Chapter 7 RADIO RESOURCE MANAGEMENT in

Chapter 7 RADIO RESOURCE MANAGEMENT in CDMA Networks Katerina Papadaki^ and Vasilis Friderikos^ Operational Research Department London School of Economics k.p.papadaki @ lse.ac.uk Centre for Telecommunications Research King's College London [email protected]

Abstract

Over the last few years wireless communications have experienced an unprecedented growth providing ubiquitous services irrespective of users' location and mobility patterns. This chapter reviews different resource management strategies for wireless cellular networks that employ Code Division Multiple Access (CDMA). The main aim of the formulated optimization problems is to provide efficient utilization of the scarce radio resources, namely power and transmission rate. Due to the fact that practical systems allow discrete rate transmissions, the corresponding optimization problems are discrete in their domains. Additionally, these optimizations problems are also non-linear in their nature. We focus on power minimization and throughput maximization formulations both for single time period and multiple period models. We provide a new method for solving resource management problems in CDMA networks, formulated as dynamic programming problems. A linear approximate dynamic programming algorithm is implemented that estimates the optimal resource allocation policies in real time. The algorithm is compared with baseline heuristics and it is shown that it provides a significant improvement in utilizing the radio network resources.

Keywords:

wireless cellular systems, radio resource management, power and rate control, approximate dynamic programming

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1.

HANDBOOK ON MODELLING FOR DISCRETE OPTIMIZATION

Introduction

Over the last decade the cumulative impact of the success of wireless networks and the Internet sparked a significant research interest on the convergence aspects of these two technologies. Due to the increased available bandwidth, mobile users are becoming increasingly demanding and sophisticated in their expectations from mobile wireless networks. This stimulates the development of advanced resource management tasks for optimal usage of the scarce resources of wireless networks. In this chapter we will describe two resource allocation problems that arise in Code Division Multiple Access (CDMA) networks. These problems arise in wireless telecommunication systems where serving mobile users is constrained by system capacity. Mobile users need two services, transmitting information to them and from them. The two problems are generally studied separately: Both are within the setting of a mobile wireless network that we describe in detail in the following.

1.1

Mobile wireless network

The main concept behind a mobile wireless system is that a geographical area is divided into a number of slightly overlapping circular "cells." Each cell contains a base station, which is responsible in transmitting (receiving) information traffic to (from) multiple mobile users within the cell. There are two types of transmission that occur within each cell: the downlink communication, where the information arrives at the base station for each mobile user and queues to be transmitted to the respective user; and the uplink communication, where each mobile user transmits information to the base station. Currently, we are witnessing a paradigm shift in mobile wireless networks from commodity voice delivery to mobile multimedia packet based transmission. Packet based transmission, which means that information (in bits) is packaged in discrete bundles of information packets, occurs in Internet like applications such as Voice over Internet Protocol (VoIP), Video Streaming, WWW and e-mail to mention just a few. For example, mobile users could be downloading files from the internet (downlink communication) or uploading files to the internet (uplink communication). There are different access systems for performing the transmission. In this chapter we are concerned with Code Division Multiple Access (CDMA) systems where multiple transmissions can occur simultaneously in each time slot. In Time Division Multiple Access (TDMA) systems the transmissions are scheduled over time since only one transmission can occur per time slot. In Frequency Division Multiple Access (FDMA) systems only transmission within different frequency bands is allowed in each time slot.

