Elsevier

Physical Communication

Volume 13, Part C, December 2014, Pages 88-98
Physical Communication

Full length article
SC-FDMA user pairing and frequency allocation with imperfect channel state information

https://doi.org/10.1016/j.phycom.2014.10.001Get rights and content

Abstract

We consider user pairing for a single-carrier frequency-division multiple-access (SC-FDMA) transmission in the uplink of a Long Term Evolution (LTE) system. Two single-antenna users each are multiplexed to the same time and frequency resource within one cell. A virtual multiple-input multiple-output (V-MIMO) system arises for each user pair if multiple receive antennas are employed at the base station. For user pairing and frequency allocation, knowledge about the channel state is necessary. According to the LTE standard sounding reference signals are used for channel acquisition and transmitted with interleaved frequency-division multiple-access (I-FDMA). In channel state acquisition, the subcarriers not included in the channel sounding procedure should be taken into account by interpolation in frequency direction in a first step. Then a prediction in time direction for the time instant of the considered subframe is required. Channel interpolation and prediction are revisited in this paper, and the influence of channel interpolation and prediction errors on the achievable data rate of the system with user pairing and frequency resource allocation is studied. Simulation results show that joint user pairing and frequency allocation combined with channel interpolation and prediction is always beneficial for static or slowly moving users. However, for high user velocity the performance approaches that of random pairing and frequency allocation or becomes even worse.

Introduction

The first Long Term Evolution (LTE) networks are currently rolled out in various countries all over the world. In order to increase the achievable data rate of the overall system assuming mobile stations (MSs) with only one transmit antenna, it is possible to pair or group users in the uplink. For user pairing NU=2 users share the same time and frequency resources within one cell, where for user grouping (NU>2) more than two users share time and frequency resources. For a good separation of the signals of the individual users of a pair/group, the number of receive antennas NR should be at least NU. Hence, a virtual (spatially distributed) multiple-input multiple-output (V-MIMO) system arises.

In this paper, we will focus on user pairing, while an extension to user grouping is straightforward. We assume that the base station (BS) measures the channels of all MSs and schedules the individual MSs’ frequency allocations based on the acquired channel state information (CSI). Joint user pairing and frequency allocation should be employed to fully realize the possible system capacity gain. Since single-carrier frequency-division multiple-access (SC-FDMA) transmission  [1] is adopted in the uplink of LTE, each user must be scheduled to a contiguous set of resource blocks (RBs), where one RB comprises 12 subcarriers. However, the joint optimization of user pairing and frequency allocation is an NP-hard problem and complexity reduced suboptimal algorithms are necessary for a practical application. This problem has been studied in  [2], where different metrics and complexity reduced user pairing algorithms have been proposed. An extension to user grouping is presented in  [3]. Also  [4] and [5] consider joint user pairing and frequency allocation and propose suboptimal algorithms for complexity reduction. All of these works assume that the BS has perfect knowledge of the channel coefficients of all users on all available subcarriers in the cell. In practice, CSI needs to be acquired by the BS. For this purpose, sounding reference signals (SRSs) can be transmitted with interleaved frequency-division multiple-access (I-FDMA) modulation  [6] in the last SC-FDMA symbol of a subframe. If SRSs are transmitted by an MS, then only every second subcarrier of the whole transmission band is included. Therefore, two MSs in one cell can transmit their SRSs in the same subframe simultaneously without overlap of the pilot symbols. To obtain updated least squares channel estimates for all MSs in the cell, two MSs each must transmit SRSs per subframe. This is done in a round robin fashion for all MSs.

For user pairing and frequency allocation the CSI should be available for every subcarrier at every time instant the MS is considered for resource allocation. Therefore, it is necessary to interpolate the CSI for the missing subcarriers in frequency direction and to predict the channel state for the point in time the scheduling should take place. This interpolation and prediction can be achieved via two sequentially applied one-dimensional linear minimum mean-squared error (MMSE) filtering processes  [7] which are revisited in this paper and adjusted to the given scenario. We analyze the mean-squared error (MSE) of interpolation and prediction for typical LTE system parameters. Then, the influence of the interpolation and prediction errors on the achievable performance of joint user pairing and frequency allocation is analyzed by numerical simulations.

The major novel contributions of this paper are as follows.

  • An MSE expression for SRSs based channel state acquisition in the LTE uplink is derived and evaluated for a typical LTE scenario.

  • The performance of joint user pairing and frequency allocation is studied for imperfect channel knowledge.

  • Based on simulation results, the influence of user velocity on user pairing and resource allocation is studied.

This paper is organized as follows. In Section  2, the system model is introduced. Channel interpolation in frequency direction and prediction in time direction is investigated in Section  3 including an analysis of the MSE. The joint user pairing and frequency allocation problem is outlined in Section  4 and different suboptimal algorithms with reduced complexity are summarized. In Section  5, numerical results for different algorithms and different channel interpolation and prediction parameters are presented. Section  6 concludes the paper.

Notation: E{}, (), and ()H stand for expectation, conjugation, and Hermitian transposition, respectively. ld(x) denotes the base 2 logarithm of x. Bold lower case letters and bold upper case letters refer to column vectors and matrices, respectively. IX denotes the X×X identity matrix. δ() stands for the Dirac impulse. [A]m,n is the element in the mth row and nth column of matrix A. |A| is the cardinality of the set A. Jν() denotes the Bessel function of the first kind and order ν.

