Continuing with a previous topic:

Multipath: Antenna Stack & Diversity Gain?
The following is a thought experiment.

Consider multipath effects to be the sum of only two signals, the desired or direct signal (D) and the multipath signal (M).

For a sum (combination) signal to experience a deep null (

say 25 dB), the two signals must arrive at the antenna aperture nearly 180 degrees out of phase and nearly equal in amplitude.

Let D and M represent the frontal area of signals propagating through space.

Constraints on D and M:

1. Equal Frontal Area: Size is less than, or equal, that of a single antenna aperture.

2. M = - D, or Integrated Field Strength of Multipath = negative Direct

In the image above, for a single antenna there is one combination that yields a null. That is; Both signals arrive at the antenna. For the stack there are 3 distinct combinations adding to a null. These 3 combinations are; both signals arrive at the center of the stack, or one signal arrives at the upper antenna and the other signal arrives at the lower antenna (2 ways).

Consider larger frontal areas, with larger integrated field strength:

1. One frontal area larger than stack aperture.

A. Direct signal frontal area greater than the stack aperture.

Nulls could not occur at the stack aperture because the Multipath would not be sufficient to cancel the larger Direct signal.

If frontal area of direct signal could be larger than the stack aperture, then the inverse could occur.

B. Multipath signal frontal area greater than the stack aperture.

Nulls could not occur at the stack aperture because the Direct would not be sufficient to cancel the larger Multipath. Multipath would dominate.

2. Both Direct and Multipath frontal areas larger in area than the stack aperture.

In this latter case, the larger stack aperture could be considered as a single antenna and would have no multipath advantage over the smaller antenna aperture.

There are uncountable combinations of direct and multipath signals, large and small frontal areas with varying amplitudes and phases. Most combinations would not result in large cancellations or deep nulls. When deep nulls result from combinations, mostly they could be analyzed as described above.

In the image, the stack has twice the aperture of the single antenna. This increased aperture allows more signal combinations. If the number of signal combinations were directly proportional to the aperture size, then a stack could have twice as many combinations as a single antenna. For the stack; 2 times possible combinations there could be 3 times as many null-generating combinations. Statistically, this represents an increase in proportion of null-generating events.

Very wide spacing, with a large gap between apertures could eliminate the possibility of both Direct and Multipath combining at the center of apertures. That could reduce the possible number of null-generating combinations at the stack from 3 to 2. Thus, very wide spacing could allow stack performance to be similar to that of a single antenna.

Unless the statistics of the Direct or Multipath signals changed, then wider, or different spacing of the stack would not greatly improve the above scenario. If widely spaced locations were found for one antenna where the Direct signal had better statistics relative to Mutipath, then positioning both antennas in those regions could provide even better results. But, that would appear to be a matter of optimal antenna positioning instead of diversity gain.

*Note: *

With normally stacked antennas a combiner cannot take advantage, or mitigate the effects, of the differing phases of separate antenna signals. To mitigate multipath or to take full advantage of signals arriving with differing phase, a combining system must provide a means to either; synchronize the phase of separate antenna signals if combined pre-detection, or neglect phase if combined post-detection.
Summary

Considering information in

the earlier post, it seems difficult to rationalize that an antenna stack provides diversity gain against multipath.

Absent a plausible mechanism, one could conclude:

Against Multipath: Stacking antennas does not provide diversity gain.

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