Radio Resource Management

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Constraints Under light traffic conditions the issue of packet scheduling from or to different mobile users is trivial as far as there are enough capacity resources to satisfy the requests by the users. The problem arises when there is heavy traffic of information and there are scarce resources for the transmission process. The main resource needed for a device to perform a transmission is power. The power needed to perform a transmission in a time slot depends on the transmission rate (bites per second) chosen for this transmission as well as the transmission rates of other transmissions that occur simultaneously. This is due to the interference that occurs between transmissions that take place in the same time slot. The interference caused by simultaneous transmissions is a drawback for CDMA systems, but nonetheless it is balanced by the higher throughput of information. Given the interference of simultaneous transmissions, managing the power resource becomes challenging since it is a non-separable function of all the transmission rates that occur concurrently. Further, the power levels needed for a transmission depend on the channel gain between the user and the base station; the channel gain is a metric that quantifies the quality of the connection between the user and the base station: Higher channel gain means better quality of the connection. It is determined by a stochastic process whose mean is a function of the distance between the user and the base station. As a mobile user moves away from the base station his channel gain decreases in such a manner that the power needed for transmission (without interference from other users) increases as a quadratic function of the distance. There is another constraint concerning the transmission process. This occurs due to the frequency bandwidth available for the transmission. This limitation results in an upper bound on the aggregate transmission rate from the transmitting device. In order to efficiently serve the mobile users, Quality of service (QoS) requirements are defined and introduced into the problem. Quality of service of mobile users can be measured by the total transmission rate achieved by users, the total delay of information packets waiting in the queue, the average queue length for each user etc. These factors can either be introduced into the objective of the problem as quantities to be maximized/minimized, or they can appear as constraints to guarantee satisfactory levels of quality of service.

1.2

The single cell problems

We describe the two problems that arise in a single cell where transmission rates need to be allocated to users in order to efficiently utilize the resources needed for the transmission process.

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In the downlink problem information packets arrive over time at the base station for each mobile user and are queued to be transmitted over a discrete time horizon, taking into account power and aggregate rate constraints. In the uplink problem information packets are queued at each mobile device to be transmitted to the base station over a discrete time horizon. In both problems the objective is to perform the transmission efficiently by either maximizing system throughput or minimizing power used while keeping quality of service at satisfactory levels. These two problems are generally studied separately. Their main difference stems from the origin of resources for the transmission. In the downlink, it is the base station that performs the transmission and thus there is one capacity constraint for each resource, whereas in the uplink it is the mobile devices that perform the transmission and thus there is a capacity constraint for each mobile user for each resource.

1.3

Literature review of CDMA downlink and uplink problems

Because in CDMA systems all mobile users share the same frequency, the interference produced during concurrent transmission is the most significant factor that determines overall system performance and per user call quality. Therefore the most crucial element in radio resource management is power control. As mobile users move within the cell their channel changes and therefore dynamic power control is required to limit the transmitted power while at the same time maintain link quality irrespectively of channel impairments. In that respect, power control has been extensively examined over the last years, and various schemes have been proposed in order to maintain a specific communication link quality threshold for each mobile user [1], [2], [3], [4]. For practical CDMA systems where there is a physical constraint on the maximum transmission power, it has been shown that by minimizing power transmission (i.e. reducing the interference between transmitting users) the maximum number of users can be served [5], [6]. These power control schemes have mainly focused on single service voice oriented communication rather than on multiservice wireless communication, where variable bit-rate packet transmission is also supported (data services). For data services, such as Internet like applications, where there is not a specific data rate requirement, not only power control but also rate control can be exploited to efficiently utilize the radio resources [6], [7]. The optimization of data packet transmission in terms of minimum time span, maximum throughput and minimum power transmission, through joint power and rate control have been studied in [8], [12]. Oh and Wasserman [7] consider a joint power and rate allocation problem. They consider a single cell system and formulate an optimization problem for a single


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class of mobiles. They show that for the optimal solution, mobiles are selected for transmission according to their channel state and if a mobile is selected, it can transmit at the maximum transmission power. A textbook dynamic programming (classical Bellman DP [13]) formulation for non-real time transmission on the downlink of a CDMA system has been developed in [12], where the link between throughput maximization and minimum time span has been discussed. A similar DP formulation appeared in [16], where the authors discussed optimal joint transmission mode selection and power control. DP for resource management on the downlink of a CDMA system has also been used in [14]. The authors focused only on throughput maximization without considering queue length evolution and showed that by optimally allocating bit-rates, using a textbook DP algorithm, tangible gains can be achieved. Furthermore, the authors in [15] used classical backward recursion DP to obtain a fair-queueing algorithm for CDMA networks, but with the assumption that all codes are available on the downlink channel. The above related work has mainly focused on DP formulation rather than implementation aspects for real-time decisions. The computational challenges that arise for the actual solution of these optimization problems have not been meticulously discussed. Textbook DP algorithms (i.e., value iteration or policy iteration) typically require computational time and memory that grow exponentially in the number of users. The inherent computational complexity render such algorithms infeasible for problems of practical scale. In this chapter, we present the work of Papadaki and Friderikos [19] that tackle the intractability of large-scale dynamic programs through approximation methods. A linear approximate DP architecture is used for near-optimal data transmission strategies on the downlink of CDMA systems. The work in this paper is closely related to algorithms used in [18]; other types of approximate DP algorithms have been discussed and developed in [20] and [21].

