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PROJECT PROPOSAL

Joint Optimization of Power Allocation and Cooperation Strategy inWireless Cooperative Networks

Phuong Thanh Tranptran@purdue.edu

Abstract

In wireless communication networks, to enhance the quality of transmission, we use more than oneantenna to achieve the transmit diversity. However, wireless devices such as mobile phones cannot have more than one antennas due to the limitation of size and complexity. Recently, cooperativecommunication has been proposed to create the so-called virtual antenna systems for circumventingthis problem. This technique achieves a diversity gain by using a combination of the relayed signal

and the direct signal. There have been several researches about optimizing the power allocation at PHY layer and scheduling at MAC layer in cooperative networks, but most of them consider these two

problems separately. In this project, I want to combine theses two problems by investigatingalgorithms that jointly optimize the power allocation and the scheduling. We will use the convexoptimization theory to find the optimal solution to this problem, and confirm our analysis by somesimulation results.

I. Introduction

Perhaps one of the most important contributions to the evolution of wireless networks in recent years has beenthe advent of MIMO technologies, which create the transmission diversity created by using multiple receive andtransmit antennas. Its has been standardized in IEEE 802.16-2004 air interface [1] and IEEE 802.16e mobileamendment [2]. Unfortunately, its not convenient when implementing it on the uplink mobile channel due tothe limitation of hardware size and complexity.

Idea about cooperative communications started from the work of Cover and El Gamal in 1979 [3], and then it isdescribed more rigorously in some papers starting from 2003 ([4] [6]). A concise tutorial about cooperativecommunications can be found in [7]. More theoretical analysis on this technique is introduced in [8]. Brieflyspeaking, in cooperative communication systems, each wireless user is assumed to transmit data as well as act asa cooperative agent for another user. The data from each user can reach the base station (BS) by at least twoways: direct transmission to BS and relayed transmission via another user [7].

Recent researches on cooperative communications focus on the following issues: on one hand, scientists aretrying to optimize the performance of these systems subject to some constraints on the wireless resourceavailable, such as optimizing the power allocation at PHY layer, optimizing the scheduling mechanism at MAClayer or optimizing the routing protocol at network layer, and so on ([9], [10], [11]); on the other hand, they arefinding some coding schemes to improve the diversity, and hence, the performance of this systems [12]. But theresearch on joint optimization or cross-layer optimization is still at the beginning.

The goal of this project is investigating carefully this problem and finding the optimal solution for that, using thetools of convex optimization theory. The work on this project follows the similar work on the MIMO-basedWiMAX network [13].

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ECE647 PERFORMANCE MODELLING OF COMPUTER COMMUNICATION NETWORKS

II. Approach

The project will be composed of four major parts:system modeling, problem formulation, analysis usingconvex optimization theory, and simulation.

A.

System Model We consider the uplink of a wireless CDMA network with two mobile users (MS) for simplicity. Each userhas a maximum transmission power limit P max . Basestation (BS) transmit a pilot signal with constantpower, MS measure the channel gain based on thissignal and report to BS. Assume the power control iscarried out perfectly. This model is similar to themodel in [9].

The system will distributed a time interval to each user

for transmitting signals. Let i be the fraction of time corresponding to user i, then2

1

1ii

=

(1)

User 1 User 1 data Idle Idle User 2dataUser 2 Idle User 1 data User 2data Idle

1 2

Fig 2. Time allocation for two users

For the time interval of user i, its divided into 2 equal-length time slots. So there are 4 time slots in total. In thefirst time slot, user 1 transmit its data, user 2 listens. In the second time slot, user 2 acts as a relay for user 1, anduser 1 is idle. In the third and fourth time slot, the role of them is reversed.

The power allocation for user i can be represented by the matrix [13]:*[ . ]i i iP E x x= (2)

where i x is a complex vector representing the transmitted signal of user i. The symbol (*) denotes the conjugate

transpose operation. The received signal of user i over subcarrier n is represented by the vector i y :

i i i i = + y H x n (3)

where n is the AWGN noise vector with zero mean and variance 1, H i is the channel gain matrix for user i; i is

the SNR of user i.

B. Problem Formulation Our purpose is maximizing the weighted sum rate of 2 users (defined in [12]), subject to the constraints of timeand power resource.

