# Power Control for Mobile Phones

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Section II: Interference Constraints:
Assumptions and Symbols Used:
1. Number of users = N
2. Number of base stations = M
3. Transmitted power of user j = pj
4. Gain of user j to base k = hkj
5. Receiver noise at base station =
6. Signal to interference Ratio = SIR
The general interference constraints that apply to any system state that at a base station (k), a user receives a signal of power (hKjPj). At the same time, the user experiences an interference that can be denoted by ij hkipi + k.
Thus, the SIR of a user j at base station (k) and under the power vector (p) can be denoted as pjkj(p) where,
hkj
kj(p) = ——
ij hkipi + k
Section III: Minimum Power Assignment (MPA) Method:
The MPA is an iterative procedure and at each step, the user is assigned to the base station at which its SIR is optimized. We can analyze the MPA for two situations:
1. Continuous power adjustment
2. Discrete power adjustment
If we denote target SIR for a user by , then, the SIR constraint of a user following the MPA procedure can be denoted as:
j
pj I j MPA (p) = min k —
kj(p)
According to the MPA iteration, i.e. p (t +1) = I MPA( p(t)), the user is assigned to the base station where the power consumed by the mobile device to attain its target SIR i.e. is minimized. This iteration is applicable with the assumption that other users corresponding to the same base station are currently maintaining a fixed transmission power level.
We shall now examine the two cases where MPA is applicable in more detail.
Section IV:…
The aim of the minimum power assignment method is to provide users of cellular communication services with an acceptable connection with minimum usage of power on the side of the user so as to elongate battery discharge time, i.e. the amount of time that it takes for the battery of the cellular device to get discharged. The use of the synchronous and asynchronous standard power control algorithms guarantee to find the minimal power level required for establishing an acceptable connection given that the interference from other users that needs to be over come to do so, characterized by the value I(p) is feasible. Asynchronous power control also indicates the robustness of the standard power control algorithm in the face of slower updating of transmission power levels by individual users. The power controlled systems and methods that are described in this report can be implemented by each individual user knowing only its own uplink gains and the total power received at each base station, i.e. a user need not be concerned about the power transmissions of other users corresponding to the same base station, thereby making the algorithm much faster and much less complex. Further development in the field of power control for mobile devices holds the potential to decrease the need for repeated recharging of cellular communication devices and of elongating the standby and talk time simultaneously.