All,
In today’s meeting Frank Wang brought up a very good question: Why does TDD SNR degrade directly with the noise floor level, but ACT has less direct degradation with increasing
noise?
First let’s look at equation (snr-3) on slide 6 of
https://www.ieee802.org/3/dm/public/adhoc/103025/jonsson_3dm_01_10_30_25.pdf:
- The second term of the equation shows that Salz SNR decreases directly with increasing noise
- The Salz SNR reduces with the average noise level in dB across the signal band: 10*log10(S_n(f))
Second let’s recall that the noise power for TDD is assumed to be just the noise floor, while the ACT noise is assumed to be noise floor plus residual echo (my analysis assumed
no echo cancellation):
- TDD: S_n(f) = S_a(f)
- ACT: S_n(f) = S_a(f) + S_ec(f)
where
- S_a(f) is the Gaussia noise floor
- S_ec(f) is the residual echo power level
Putting the two steps above together we get that the Salz SNR decreases with the average of noise in dB:
- TDD: 10*log10(S_a(f))
- ACT: 10*log10(S_a(f) + S_ec(f))
The echo term in the ACT Salz SNR noise term means that:
- Everything else being equal, the ACT Salz SNR is going to be lower than TDD Salz SNR in very low noise environments
- The TDD Salz SNR will decrease dB-for-dB with increasing noise
- The ACT Salz SNR will decrease slower, until the echo noise, S_ec(f), becomes trivial compared to the noise floor, S_a(f)
The plot and table below show an example assuming that the average echo contribution to the Salz SNR is equivalent to 1e-5mW.
|
Noise Floor [dBm/Hz] |
|
Noise Floor [mW/Hz] |
Noise Floor across 3GHz [mW] |
Noise Floor across 2.8GHz [mW] |
Residual Echo [mW] |
|
TDD Noise [mW] |
ACT Noise [mW] |
|
TDD Noise [dBm] |
ACT Noise [dBm] |
|
-150 |
|
1E-15 |
0.000003 |
2.8125E-06 |
1.00E-05 |
|
3.00E-06 |
1.28E-05 |
|
-55.2 |
-48.9 |
|
-149 |
|
1.26E-15 |
3.78E-06 |
3.5407E-06 |
1.00E-05 |
|
3.78E-06 |
1.35E-05 |
|
-54.2 |
-48.7 |
|
-148 |
|
1.58E-15 |
4.75E-06 |
4.4575E-06 |
1.00E-05 |
|
4.75E-06 |
1.45E-05 |
|
-53.2 |
-48.4 |
|
-147 |
|
2E-15 |
5.99E-06 |
5.6117E-06 |
1.00E-05 |
|
5.99E-06 |
1.56E-05 |
|
-52.2 |
-48.1 |
|
-146 |
|
2.51E-15 |
7.54E-06 |
7.0647E-06 |
1.00E-05 |
|
7.54E-06 |
1.71E-05 |
|
-51.2 |
-47.7 |
|
-145 |
|
3.16E-15 |
9.49E-06 |
8.8939E-06 |
1.00E-05 |
|
9.49E-06 |
1.89E-05 |
|
-50.2 |
-47.2 |
|
-144 |
|
3.98E-15 |
1.19E-05 |
1.1197E-05 |
1.00E-05 |
|
1.19E-05 |
2.12E-05 |
|
-49.2 |
-46.7 |
|
-143 |
|
5.01E-15 |
1.5E-05 |
1.4096E-05 |
1.00E-05 |
|
1.50E-05 |
2.41E-05 |
|
-48.2 |
-46.2 |
|
-142 |
|
6.31E-15 |
1.89E-05 |
1.7746E-05 |
1.00E-05 |
|
1.89E-05 |
2.77E-05 |
|
-47.2 |
-45.6 |
|
-141 |
|
7.94E-15 |
2.38E-05 |
2.234E-05 |
1.00E-05 |
|
2.38E-05 |
3.23E-05 |
|
-46.2 |
-44.9 |
|
-140 |
|
1E-14 |
0.00003 |
2.8125E-05 |
1.00E-05 |
|
3.00E-05 |
3.81E-05 |
|
-45.2 |
-44.2 |
|
-139 |
|
1.26E-14 |
3.78E-05 |
3.5407E-05 |
1.00E-05 |
|
3.78E-05 |
4.54E-05 |
|
-44.2 |
-43.4 |
|
-138 |
|
1.58E-14 |
4.75E-05 |
4.4575E-05 |
1.00E-05 |
|
4.75E-05 |
5.46E-05 |
|
-43.2 |
-42.6 |
|
-137 |
|
2E-14 |
5.99E-05 |
5.6117E-05 |
1.00E-05 |
|
5.99E-05 |
6.61E-05 |
|
-42.2 |
-41.8 |
|
-136 |
|
2.51E-14 |
7.54E-05 |
7.0647E-05 |
1.00E-05 |
|
7.54E-05 |
8.06E-05 |
|
-41.2 |
-40.9 |
|
-135 |
|
3.16E-14 |
9.49E-05 |
8.8939E-05 |
1.00E-05 |
|
9.49E-05 |
9.89E-05 |
|
-40.2 |
-40.0 |
|
-134 |
|
3.98E-14 |
0.000119 |
0.00011197 |
1.00E-05 |
|
1.19E-04 |
1.22E-04 |
|
-39.2 |
-39.1 |
|
-133 |
|
5.01E-14 |
0.00015 |
0.00014096 |
1.00E-05 |
|
1.50E-04 |
1.51E-04 |
|
-38.2 |
-38.2 |
|
-132 |
|
6.31E-14 |
0.000189 |
0.00017746 |
1.00E-05 |
|
1.89E-04 |
1.87E-04 |
|
-37.2 |
-37.3 |
|
-131 |
|
7.94E-14 |
0.000238 |
0.0002234 |
1.00E-05 |
|
2.38E-04 |
2.33E-04 |
|
-36.2 |
-36.3 |
|
-130 |
|
1E-13 |
0.0003 |
0.00028125 |
1.00E-05 |
|
3.00E-04 |
2.91E-04 |
|
-35.2 |
-35.4 |
I hope that this explanation helps. Please let me know if you have any questions or comments.
Ragnar
To unsubscribe from the STDS-802-3-ISAAC list, click the following link: https://listserv.ieee.org/cgi-bin/wa?SUBED1=STDS-802-3-ISAAC&A=1