# Narrowband instantaneous power

#### cooltafel

Joined Mar 20, 2018
8
Hey all,

I got stuck on a homework question about narrowband instantaneous power.

First of all, the description of the quesion:
Assume a mobile traveling at a velocity of 20 km/h receives two multipath components at a carrier frequency of 1000 MHz. The first component is assumed to arrive at τ = 0 μs with an initial phase of 0° and a power of −50 dBm, and the second component which is 3 dB weaker than the first component is assumed to arrive at τ = 1 μs, with an initial phase of 30°.

If the mobile moves directly toward the direction of arrival of the first component and directly away from the direction of arrival of the second component, compute the narrowband instantaneous power for t = 0 s.

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I made an attempt in Matlab, here is the code:
Code:
power1 = -50;
gain1 = 10^((power1 - 30)/10);

gain2 = gain1/2;

narrowband_power = (abs(sqrt(gain1)*exp(0)+sqrt(gain2)*exp(1i*30)))^2;

fprintf('Narrowband instantaneous power: %i [nW]\n', narrowband_power*10^9);

My question is: How should the initial phase of the second component be considered in the calculations?
In my code I put the initial phase in the exponent of the second component. Is that the correct way?
I am asking this, because there are some follow-up questions that require this initial phase.

Thanks in advance for the effort and help!

Greetings