# Noise power at receive antenna with finite transmit SNR?

I have seen a few examples of link budgets, and they all assume that the total noise at the Rx is just going to be -174 dBm + 10 log BW. However, this seems to me to assume that the transmit signal is perfect and the SNR is the transmit power (dB) minus the noise floor (followed by the noise figure of the Rx chain etc).

I'm having a bit of trouble reasoning through what the effect of a finite SNR on the transmit side would do to the receive noise. Clearly, the signal level is much higher, but if the Tx SNR is relatively bad to begin with (e.g., 10 dB), what is the received SNR going to be? I assume that the finite Tx SNR should have some effect, right?

To make things a bit more concrete, let's say radiated Tx power is 30 dBm, path loss is 100 dB, and we have a 100 MHz wide signal with no antenna gain (or loss). The analyses that I've seen would say the SNR coming off the antenna is 30 dBm - 100 dB - (-174 + 10log 100 Mhz) = 24 dB. But how can I calculate the SNR if we further assume the Tx SNR was only 10 dB (or 20 dB, or 50 dB)?

Figure out the contribution of the transmitter noise at the receiver. If it is much lower than the receiver noise, then you can ignore it. If it is much larger than the receiver noise, then you can ignore the receiver noise. If the two noise sources are comparable in power, you'll have to combine them to find the overall SNR of your system.

For example, in your example (+30 dBm Tx, 10 dB SNR, 100 dB path loss), you have +20 dBm noise at the transmitter. -80 dBm arriving at the receiver.

Since these numbers are more than 10 dB apart, you can very nearly ignore the receiver noise and your received SNR will be very close to the transmitted SNR of 10 dB.

If you really want to be very careful about things, -94 dBm is about 0.4 pW, and -80 dBm is 10 pW. So the total noise power referenced to the receiver input is 10.4 pW or -79.8 dBm. So your SNR is about 9.8 dB rather than 10 dB.

With 20 dB transmit SNR, your two noise sources will be nearly equal, requiring the full calculation of the total noise power.

With 50 dB transmit SNR, the transmitter noise will be insignificant and your calculation of 24 dB SNR based on receiver noise alone will give you the overall SNR.

How about -150 dbc/rtHz phase noise spec, out of the transmitter?

Given this is power, we know an otherwise unused 10KHz slice of spectrum near the carrier that has no modulation energy within the 10KHz, will have -150 + 10*log10(10,000Hz) = -150+40 = -110dBm of noise power, if the transmitter is outputting only 1milliWatt of power. At 1 watt, the phase noise (both AM and PM are in this), is -110+30 = -80dBm.

At some point, radios within moderate distance (10 feet, at a fire or auto accident) but using channels near the same carrier or even using adjacent carriers, will be DE-SENSING each other.

Thus not only does AM noise with NRZ, or AM+PM with 64QAM, degrade the desired receiver sensitivity, but PhaseNoise will degrade the SNR of adjacent-channel (or merely near-channel) receivers.

• Um, wow. Hadn't even considered that kind of thing. Thanks for catching me off-guard (honestly). Dec 21, 2018 at 2:30
• The manufacturer had a lines-down problem. They could not understand why the previous generation of radios, made with dozens of those tiny square-metal-can 50ohm in, 50ohm out modules, worked just fine (tho burned lots of power, so a relatively brief time between recharges). Yet the new radios, with the modules replaced with all the circuits collapsed onto silicon, could not meet the -150dBc requirements. Turns out they had no theory for predicting phasenoise in their circuits. Using Tj = Vnoise/SlewRate,I showed them how the Prescaler needed to be a LOW NOISE design. Needed a low noise FF. Dec 21, 2018 at 2:46