Sum two different coverage models

Is there a way to sum two different coverage outputs? I have two different transmitters and have plotted the output of each on the same coverage map. I notice that it appears to do the equivalent of a 'max hold' where the field patterns from the separate transmitters overlap. Is there a way to sum the field patterns from the separate transmitters? I realise that this would effectively assume zero phase diference at all points of interaction, but that suits what I am aiming to do.

So far I have tried converting the output of the coverage .Data to an array. This provides the lat, long, and dB output for each transmitter. What I can't work out is how to sum these arrays when the lat and long values are different (as the transmitters are in different locations). In an ideal world, I would then convert the summed arrays back into a coverage map of the result.

Any help much appreciated.

% horn antenna setup
tx_horn = horn("Height", 0.06, "Width", 0.16, "Length", 0.10, "FeedHeight", ...
    0.04, "FeedWidth", 0.002, "FlareHeight", 0.216, "FlareLength", 0.15, ...
    "FlareWidth", 0.266);

% transmitter array setup
f = 1.3e9;                              % Frequency
c = 299792458;                          % Speed of light
wl = c / f;                             % Wavelength

M = 2;                                 % Number of elements on each row
N = 2;                                 % Number of elements on each column
dy = 0.5 * wl;                         % Spacing between row elements (m)
dz = 0.5 * wl;                         % Spacing between column elements (m)
ura = phased.URA([N M], [dz dy], 'Element', tx_horn);

% transmitter setup
tx1 = txsite('Latitude', 52.36364, ...
        'Longitude', -3.77767, ...
        'TransmitterFrequency', f, ...
        'Antenna', ura, ...
        'AntennaHeight', 5, ...
        'TransmitterPower', 50, ...
        'AntennaAngle', 90);

tx2 = txsite('Latitude', 52.36369, ...
        'Longitude', -3.78150, ...
        'TransmitterFrequency', f, ...
        'Antenna', ura, ...
        'AntennaHeight', 5, ...
        'TransmitterPower', 50, ...
        'AntennaAngle', 90);
 
% coverage output
e_max = -20;
e_min = -60;
e_step = 1;

cov1 = coverage(tx1, 'close-in', 'SignalStrengths', e_min:e_step:e_max, 'ColorLimits', [e_min e_max]);
cov2 = coverage(tx2, 'close-in', 'SignalStrengths', e_min:e_step:e_max, 'ColorLimits', [e_min e_max]);

% convert to arrays for summing?
tx_array1 = table2array(cov1.Data);
tx_array2 = table2array(cov2.Data);

% What next?

Answer 1

[Walter Roberson]

You could probably extract the lat and long vectors from tx_array1 and tx_array2 and do scatteredInterpolant() to construct interpolating objects with interpolation method set to 'none'. After that would be a matter of inventing common query points. Then query each of the scattered interpolant objects at the common query points.

Now,

result = zeros(size(QUERY_RESULT1));
mask1 = isnan(QUERY_RESULT1);
mask2 = isnan(QUERY_RESULT2);

tmask = ~mask1 & ~mask2;
result(tmask) = QUERY_RESULT1(tmask) + QUERY_RESULT2(tmask);

tmask = ~mask1 & mask2;
result(tmask) = QUERY_RESULT1(tmask);

tmask = mask1 & ~mask2;
result(tmask) = QUERY_RESULT2(tmask);

%mask1 & mask2 is nan in both places. The output result for there should be
%0, which we already got by initializing the result array to 0.

[Barney]

Thanks for the answer. I'm new to using scatteredInterpolant, so appreciate any information.

Just to clarify, are you suggesting taking a scatteredInterpolant as follows:

QUERY_RESULT1 = scatteredInterpolant(tx_array1(:, 1), tx_array1(:, 2), tx_array1(:, 3), 'linear', 'none');

(and the same for tx_array2).

then querying each with the lat/long values of each and summing the values where they share lat and long references?

[Walter Roberson]

Almost right

QUERY_RESULT1 = scatteredInterpolant(tx_array1{:, 1}, tx_array1{:, 2}, tx_array1{:, 3}, 'linear', 'none');

because tx_array1 is a table.

You would do something along the lines of

N = 100;

lat1 = tx_array1{:,1};
lon1 = tx_array1{:,2};
data1 = tx_array1{:,3};
lat2 = tx_array2{:,1};
lon2 = tx_array2{:,2};
data2 = tx_array2{:,3};
[minlat1, maxlat1] = bounds(lat1);
[minlon1, maxlon1] = bounds(lon1);
[minlat2, maxlat2] = bounds(lat2);
[minlon2, maxlon2] = bounds(lon2);
F1 = scatteredInterpolant(lat1, lon1, data1);
F2 = scatteredInterpolant(lat2, lon2, data2);
latLB = min(minlat1, minlat2);
latUB = max(maxlat1, maxlat2);
lonLB = min(minlon1, minlon2);
lonUB = max(maxlon1, maxlon2);
latq = linspace(latLB, latUB, N);
lonq = linspace(lonLB, lonUB, N+1);

[LatQ, LonQ] = ndgrid(latq, lonq);
QUERY_RESULT1 = F1(LatQ, LonQ);
QUERY_RESULT2 = F2(LatQ, LonQ);

result = zeros(size(QUERY_RESULT1));
mask1 = isnan(QUERY_RESULT1);
mask2 = isnan(QUERY_RESULT2);
tmask = ~mask1 & ~mask2;
result(tmask) = QUERY_RESULT1(tmask) + QUERY_RESULT2(tmask);
tmask = ~mask1 & mask2;
result(tmask) = QUERY_RESULT1(tmask);
tmask = mask1 & ~mask2;
result(tmask) = QUERY_RESULT2(tmask);

%be careful, long corresponds to x and lat corresponds to y
surf(result, LonQ, LatQ, 'edgecolor', 'none')

[Barney]

Thanks Walter.

A couple of slight tweaks - I had used the table2array function to generate the tx_arrays, so consequently I can use round brackets rather than curly braces to set the lat and lon variables. Also, for my personal preference, I have reordered the variables in the surf plot to be as follows:

surf(LonQ, LatQ, result, 'edgecolor', 'none')

Thanks again for your help, I really appreciate it.

[Walter Roberson]

I don't know what I was thinking, putting the result before the other information !