The assumption that S/N is determined by directivity is correct, anyway this
is a theorical perspective assuming perfect and noiseless receivers.
In the real life this concept works if the band noise is consistent and if
antenna losses are not too big compared with the receiver NF and dynamic
range whose are both easyer obtained when the transmission mode allows the
use of narrow BW (CW or better slow CW as it's common with the 137 KHz
band).
The thread becomes quickly much less easy (real) with AM or SSB where the
receiver ground floor is typically much worse because of the wider BW
involved and the antenna losses must be less of the same amount.
The use of extremely low noise preamplifiers to recover NF with high losses
antennas, inevitably lead to overload problems and distortions whose facts
will disrupt the available S/N, independently by the antenna directivity.
A very small antenna can certainly be modeled as a current source and the
moderate distance between several of this points prevent problems of
reception diversity. In the other hand, if the signal available from the
array is not adequate to the receiver NF and BW, a system with the highest
directivity but too hevy losses is practically not useable.
73,
Mauri I4JMY
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