Elsevier

Computer Networks

Volume 104, 20 July 2016, Pages 43-54
Computer Networks

Entropy-based active learning for wireless scheduling with incomplete channel feedback,☆☆

https://doi.org/10.1016/j.comnet.2016.05.001Get rights and content

Abstract

Most of the opportunistic scheduling algorithms in literature assume that full wireless channel state information (CSI) is available for the scheduler. However, in practice obtaining full CSI may introduce a significant overhead. In this paper, we present a learning-based scheduling algorithm which operates with partial CSI under general wireless channel conditions. The proposed algorithm predicts the instantaneous channel rates by employing a Bayesian approach and using Gaussian process regression. It quantifies the uncertainty in the predictions by adopting an entropy measure from information theory and integrates the uncertainty to the decision-making process. It is analytically proven that the proposed algorithm achieves an ϵ fraction of the full rate region that can be achieved only when full CSI is available. Numerical analysis conducted for a CDMA based cellular network operating with high data rate (HDR) protocol, demonstrate that the full rate region can be achieved our proposed algorithm by probing less than 50% of all user channels.

Introduction

A challenging open problem in wireless networks is the efficient allocation of limited and time-varying resources among multiple users to satisfy their requirements. The problem is exacerbated by the highly dynamic nature of wireless channels due to multiple superimposed random effects caused by mobility and multi-path fading. In many cases, acquiring extensive information on wireless channel characteristics is simply infeasible as a result of prohibitive overhead costs and hard constraints. In yet other cases, the wireless channel may be highly non-stationary that by the time the information is obtained, it becomes outdated due to channels’ fast-changing nature. Hence, scheduling decisions should be made based on partial and outdated channel state information.

One of the main assumptions in prior works [2] is that the exact and complete channel state information (CSI) of all users is available at every time slot. Under this assumption, the seminal work by Tassiulas and Ephremides has shown that the opportunistic Max-Weight scheduling algorithm is throughput-optimal, i.e., it can stabilize the network whenever this is possible [2]. Max-Weight algorithm is a simple index policy which schedules the user with the largest queue length and rate product at each time slot.

In this paper, we investigate scheduling in a multi-user downlink wireless network where only partial channel state information can be acquired due to the band-limited feedback channel (Fig. 1). We present a joint CSI acquisition and scheduling algorithm which operates without any a priori knowledge on the distribution of channel states. The proposed algorithm tracks the states of the channels by using a learning algorithm and by judiciously probing a set of users whose channel states may have changed. At each slot, the algorithm schedules a user among the set of probed users, which has the highest queue backlog and transmission rate product.

Our work relies on a recent learning and optimization framework developed in [3], wherein the exploration and exploitation trade-off is explicitly quantified as a multi-objective meta optimization problem. In this paper, we investigate a trade-off between scheduling a user with the highest queue-rate product (exploitation), and probing of users with outdated channel observations (exploration). The solution of this trade-off problem requires the prediction of the instantaneous user channel states, and the measurement of the associated level of uncertainty in the prediction. We adopt a Bayesian approach, and use Gaussian processes as a state-of-the-art regression method to predict the instantaneous user channel states.

Gaussian process regression is a powerful nonlinear interpolation tool, where the inference of continuous values are made with respect to a Gaussian process prior [4]. Although the inference of instantaneous channel gains is with a Gaussian process prior, this does not assume that the underlying channel model is Gaussian. In fact, as demonstrated by our numerical experiments, our approach is applicable to a wide range of channel models including time-correlated and even non-stationary channels. Another unique feature of our algorithm is that the uncertainty in the predicted channel state is quantified explicitly by the entropy measure from the information theory. Our algorithm weighs the level of uncertainty eliminated by probing a channel against the aspiration to schedule the user with the maximum weight to determine a set of users probed at every slot.

Our contributions are summarized as follows: i-) we first define a general Max-Weight-like policy which makes scheduling decisions based on the predicted values of instantaneous channel rates rather than their exact values. Based on the channel prediction errors, we define the achievable rate region of this algorithm as compared to the full rate region achieved by the Max-Weight algorithm with complete CSI. Specifically, we analytically show that with this policy, ϵ fraction of the full rate region can be obtained. We also explicitly compute ϵ under certain conditions; ii-) Next, based on this general policy we investigate a multi-objective framework where the exploration and exploitation tradeoff of probing different users is identified. In this framework, the information obtained by probing a user channel is modeled with the help of Shannon’s entropy formula according to the past observations of the channel; iii-) Then, we specify in detail our channel predictor used to predict instantaneous CSI, and suitable for both stationary and non-stationary channels based on Gaussian Process Regression; iv-) Lastly, we perform an extensive number simulations using High Data Rate (HDR) protocol [5] with a realistic channel model. We compare the performance of our algorithm with that of the state-of-the-art channel prediction method based on Autoregression (AR) [6].

The organization of our paper is given as follows: Section 2 summarizes the literature on opportunistic algorithms scheduling with a partial CSI, and learning methods previously used for the control of wireless networks. Section 3 presents the system model used in this paper. In Section 4, the general Max-Weight type policy and its performance in terms of achievable rate region are presented. In Section 5, GPR is explained in detail. The performance of the proposed algorithm is evaluated numerically in Section 6. Finally, we conclude the paper in Section 7.

