Distributed Power Control in Cellular and Wireless Networks - A Comparative Study Vijay Raman, ECE, UIUC 1 Why power control? Interference in communication systems restrains system capacity In cellular systems - cochannel interference due to channel reuse In wireless networks - interference from neighboring nodes due to uncoordinated access Interference mitigation procedures involve: Designing systems to tolerate low signal-to-noise ratio by using, for eg., efficient modulation and coding schemes Efficient cell planning - in case of cellular systems Dynamic channel allocation based on traffic and propagation conditions - for cellular and multichannel wireless networks Power control to reduce the effect of interference - can be done in addition to above schemes 2 What is power control? Adjust the power of each transmitter for a given channel allocation such that the interference levels at the receiver locations are minimized. Requirement Maintaining adequate transmission quality on the intended communication 1
link is a default requirement Consequence Reducing transmit power at a certain link will make it vulnerable to more interference Power control problem is not trivial Notes: The transmit power of one user is directly proportional to the interference caused to other users. Therefore, decreasing transmit power will reduce the interference levels at the users. However, reducing the power levels may disrupt the communication link. The goal of the power control algorithm is to therefore reduce interference while maintaining adequate signal quality at the intended receiver. 3 Power control in cellular systems - Performance analysis 1 Quality of a communication link in cellular systems is usually measured in terms of carrier-to-interference (C/I) ratio Assuming a high capacity, interference limited system, the C/I ratio as perceived by a mobile in cell i is given by, Γ i = P rx,i where P rx,i is the received power at mobile i and I j is the interference from a cell j i 1 J. Zander, Performance of optimum transmit power control in cellular radio systems, IEEE Transactions on Vehicular Technology, Feb. 1992. j i I j 2
4 Performance analysis (2/3) If P i is the transmit power by a base station in cell i and G ij is the link gain between a mobile in cell i and a base station in cell j, we get Γ i = G iip i G ij P j j i If there are Q cells operating on a same channel at a given instant, then where, Γ i = P i Q P j Z ij P i j=1 Z ij = G ij G ii is a stochastic variable denoting the normalized link gain Γ i will also be a stochastic variable 5 Performance analysis (3/3) The distribution of Γ is defined as, F (γ) = P r{γ γ} = 1 Q Q P r{γ j γ} = 1 Q j=1 Q F j (γ) j=1 If γ 0, called system protection ratio, is the minimum C/I ratio required for a successful transmission, then the performance measure is the interference probability, F (γ 0 ) = P r{γ γ 0 } Notes: Here, Γ indicates the C/I level at some randomly chosen mobile. Because the C/I level at a mobile is affected by all the Q co-channel cells, the distribution of Γ at a randomly chosen mobile is the weighted sum of the distributions of the C/I levels at all the co-channel cells. The weights are assumed to be the same ( 1 Q ) for all the cells, implying that all the cells affect equally. 3
6 Idea behind the power control algorithm Preposition 1 With probability one, there exists a unique maximum achievable C/I level The maximum is given by γ = max{γ P 0 : Γ i γ, i} γ = 1 λ 1 where λ is the largest eigen value of the matrix Z. The power vector P achieving this maximum is the eigen vector corresponding to λ The proof follows directly from Perron-Forbenius Theorem noting that Z is a non-negative matrix of full rank with probability one Notes: The following definition may be useful to understand the Preposition 1. The definition of achievable C/I level be stated as follows: The C/I level γ is achievable if there exists a power vector P 0 such that Γ i γ for all cells i. Based on this definition of achievable C/I levels, all that the preposition says is, there exists a unique maximum achievable C/I level. Furthermore, the unique maximum is in fact reached when the C/I levels are balanced such that Γ i = γ, i. By P 0 we mean that the powers are non-negative. Further, we can understand that if the maximum achievable C/I is non-zero then P cannot be zero for any i. Finally, Preposition 1 suggests for which C/I level the system is stable, i.e., the C/I balance could be reached. 7 Optimum power vector Preposition 2 At least one optimum power vector has the form, P i = 0, P i 0, i R i / R where R = {i : Γ i < γ 0 } 4
