Electromagnetic Waves, Antennas, and RF: Detailed GNSS Link-Budget Example from Satellite EIRP to Interference Margin

Electromagnetic Waves, Antennas, and RF: Detailed GNSS Link-Budget Example from Satellite EIRP to Interference Margin

This extended worked example combines the main results of EM24–EM28 into one GNSS-style link calculation. The goal is to begin at the satellite transmit reference plane, propagate the signal through free space, determine the received carrier Power, form the receiver noise density and G∕T, calculate C∕N₀ and finite-bandwidth C∕N, compare against a receiver requirement, and finally determine how much additive noise-like interference can be admitted before the requirement is reached [1, 2, 3].

The numerical values are intentionally illustrative. The carrier frequency is GPS L1-like, but the quoted EIRP, receiver threshold, implementation losses, and noise temperature should not be interpreted as a universal GPS specification. Actual values depend on satellite block, signal component, geometry, antenna pattern, propagation conditions, receiver design, and the reference plane at which each quantity is specified.

1. Link assumptions and reference plane

Use the following notional link:

f	= 1.57542 × 109 Hz,	(1)
r	= 20,200 × 103 m,	(2)
EIRP	= 27.0 dBW,	(3)
Latm	= 0.50 dB,	(4)
Lpol	= 0.50 dB,	(5)
Lmisc	= 1.00 dB,	(6)
Gr	= 2.00 dBi,	(7)
Tsys	= 400 K,	(8)
Bn	= 2.00 × 106 Hz,	(9)
req	= 42.0 dB-Hz.	(10)

The total non-free-space loss is therefore

(11)

The receive antenna gain and system noise temperature are assumed to be referred consistently to the same receiver input reference plane. This is essential: a feed loss, radome loss, or mismatch loss must not be subtracted again if its effect has already been absorbed into the quoted G∕T or T_sys.

2. Frequency, wavelength, and geometry

The wavelength is

(12)

where

(13)

Thus

λ	=	(14)
	≈ 0.190294 m.	(15)

So the L1-like carrier wavelength is about 19.0 cm.

The range r = 20,200 km is used here as a simple GNSS-scale slant range for the worked calculation. In a real receiver the instantaneous satellite-to-user slant range varies with satellite elevation and user geometry.

3. Satellite EIRP

Equivalent isotropically radiated power is the product of transmitter power and transmit antenna gain, after losses ahead of the antenna have been accounted for:

(16)

in linear units, or

(17)

in decibel form.

For this example the satellite directional EIRP toward the user is already given:

(18)

The corresponding isotropic-equivalent linear power is

PEIRP	= 1027∕10 W	(19)
	≈ 501.2 W.	(20)

This does not mean that the transmitter necessarily dissipates 501 W of RF power. EIRP includes antenna directivity and represents the isotropic transmitter power that would create the same far-field power density in the specified direction.

4. Free-space path loss

From the Friis relation, free-space path loss is

(21)

In decibels,

(22)

Substitution gives

LFS,dB	= 20 log 10	(23)
	≈ 182.503 dB.	(24)

Hence

(25)

The linear path-loss ratio is enormous:

(26)

This is geometric spreading and receive-aperture scaling, not absorption of energy by empty space.

5. Received carrier power

The received carrier power at the chosen receiver reference plane is

(27)

Therefore

C	= 27.0 − 182.503 − 2.00 + 2.00	(28)
	= −155.503 dBW.	(29)

Thus

(30)

In dBm,

(31)

In watts,

(32)

6. Receiver thermal-noise density

For system noise temperature T_sys, the available thermal-noise power spectral density is

(33)

where

(34)

At T_sys = 400 K,

N0	= (1.380649 × 10−23)(400)	(35)
	= 5.522596 × 10−21 W/Hz.	(36)

In logarithmic units,

N0,dBW/Hz	= 10 log 10(k) + 10 log 10(400)	(37)
	= −228.599 + 26.021	(38)
	= −202.579 dBW/Hz.	(39)

Therefore

(40)

7. Receiver G∕T

The receiver figure of merit is

(41)

For the assumed receive antenna and system temperature,

G∕T	= 2.00 − 10 log 10(400)	(42)
	= 2.00 − 26.021	(43)
	= −24.021 dB/K.	(44)

Thus

(45)

8. Carrier-to-noise-density ratio C∕N₀

There are two useful ways to calculate C∕N₀. Performing both provides an excellent consistency check.

8.1 Method A: carrier power minus noise density

Because carrier power is in dBW and noise density is in dBW/Hz,

(46)

Hence

C∕N0	= −155.503 − (−202.579)	(47)
	= 47.076 dB-Hz.	(48)

Therefore

(49)

8.2 Method B: the end-to-end G∕T equation

Using the complete link-budget relation,

(50)

Substitution gives

C∕N0	= 27.0 − 182.503 − 2.00 − 24.021 + 228.599	(51)
	= 47.076 dB-Hz,	(52)

exactly matching Method A to rounding.

In linear units,

(53)

The unit “Hz” appears because a power is divided by a power spectral density.

9. From C∕N₀ to finite-bandwidth C∕N

For an ideal equivalent noise bandwidth B_n,

(54)

Therefore

(55)

and in decibels,

(56)

For B_n = 2.00 MHz,

(57)

so

C∕N	= 47.076 − 63.010	(58)
	= −15.934 dB.	(59)

Thus

(60)

The corresponding total thermal noise power is

NdBW	= −202.579 + 63.010	(61)
	= −139.568 dBW,	(62)

or

(63)

This is substantially larger than the carrier power, which is Normal for spread-spectrum GNSS reception before correlation and signal processing.