2 2*

2,1 1

max logi

i i i i i i i iP

i i

WSR w C w E I H PH

= =

= = + (4)

subject to: - time constraint (1)

Fig 1. System model

BASE STATION

C h a n n e

l S t a t e

I n f o r m a t

i o n

PowerAllocation

Schedulin g

User 1

User 2

Feedback Channel

Control Channel

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ECE647 PERFORMANCE MODELLING OF COMPUTER COMMUNICATION NETWORKS

- power constraint: ( )2

1

1i ii

E Tr =

P (5)

- rate constraint (for fairness): *2logi i i i i i E I H PH R + (6)

C. Analysis

We will show this problem is a convex optimization problem. For solving this problem, we can use theLagrangian dual method [14]. For simplicity, assume that the channel state information (CSI) can be estimatedperfectly and sent back to BS with no error.

D. Numerical results

For the purpose of verifying and illustrating the mathematical analysis, this project will provide some simulationresults by running MATLAB program to execute the algorithm that is found from analysis. The channel gainmatrices, which are Gaussian i.i.d complex random variables will be created and some plots about theconvergence rate of the algorithms in some different condition will be provided.

III. Expected Outcomes

The first and most significant deliverable of this project will be a procedure to determine the jointly optimalsolution for the power allocation and scheduling problem, together with the detailed proof based on theory of convex optimization. In addition, to visually illustrate this result, some numerical results getting by running thealgorithm on computer will also be delivered (II.D).

References

[1] IEEE Standard 802.16-2004: IEEE Standard for Local and Metropolitan Area Networks Part 16: AirInterface for Fixed Broadband Wireless Access Systems, Oct. 2004.[2] IEEE Standard 802.16e-2005: IEEE Standard for Local and Metropolitan Area Networks Part 16: AirInterface for Fixed and Mobile Broadband Wireless Access Systems - Amendment 2: Physical and MediumAccess Control Layers for Combined Fixed and Mobile Operation in Licensed Bands, Feb. 2006.[3] T. M. Cover and A. A. E. Gamal, Capacity Theorems for the Relay Channel, IEEE Trans. Info. Theory ,

vol. 25, no. 5, Sept. 1979, pp. 57284.[4] A. Sendonaris, E. Erkip, and B. Aazhang, User Cooperation Diversity Part I and Part II, IEEE Trans.Commun. , vol. 51, no. 11, Nov. 2003, pp. 192748.[5] J. N. Laneman, G. W. Wornell, and D. N. C. Tse, An Efficient Protocol for Realizing Cooperative Diversityin Wireless Networks, Proc. IEEE ISIT , Washington, DC, June 2001, p. 294.[6] T. E. Hunter and A. Nosratinia, Diversity through Coded Cooperation, submitted to IEEE Trans. WirelessCommun. , 2004.[7] Aria Nosratinia, Ahmadreza Hedayat, Cooperative communications in Wireless Networks, IEEE Comm.

Mag. , Oct 2004.[8] K.J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski, Cooperative Communications and

Networking, Cambridge University Press, 2009.[9] Bin Wang, Dongmei Zhao, Optimum Power Distribution for Uplink Channel in a Cooperative WirelessCDMA Network, ICC2008 Proceedings. [10] Somsak Kittipiyakul, Tara Javidi, Relay Scheduling and Cooperative Diversity for Delay-Sensitive andBursty Traffic.[11] Zhengguo Sheng, Zhiguo Ding, Kin K Leung, D. L. Goeckel, and D. Towsley, Error Performance Boundsfor Routing Algorithms in Wireless Cooperative Networks, ACITA 2008.[12] Xiaoyong Guo, Xiang-Gen Xia, Distributed Linear Convolutive Space-Time Codes for AsynchronousCooperative Communication Networks, IEEE Trans. Wireless Comm., Vol. 7, No. 5, May 2008. [13] Jia Liu, Y. Thomas Hou, Optimal Downlink Power Allocation and Scheduling for MIMO-based WiMAXAccess Network, submitted to IEEE Journal on Selected Area of Communications. [14] Stephen Boyd, Lieven Vandenberghe, Convex Optimization , Cambridge University Press, 2004.