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Introduction

Power Control in communication systems refers to the computation of the optimal transmit power settings of the terminals in a network, so as to maximize network capacity, subject to basic minimum service levels being met for each terminal. Power control is of particular importance in wireless communication systems, due to the interference between different signals at the receiver.

Power control in 1st generation wireless networks was a relatively simple problem because of the enforced separation in resources i.e. FDMA networks used separate frequencies between different terminals, with a significant gap/guard band between the two. This meant that the primary aim of power control was to ensure that there was sufficient received power so as to cross the noise threshold. Interference between terminals was a relatively small problem. This still remains the case in satellite networks and other systems.

However, when cellular networks came into operation, the power control problem started taking center-stage. Since cellular networks aggressively re-use frequencies so as to maximize capacity, inter-cell interference started becoming the dominating source of impairment; as a result the network was "interference constrained" in capacity.

[Gupta and Kumar]'s work demonstrated the relation between interference and network capacity in any interference controlled network, with random placement of nodes and a very standard fading model. This paper clearly shows that the key importance of power control in cellular networks.

Theoretically, power control can be formulated and solved as a convex_optimization problem. In real-life power control is far more complex. This is due to relative movement of the remotes, lack of instantaneous information regarding individual link conditions and limited signaling capacity. We shall discuss these issues individually. wcdma

Power control in cellular networks

Power control in cellular networks is the task of letting the terminals know what power they should transmit on. The network typically has limited flexibility for adjusting its own transmission power adaptively (partly because it is part of the network planning exercise and determines the cell edges, and partly because cellular terminals use the network transmission power as a beacon to determine path loss). How complex or simple this task is depends on one or more of the following factors

Issues in cellular power control

Sensing channel conditions

The key to setting the optimal power allocation is to be able to know the conditions of the channel between the network and each terminal. Unfortunately, cellular systems operate in a highly dynamic environment, due to the terrain and the mobility of the users. In an urban environment, the primary path is typically a NLOS path reflecting off different intermediate reflectors and small changes in the user's location can lead to large changes in the path condition. Also, the amount of signaling bandwidth available between the network and the terminal in the forward direction (signaling of power control messages) is limited.

In TDD systems, channel reciprocity can be assumed by the network, if the frame size is small enough. In other words, the terminal can compute the condition of the forward channel (from the network to itself) and use the same for the return channel (from itself to the network). However, this will not work in FDD systems, where the frequencies for forward and reverse link operations are different and there is substantial frequency sensitive interference.

Bandwidth and latency of the control channel

An oft misunderstood issue in power control is the ability of the network to control the remotes. This depends upon three things; reaction time of the network (depends on its computing ability) and the communication channel between the network and the remotes.

Most modern wireless networks, for example, UMTS?, LTE, EVDO and WiMAX provide a multiplicity of dedicated mechanisms for power control related communication. In UMTS, this happens through the fast power control mechanisms; similar mechanisms exist in others. However, all of these mechanisms have limited bandwidth and further, a minimum latency (this includes both the scheduling delay i.e. gap between control channel allocations and the actual transfer delay). Further, it is nearly impossible to schedule power control messages to all remotes at the same time (something that is implicitly assumed by nearly all power control algorithms). Further, bandwidth considerations mean that the resolution and information content of power control messages is limited, which can lead to severe non-convergence effects, especially when there are a large number of remotes.

A further problem is the problem of loop-gain. When the network invokes the power control algorithm, it has to take into account existing power control messages already transmitted which either have yet to take effect, or, more often, whose effect is yet to be reflected in the measurements.

Identifying interfering users

In older systems, built around voice usage, with relatively long, continuous transmission, the number of terminals active simultaneously was relatively easy to identify. Even in CDMA networks (see below), terminals are transmitting semi-continuously, with different operating codes, so this determination is easy. However, in older GPRS networks and modern OFDM networks, users are assigned slots and resources in a frame-by-frame manner and thus the interfering set changes at a very fast rate.

