International Journal of Antennas and Propagation

Volume 2015, Article ID 125653, 14 pages

http://dx.doi.org/10.1155/2015/125653

## Analysis of Synchronization Impairments for Cooperative Base Stations Using OFDM

^{1}Huawei Technologies, European Research Center, 80892 Munich, Germany^{2}Pontificia Universidad Católica de Chile, 7820436 Santiago, Chile^{3}Technische Universität Berlin, 10623 Berlin, Germany^{4}KU Leuven, 3001 Leuven, Belgium

Received 21 August 2014; Revised 10 February 2015; Accepted 12 February 2015

Academic Editor: Feifei Gao

Copyright © 2015 Konstantinos Manolakis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Base station cooperation is envisioned as a key technology for future cellular networks, as it has the potential to eliminate intercell interference and to enhance spectral efficiency. To date, there is still lack of understanding of how imperfect carrier and sampling frequency synchronization between transmitters and receivers limit the potential gains and what the actual system requirements are. In this paper, OFDM signal model is established for multiuser multicellular networks, describing the joint effect of multiple carrier and sampling frequency offsets. It is shown that the impact of sampling offsets is much smaller than the impact of carrier frequency offsets. The model is extended to the downlink of base-coordinated networks and closed-form expressions are derived for the mean power of users’ self-signal, interuser, and intercarrier interference, whereas it is shown that interuser interference is the main source of degradation. The SIR is inverse to the base stations’ carrier frequency variance and to the square of time since the last precoder update, whereas it grows with the number of base stations and drops with the number of users. Through user selection, the derived SIR upper bound can be approached. Finally, system design recommendations for meeting synchronization requirements are provided.

#### 1. Introduction

Base station cooperation, also known as coordinated multipoint (CoMP), is an ambitious multiple-antenna technique, where antennas of multiple distributed base stations and those of multiple terminals served within those cells are considered as a distributed multiple-input multiple-output (MIMO) system [1–3]. In the downlink, also known as joint transmission (JT) CoMP, signal preprocessing at the base stations is applied to eliminate the intercell interference and to enhance the spectral efficiency. In the simplest case, data symbols are precoded with the pseudoinverse of the MIMO channel matrix; this method is known as zero-forcing (ZF) precoding [4]. Using ZF precoding, system performance becomes close to optimal in the high signal-to-noise ratio (SNR) regime, as shown in [5]. Deployment concepts for JT CoMP and field trial results have been reported in [6], whereas recent progress can be found in [7, 8]. The role of CoMP and integration aspects into next generation cellular systems are highlighted in [9]. Finally, an overview on cooperative communications can be found in [10].

The combination of MIMO techniques with orthogonal frequency division multiplexing (OFDM) has been a successful concept for broadband cellular networks and has enabled a significant increase of the spectral efficiency during the last years [11, 12]. However, it quickly became clear that precise synchronization is vital for realizing the potential of MIMO-OFDM systems. It is known from [13] that the carrier frequency offset (CFO) causes intercarrier interference (ICI) as well as a phase drift on all OFDM subcarriers, known as common phase error (CPE). The sampling frequency offset (SFO) is also a source of ICI and implies a phase drift that grows linearly with frequency, thus affecting each subcarrier differently. Accurate maximum likelihood (ML) tracking algorithms have been developed and optimized for single-user point-to-point MIMO-OFDM in [14], whereas synchronization for multiuser MIMO within one cell has been studied in [15]. For the OFDM-based multiuser uplink, a signal model and compensation techniques have been developed in [16].

