### The MUF and SNR Distribution: Choosing the Best Frequency in VOACAP

You have now run the prediction and are anxious to operate between the chosen locations on the frequencies you entered. There are two things to discuss in our analysis:

• What is the best of our frequencies?
• What is the predicted SNR (Signal-to-Noise) distribution on that frequency?

#### The Meaning of MUF

In VOACAP, the MUF (maximum usable frequency) is a statistical concept. The MUF is defined here as the median maximum usable frequency for a given ionospheric path, month, SSN and hour. On each day of the month at this hour, there is a maximum observed frequency (MOF) for a mode. The median of this distribution is called the MUF. Therefore, it is not the maximum usable frequency in terms of communications.

In other words, the MUF is the frequency for which ionospheric support is predicted on 50% of the days of the month, ie. 15 days out of 30 days. So on a given day communications may or may not succeed on the frequency marked as the MUF.

To ensure a good communication link between two locations, the operating frequency is typically chosen below the predicted MUF. It is often claimed that the optimal operating frequency lies somewhere between 80-90% of the MUF (e.g. if the MUF is 10 MHz, the optimal frequency would be around 8-9 MHz). However, in VOACAP it is the predicted SNR distribution using Complete System Performance methods (e.g. Methods 20, 21, 22 or 30) that determines which frequencies provide an acceptable grade of service.

#### The MUFday

The MUF is also related to another parameter, MUFday. The value of the MUFday is the fraction of the days in a month at that hour that the operating frequency is below the MUF for the most reliable mode (that is, the mode with the highest reliability of meeting the required SNR). The mode and the associated data shown below the user-specified frequencies are always the most reliable mode. For a more detailed discussion, see Calculating MUFdays.

#### SNR, SNR10 and SNR90: The Predicted SNR Distribution

The SNR distribution tells us what grade of service is to be expected over the days in the month on a given frequency at a given hour. A statistical method is used to determine the grade of service over 27 days (SNR90), 15 days (SNR) and 3 days (SNR10) out of 30 days. However, it does not tell you which days are good or which days are bad.

Below are the four SNR output parameters needed for analysis:

```   1.0 13.1  6.1  7.2  9.7 11.9 13.7 15.4 17.7 21.6 25.9  0.0  0.0 FREQ
F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2   -    -  MODE
80   63   69   78   83   78   68   28  -39  -58   -    -  SNR
26.7 12.4 13.8 21.2 26.7 26.8 26.8 26.8 26.8 13.3   -    -  SNR LW
18.5  7.6  7.1  7.8 12.7 22.2 25.7 25.7 25.7  7.6   -    -  SNR UP
54   51   55   57   56   51   41    1  -66  -71   -    -  SNRxx
```

The SNR indicates the dB-Hz value that can be maintained on 50% of the days (ie. on 15 days) in the month. In our example above on 11.9 MHz, the SNR value is 83 (dB-Hz).

The SNRxx (ie. SNR90, provided the REQ.REL. is 90%) indicates the dB-Hz value that can be maintained on 90% of the days (ie. on 27 days) in the month. In our example above on 11.9 MHz, the SNRxx value is 56 (dB-Hz). This can be calculated as SNR - SNR LW (or 83 - 27 = 56 in our example).

And finally, the SNR10 (calculated as SNR + SNR UP) is the dB-Hz value that can be maintained on 10% of the days (ie. on 3 days) in the month. In our example above on 11.9 MHz, the SNR10 value is appr. 96 (dB-Hz).

The two most prominent parameters to consider in search of the best frequency are the SNR and SNR90 values. As a rule of thumb, look for the highest SNR value and the highest SNR90 value. Let us assume that the required SNR we wish to maintain in our circuit is 67 (not a good but still a reasonable listening quality in international broadcasting). We will see that the SNRxx is below 67 at all our frequencies which means none of them cannot maintain that grade of service on 27 days out of 30 days. Then we will need to look for the highest SNR. Of our frequencies, the best would be 11.9 MHz with the SNR value of 83.

#### Conclusion: MUFday and SNR

In conclusion, 11.9 MHz is the best candidate for the operating frequency at 01 UTC during that month. 11.9 MHz is also below the predicted MUF of 13.1 MHz for that mode.

#### The RPWRG and the REL

Let us expand our example above by adding two other output parameters (RPWRG and REL) as follows:

```
1.0 13.1  6.1  7.2  9.7 11.9 13.7 15.4 17.7 21.6 25.9  0.0  0.0 FREQ
F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2 F2F2   -    -  MODE
80   63   69   78   83   78   68   28  -39  -58   -    -  SNR
13   16   12   10   11   16   26   66  133  138   -    -  RPWRG
0.74 0.24 0.57 0.74 0.78 0.70 0.51 0.03 0.00 0.00   -    -  REL
26.7 12.4 13.8 21.2 26.7 26.8 26.8 26.8 26.8 13.3   -    -  SNR LW
18.5  7.6  7.1  7.8 12.7 22.2 25.7 25.7 25.7  7.6   -    -  SNR UP
54   51   55   57   56   51   41    1  -66  -71   -    -  SNRxx
```

The RPWRG is related to the SNR90 and REQ.SNR. In our example above, the REQ.SNR was set to 67. The RPWRG (the required power gain) parameter tells us how many desibels are needed in the communication system to achieve the SNR90 value of 67. It is calculated as REQ.SNR - SNRxx (or 67 - 56 = 11 on 11.9 MHz). As the value of the RPWRG is positive in our example, it means that many desibels are needed for our system; if the value had been negative, that many desibels would have been in excess (ie. unnecessary) to achieve the required SNR for 27 days out of 30 days.

This parameter relates to the (communication) system design. In our example on 11.9 MHz, we should consider what measures we could take to add the necessary 11 desibels to the system: doubling the transmitting power would give us 3 desibels, using a more powerful transmitter antenna could give us a few desibels more, and at the receiving end we could choose, say, a 3-element Yagi instead of the whip antenna which would still contribute some more desibels.

The REL is related to the SNR and REQ.SNR, and is defined as a circuit reliability factor. It tells us the percentage of days in the month when the SNR value will equal to or exceed the REQ.SNR. The SNRxx tells us which SNR value can be achieved on 90% of the days (27 days) in the month. If the SNRxx would have been 67, then the value of REL had been 0.90 (or 90%, which is the REQ.REL. we have specified) and the RPWRG would have been zero (0).

### Conclusion: REL (Reliability)

The REL value of 0.78 on 11.9 MHz suggests that the required SNR of 67 can be achieved on 78% of days in the month. To translate the percentage value to the number of days, take a look at the Z Tables. We will see that 78% equals to 23 days.

For a more detailed discussion on how the REL value is calculated, see the article Maintaining the Required Grade of Service.