I tried a few things to understand where the problem lies. I have to say I am not an expert in this field and I will not find out if thre is a better equation but at least I found a few minor bugs here and there, and made at least the implicit function works but not with the expected P target value , neither with the expected shape . So I wonder if there is still a problem either due to the constants or how we implemented the equations (I did a few variations around the "official" one , but no one gave a satisfatory behaviour)
so to know what typical P value the equation would return for a given h,R pair, I did first a contour plot by generationg a meshgrid for h and R.
you can see that P lies in the range 100 to 130 dB , to this explains why implicit would not any solution if the P target = 10 dB, way out what is to be expected - so again, if P should be 10 dB, then we have a problem either with the constants and / or how we wrote that equation; also P was missing in the function evaluation with implicit
f = A./(1+a*exp(-b*(atan(h./R)-a)))+10*log10(h.^2+R.^2)+B1;
f=@(h,R) A./(1+a*exp(-b*(atan(h./R)-a)))+10*log10(h.^2+R.^2)+B1 - P
fimplicit(f,[500 4500 500 4500])