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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.

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 [

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 [

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 [

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

The paper is organized as follows. In Section

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

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

Transmitter and receiver have individual sampling periods

By following similar arguments as the ones leading to equation

The model given by (

Returning to the model, it can be observed in (

In practical system implementation, the carrier and sampling frequency clocks of a transmitter or receiver are derived from the same reference, that is, from the same local oscillator. Thus, for the product of an arbitrary

Considering this relationship in (

The derivations up to here have been presented including both CFO and SFO for the sake of completeness, as well as for further reference. Expressions (

Expressions (

Now we specialize the model obtained in Section

It is to be noted that channel estimation errors and CSI delays due to the feedback and the backhaul network are not considered in this work. Their effect on JT CoMP is important and might even overwhelm the effects of imperfect synchronization, which we are analyzing here. A distinct analysis by the authors which includes the effect of imperfect channel knowledge and derives the resulting performance limitations can be found in [

Transmissions are precoded on each OFDM subcarrier

Next, consider

The following section contains an in-depth analysis of the impact of synchronization impairments onto the performance. It is organized as follows: first, we study the power of a user’s self-signal (useful signal) and then the IUI and ICI. Next, we show that ICI is small compared to IUI and provide analytical expressions for the mean SIR. Finally, we highlight the value of user selection and show its impact onto the performance.

Conceptually, the rise of IUI and ICI due to imperfect synchronization can be understood as a dispersion of the energy allocated on a specific subcarrier of a specific user to other users (IUI) and to other subcarriers (ICI). This implies a drop of the self-signal power and a rise, on that user and that subcarrier, of the power of IUI and ICI from other users’ and other subcarriers’ losses. In what follows, we proceed under the assumption that data symbols are statistically independent between users and across subcarriers; that is,

Since there is statistical independence between data symbols, channel coefficients, and synchronization parameters, the mean power of the user’s self-signal (

In a first step, we analyze

For transmission from one base station, that is, for case

Result (

If we further consider the case in which the CFOs of the base stations are Gaussian i.i.d. with zero mean and variance

The derivation of the mean power of the IUI (

Following similar steps as before, now for (

The relative magnitudes of the power terms derived so far in this section are analyzed next. A simple expression for the mean ICI-to-IUI power ratio of a user

Regarding the ratio

We will now neglect the ICI and define the mean SIR (self-user signal-to-IUI ratio) by the ratio between (

The SNR gains in JT CoMP are increased if a scheduler selects the appropriate users to be jointly served on the same time and frequency resources. As shown in [

Considering now an idealized scenario, from the precoding point of view, with orthogonal channel vectors of equal power among the users, scenario which has been analyzed in [

It should be clarified at this point that (

The signal model given in Section

What indeed changes in OFDMA is the channel statistics for each user after resource allocation. Therefore, if intended to evaluate the overall performance of a coordinated multipoint system using OFDMA, the general mean power expressions (

In this section, the received power of a user was studied in relation to the interference from other users and other subcarriers, in a multicellular multiuser downlink with cooperative base stations. Closed-form expressions and accurate approximations for all relevant terms were derived. Moreover, it was demonstrated that interuser interference has the most relevant effect. Finally, the impact of the radio channel was investigated and analytical SIR expressions were derived for zero-forcing precoding.

In this section, analytical results of Section

A JT CoMP scenario is considered, where a cooperation cluster of

At time instant

The oscillator accuracy Osc, typically specified in parts per million (ppm) or parts per billion (ppb), relates to the standard deviation of the resulting carrier frequency as

Typical 3GPP LTE parameters are used, specified in [

Figure

Mean power of interuser and intercarrier interferences in a Rayleigh fading channel. Here, 7 base stations serve 3 and 6 users, respectively. Analytical results are shown by lines, while markers show numerical evaluations.

First of all, Figure

Figure

Mean SIR over time for Rayleigh fading channel and SIR upper bound. Here, 7 base stations using oscillators of accuracy given by Osc serve jointly 6 users. Analytical results are shown by lines, simulations by markers.

For the Rayleigh fading channel, the analytical expression (

Figure

Mean users’ SIR 10 ms after most recent precoder update, for the Rayleigh fading and upper bound. Here, 7 base stations serve jointly from 2 to 6 users. Analytical results are shown by lines, simulations by markers.

In this section, synchronization requirements for OFDM-based JT CoMP and ways to meet them are discussed. It can be seen from Figure

Other schemes, also for base stations with no GPS connection, suggest that base stations are connected via Ethernet to the backhaul network, over which, and by using a network synchronization protocol such as IEEE1588 [

An exact signal model for multiuser multicellular systems using OFDM was derived, for transmissions impaired by individual carrier and sampling frequency offsets on every transmitter and receiver branch. The model was specialized to the downlink of systems with cooperative base stations, where precoding with the inverse of the channel matrix was considered. It was analyzed how carrier frequency misalignments among the cooperative base stations decrease the power of the self-user’s signal and cause interuser and intercarrier interference. Closed-form exact expressions and accurate approximations were derived for the mean power of the above signals and it was shown that, for practical purposes, the interuser interference dominates on the intercarrier interference. Analytic expressions were also derived for the mean SIR, for Rayleigh fading channel conditions as well as an SIR upper bound for cooperative systems using zero-forcing precoding. The mean SIR decreases quadratically with time and is inversely proportional to the variance of the base stations’ frequency offsets. It grows with the number of base stations and drops with the number of users jointly served by them on the same time and frequency resource. From a practical point of view, when a high SIR is targeted, synchronization requirements can be fulfilled by using at the base stations OCXOs locked either to a precise GPS reference or to an accurate clock signal provided through the backhaul network.

The constants

We analyze

For the first case

Consider the function

Let

First, if

Next, using (

This work was done during Konstantinos Manolakis doctoral studies at the Technische Universität Berlin, Germany.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors would like to acknowledge the Deutsche Forschungsgemeinschaft (DFG) for support within project