AN UPLINK POWER CONTROL ROUTINE FOR QUALITY-OF-SERVICE EQUALIZATION IN WIRELESS DATA TRANSFER NETWORKS CONSTRAINED TO EQUIDISTANT POWER LEVELS

Background. Power control is a process of adjusting transmitter power output in a communication system to achieve satisfactory performance within the system. In wireless data transfer networks, this process refers to uplink connection, when information about the transmitter power output is sent to the base station, whereupon the power is adjusted in accordance with one or more transmit power control commands received in the downlink. The uplink power control is intended to ensure quality of service declared by the system provider including maintaining a sufficient signal-tonoise ratio and link data rate, reducing interference, overloading, and preserving the battery life. Objective. Whereas the sum of power levels is constrained to the grand total of the powers transmitted in the uplink off all the transmitters, the quality-of-service equalization is a fundamental task. Henceforward, for a set of equidistant power levels, the goal is to achieve the quality-of-service equalization by non-decreasing powers when moving away from the base station with using the distances from the mobiles to the base station. Inasmuch as the uplink power grand total is “allowed”, the sum of all the powers should be as much as closer to the grand total. Methods. Principally, ratios of distances to the base station are calculated using an initial value of the path loss exponent. Then the case of the overloaded network is checked out. After that, the base station power responses are calculated using the ratios and the principle of the equal quality of service, wherein the received uplink power should be closely the same for all the users by every uplink transmission. If the farthest/closest transmitters’ powers are out of the power range, they are set down/up to the proper maximum/minimum. The path loss exponent is decreased if the proper maximum is re-violated. Finally, the base station power responses are rounded to values within a set of power levels. Results. The suggested algorithm deals with powers in watts fitting wireless data transfer networks working in shallow areas (like Wi-Fi, Bluetooth, etc.), for which the number of power levels is relatively great and the range of active uplink transmission powers is relatively narrow. The routine which implements the algorithm still can be optimized depending on the programming environment and paradigm. For instance, C++ and Python will fit for speeding up the performance. Nevertheless, the routine would not sustain the UMTS update frequency, unless a network works with a few tens of users. Conclusions. The uplink power control routine stated with the six algorithmic items effectively equalizes quality of service in shallow wireless data transfer networks, where user uplink powers are constrained to equidistant power levels in watts. It is not a one-step but a multi-step process during which four types of conditions are successively tried to get satisfied. Eventually, the factual sum of all the powers transmitted in the uplink may become “harmlessly” less than the grand total.


Introduction
Power control is a process of adjusting transmitter power output in a communication system to achieve satisfactory performance within the system. In wireless data transfer networks, this process refers to uplink connection, when information about the transmitter power output is sent to the base station (mobile-to-base), whereupon the power is adjusted in accordance with one or more transmit power control commands received in the downlink (which follows the uplink) [1,2]. The uplink power control is intended to ensure quality of service declared by the system provider [3,4]. This also includes maintaining a sufficient signal-to-noise ratio and link data rate, reducing interference, overloading, and preserving the battery life [5].
One of the most important aspects of the quality-of-service principle is ensuring equal access for all the users. Along with that, reducing interference relates to effective spectrum management [6,7]. The latter is very important for overall wireless communications, which have been growing dramatically. All these items are thoroughly intertwined influencing each other. Thus, ensuring quality-of-service equalization additionally helps to sustain the increasing transmission of radio waves, which threatens not only with interference, but also with plausible health issues [8].
In general, the base station manages a definite set of power levels of the transmitters/mobiles linked to it. This is the centralized power control [6]. Obviously, the performance of the base station cannot be compromised by high power local mobiles which may tend to mask out weaker mobiles farther away from the base station. Therefore, transmit power output of the nearer mobiles is decreased, whereas the farther mobiles are adjusted to have higher transmit power outputs [8,9].
For instance, a table of GSM power levels is defined, and the base station controls the power of the mobile by sending a GSM "power level" number/tag/identifier. The mobile then adjusts its power by an appropriate accuracy: at the maximum power levels it is typically ±2 dB, whereas this relaxes to ±5 dB at the lower levels. The power level numbers vary according to the GSM band in use [3,4] The UMTS uses its own conception of uplink power control [1,2,6]. The transmitter is capable of changing the output power with a step size of 1, 2, and 3 dB depending on a set of transmit power control commands. Thus, once the set is for "down"/"up" within the most accurate power control range, the transmit power is reduced/increased by 1 dB; otherwise the transmit power is not changed.
The main problem in such a power adjustment is that it is too slow. Indeed, GSM cellular systems has their update frequency of 2 Hz. The UMTS updates powers at 1500 Hz, but it reacts against weaker or stronger signal (received by the base station) only with a single step, so abrupt changes of signal power are impossible to compensate [6,10].
Contrary to the centralized power control, mobiles can be allowed to update their powers autonomously, considering quality of service they perceive [8]. As the mobiles become independent of the base station, they can be considered as selfish agents (players) who try to maximize their utilities (i. e., throughput and connectivity) [6]. Then methods of decision-making theory are applicable. Thus, non-cooperative game theory models of wireless network power control claim that the selfish mobiles maximizing their own utility are opposed to maximizing the overall performance of the wireless data transfer network, in which the mobiles operate [6,7]. Then, with a utility function assigned for each mobile, the most stable and advantageous situation in the game is determined. However, substantiation of the utility function relies only on distances from the mobiles to the base station, rather than distances between each pair of mobiles [6]. This does not improve measuring interference if to compare the game theory approach to both the table-of-powerlevels and one-step-adjustment approaches mentioned above. Besides, re-calculation of the power according to the most favorable situation becomes exponentially slow when the number of mobiles operating simultaneously linearly increases.

