# Multiple log-normal signals

In cellular networks, interference does not come from only
one source but from many
co-channel transmitters. In a hexagonal reuse pattern the number of interferers typically is six.
At least two different methods are used to estimate the probability distribution of
the joint interference power accumulated from several log-normal signals.
Such methods are relevant to estimate the joint effect of multiple interfering signals with shadowing.
Fenton and Schwartz
and Yeh both proposed to approximate the pdf of the joint interference power by a log-normal
pdf, yet neither could determine it exactly.

## Fenton

The method by Fenton assesses the logarithmic mean and
variance of the joint interference signal directly as a function of the logarithmic means and variances
of the individual interference signals. This method is most accurate for small standard deviations of
the shadowing, say, for less than 4 dB.
## Schwartz and Yeh

The technique proposed by Schwartz and Yeh is more accurate
in the range of 4 to 12 dB shadowing, which corresponds to the case of land-mobile radio in the VHF and
UHF bands. Their method first assesses the logarithmic mean and variance of a joint signal produced
by cumulation of two signals. Recurrence is then used in the event of more than two interfering
signals. A disadvantage of the latter method is that numerical computations become time consuming.

### Schwartz & Yeh

Disclaimer: Executable software programmes are provided with no
guarantee whatsoever. See License.

See also tabulated results for 0, 6, 8.3 and 12 dB of shadowing.

Besides these methods, by Fenton and Schwartz and Yeh, a number of alternative (and often
more simplified) techniques are used. For instance in VHF radio broadcasting, signals fluctuate with
location and with time according to log-normal distributions. Techniques to compute the coverage of
broadcast transmitters are in CCIR recommendations.
Outage probabilities for systems with multiple Rayleigh fading and shadowed signals can however be computed easily
without explicitly estimating the joint effect of multiple shadowed signals.

Thanks to Ramjee Prasad for making portions of the SPEC algorithm available to us.