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# Equivalent Noise Figure of parallel devices in chain

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#### crazyboy

##### Newbie level 6
How to calculate the equivalent Noise Figure of receiver system with parallel inputs ? Suppose my system have 2 receiving antennas. Each antenna having a LNA with 3dB Noise Figure and Gain 10dB. I'm going to combine the power from 2 antennas and amplify over an amplifier having a Noise Figure of 5 dB with Gain 10dB. So how to calculate the equivalent Noise figure of this system ?

How can we apply Friss-Noise transmission formula in this type of problem? is it F1 + (F2-1)/G1 ? Here I have 2 parallel inputs to second stage amplifier so how can F1 will be decided ? is it some combination of two inputs ?

I think, you need to specify the relation of both antenna signals before.

In fact the system input is not "parallel". The low-noise amplifier must look to a specified source impedance, preferably 50 Ohms. Your two antennas are not connected "in parallel" but you must use a power combiner to get antenna outputs from two (or more) antennas to be summed to a common port which then becomes a signal source for the LNA.

The noise figure of such system is not easy to define. LNA input NF is usually taken for calculation using the Friis' formula. Noise coming from one or more antennas then depend upon what such antennas "see" by their radiation pattern. There is a full science on such problems, named radiometry.

For example the 4G cellular system LTE use by definition (and mandatory in all test specifications) two antennas connected to 2 independently receivers (for MIMO operation).

The Noise Figure, SNR, Gain, and Sensitivity, of each receive system is analyzed separately.

Finlay, when the two receivers are put to work together, the combined sensitivity of the system is defined.

Usually (but not mandatory) the combined sensitivity of two identical receivers is 3dB better than of a single one.

crazyboy

### crazyboy

Points: 2
Usually (but not mandatory) the combined sensitivity of two identical receivers is 3dB better than of a single one.
Applies to identical signals (phase and magnitude) from both antennas.

Diversity systems (e.g. for LTE) are used because you don't expect good signals from both antennas. Even if both signals are good, they may be out of phase, so they can't be simply added after the LNA. Diversity receiption either involves a select switch or separate receiver channels.

Diversity has different meaning than MIMO.
Diversity can use a single receiver and two switched antennas to find the best propagation path at a time, when MIMO use two antennas and two receivers working in the same time, receiving two separate propagation paths.
In a digital wireless system, Diversity is designed to give better coverage (wider area), when MIMO is designed to give better data throughput.

RiffMaster

### RiffMaster

Points: 2
Diversity has different meaning than MIMO.
Yes, thanks for clarifying. The setup in the original question "combine the power from 2 antennas" describes none of both concepts. It only works for in-phase antenna signals.

To vfone: The original question was about SYSTEM NOISE FIGURE. The definition of SENSITIVITY concerns S/N or Eb/No, therefore in/phase signals are referred to above noise power which is random.

Thanks for a clear distinction between MMO and diversity!

vfone: Both antennas are identical and looking at same portion of sky. So I can assume the input noise and signal powers are almost same in both antennas. As I combining the powers in almost same phase (using delay lines), can I follow this thumb rule of "3dB better" for Noise Figure as well ? or its meant for Sensitivity only? Can you send me any article regarding the same ? Thanks a lot for all replies

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Noise power and noise figure has nothing to do with phasing. Thermal noise is a random process due to randomly moving charges. Please follow my advice above.
If your antenna(s) look to the ground or to a vegetation wall, they will generate ~300 K at their ports. If you combine outputs of two or more such antennas, the combined output will stay the same. If one or both antennas look to the cold sky, their (combined) noise output may be lower The difference requires to study their radiation patterns; best you can do is to measure the noise power before or after LNA.
With signals, the situation may be different. One signal will pass its separate paths through both antennas, and then phasing will define the signal power at LNA input.

MIMO can increase sensitivity by 3dB because MOMI use spread spectrum CDMA technologies. According to CDMA properties, if use two receiver antennas, the signals is doubled, but noise is still white noise, so sensitivty improves 3dB. If use four antennas, improves 6dB.
But if your signal is not CDMA, then can't get the improvement. Diversity technologies normally only select the better path of the two paths. There also may use combination of the two path signals, but it is not mature, and is hard to evaluate. Anyway, the best of diversity is 3dB.

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