2.

Problem Definition

In this section we define the capacity constraints and explain the relationship between power and transmission rates. We define the parameters and variables and set the notation for the rest of the chapter for both the uplink and the downlink problems. Uplink Consider a single cell in a CDMA cellular radio system where A^ active mobile users share the same frequency channel. Each mobile user can transmit to the base station with power pi that is in the range 0 < Pi < Pi, where pi is the power capacity for mobile user i. We denote the channel gain or link gain between user i and the base station by gi'. the higher the value of Qi, the better the quality of the connection between the user and the base

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station. We define the problem for a short time interval, a time slot, such that Qi is stationary. Given that the mobile users are using power given by the power vector P — {PI^P2,"",PN) and their channel gain is given by the channel vector S= (^1) ^2, ••., 5iv), we define the Signal-to-Interference-Ratio (SIR), denoted by 7i, for mobile i, as: 7,(p) ^

^^^^-y—-, 1 < i < A^

(7.1)

EjîgjPj + i + i' where / > 0 is the inter-cell interference noise (i.e. interference that occurs from neighboring cells) and u > 0 is the power of background and thermal noise at the base station. Both / and u are considered to be fixed for the current analysis. The realized data rate of a mobile user depends on many factors, however the SIR is an important measure that is directly related to the transmission rate of a mobile. We let Vi e ^ denote the transmission rate for mobile user z, where i?^ is the set of allowable rates and r = (ri, ...,rAr) is the corresponding vector of transmission rates. Then assuming a linear relationship between the SIR (7^) and the transmission rate (r^) we have: Vi W - - IT

(7.2)

where W denotes the spreading bandwidth, and F = E^/h is the bit-energyto-interference-power-spectral-density ratio for each mobile that we assume to be the same for all mobile users. V gives the probability of a bit transmitted erroneously. Equations (7.1) give 7^ in terms of the power vector p. Given that the rate allocation decisions are based on the SIR's we would like to have the power of each user pi in terms of the 7i's. We can rewrite (7.1) as: 9iPi ^N

Ylj=i 9jPj - 9iPi + 1 + ^ which is equivalent to: N

9iPi = I X^^jPj + I + J^\ T-J— Summing over i and rearranging terms yields:

.7 = 1

^

^j

= l 1+7,-

(7.3)

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Radio Resource Management Substituting (7.4) into (7.3) gives:

I+u li l - E f . i l ^ ^ ^ ( l + 7i)

Pi

(7.5)

The above expression gives the required power to perform the transmission for mobile user i when the transmission targets are set to 7 = (71, ...,77v). It is easy to show [9] that there exist feasible powers p to perform the transmission, given by (7.5), when the following condition holds: N

7j < 1 1 + 7j

^

(7.6)

Note from (7.5) that the power needed from mobile i to perform a transmission with SIR target 7^ does not solely depend on 7^ but on the SIR targets of all the users i.e. the entire SIR vector 7. This is due to the interference caused in a CDMA system when simultaneous transmissions take place. As can be seen from (7.5), the channel gain gi of user i plays an important role in the power needed to perform a transmission. A user with a good channel (high Qi) needs less power than a user with a bad channel (low gi). Further, when a single user transmits in a time slot then to achieve a target SIR 7^ his allocated power needs to be pi = li^-^ (see equation (7.1)). However, as can also be seen from (7.1) when other users transmit in the same time slot, user i needs to increase his power considerably to counteract the interference caused by other transmissions, in order to achieve the same 7^ target. Because of the maximum power limit at each mobile. (7.7)