Considering distributed JT CoMP, cooperative base stations are located at different sites, which implies that their frequency up- and downconverters are driven by their own local oscillators, while sampling frequencies also differ among them. Signal modeling of JT CoMP with individual offsets in carrier and sampling frequencies in [17] revealed that orthogonality between multiple users’ data signals is misaligned and interuser interference (IUI) arises. First insights into the performance degradation were obtained by numerical evaluation. In chapter 8 of [18], the sensitivity of CoMP to the CFO was analyzed for a scenario with two cooperating base stations. Similar observations have been reported in [19, 20], whereas methods for estimating multiple CFOs based on training signals have been developed in [21]. The problem of nonsynchronized cooperating base stations has been also investigated in [22–24], where the focus has been on how to estimate and compensate the multiple CFOs. In [25], propagation delay differences were also included for transmissions from distributed base stations with multiple CFOs. In [26], a scheme for synchronizing base stations has been proposed, based on a time-slotted round-trip carrier synchronization protocol. The implementation of Global Positioning System- (GPS-) based synchronization for distributed base stations in an outdoor testbed has been reported by the authors in [27]. More recently, an over-the-air synchronization protocol has been proposed in [28], which is also applicable for networks with a large number of access points. A survey on physical layer synchronization for distributed wireless networks can be found in [29].

The first objective of the present paper is to investigate the synchronization requirements for base-coordinated multicellular MIMO networks. A major contribution of this work is the derivation of an* exact* signal model capturing the joint effect of multiple CFOs and SFOs at transmitters and receivers in a MIMO-OFDM system and over the time. Based on this model, it is shown that the impact of the SFO is negligible compared to the one of the CFO. Application of the model to the distributed CoMP downlink with ZF precoding leads to analytical closed-form expressions for the mean power of the users’ self-signal, interuser, and intercarrier interferences. It is found that the interuser interference is the dominant source of signal degradation and that synchronization requirements for cooperating base stations are very high, compared to the ones in single-cell transmission. The mean signal-to-interference ratio (SIR) is analyzed and is approximately found to degrade quadratically with time and to be inversely proportional to the variance of the base stations’ CFO. The SIR further grows with the number of base stations and drops with the number of users. In addition to the SIR analysis for the Rayleigh fading channel, an SIR upper bound is derived, which can be approached by appropriate user selection. Finally, recommendations for practical synchronization of distributed wireless networks are given.

The paper is organized as follows. In Section 2, a general signal model for a MIMO-OFDM communication system in the presence of multiple CFOs and SFOs is derived. In Section 3, the model is applied to the CoMP downlink and expressions are derived for mobile users’ self-signal, interuser, and intercarrier interferences. Analysis in Section 4 leads to closed-form expressions for the mean power of the above signals and the resulting SIR. The system performance is evaluated analytically and verified by means of simulations in Section 5. Synchronization requirements are established and practical methods to fulfill them are discussed in Section 6. Finally, conclusions are summarized in Section 7.

#### 2. General Signal Model for Distributed MIMO-OFDM Systems

In the following, a distributed MIMO network is considered with an arbitrary number of antenna branches at every base station and at every user. The cellular network uses OFDM for the air interface, with subcarriers, which are indexed with in the range . An entire OFDM symbol is samples long, equal to samples plus the number of samples of the cyclic prefix. Integer indexes successive OFDM symbols and is hence a measure of time.

Each base station and each mobile are assumed to have their own carrier and sampling frequency, within typical ranges. The total number of transmit branches is . Each transmit branch (can be a base station in the downlink or a user in the uplink), denoted by subindex , has its individual sampling period , carrier frequency and respective initial phase parameters and . In Figure 1, it is shown for a point-to-point transmission how sampling and carrier offsets misalign analog-to-digital and digital-to-analog conversion, as well as frequency conversion, respectively. The corresponding receiver parameters are denoted as , , , and , while symbol is used for . The digital modulation of subcarrier on transmit branch is represented by the complex-valued symbol . Due to different sampling timings between transmit branches of different base stations (downlink) or among mobile users (uplink), the intercarrier spacing is transmit-branch-specific and measures Hertz. The ideal carrier frequency is denoted by and the ideal sampling period with . For any transmitter or receiver, its CFO and SFO are defined as the the deviation from the ideal carrier frequency and sampling period, respectively. The complex baseband-equivalent frequency response of the passband channel between transmitter and receiver at frequency is denoted by . It includes frequency-flat path loss and shadow fading as well as frequency-selective small-scale fading.