This implies that we can limit our search for optimum power vectors to those vectors with positive components for those cells where the required C/I is achieved Notes: From this preposition, we can understand that the optimum power vector does not guarantee the required C/I, γ 0 for all users. Instead, we have to shut off users that cannot achieve the required C/I level. This suggests a means by which a power control algorithm has to operate. The Preposition 1 should be applied to the subset of users so formed (after eliminating those users who have Γ i < γ 0 ), and see if the protection ration γ 0 can now be achieved for all the users. If not, we have to again shut-off few users, and continue so on! In other words γ in Preposition 1 is not same as γ 0. The power control algorithm tries to make γ at least as good as γ 0 (i.e, it tries to make γ γ 0 ) by eliminating users that cannot achieve γ 0. 8 Global power control algorithm The goal of the power control algorithm is to minimize the interference probability and find the optimum power vector P 0 to achieve the greatest C/I ratio, γ that all the mobiles are jointly capable of achieving Shut-off transmissions in those links that has a C/I level less than the protection ratio, for eg. by handing over to another cell 9 Implications Implementing such an algorithm is difficult as it assumes a global knowledge of the channel gains of all the links Estimating the channels gains require significant measurement effort Even if a measurement is possible, the amount of data required to be communicated to the controller would be enormous for a reasonably sized network Motivates a distributed implementation of the power control algorithm 5
However, handing over mobiles that do not have sufficient C/I may increase the interference in the cell to which it has been handed over. No means to address this problem yet Notes: When there is a hard handover, the centralized power control algorithm will work exactly as mentioned in the sections so far. When a mobile cannot achieve the protection ratio in a cell, then it will be handed over to another cell where the mobile may potentially achieve the protection ratio (which may be due to better link characteristics). 10 Distributed power control algorithm 2 Distributed algorithm involves controlling the transmit power of the mobiles and their corresponding base stations without involving some central controller C/I measurements in the cell itself would affect the transmit power in the cell The power control algorithm is again based on cell-removal technique based on the following balancing algorithm P ν+1 i where ν denotes time = βp ν i P (0) = P 0, ( ) P 0 > 0 1 + 1 Γ (ν) i, β > 0 Notes: The distributed algorithm is implemented as follows: Each node starts with an initial equal power and measures the resulting C/I ratio. If the C/I values are greater than γ 0 for all the cells then the algorithm will stop. Else, the balancing algorithm described in the section is operated for some L steps. At an intermediate step if all the mobiles have C/I greater than the protection ration, then the algorithm stops. Otherwise, after L steps, the cell with the least initial C/I level is removed and the algorithm is repeated by reseting the power levels of all cells to an equal value. 2 J. Zander, Distributed cochannel interference control in cellular radio systems, IEEE Transactions on Vehicular Technology, Aug. 1992. 6
11 Implications of the distributed algorithm If we assume a slow-fading multipath channel, the factors affecting the link gain Z will be mainly the large scale fading The gains can be considered constant for the duration of the algorithm if the algorithm converges within the coherence time of the shadow fading process. This in turn requires high C/I estimation rate Multipath channel variations may however, corrupt the measurements, which in turn will determine the maximum possible iteration rate C/I measurements are therefore slow and less accurate 12 Implications of the distributed algorithm Such an algorithm may be useful for cellular systems with large or moderate cell sizes, but more careful study is required for indoor and small cell scenarios (where propagation changes rapidly) Moreover, a completely distributed algorithm is not possible as knowledge of C/I is required for cell removal [J. Zander 92] Distributed algorithms where users evolve their powers unanimously to a desired prefixed target C/I ratio has been proposed in the literature 3 Notes: 1) The distributed algorithm is easier to implement than a centralized algorithm as it is computationally simpler (as computations are distributed) and can operate with limited knowledge of the channel states (rather than a system-wide knowledge). 2) Because the distributed power control algorithm uses only a limited knowledge of the C/I values, it cannot be optimum. However, the distributed algorithm that is discussed approximates the centralized algorithm in the way it is formulated. The idea behind both the centralized and distributed algorithms are the same - eliminate users that cannot achieve the protection ratio. Though the centralized and the distributed schemes perform 3 G.J. Foschini and Z. Miljanic, A simple distributed autonomous power control algorithm and its convergence, IEEE Transactions on Vehicular Technology, Nov. 1993. 7