Pi g2 ^ - - - ^ 9N î^d that there exists a feasible vector 7 = ( 7 1 , . . . , 7^^) that satisfies (7.19)-(7.21), For each feasible vector 7, the objective (7.18) is minimized by reassigning 7^ 's such that 71 > 72 > . . . > 7iV

Lemma 7.1 becomes intuitively plausible when we observe the structure of the objective function (7.18). The objective is to minimize both the sum in the numerator and the denominator of the objective. In the sum of the numerator the terms r ^ have coefficients ^^ where as in the sum of the denominator l+7j

9j

the coefficients are all the same. Thus, apart from their channels QJ the users are indistinguishable in the objective. Given a feasible assignment of SIRs it is always better to reassign the users' SIRs according to the order of their channels. However, the question is what is the optimal SIR vector irrespective of the order of its elements. Berggren and Kim propose the following heuristic, based on the above result, that they call Greedy Rate Packing (GRP): Greedy Rate Packing L E T : 7* = 0, foralH = 1,...,A^. F O R i = iTO N D O : I

7i

max < "ji e L :

7i

.tt^ + î

< 1 — max

9jPi

(7.22)

Starting with the user with the highest link gain, GRP iteratively allocates the maximum SIR that is feasible with respect to the current power constraints. A^ The total SIR achieved from GRP is 7* = J2i=i li- The GRP heuristic ignores the constraint (7.19) of meeting the SIR target 7. However, as long as 7* is high


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enough the heuristic provides a good solution. Berggren in [9] shows that out of all feasible SIR assignments that will give total throughput equal to 7*, the GRP assignment requires the minimum power. Thus, they show that by replacing the SIR target 7 by 7* in (7.19): N

X;7i-7*

(7.23)

the GRP heuristic gives the optimal solution to the problem of minimizing (7.18) subject to (7.23), (7.20) and (7.21). If we let MUP{^) be the set of the SIR vectors that solve the problem (7.18)-(7.21), then the question becomes what is the SIR vector that solves the MUF problem and maximizes 7. We can write this as follows: N

max E ^ i

s.t

^ eMUP i^lj]

(7.24)

(7.25)

Berggren and Kim do not provide a solution to the above problem but they do consider a special case where the power capacity of mobile i, pi is large compared to the interference plus noise, I + u, and thus the power constraints (7.20) are reduced to the following simple form:

They also assume that the transmission allowable rates, and thus the corresponding SIRs, are geometrically related. Suppose the set of allowable rates g^ = { 0 , r ( ^ ) , . . . , r W } where r(^+^) - iJ.r^'\ 1 0 and r^^). They show that for a rate allocation that maximizes throughput (and thus SIR) subject to (7.26), it is suboptimal to use the rates A^\ . . . , A^^ more than /i— 1 times each. Thus when /i — 2, which is often the case in practice, it is suboptimal to use any of the rates more than once. Thus the GRP can be modified to the MGRP to allocate rates (SIRs) to users in a similar manner but to never use the same rate twice. Berggren and Kim using this result show that the MGRP gives maximal throughput subject to (7.26) and the assumption of geometric rates. A similar heuristic is formulated for the downlink problem. The GRP heuristic is very power efficient but it does not take into account the packet delays in the queues. As we will see in the numerical results of section 7.4, where we compare it with a queue sensitive scheme, it consumes low power, but it cannot cope with service requirements when the system operates close to capacity.

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3.2


Maximum Throughput - uplink

An interesting formulation for the Uplink is considered by Kumaran and Qian [11]. They consider the problem of maximizing throughput subject to power constraints. However, they assume that the rate r^ is concave with respect to 7^, contrary to our assumption in (7.2) that they have a linear relationship. Their assumption is based on the Shannon formula for the AWGN Gaussian channel (see [23]) where: n - / i l o g ( l + 7^) We use the substitution ai = j constraints: yaj ^

(7.27)

^ on the power constraints (7.8) to derive

+ ^(^-^)