Consider a WiMAX system, for example, where there are 10 users, A_0_ to A_9_. However, for a given frame, subchannel 1 in slot 1 is allocated to A_0_, A_3_ and A_8_, whereas subchannel 2 in slot 2 is given to A_4_, A_5_ and A_7_. Clearly, A_0_ is not interfering with A_7_. However, most networks lack the ability to tie in power control at such a fast rate. Also, the WiMAX air interface does not allow changes to the power setting on such a slot by slot manner i.e. there is no option to set transmit power along with an allocation in the uplink map.

Techniques of power control

The power control function in any wireless network can be divided into

• The measurement mechanism (periodicity, format, spread)
• The power adjustment algorithm
• The feedback mechanism

The key to this is the algorithm, but the measurement and feedback loop should not be underestimated; they can strongly affect the form of power control algorithm which will work or not work. In this section, we review some of the types of algorithms which have been employed for this purpose.

Centralized vs distributed power control

The existence of asymptotically optimal distributed algorithms (both in cooperative and non-cooperative modes) is well proven in multiple disciplines (see article on distributed control. Distributed algorithms are applicable to the power control scenario as well; strong advantages of distributed control include scaling (with more and more terminals), relatively less use of the signaling channel, etc. This has been studied in a theoretical setting by [Zander92], [Grandhi94], [Foschini93][ and others.

Distributed power control algorithms are executed by the terminals and they work on the basis of the terminals own transmission power P_i_(n) in the nth time instant and the measured link condition _i_(n) corresponding to the same transmission. The algorithm works by updating the transmission power from the nth to the (n+1)th instant by some arbitrary constant c_i_(n) i.e. P_i_(n+1) = c_i_(n)P_i_(n). It has been shown that for some conditions on the sequence c_i_, the power vector converges asymptotically (in some cases weakly) to the optimal transmission vector. Different algorithms work on different mechanisms to compute the best value of c_i_(n)

A key concern for distributed algorithms (to some little extent, centralized algorithms as well) is the convergence time; if the situation is stationary then convergence time does not matter; however, if the average network condition is changing, then the convergence time for the power control algorithm has to be faster than the rate of change.

A second concern is the possibility of instability; specifically, sudden events causing a reaction from the entire active mobile population, leading to temporary network outages. How fast this kind of situation can be detected and mitigated is a property of the algorithm being used. Many networks which support distributed power control allow a central controller to damp

 the behaviour of the terminals through broadcasts; thus
 trading off convergence time for stability

Joint power control

Modern air interfaces allow adaptibility in multiple dimensions. In addition to active transmit power management as described above, they also allow dynamic "on the fly" modification of the encoding scheme, the modulation scheme, the beam forming characteristics, etc. A unidimensional power management algorithm, which assumes that all other conditions remain stationary for the duration of the power control loop time will thus likely to be suboptimal in the best case and subject to significant thrashing in the worst case.

However, optimization in two dimensions, such as scheduling and power control is extremely difficult and can be of non-linear complexity, especially when the two-dimensional surface is not well-behaved. Many joint scheduling algorithms work by alternately optimizing one parameter while leaving the other constant, for example [Elbatt04] Joint power control and beamforming has also been proposed [Farokh98]

Related links

Umts power control, LTE power control?

References

[Elbatt04] Elbatt, Ephremides, "Joint Scheduling and Power Control for Wireless ad hoc networks", IEEE Transactions on Wireless Communications, January 2004 [Farokh98] Farokh Rashid-Farokhi, K.J.Ray Liu, Leandros Tassiulas, "Transmit Beamforming and Power control for Cellular Wireless Systems", IEEE JSAC, Oct 1998 [Foschini93] Foschini, Miljanic, "A Simple Distributed Autonomous Power Control Algorithm and its Convergence", IEEE Transactions on Vehicular Technology, 1993 [Grandhi94] Grandhi, Vijayan, Goodman, "Distributed Power Control in Cellular Radio Systems", IEEE Transactions on Communications, 1994 [Gupta and Kumar] Gupta, Kumar, "On the capacity of wireless networks", IEEE Transactions on Information Theory, 2000 [Zander92] Zander, "Performance of optimal transmitter power control in radio-networks", IEEE Transactions on Vehicular Technology, 1992 Categories: Wireless

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