Problem statement
Whereas the sum of power levels is constrained to the grand total of the powers transmitted in the uplink off all the transmitters, the quality-of-service equalization is a fundamental task [1,2,7,9,11]. Power levels can be equidistant like in GSM tables, but their selection might be driven by distances from the mobiles to the base station. These distances are estimated by a GPS navigation technique, which is presumed to be used in the game theory approach as well. Henceforward, for a set of equidistant power levels, the goal is to achieve the quality-of-service equalization by non-decreasing powers when moving away from the base station with using the distances. Inasmuch as the uplink power grand total is "allowed", the sum of all the powers should be as much as closer to the grand total.

Parameters used for uplink power control
A number of active transmitters N is determined automatically. So, there are seven types of parameters used for uplink power control. Some of these parameters are defined by the system, the rest of them are measured.
The system-defined parameters are: 1. An initial (nominal) value of the path loss exponent  . Values of exponent  are normally in the range of 2 to 4, where  becomes greater for propagation of radio waves in relatively lossy environments. The path loss exponent can reach values in the range of 4 to 6 in covered environments (buildings, basements, sport-arenas, etc.). As the time goes by (say, in years),  can be increased if the area where a base station operates becomes overbuilt with various architectural constructions.
2. A maximum-tolerated grand total  p of the powers transmitted in the uplink off all the transmitters (either in dBm or watts). Value  p depends on the capacity of the network. Occasionally,  p can be expressed as a maximal number of user transmitters which could effectively simultaneously work within a scope of the same base station. 3. A maximally possible transmitter power output max p (either in dBm or watts).

A minimally possible transmitter power output 0
p (either in dBm or watts).

A set of uplink power levels
As these L levels are assumed to be equidistant, Thus, the closest transmitter has the greatest index, and the farthest transmitter has index 1. Obviously, powers

Ratios of distances to the base station
The reduction in power density of radio waves as they propagate through space is called path loss. Path loss is a major component in the analysis and design of the link budget of a wireless data transfer network. If a transmitter is distanced by d meters from a receiver, then the path loss in the simplified form is estimated in dB as where system losses are included into the path loss exponent. If a transmitted power is transmit p , and the received power is rec p , then path loss (3) Hence, quality of service can be equalized by taking into account factor  d in (4) for each pair of active transmitters. This is why ratios of distances by the path loss model (3) will be used further. Ratios (5) are calculated by the base station, which is assumed to "know" the path loss exponent over the area wherein this station operates.

User power requests and base station power responses
The base station is tasked to map power requests Descending order (7) is necessary due to (2) and (4). If (6) and (7) hold then the powers are not corrected: Otherwise, they are corrected so, that Meanwhile, the difference by (9) should be minimized. In particular, the marginal case in (9) is plausible and acceptable.

A case of the overloaded network
If, occasionally, holds, then the farthest-from-the-base-station transmitters whose distances are x returns the integer part of x , will be turned off: and only power requests Those off N farthest-from-the-base-station transmitters will receive a command in the following downlink to turn off. Nevertheless, such a turn-off is not permanent. The turned-off transmitter becomes inactive just for a period of a single update (e. g., for 1/1500 s in the UMTS). After that, it is likely the transmitter will start searching for another network, if the current network continues disconnecting it by sending "zero" power responses (16).

