Signal power calculation formula derivation step
Signals can be divided into energy limited signals and power limited signals. If the power of the signal is limited, it is called a power limited signal, referred to as a power signal. The energy of the power signal is infinite. It has a large impact on the performance of the communication system and determines the voltage and electromagnetic field strength of the transmitter in the wireless system.
The energy E and power P of the continuous time signal f(t) are defined as:
The energy E and power P of the discrete time signal f(k) are defined as:
If the signal energy is limited, ie 
And 
, the signal is called the energy signal; if the signal power is limited, 
And E approaches 
, this signal is called the power signal. A power limited signal is a signal with an average power greater than zero and limited.
The power of a limited power signal is greater than zero and limited, and the energy is infinite.
A signal cannot be both a power signal and an energy signal, but it can be neither a power signal nor an energy signal. In general, periodic signals and random signals are power limited signals [2].
How to judge the power signal and energy signal?
The energy and power of a signal is a basic concept or general concept in signal and system analysis. Its definition does not specifically consider the situation of taking care of a particular signal. In layman's terms, time does not exist for you, nor does it die for you. Past, present and future are the time frames that the discipline of signals and systems needs to focus on. For broad adaptability, the integration time of these two basic concepts is infinite.
According to the characteristics of the two signals, the periodic signal in the infinite time is a power limited signal, and the energy signal must be a non-periodic signal. The aperiodic signals are further divided into three types. One is the energy signal: a pulse signal with a limited duration, and 
Time, 
One is a power signal: a signal with a limited duration but a limited amplitude; one is neither a power nor an energy signal, when 
Time, 
.
(Premise: the propagation of obstacles between the transmitting end and the receiving end, such as the connection signal between the satellite and the mobile phone)
Friis formula:
Pr(d): received signal power Pt: transmit power Gt: transmit antenna gain Gr: receive antenna gain λ: wavelength (m)
d: distance between transmitter and receiver (m)L: loss independent of propagation (transmission line attenuation, filter loss, antenna loss)
Note: The unit of power and gain is W
Can be rewritten from the above formula to Pr, which is a non-functional form of Pr(d)
Assuming no loss in the ideal state, L = 0, f = c / λ, adding the constants, you can calculate:
If you change the Pr, Pt, Gt, and Gr units to mW, you can deduce the following formula.
The unit commonly used to represent power in the wireless concept generally uses dbm, dbi, and the conversion relationship with W is as follows
In the case of d"50m,
Can be calculated as
If you change the Pr, Pt, Gt, and Gr units to mW, you can deduce the following formula.
The path loss formula is
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