Shadowed areas and interference at cell borders pose challenges for future wireless broadband systems. A potentially powerful remedy would be coordinated multipoint (CoMP) transmission, using remote radio heads or coordination between cellular base station sites. It can overcome interference limitations in cellular radio networks and also provide coverage gains. The first steps towards support for CoMP have recently been added to the 3GPP LTE standard in Release 11 [1].

CoMP techniques for downlink transmission are often categorized into two groups [2, 3]. With joint transmission (JT), sometimes referred to as joint processing, user data is transmitted via several access points. The second group uses coordination for interference avoidance without sharing user data, using, e.g. joint scheduling (JS) and/or joint beamforming (JB) (see, e.g. [4]). The later techniques are often considered to require less backhaul capacity and to be more robust to inaccurate channel state information at transmitters (CSIT). Joint transmission can provide higher potential gains in spectral efficiency at full load (see, e.g. [3, 5]), by converting harmful interference power into useful signal power. For example, coherent JT CoMP was in [6] found to have the theoretical potential to multiply the spectral efficiency at 10% outage by a factor of 5 for terminals and base stations with single antennas. These gains are especially important for users at cell edges [7].

However, much less spectacular results are provided by recent system level simulations. Evaluations of coherent JT CoMP within 3GPP have resulted in gains in average spectral efficiency of below 27% for homogeneous deployments using 4×2 MIMO transmission [8].

These large discrepancies raise questions that have motivated our research: What reduces the large potential gains of JT CoMP? Can large improvements be obtained for most users, or only for a small subset of users, e.g. those close to cell edges? What combinations of scheduling strategies and beamforming algorithms are efficient for realistic coordination topologies, propagation conditions and CSIT quality?

Answering such questions requires a joint study of multiple aspects of the problem and their interactions, in particular the assumed propagation environment, the cooperation architecture, the CSIT quality, physical layer techniques, scheduling and the grouping of users who participate in cooperation. We here investigate an important subset of these issues for downlinks of orthogonal frequency-division multiplexing (OFDM) systems, mainly considering frequency-division duplexing (FDD). One focus is the effect of imperfect CSIT due to mobility. To obtain results for realistic propagation conditions, we mainly use measured channels from channel sounding signals in an urban environment for 20-MHz OFDM downlinks. The measurements use simultaneous transmissions from three single antenna sites to a moving terminal. Large numbers of combinations of user positions are investigated and CSIT is obtained by Kalman channel predictors. These provide the best attainable quality of imperfect channel estimates.

Preliminary results obtained under these conditions were reported in [9]. A robust linear precoder performed joint coherent transmission from the three single antenna base stations to three single antenna terminals. These moved along randomly selected segments along the measured route at pedestrian velocities. The performance was here improved greatly for a minority of user sets by using JT CoMP, as compared to using conventional cellular transmission. However, the average spectral efficiency over all investigated sets of user positions was reduced. Such rather pessimistic results (obtained with imperfect CSIT) would be consistent with those recently reported in [8] that assumed perfect CSIT.

New results presented here are significantly more positive for the potential of JT CoMP: Large gains are obtained for a large majority of investigated user positions.

### 1.1 Contributions

We investigate and develop a transmit strategy for coherent JT CoMP by a step-by-step evaluation of its various components and interactions, leading to the following main conclusions and results.

First, one issue with CoMP is that significant coordination delays over backhaul links might eliminate the potential for CoMP gains. We show that channel prediction enables large average performance gains when using linear coherent joint transmission at pedestrian velocities for total delays of over 20 ms at 2.66 GHz. For lower delays, the same conclusion holds for higher-mobility users. CoMP would, e.g. remain possible at 500 MHz carrier frequencies for velocities up to 120 km/h, if the total delays are 5 ms.

Second, two parts of a JT CoMP design that are crucial for the average performance gains are the means for resource allocation over frequency-selective OFDM downlinks and the user grouping, i.e. the formation of groups of users who will share a particular time-frequency resource block.

We here introduce and evaluate a user grouping scheme with very low complexity, ‘User groups provided by cellular scheduling’. This user grouping strategy is based on local scheduling in the base stations, and it can (but does not have to) utilize already existing scheduling algorithms. In many papers with 2 to 3 base stations and single-carrier transmission, the authors have intuitively used a user grouping scheme similar to this, often with all users placed at the same distance to their nearest base station site. However, to the best of our knowledge, this has never been compared with other schemes nor is it usually motivated by the authors using it. At much lower complexity than, e.g. greedy user selection, this strategy provides spatially good (although not optimal) user groups that improve the sum rate performance when using linear precoding. It preserves multiuser diversity gains and also requires less feedback and less backhaul capacity than alternative strategies proposed previously. For systems with many users, the backhaul demand for transmission control can even be significantly lower than that for JS/JB CoMP. Using this scheme, JT CoMP can improve the sum capacity for essentially all investigated combinations of user positions. On average over random sets of user positions, it is increased by up to 54% as compared to cellular transmission, with imperfect CSIT at full system load.

