Richard (G3CWI) published an interesting blog article Comparison of groundwave performance of Small Transmitting Loop and Quarterwave GP summarising a recent WSPR test on 40m over 20km distance.

This article is a walk through of the expected WSPR receive S/N for the case of the 20mW tx on a quarter wave vertical.

## 100% efficient tx and rx antenna systems

Ground wave suffers attenuation due to two key components:

- dispersion of energy as the wave spreads out from the source; and
- absorption of energy in heating the soil.

Item (1) is simply inverse square law effect, and Norton provides us with several approximations for estimating (2) from Sommerfields work.

Calculate efficiency of vertically polarised antenna from far field strength uses Norton's f5 approximation for ground wave attenuation.

Above is a calculation for a 100% efficient transmitter. (The trick to getting this is to leave the *measured field strength* field empty and the calculator will insert the value that gives 100% efficiency.)

So the next question is what ambient noise level might we expect in a rural setting on 40m.

ITU-R P.372-12 gives us guidance, suggesting the median ambient noise figure (NF) at 7MHz in a rural precinct is 44.6dB. This will dwarf the NF of a good HF receiver which will be better than 15dB without preamp, so we will run with total NF of 44.6dB.

Let us now calculate the signal to noise ratio (S/N) in 2.5kHz noise bandwidth of the rx signal of -7.1dBµV/m with NF of 44.6dB. We will assume that the rx antenna is a 100% efficient QW vertical with directivity 3 (gain 4.77dBi).

Again a handy online calculator can be used, Field strength / receive power converter.

Above is the input data for the problem. The use of 2500Hz noise bandwidth is to obtain results in terms of WSPR's reference for S/N reports.

Above the results contains at the end, the rx S/N which is 2.46dB.

## Real world corrections

### Rx antenna

Because the external noise is much greater than the rx internal noise in this scenario, small reduction in rx antenna efficiency and gain will not significantly alter the rx S/N ratio, though it will reduce the received power.

### Rx ambient noise

Rx ambient noise varies with location, time, polarisation, neighbourhood effects, atmospherics etc. The ambient noise scenario modelled here is for a rural precinct, and city noise could easily be 10dB or more worse. Rx ambient noise in this scenario dominates total noise, and any difference would roll directly into rx S/N.

### Interference

A further source of noise is unwanted signals. Because of the uncoordinated way in which WSPR works, there is a significant risk of interference from stations that might reduce the S/N ratio observed on the desired signal.

### Tx antenna

The tx antenna used for Richard's experiment is likely to have an efficiency of perhaps -1dB give or take, and that would directly roll into observed rx S/N ratio.

### Ground parameters

Soil is not homogenous, and ground type for Richard's test is unknown. Soil type has a significant effect on path loss over such a long ground wave path, and that rolls directly into observed S/N ratio.

## In the event

Richard collected 169 paired observations of two transmitters received at one receiver 20km distant on 40m.

The observed median S/N ratio for the transmitter discussed in this article was 1dB, which is quite in keeping with the prediction of 2.5-1=1.5dB for a typical antenna over an ‘average ground' path with typical rural ambient noise.

There is a great deal of uncertainty in the estimate, and the largest element would be the soil type assumed, next would be the ambient noise at the receiver. Nevertheless, the article describes a process for estimating the performance and the estimate is improved by better knowledge of all the influencing parameters.

## References / links

- ITU-R. Jul 2015. Recommendation ITU-R P.372-12 (7/2015) Radio noise.
- Norton, KA. Dec 1941. The calculation of ground wave field intensity over a finite conducting spherical earth. Proc IRE, vol 29, pp 623-639.
- ———. Oct 1936. The propagation of radio waves over the surface of the earth and in the upper atmosphere Part I. Proc IRE, vol 24, pp 1367-1387.
- ———. Sep 1937. The propagation of radio waves over the surface of the earth and in the upper atmosphere Part II. Proc IRE, vol 25, pp 1203-1236.