Raw calculation of the base station power responses
Ensuring the equal quality of service implies an equal received uplink power for all the users by every uplink transmission. This means that, for the neighboring transmitters, It follows from (18) that the uplink power of i -th transmitter should be set at Obviously, Then power of every farther transmitter is expressed by the closest one with (20): Then, using marginal case (13) and the-closesttransmitter expression (21), So, the nominally appropriate uplink power of the closest transmitter is and nominally appropriate uplink powers of the remaining transmitters are

Setting down/up to the proper maximum/minimum
When a cycle of the raw calculation of the base station power responses is completed, there is a subtask to check whether conditions (10) and (11) Theoretically, both cases (26) and (29) are possible. The case with rectifying situation (29) always follows the case with rectifying situation (26). However, even after having re-corrected powers by (31), there still can be a violation (re-violation) of condition (10). Then the path loss exponent is adjusted "manually".

Adjusting the path loss exponent
If (10) is re-violated after having rectified situation (29), the path loss exponent, despite the real losses in the surrounding environment, is decreased "manually". It is a subtask wherein the path loss exponent must be minimally decreased down to value  * such, that conditions (10) and (11) hold both at this value. In fact, *  will become a maximally possible value of the path loss exponent, at which conditions (10) and (11)  is executed until (10) and (11)  .
The sequence of assignments (36) and either (37) or (38) is repeated while    , where  is an insignificant change (either decrement or increment) of the path loss exponent.

Uplink power control with equidistant power levels
After the raw calculation of the base station power responses is complete and conditions (10) and (11)  Firstly, remainders The single bottleneck is in those iterations occurring after the raw calculation.

Examples of the uplink power control routine application
For exemplifying the uplink power control routine application, let   4 as it normally is for areas with city buildings and constructions. Note that powers are in watts. Fig. 1 shows a location example of 800 active users (transmitters) with sufficiently great range of uplink powers and their levels. The uplink powers are corrected according to Fig. 2. A result of some limitations to the network is hardly seen in Fig. 3, but it is well seen in the corresponding Fig. 4. A location example with turning the farthest users (transmitters) off is in Fig. 5, whereupon Fig. 6 shows a trivial distribution of grand total of the powers transmitted in the uplink.
Those illustrations are much simplified but they give a general imagination of what results of the routine application are expected. Another important property is the time performance, which is better for cases like that in Fig. 6 (the result in Fig. 6 is obtained in about 25 times faster than that in Fig. 4). By the way, increasing the number of power levels does not retard the time of the routine execution.

Discussion
The suggested algorithm is directed to work with powers in watts. A transition to decibel-milliwatts can be done but it is not worth for wireless data transfer networks working in shallow areas (like Wi-Fi, Bluetooth, etc.), for which the number of power levels is relatively great and the range of active uplink transmission powers is relatively narrow. The routine which implements the algorithm still can be optimized depending on the programming environment and paradigm. For instance, C++ and Python will fit for speeding up the performance.
Nevertheless, the routine would not sustain the UMTS update frequency. Experiments show that it takes no shorter than 0.5 to a few milliseconds for correcting the power requests within a network with a few hundreds currently active users. However, networks with a few tens of users process their power requests much faster (no longer than 0.5 ms that fits the UMTS update frequency). Moreover, the routine could be sped up by an appropriate implementation of dichotomization [12] by (32) -(38).
An apparent advantage of the uplink power routine is that it is capable to smooth much the distribution of uplink powers. Increasing the number of power levels seemingly improves the smoothness (compare Fig. 4 to Fig. 2) without significant delays in performance.

Conclusions
The uplink power control routine stated with the six algorithmic items is intended for quality-ofservice equalization in wireless data transfer networks, where user uplink powers are constrained to equidistant power levels in watts. The routine is based on calculating ratios of distances to the base station and involving a set of uplink power levels, which allow approximating to the equalization by smoothing uplink powers' distribution. It is not a one-step but a multi-step process during which conditions (13), (10), (11), (25) are successively tried to get satisfied. Eventually, condition (13) may fall out due to power level constraint (25), and condition (9) becomes true. The carried out research can be furthered in order to optimize the time of the routine execution.