lengcallrobot

Dear every members, esecially Pokemon.

The below description is my problem:

Variable : a, b, c, dx, P, Pn, a', b', c', Clim and dR
Intermedia variable: S, R1, R2, PdB
For symplification : PdB = 10 log10(P) or P=10^(PdB/10)
For symplification : S=P/Pn
For symplification : R1=10^((1/10)*(PdB - a(dR-dx)^b - c))
For symplification : R2=10^((1/10)*(PdB - a'dR^b' - c'))

The equation to be solve is: f(dR) = S^2 R1 R2 - (2^(2 Clim) - 1)(1 + S(R1 + R2)) = 0
From this equation, Find dR in function of other variables.

Note that the varialble " b " is not an integer

Hope our member can help me.
Sorry Na if my question is stupid or disturb all of you.

Take care.

Pokemon

I have question about R1, R2, and f(dR) cos the formula is abit not clear is that R1 n R2 = 10 power to (1/10)*(PdB - a(dR-dx)^b -c) and (1/10)*(PdB - a(dR-dx)^b -c) right?

and f(dR) = S^2R1R2 is (S^2) * R1 * R2 right?

for my idea you take PdB put into R1 and R2, then find R1 * R2 and R1 + R2
Than put everything into f(dR)=0, then find dR.

What class is that and what chapter?

lengcallrobot

Thank for your quick reply Pokemon.

R1 = 10 power [(1/10)*(PdB - a(dR-dx)^b - c)]
R2 = 10 power [(1/10)*(PdB - a'(dR^ b') - c')]

where a different from a' (another variable independant from a, not a conjugate)
similarely for b and b', and c and c'.

f(dR) = R1*R2*(S^2) - (2^(2*Clim) - 1)*(1 + S*(R1 + R2)) = 0

Actually, I also think ask what you suggest by represent (R1+R2)=s and R1*R2 = p
than use the equation X^2 - sX + p = 0 to find R1 and R2 and then to find dR.
However, I have only one equation but 2 variables.

Thank you anyways for your effort.
I will try the find the way out today (by using approximation method some where)
and if I can, I will informe you as well.

Best regards

lengcallrobot

Oh! I just forget to answer your question.

This problem is my research work, not a mathematic class.

Clim : required channel capacity for MIMO (Multiple Input Multiple Output) transmission scheme.

dx : cross point distance between the channel capacity in direct link and relay link.
dR : optimum position to place a relay node.

other variables also have meaning but as for Mathematicien, the meaning of those variables are not so important, then just skip for short.

Thank you so much.

Pokemon

Is that any relationship between a and a', b and b', c and c'?
I can short R1 = p/(10 power to [(a(dR-dx)^b + c)] and R2 = R1 = p/(10 power to [(a'(dR-dx)^b' + c')]

I don't thing you can use X^2 - sX + p = 0 (s=R1+R2, p = R1*R2)

What I mean maybe you can short R1+R2 and R1*R2, so when you put into f(dR) it will be easy to see.

I have not working on math for long long time and I m kind busy to now cos I taking 3 class with full time work. If I have and more idea I will let you know. I need abit more time

lengcallrobot

Thank you Pokemon.

You are right for shorting R1 but R1 cannot be equal to R2 because of :
. In R1, the distance is (dR-dx) but in R2, the distance is only (dR).
. No relationship between a, a', b, b', c, and c' because a, b, and c are the coefficient
of the Roof-to-Ground pathloss model and a', b', and c' are the coefficient of
Roof-to-Roof pathloss model. No correlation between these two model.

I used try as what you suggest but the problem is that I cannot expend the term (dR-dx)^b
since b is unknow at the time of simplifying the formular( but is know during numerican application), and b is not an integer number (as I mentioned before).

I also used try to put log10 to eliminate 10 power... but cannot be done. I will try it again today.

Thank for taking care of me.
Best regards.

Pokemon

Where do you get this question from or who give it to you? Do you have it write in khmer?
I remember I saw that type of question some where one time. sometime they have rule or technical to do that, and that is very high math too not much people can do that too.
If you have book or it write in khmer send that to me maybe I have idea about that.

lengcallrobot

Thank you Pokemon. But tell you the true, this is what make me unsleepy. It is my research work. I am now 2nd year Ph.D in Electrical and Electronic Engineering in Tokyo Institute of Technology, Japan. Those equation is my research work, I need to solve this in order to publish my journal. I have many satisfy simulation results and I also can use Matlab to solve that problem numerically. However, my advisor still want me to find the solution theoritically by solving this equation. Moreover, that equation already simplified by many assumtions.

That all the raison I cannot sleep.

Thank you very much for your kindness.

__________________
May God bless our lovely country !

Pokemon

oh I see. What I know for most difficult math most time they have rule or only one way to it. Unless u done alot of that type of questions. I did research when I was in high school cos I want to best math student, some of the question i so crazy you have to add some the right number to get the answer or like you have remember how to do it more they find the way how to do it.

You are very high class man. for me I dont have much time to study cos I have to work need money.

lengcallrobot

Thank you Pokemon, I do not count the output as mentioned before. What is make me happy and warm is your heart.

You know, I also try to use symbolic math library in Matlab and Mathematica to solve this problem, unfortunately, both of them fall to solve it. I guess if one of them can solve it, I may have chance to solve it too, but now... nothing I can say.

Thank you very much for your time and your warm heart.
Take care with love.

__________________
May God bless our lovely country !