Further Analysis on Resource Allocation in Wireless Communications Under Imperfect Channel State Information

For practical wireless transmissions, a transmitter cannot always receive the channel state information (CSI) p erfectly due to feedback delay, estimation error and quantization error. Therefore, the prescribed quality of service (QoS) requirements, such as bit error rate (BER), can not be guaranteed and the system performance will then be degenerated. In this pap er, the resource allocation for wireless transmission with theDoppler effect is investigated, and a new resources allocation meth od based on the system dynamics is developed. It is shown that, unlike the existing resource allocation methods based on me an feedback, the new method in this paper can not only reduce the effect of imperfect CSI on the given BER, but also improve the efficiency of resource allocation. The wireless systems equ ipped with the new resource allocation scheme behave with strong r obustness with respect to the change of the correlation coeffi cient. In addition, by properly choosing the control parameters, the scheme can further improve the allocation efficiency with the satisfied QoS. Simulation results are given in support of thegood performance of the proposed new scheme. I. I NTRODUCTION T HE quality of service (QoS) requirement in wireless systems is highly dependent on the accuracy of the channel state information (CSI) obtained by the transmitte r. Most authors assume that the transmitter receives the CSI perfectly when considering resource allocation in wireles s communications [1] [2]. The assumption is reasonable for wireline systems while impractical for wireless systems. I n wireless communication system, the transmitter only obtai ns partial CSI due to channel estimation errors and feedback delays. It will cause the system performance degradation because the QoS requirements can not be guaranteed. For example, the bit error rate (BER) will increase when the real channel gain is smaller than the received channel gain. This motivates us to study effect of imperfect CSI on the resource allocation performance in wireless communications. Generally, when analyzing the partial CSI, there are two kinds of feedback are considered [3]: Mean feedback and Covariance feedback. In the case of mean feedback, the channel distribution is modeled at the transmitter as h ∼ N (μ, α), D. Huang and CY. Miao are with the School of Computer Engineer i g, Nanyang Technological University, Singapore. e-mail: hu0 013ng@ntu.edu. sg, ascymiao@ntu.edu. sg ZQ. Shen is with the School of Electrical and Electronic Engi neering, Nanyang Technological University, Singapore. e-mail: zqs hen@ntu.edu. sg ZH. Man is with the Faculty of Engineering& Industrial Sciences, Swinburne University of Technology, Australia. e-mail: zm an@swin.edu. au C. Leung is with the Department of Electrical and Computer En gineering, The University of British Columbia, Canada. e-mail: cleung @ece.ubc. ca where the meanμ denotes an estimate of channel based on the feedback, andα represents the covariance of the estimation error. For the case of covariance feedback, the channel distribution is modeled ash ∼ N (0, Σ), which denotes the channelh varies too rapidly such that the transmitter cannot track its mean. Recently, many authors have investigated different transmission model under partial CSI [3]-[7]. [4] investigates a n adaptive modulation schedule and the problem of maximizing the information transfer rate in both cases are presented in [3]. An adaptive MIMO-OFDM based on channel mean feedback is studied by [6]. For the case of partial CSI caused by Doppler effect, there are still not publications on the dyna mics analysis of allocation schedule up-to-date. When analyzin g the dynamics of the transmission model, we find that the efficiency of an allocation schedule can be further improved by introducing appropriate parameters. In this paper, a system dynamics analysis model for analyzing the effects of partial CSI on the allocation schedule is developed. We first analyze the effects of partial CSI on BER. More concretely, the transmission is affected by Doppler effect, leading the channel gain to keep changing. We then apply the mean feedback to model the transmission. Based on the given system model, we analyze the system dynamics under different parameter values. Since the deriv ed difference equations are nonlinear, we linearize it and ana lyze the stability of equilibrium point. We find that the system is locally asymptotically stable in the case of appropriate parameter values. We also find that the equilibrium point changes according to the introduced parameters. Simulatio n results show that that the proposed allocation schedule not only suppresses the effect of the correlation coefficient, b u also improves the efficiency of resource allocation by selec ting appropriate parameters. The paper is organized as follows. In Section II, the system model is described and the allocation schedule is formulate d. S ction III presents the system dynamics analysis model and the new allocation schedule is derived. Simulation example results are shown in Section IV. Section V gives conclusions . II. PROBLEM FORMULATION Consider the downlink of a base station (BS) with a receiver (Rx). The transmission schedule is illustrated in Figure 1. Under the condition that the channel delay is ignored, the bi t error rate (BER) for an additive white Gaussian noise (AWGN)