Third, a main mechanism behind the sometimes disappointing performance of JT CoMP is highlighted: The different distances involved from sets of transmitters to the different receivers will often generate hard-to-invert joint channel matrices. This results in precoders with large differences in the scaling of their elements. A joint linear precoding design under a per-antenna power constraint is then forced to reduce the transmit powers of the closest base station to a user far below the allowed power to obtain a balanced solution. This effect reduces the total transmit power for a cluster of transmitters that participate in joint transmission, often with the result that out-of-cluster interference and noise reduce performance below that of single-cell transmission. The proposed user grouping strategy alleviates this problem.

Finally, since the CSIT is uncertain, robust techniques for joint precoder design are of interest. The robust linear precoder (RLP) design, introduced in [9], is here investigated further and is developed into a versatile tool for design of linear joint precoders. Robust design is most easily performed for mean square error (MSE) criteria. The RLP is here designed to optimize more general criteria by using a low-dimensional iteration over weighting matrices in a closed-form robust precoder design. We here provide sufficient conditions for the closed-form robust design to minimize a weighted sum of intracluster interference and transmit powers under imperfect CSIT accuracy for known second-order moments of the statistical uncertainties. We also show that imperfect CSIT due to quantization is straightforwardly included into the design. We investigate under what conditions a robust JT design provides benefits by comparing to a simple zero-forcing (ZF) design. Also, we observe that the interplay between channel prediction errors, opportunistic scheduling and precoder design increases the multiuser scheduling gain when using CoMP, relative to single-cell transmission.

These results, taken together, in our opinion indicate that large performance gains are indeed possible by using linear JT CoMP techniques that can be designed with reasonable computational complexity.

### 1.2 Assumptions, design choices and related work

The potential for coherent JT CoMP was shown in [10] to be highest for low-mobility users, as compared to joint scheduling and to the use of noncoherent JT CoMP. We therefore here focus on coherent JT CoMP, also referred to as network multiple-input multiple-output (MIMO) or multi-cell MIMO (see, e.g. [5, 6, 11, 12]), for low-mobility users.

Although, the largest gains are achieved with nonlinear precoding techniques such as dirty paper coding [6], complexity currently makes nonlinear precoding unfeasible for most realistic systems. We here focus on a low-complexity linear precoding solution. Zero-forcing linear precoders [13] are here a frequently studied alternative.

Coordination over a very wide area would provide the highest performance, but would be unrealistic due to computational complexity, delay constraints and capacity constraints in the fixed network. Therefore, we consider the use of CoMP within limited coordinated sets (clusters) of *N* transmitters distributed over *N*_{
B
} cells. In cellular transmission, the transmitters belonging to each cell are coordinated, but they are uncoordinated to the transmission in other cells. In CoMP that uses clustered joint transmission, the aim is to suppress the intracluster interference when jointly transmitting to *M*_{
g
} users. With perfect CSIT, the intracluster interference can then be eliminated by phase cancellation when *N*≥*M*_{
g
}.

The cluster size, i.e. the number of cooperating cells per cluster, involves a trade-off. A larger size ideally provides larger gains relative to cellular transmission, since a lower fraction of users are then located at cluster edges, but introduces a higher computational burden. Investigations in [11, 14] show that a cluster size above 7 to 9 cells will not provide large additional gains for systems with MIMO links. In [15], for few base station antennas, a cluster that used transmitters at three separate sites was adequate to attain most of the achievable CoMP gains (see also [16]). Our evaluations in Sections 6 and 7 focus on a cluster size of three sites, partially motivated by the results of [15] and partially due to the limitations of our measurements.

An important aspect is to limit the remaining intercluster interference. An interesting scheme proposed in [14] and further evaluated in [17] uses cluster-specific antenna tilting and power control for this purpose. We have in our investigations adjusted the interference statistics to approximate the one that would be generated by the scheme of [14].