Section snippets

Related work

It was shown that Max-Weight algorithm scheduling the user with the highest queue backlog and transmission rate product at every time slot is throughput optimal [2]. An important assumption of Max-Weight algorithm is that it requires complete knowledge of channel states at the beginning of each time slot. Investigating the performance of Max-Weight algorithm with incomplete CSI has been an active research area, and we classify the previous works on this area into two main categories: in the

System model

We consider a multiuser downlink network with N users and a single base station (BS) as shown in Fig. 1. Time is slotted, and a non-interference model is adopted, where only one user transmits at any given time slot, and there is no interference from neighboring cells. Each user channel experiences independent quasi-static Rayleigh fading, in which the channel gain is constant over the duration of a time slot 1

A General result

In this section, we study the scheduling problem with incomplete CSI over general fading channel model without assuming a priori channel distribution. Let π(η) be a joint policy which employs an arbitrary channel prediction algorithm η to predict the channel states at each slot. The quantity c^n(η)(t) is the estimated CSI of user n at the beginning of time t under policy η. Let R^n(η)(t) denote the predicted transmission rate of user n at time t which is defined according to (1) by replacing cn(

Predicting channel states using Gaussian process regression

The implementation of MOSF algorithm involves predicting Rn(t) by employing a particular prediction algorithm η, and measuring In(t) for each channel. The prediction of a variable such as Rn(t) is known as the regression problem in pattern recognition literature. In this work, we employ Gaussian Process Regression (GPR) to track the variation of channel states.

Let Dn(t)=(cn,τn) denote the set of observations of channel n at the beginning of time slot t, where cn={cn1,cn2,,cnw} denotes the set

Numerical analysis

In our simulations, we model a single cell CDMA downlink transmission utilizing high data rate (HDR) [5]. The base station serves 16 users and keeps a separate queue for each user. Time is slotted with length Ts=1.67 ms as defined in HDR specifications. Packets arrive at each slot according to Bernoulli distribution: The size of a packet is 128 bytes which corresponds to the size of an HDR packet. The wireless channel is modeled as correlated Rayleigh fading channel according to Jakes’ model

Conclusion

In this paper, we considered scheduling in a downlink multi-user setting, where the base station can only probe a limited number of users due to the limited bandwidth on the uplink feedback channel. We have presented a joint scheduling and channel probing algorithm that can operate in a stationary and non-stationary network scenarios. The algorithm is based on an active learning framework that quantifies the reward of learning the current state of the system by using the entropy measure. Based

Mehmet Karaca received the BS degree in Telecommunication Engineering from Istanbul Technical University, Istanbul, Turkey in 2006 and the MS and PhD degrees in Electronics Engineering from Sabanci University, Istanbul, Turkey in 2008 and 2013, respectively. He worked as a wireless systems engineer at Airties Wireless Networks, Turkey for two years. He is currently postdoctoral researcher at Lund University, Sweden. His research interests include the design and analysis of scheduling and

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  • Mehmet Karaca received the BS degree in Telecommunication Engineering from Istanbul Technical University, Istanbul, Turkey in 2006 and the MS and PhD degrees in Electronics Engineering from Sabanci University, Istanbul, Turkey in 2008 and 2013, respectively. He worked as a wireless systems engineer at Airties Wireless Networks, Turkey for two years. He is currently postdoctoral researcher at Lund University, Sweden. His research interests include the design and analysis of scheduling and resource allocation algorithms for wireless networks, stochastic optimization and machine learning, the next generation IEEE WLANs.

    Ozgur Ercetin received the BS degree in electrical and electronics engineering from the Middle East Technical University, Ankara, Turkey, in 1995 and the MS and PhD degrees in electrical engineering from the University of Maryland, College Park, in 1998 and 2002, respectively. Since 2002, he has been with the Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul. He was also a visiting researcher at HRL Labs, Malibu, CA, Docomo USA Labs, CA, and The Ohio State University, OH. His research interests are in the field of computer and communication networks with emphasis on fundamental mathematical models, architectures and protocols of wireless systems, and stochastic optimization.

    Tansu alpcan received the B.S. degree in electrical engineering from Bogazici University, Istanbul, Turkey in 1998. He received the M.S. and Ph.D. degrees in electrical and computer engineering from University of Illinois at Urbana-Champaign in 2001 and 2006, respectively. His research involves applications of distributed decision making, game theory, optimisation, and control to various security and resource allocation problems in complex and networked systems. He is recipient of multiple research and best paper awards from UIUC and IEEE. He has played a role in organization of several workshops and conferences such as IEEE Infocom, ICC, GameComm, and GameSec as TPC member, associate editor, co-chair, chair, and steering board member. He is the (co-)author of more than 100 journal and conference articles, an edited volume, as well as the book “Network Security: A Decision and Game Theoretic Approach” published by Cambridge University Press in 2011. He has worked as a senior research scientist in Deutsche Telekom Laboratories, Berlin, Germany, between 2006-2009, and as Assistant Professor in Technical University of Berlin from 2009 until 2011. He has joined the Department of Electrical and Electronic Engineering in the University of Melbourne as Senior Lecturer in October 2011.

    A preliminary version of the paper was presented at the International Workshop on Smart Communication Protocols and Algorithms (SCPA) co-located with IEEE ICC in Ottawa, Canada on June 2012 [1].

    ☆☆

    This work was in part done when Mehmet Karaca was with Sabanci University, Istanbul, Turkey.

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