10. Required threshold and clean-link margin

Assume this particular receiver requires

(64)

for the operating mode under consideration. This value is a receiver-design assumption, not a universal GNSS constant.

The clean-link margin is

Mclean	= clean − req	(65)
	= 47.076 − 42.0	(66)
	= 5.076 dB.	(67)

Therefore

(68)

At 2 MHz the same threshold would correspond to

(C∕N)req	= 42.0 − 63.010	(69)
	= −21.010 dB.	(70)

The difference between the clean C∕N = −15.93 dB and the threshold-equivalent C∕N = −21.01 dB is again 5.08 dB, as expected.

11. Allowable additive interference density

Now suppose an admitted interferer can be modeled as additional uncorrelated, noise-like spectral density J₀ at the same receiver reference plane. The effective carrier-to-disturbance density becomes

(71)

Factor out N₀:

(72)

Thus the interference-induced degradation is

(73)

At the allowable limit, the interference consumes the entire clean-link margin:

(74)

Therefore

(75)

which yields

(76)

Using M_clean = 5.076 dB,

max,lin	= 105.076∕10 − 1	(77)
	≈ 2.218.	(78)

In decibels,

(79)

This is the maximum additive noise-like interference-density ratio permitted by the assumed 42 dB-Hz threshold and the nominal clean link.

12. Convert the allowable interference to absolute units

Because

(80)

the maximum admitted interference density is

J0,max	= N0 + max	(81)
	= −202.579 + 3.460	(82)
	= −199.119 dBW/Hz.	(83)

Therefore

(84)

If the same noise-like density occupies the full 2.00 MHz receiver noise bandwidth, the admitted in-band interference power is

Jmax	= J0,max + 10 log 10Bn	(85)
	= −199.119 + 63.010	(86)
	= −136.109 dBW.	(87)

Thus

(88)

13. Equivalent interference temperature

Because thermal-noise density is N₀ = kT_sys, a noise-like interference density can be represented by an equivalent temperature

(89)

Using the ratio form is simpler:

(90)

At the allowable limit,

TJ	= (2.218)(400)	(91)
	≈ 887 K.	(92)

The effective disturbance temperature is then

(93)

The large temperature value does not imply that the physical receiver is at 1287 K; it is an equivalent noise-temperature representation of the admitted interference.

14. Why allowable J∕S can be positive

In a GNSS link it is common for the desired spread-spectrum carrier to be below the total wideband thermal-noise power before correlation. The same can be true relative to admitted broadband interference.

At the interference limit,

(94)

while

(95)

Therefore

J∕S	= J − C	(96)
	= −136.109 − (−155.503)	(97)
	= 19.394 dB.	(98)

Thus

(99)

at the same point where the effective C∕N₀ has only fallen from 47.08 to 42.0 dB-Hz.

This is not a contradiction. J∕S compares integrated powers, while degradation in this model is governed by the ratio of interference spectral density to thermal-noise spectral density. Bandwidth, spectral overlap, receiver filtering, correlation properties, front-end linearity, and signal structure matter. Consequently, J∕S alone is not a universal predictor of GNSS receiver performance [2].

15. Compact end-to-end budget table

16. Sensitivity rules worth remembering

The completed budget makes several useful one-line sensitivity rules visible:

• A +1 dB change in satellite EIRP produces a +1 dB change in C∕N₀.
• A +1 dB increase in path or implementation loss produces a −1 dB change in C∕N₀.
• A +1 dB improvement in receiver G∕T produces a +1 dB change in C∕N₀.
• Doubling system temperature reduces G∕T and C∕N₀ by 3.01 dB.
• Doubling receiver bandwidth reduces C∕N by 3.01 dB but leaves C∕N₀ unchanged.
• Additive noise-like interference must be combined in linear power or spectral-density units before converting back to dB.

These rules are useful for rapid link-budget sanity checks, but they do not replace careful reference-plane bookkeeping.

17. Scope of the interference calculation

The interference result in this example is intentionally restricted to an additive, uncorrelated, noise-like disturbance that is admitted through the receiver bandwidth without causing front-end saturation or nonlinear behavior. Narrowband continuous-wave interference, swept interference, pulsed interference, signals with strong spectral structure, AGC effects, quantizer overload, intermodulation, correlator effects, and antenna-array spatial rejection require more detailed models. In those cases the scalar J₀∕N₀ calculation here remains a useful baseline, but it is not sufficient by itself.

18. Julia numerical check

The companion file EM28E2_gnss_link_budget_check.jl reproduces the complete chain numerically and verifies the threshold-crossing value of J₀∕N₀. It also evaluates the effective C∕N₀ over a sweep of interference-density ratios for comparison with the final figure.

Summary

Beginning with a directional satellite EIRP of 27.0 dBW, an L1-like 20,200 km free-space link gives

(100)

After 2.0 dB of other losses and 2.0 dBi of receive gain, the received carrier is

(101)

For T_sys = 400 K,

(102)

and therefore

(103)

Across 2 MHz,

(104)

For an illustrative 42.0 dB-Hz receiver requirement, the clean margin is 5.08 dB. Under the additive noise-like interference model, this allows

(105)

before the threshold is reached.

References

References