Near accurate CSIT is important for multi-user MIMO [18] and for coherent JT CoMP [19]. We here evaluate schemes under the imperfect CSIT that would be due to the main unavoidable causes: noisy estimates and outdated CSIT due to signaling delays. Users are assumed to move at pedestrian velocities at 2.66 GHz. This setting results in large channel estimation errors due to outdating when channel prediction is not used. It has previously not been clear if the use of channel prediction helps CoMP performance in a significant way. Promising results based on simulations were reported in [19], using adaptive recursive least squares prediction. A preliminary simulation study in [20] investigated a two-user, two-cell scenario. The recent paper [21] investigated this question theoretically, in the limit of large numbers of antennas per base station, but did not use a per-base station transmit power constraint, so it is hard to draw conclusions from these results.

Channel predictors are here assumed to be located in the user terminals. They report the predictions to their strongest base station. The base stations then transmit the reports over a backhaul link to a central control unit (CU) for the cluster which jointly designs the beamformers.

Kalman prediction of MIMO OFDM channels, outlined in Section 3 and Appendix 1 has been investigated in, e.g. [22, 23]. We here investigate its use in a CoMP setting, focusing on two requirements that are peculiar to this setting: (1) Transmit antennas located at different sites will be at different distances while their channels, with differing signal-to-interference-and-noise ratio (SINR), have to be estimated jointly. The weakest signals will in general be estimated with the lowest accuracy. The effects of this on the choice of pilots, the resulting precoder matrices and capacity performance need to be understood. (2) Channels may need to be predicted over long prediction horizons, due to the coordination delays.

Since significant model errors will be present, the precoder (the set of joint beamformers) should furthermore be designed to be robust with respect to (w.r.t.) the expected errors. Implementation without unrealistic computational complexity is here in focus, so we will restrict attention to linear precoders. We mainly use a versatile scheme with reasonable design complexity, the iteratively adjusted RLP introduced in [9] and further developed in Section 5 and in Appendix 2. This averaged robust design is used since it is less conservative than the minimax schemes in, e.g. [24, 25]. A useful property of the RLP is that the channel uncertainty in the form of covariance matrices that are provided by Kalman predictors can be directly used in its adjustment.

In the optimization of a criterion such as the weighted sum capacity for the involved terminals, the RLP design utilizes the analytical solution to an MSE-optimal linear robust precoder and iteratively optimizes over criterion weights used by this design. This MSE-optimal analytical solution constitutes a special case of robust feedforward control filters for dynamic (frequency-selective) systems, previously developed in [26–28]. Robust linear precoders that minimize MSE by averaging over CSIT uncertainty have more recently been highlighted for multiple-input single-output (MISO) transmit schemes by [29, 30] and for multiuser and MIMO downlinks in [24, 31]. Very few solutions have been proposed for robust linear precoder design for more general performance criteria.

Many proposals form user groups for CoMP, as, e.g. [32, 33], by first forming the user group and then allocating it to a transmission resource. This can provide groups with spatially compatible users, but may sacrifice some of the potential multiuser scheduling gain, since the frequency-domain variability of channels to users is not taken into account. Another approach is to use a greedy algorithm as in, e.g. [34–36] that assigns one user at a time to a given resource, forming a near-optimal solution both in terms of spatially compatible users and exploiting multiuser diversity. This, however, requires repeated pre-evaluation of beamformers, resulting in a high complexity. Greedy user grouping will in Section 7 be compared to the user grouping scheme we propose, but due to high complexity, we use a block-fading model rather than the whole measured channel statistics for this particular comparison.

*Notations*

In the following, \mathit{\u0112}\left[\xb7\right] averages over the distribution of channel model errors, *E*[·] averages over the statistics of noise and message symbols, ∥·∥ denotes the 2-norm of a vector, tr(·) is the trace of a matrix, Re(·), (·)^{T} and (·)^{∗} denote the real part, the transpose and the Hermitian transpose of a matrix, respectively. The unit matrix is denoted *I*. For simplicity, we shall enumerate the users such that users {1,…,*M*_{
g
}} are in the selected user group for the subcarriers considered. The Kronecker delta function is denoted *δ*_{
i
j
}. Unless otherwise explicitly stated, (·)_{
j
n
} denotes element (*j*,*n*) and (·)_{
j
} denotes column *j* of a matrix or the *j* th element of a vector. The indices *i* and *m* are user indices, *j* and *n* are base station indices, *t* and *τ* are time indices and *k* and *q* are subcarrier indices. We shall denote the base station that, on average over all subcarriers and over the small-scale fading, has the strongest channel gain to a user as that user’s master base station.