TX PSD by region. Frequencies referenced to Link A’s carrier:

Region	Range	TX PSD
In-band	$-0.5$ to $+0.5$ BW	0 dBc
Transition	$+0.5$ to $+0.75$ BW	0 to $-30$ dBc
Stop band	$	f

The negative-frequency side mirrors the positive side. The positive-frequency region from 0.5 to 0.75 BW is the segment of interest, because Link B’s receiver is centered at exactly $+1$ BW.

Step 3 — RX selectivity at each bin. Link B’s filter is centered at $+1$ BW from Link A. At bin frequency $f$:

$$H(f-1\text{BW})={\left[1+{\left(\frac{|f-1|}{0.5}\right)}^{16}\right]}^{-1}$$

At the region boundaries:

TX frequency	RX offset (normalized)	RX attenuation
$f=0$ (TX carrier)	2.0	−48.2 dB
$f=+0.5$ (TX band edge)	1.0	−3.0 dB
$f=+0.75$ (transition end)	0.5	$\approx$ 0 dB
$f=+1.0$ (RX center)	0.0	0 dB

Step 4 — Dominant integration region. The integrand $P_{TX}(f)\cdot H(f-1)$ peaks sharply at $f\approx +0.5$ BW. At that bin: TX is at full power (0 dBc) and the RX attenuation is exactly −3 dB — the largest product in the entire integration window. Bins from $f\approx 0.35$ to $0.50$ BW contribute the bulk of the leaked power. Beyond $f=0.5$ BW the TX drops steeply into its transition band while the RX opens fully; the falling TX wins, and the integrand collapses.

Three regions summarized:

Region	TX level	RX attenuation	Relative contribution
$f<0$	0 dBc	> 56 dB	Negligible
$0<f<0.5$	0 dBc	48 → 3 dB	Dominant (peak near 0.5 BW)
$f>0.5$	−30 dBc → deep	0 → 0 dB	Secondary

Step 5 — Result. Numerical integration over 500 bins, $\pm 5$ BW window:

$$\text{NFD}(1\text{BW})=10{\log }_{10}\left[\frac{{\sum }_k{P}_{TX}(f_k)}{{\sum }_k{P}_{TX}(f_k)\cdot H(f_k-1)}\right]\approx 37\text{dB}$$

The coordination threshold for this scenario is 30 dB. The link clears by 7 dB. The interactive widget below (§14) reproduces this result: set $\Delta F=1.00$ BW, select ETSI Class 4.

Why the band edge dominates. The RX filter transitions from −3 dB to −48 dB over the same 14 MHz range where the TX is still at 0 dBc. The integrand peak is pinned at the TX band edge. Any mask error that widens the TX band — incorrect bandwidth field, floor artifact at the shoulder, fallback to a broader regulatory envelope — shifts spectral power into this peak region and directly inflates the denominator. A 3 dB error at the shoulder translates to a 2–4 dB drop in NFD at $\Delta f=1$ BW.

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VI. When NFD Fails — The Limits of the Model

§13 NFD is a spectral convolution. Its outputs are exactly as reliable as its inputs. Several physical scenarios violate the underlying assumptions in ways that mask parameters alone cannot capture.

Wideband PA noise. The TX mask describes the modulated signal’s power spectral density. It does not describe broadband noise injected by a power amplifier operating near or at saturation. At saturation, the PA’s noise figure rises and its output noise floor — white, unrelated to the modulation — can sit 10–20 dB above the shot-noise floor across the full spectrum, well above what the emission mask specifies for out-of-band frequencies. A co-located receiver experiencing this sees an interference floor that NFD does not predict. The correct diagnostic is a wideband spectrum measurement at the antenna port, not a mask calculation.

Intermodulation from multiple co-area transmitters. NFD is computed pairwise. When three or more high-power transmitters share an antenna structure, third-order intermodulation products from any two of them appear at $2f_1-f_2$ and $2f_2-f_1$. At close frequency spacings these products land near the transmitting frequencies — potentially inside a third link’s receive band. The pairwise NFD between those two transmitters and the third receiver will pass, because neither transmitter individually produces a direct emission at the IM frequency. The IM product is a nonlinear artifact that requires a power budget analysis of the combined output stage, not a spectral convolution of individual emissions.

Near-field coupling at co-sited antennas. NFD assumes far-field radiation and free-space path loss between antennas. At co-sited installations where antenna separation is small relative to the wavelength — sub-metre spacing at 11 GHz, where $\lambda \approx 27$ mm — coupling between antennas is dominated by near-field effects that are orders of magnitude stronger than any far-field model predicts. Measured antenna-to-antenna isolation at the installation is the only valid input to the interference budget; computed NFD is not applicable.