Section snippets

System model

In this section, we first consider the frequency allocation aspects of an LTE uplink transmission. Second, the frequency domain transmission model for an SC-FDMA transmission is introduced.

Channel interpolation and prediction

For resource allocation, up-to-date CSI is necessary. The sounding reference signals (SRSs), which are used in LTE, are introduced in the first part of this section. Taking into account the structure of the SRSs, a filter for interpolation in frequency direction is derived, which is used to interpolate CSI for subcarriers without SRSs. Then, we consider CSI prediction in time direction based on SRSs and interpolated CSI, respectively, for subframes where no SRSs are transmitted. In the last

Joint user pairing and frequency allocation

Based on the CSI acquisition discussed in the previous section, this section considers joint user pairing and frequency allocation. First, the capacity maximization problem under fairness and allocation constraints is stated. Subsequently, the optimal solution to the problem is addressed. Furthermore, several suboptimal algorithms with significantly reduced complexity are discussed.

Numerical results

The simulation parameters used for the following results can be found in Table 1. First, we investigate the achievable data rate of the system versus the signal-to-noise ratio (SNR). User pairing and resource allocation is conducted based on the interpolated and predicted CSI, and the achievable data rate of the system is evaluated according to the true CSI. For the simulations, perfect knowledge of the user velocity and statistical channel properties is assumed. Fairness is not analyzed in the

Conclusions

In this paper user pairing and frequency allocation has been studied for imperfect channel state information. Based on the scenario given by the LTE standard, MMSE filters for channel interpolation in frequency direction and channel prediction in time direction have been derived. The MSE for channel acquisition has been analyzed and it has been shown that for a user velocity of up to 50 km/h a good prediction performance is obtained, if SRSs are transmitted for every user in every fifth

Michael A. Ruder was born in Nuremberg, Germany, in 1982. He received the Dipl.-Ing. degree in electrical engineering from the Friedrich–Alexander-University Erlangen-Nürnberg (FAU), Germany, in 2008.

Since 2008 he is a Research Assistant and a Ph.D. student at the Institute for Digital Communications, formerly Chair of Mobile Communications, of the Friedrich–Alexander-University Erlangen-Nürnberg (FAU). His current research interests include wireless communications, detection, equalization and

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Michael A. Ruder was born in Nuremberg, Germany, in 1982. He received the Dipl.-Ing. degree in electrical engineering from the Friedrich–Alexander-University Erlangen-Nürnberg (FAU), Germany, in 2008.

Since 2008 he is a Research Assistant and a Ph.D. student at the Institute for Digital Communications, formerly Chair of Mobile Communications, of the Friedrich–Alexander-University Erlangen-Nürnberg (FAU). His current research interests include wireless communications, detection, equalization and parameter estimation, resource allocation, combinatorial optimization, convex optimization, MIMO systems, GSM/EDGE, and LTE (Advanced).

Anamaria Moldovan was born in Turda, Romania. She received the M.Sc. degree in Communications and Multimedia Engineering from the Friedrich–Alexander-University Erlangen-Nürnberg (FAU), in 2014. Currently, she is a PhD student at the Institute for Digital Communications at FAU. Her main research interests include Terahertz Communications, convex optimization, statistical signal processing and MIMO systems. In 2014, she received the DAAD-Award for outstanding achievements of the foreigner students in Germany.

Wolfgang H. Gerstacker received the Dipl.-Ing. degree in electrical engineering from the University of Erlangen-Nürnberg, Erlangen, Germany, in 1991, the Dr.-Ing. degree in 1998, and the Habilitation degree in 2004 from the same university. Since 2002, he has been with the Chair of Mobile Communications (now renamed to Institute for Digital Communications) of the University of Erlangen-Nürnberg, currently as a Professor.

His research interests are in the broad area of digital communications and statistical signal processing and include detection, equalization, parameter estimation, MIMO systems and space-time processing, interference management and suppression, resource allocation, relaying, cognitive radio, and sensor networks. He has conducted various projects with partners from industry. He is a recipient of several awards including the Research Award of the German Society for Information Technology (ITG) (2001), the EEEfCOM Innovation Award (2003), the Vodafone Innovation Award (2004), a Best Paper Award of EURASIP Signal Processing (2006), and the “Mobile Satellite & Positioning” Track Paper Award of VTC2011-Spring. He is a Senior Member of IEEE.

Dr. Gerstacker is an Editor for the IEEE Transactions on Wireless Communications since 2012. Furthermore, he is an Area Editor for Elsevier Physical Communication (PHYCOM), and has served as a Lead Guest Editor of a PHYCOM Special Issue on “Broadband Single-Carrier Transmission Techniques” (2013). He has been a Member of the Editorial Board of EURASIP Journal on Wireless Communications and Networking from 2004 to 2012. He has served as a Member of the Technical Program Committee of various conferences. He has been a Technical Program Co-Chair of the IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom) 2014 and a Co-Chair of the Cooperative Communications, Distributed MIMO and Relaying Track of VTC2013-Fall.

This paper has been presented in part at the First International Black Sea Conference on Communications and Networking (BlackSeaCom 2013), Batumi, Georgia, July 2013.

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