Figure 1: Illustration of the carrier sense threshold this elimination based on the global view of the system, the main balancing procedure (discussed in Section 10), which is computationally intensive is distributed in the distributed algorithm. Furthermore, the cell-removal process can be implemented by proper co-ordination with the handoffs. 3) We have to understand that the distributed algorithm presented in this paper provides a framework for understanding the means for achieving an optimal (or near optimal) performance in cellular systems. However, these papers do not provide the means for fairness in the power control algorithms. A distributed power control scheme that addresses fairness is proposed by M. Xiao and Ness.B. Shroff in A Utility-Based Power Control Scheme in Wireless Cellular Systems (IEEE/ACM Transactions on Networking, April, 2003). 13 Power control in wireless networks Interference mitigation in IEEE 802.11-type networks is mainly aimed at improving spatial reuse [J. A. Fuemmeler, N.H. Vaidya, and V.V. Veeravalli] Few power control algorithms focus on reducing energy consumption by wireless nodes [S. Agrawal, R.H. Katz, S.V. Krishnamurthy, and S.K. Dao] Carrier sensing in 802.11 networks makes power control in 802.11 WLANs to be dependent on another quantity called carrier sense threshold Notes: 1) Transmissions in ad-hoc networks are uncoordinated and random, 8
Figure 2: First order starvation in wireless networks rather than a coordinated and scheduled access as in the case of cellular systems. Therefore, power control in wireless networks is (in a sense) difficult than that in cellular systems. 2) The CS-threshold value will essentially let a mobile to decide whether to transmit or not. In other words, a mobile will transmit if the power received from some other (potentially interfering) mobile is lower than its CS-threshold. Thus, choosing the right CS-threshold value is important to make good transmit decision and thereby decide the number of simultaneous transmissions possible. Choosing a very high CS-threshold value may result in more simultaneous transmissions that may result in a collision (as the power of a colliding transmission will fall below the CS-threshold value, which therefore cannot be sensed by a mobile), while choosing a very small CS-threshold may result in a conservative system that will have very little simultaneous transmissions (as the power from a distant, potentially noncolliding transmission may still be above the CS-threshold, leading to a deferred transmission). 14 Key problems in power control 4 Asymmetric links Introduces first order starvation First order starvation can be avoided by achieving symmetry through joint tuning of transmit power and carrier sense threshold Suggested solution is to maintain the product of carrier sense threshold, p cs and transmit power, p t of a node constant, i.e., p cs p t = β 4 V.P. Mathre, K. Papagiannaki, and F. Baccelli, Interference mitigation through power control in high density 802.11 WLANs, IEEE Infocom 07. 9
Figure 3: Second order starvation in wireless networks Interestingly, Fuemmeler, et al. arrive at the same solution for improving spatial reuse in ad-hoc networks Notes: The intuition behind setting p cs p t = β is that, when we reduce the transmit power will also come down. We can therefore have more simultaneous transmissions, which can be achieved by increasing the CS-threshold value of the mobiles (as discussed in the notes for the previous section). 15 Key problems in power control (2/2) Power control may still have to address the second order starvation Algorithms to address fully the second order starvation is an open problem 16 Discussions How to perform power control in macro-diverse wireless networks? Involves a dense deployment of access points to which a mobile client can interact [e.g., DAIR] R.D. Yates provides a power control framework for macrodiverse cellular systems Can we have the Access Points (APs) in wireless network interact among themselves to exchange power control information May include channel gains, traffic loads, CS threshold values (if not uniform), etc. 10
Possible in dense infrastructure-based networks How to perform power control when there are multiple channels? Power reduction for a user moving from channel c to c may increase the interference to users currently on channel c Notes: 1) A water-filling based power control algorithm is totally different from the algorithms that are discussed in this presentation. In water-filling, the users are all assumed to be independent and the powers are allocated to the users based on their noise levels, such that the total power allocated to all the users is less than a maximum available power. In wireless networks, the transmit power of one user will affect the interference to other users. 2) If the wireless nodes can exchange the information on their relative traffic load, channel gains, etc. then better power control decisions can be made. The mobiles can predict the potential interference better and use a more accurate transmit power to overcome the interference. 11