Reciprocal mixing and LO phase noise. The 8-pole Butterworth selectivity models the IF filter’s amplitude response. It does not model the effective selectivity degradation from local oscillator phase noise, which limits stop-band performance through a different mechanism: a strong adjacent-channel signal beats against the LO’s noise sidebands to produce an in-band noise floor. At frequency offsets of one to two channel widths — where NFD calculations are most often contested — the binding selectivity limit for a receiver with LO phase noise above −110 dBc/Hz at 1 MHz offset is the phase noise density, not the IF filter roll-off. This is not captured by any spectral mask convolution. Equipment specifications that quote selectivity in this regime should reference measured phase noise, not filter order.

The NFD model is valid in its nominal regime: two stations, defined spectral masks, far-field propagation, linear transmitters. The scenarios above do not constitute failure of the coordination procedure — they constitute conditions outside its defined scope.

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VII. Interactive NFD Convolution

§14 The following widget computes NFD numerically using 500-bin discrete integration over parametric approximations of the FCC Part 101.111(a) and ETSI EN 302 217-2 Class 4 emission mask envelopes, against an 8-pole Butterworth receiver selectivity model. The shaded overlap area is the denominator integral — the power that leaks through the receiver filter. As $\Delta f$ increases, the RX mask (blue) shifts away from the TX emission peak (gold) and the overlap shrinks.

The low-power mode toggle applies the −13 dBm/MHz absolute floor to the TX mask, simulating a transmitter operating below the threshold at which the relative mask is the binding constraint.

NFD CONVOLUTION

ΔF: 1.00 BNFD: 15.8 dB

FREQUENCY OFFSET ΔF1.00 × BW

0 (co-channel)4.5 BW

FCC PART 101ETSI CLASS 4LOW-POWER MODE

Gold: TX PSD mask centered at 0. Blue: RX selectivity shifted by ΔF. Shaded area: overlap integral — the NFD denominator. Low-power mode applies the FCC −13 dBm/MHz absolute emission floor, lifting the out-of-band level and degrading NFD.

The parametric masks here are simplified regulatory envelopes. In actual coordination, the mask shape in the transition region — between the passband edge and the stop-band floor — is the determinative factor. Vendor test reports for the specific radio model will generally show steeper roll-off than the regulatory envelope, producing higher NFD values.

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Conclusion

NFD is a deterministic calculation. Given the TX power spectral density mask and the receiver selectivity characteristic, the result at any frequency offset is uniquely specified by the convolution integral. There is no measurement uncertainty, no propagation variable, and no frequency planning judgment involved. If the software produces a conflict that the math does not support, the software’s inputs are wrong.

The two traps described here — the low-power absolute floor and the CCDP bandwidth artifact — account for a disproportionate share of false conflicts in North American fixed microwave coordination databases. Both produce lower NFD values than the physical system warrants. Both are recoverable through manual recalculation with correct inputs, within the ISED technical analysis procedure, without field measurements or hardware changes.

A coordination engineer who understands the NFD integral can read an EMC report backwards from the conflicting value to the mask parameters that produced it, identify which parameter is wrong, and write a technically defensible correction. One who treats NFD as a black-box output cannot.

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References

1. International Telecommunication Union — Radiocommunication Sector, “Frequency and distance separations,” Recommendation ITU-R SM.337-6, Geneva, 2008.

2. European Telecommunications Standards Institute, “Fixed Radio Systems; Characteristics and requirements for point-to-point equipment and antennas; Part 2: System-dependent requirements for digital systems operating in frequency bands where frequency co-ordination is applied,” ETSI EN 302 217-2 V3.2.2, Sophia Antipolis, 2021.

3. U.S. Code of Federal Regulations, “Emission limitations,” 47 CFR § 101.111, Federal Communications Commission, Washington, DC.

4. Innovation, Science and Economic Development Canada, “Spectrum Utilization Policy, Technical and Administrative Requirements for Fixed Earth Stations Operating in Frequency Bands Shared with Terrestrial Radiocommunication Services,” TN-360, Ottawa.

5. International Telecommunication Union — Radiocommunication Sector, “Considerations in the development of criteria for sharing between the terrestrial fixed service and other services,” Recommendation ITU-R F.758-7, Geneva, 2019.

6. H. W. Ott, Electromagnetic Compatibility Engineering. Hoboken, NJ: John Wiley & Sons, 2009, ch. 11.