In this paper, we study feedback optimization problems that maximize the users' signal to interference plus noise ratio (SINR) in a two-cell multiple-input multiple-output broadcast channel. Assuming the users learn their direct and interfering channels perfectly, they can feed back this information to the base stations (BSs) over the uplink channels. The BSs then use the channel information to design their transmission scheme. Two types of feedback are considered: 1) analog and 2) digital. In the analog feedback case, the users send their unquantized and uncoded channel state information (CSI) over the uplink channels. In this context, given a user's fixed transmit power, we investigate how he/she should optimally allocate it to feed back the direct and interfering (or cross) CSI for two types of BS cooperation schemes, namely, multicell processing (MCP) and coordinated beamforming. In the digital feedback case, the direct and cross link channel vectors of each user are quantized separately, each using the random vector quantization scheme, with different size codebooks. The users then send the index of the quantization vector in the corresponding codebook to the BSs. Similar to the feedback optimization problem for the analog feedback, we investigate the optimal bit partitioning for the direct and interfering link for both types of cooperation. We focus on regularized channel inversion precoding structures and perform our analysis in the large system limit in which the number of users per cell (K) and the number of antennas per BS (N) tend to infinity with their ratio β = (K/N) held fixed. We show that for both types of cooperation, for some values of interfering channel gain, usually at low values, no cooperation between the BSs is preferred. This is because, for these values of cross channel gain, the channel estimates for the cross link are not accurate enough for their knowledge to contribute to improving the SINR and there is no benefit in doing BS cooperation under that condition. We also show that for the MCP scheme, unlike in the perfect CSI case, the SINR improves only when the interfering channel gain is above a certain threshold.

This paper considers base station (BS) cooperation in the form of coordinated beamforming, focusing on min-max fairness in the power usage subject to target SINR constraints at each single-antenna user. We show that the optimal beamforming strategies have an interesting nested zero-forcing structure. In the asymptotic regime where the number of antennas at each BS and that of users in each cell both grow large with their ratio tending to a finite constant, the dimensionality of the optimization problem that needs to be solved is greatly reduced, and only knowledge of statistics is required to solve it. The optimal solution is characterized in general, and an algorithm is proposed that converges to the optimal transmit parameters, for feasible SINR targets. For the two cell case, a simple single parameter characterization is obtained. These asymptotic results provide insights into the average performance, as well as simple but efficient beamforming strategies for the finite system case. In particular, the asymptotically optimal beamformers only require the BSs to have local instantaneous channel state information; the remaining parameters of the beamformers can be calculated using channel statistics, thereby reducing the channel state information estimation and signaling overhead.

We consider a multiuser system where a single transmitter equipped with multiple antennas (the base station) communicates with multiple users each with a single antenna. Regularized channel inversion is employed as the precoding strategy at the base station. Within this scenario we are interested in the problems of power allocation and user admission control so as to maximize the system throughput, i.e., which users should we communicate with and what power should we use for each of the admitted users so as to get the highest sum rate. This is in general a very difficult problem but we do two things to allow some progress to be made. Firstly we consider the large system regime where the number of antennas at the base station is large along with the number of users. Secondly we cluster the downlink path gains of users into a finite number of groups. By doing this we are able to show that the optimal power allocation under an average transmit power constraint follows the well-known water filling scheme. We also investigate the user admission problem which reduces in the large system regime to optimization of the user loading in the system.

Channel state information (CSI) at the base stations (BSs) can significantly increase the spectral efficiency in single and multi-cell broadcast channels. Assuming the users learn their direct and interfering channels, they can feed back this information to the BSs over the uplink. The BSs then form channel estimates which they use to design their transmission scheme. Clearly, the quality of these estimates affects system performance. In this paper, we study limited feedback in a two-cell MIMO broadcast channel. For a fast transfer of CSI, we consider the analog feedback scheme where the users send their unquantized and uncoded CSI over the uplink channels. In this context, given a fixed user's transmit power, we investigate how a user should optimally allocate this power to feed back the direct and interfering CSI for two types of base station cooperation schemes, namely, network MIMO and coordinated beamforming. We focus on regularized channel inversion precoding structures and perform our analysis in the large systems limit in which the number of users per cell (K) and the number of antennas per BS (N) tend to infinity with their ratio β = K/N held fixed.

In a multicell network, the quality of the channel state knowledge at the base stations (BSs) affects system performance. When this knowledge is acquired through a quantized feedback scheme, its quality is roughly determined by the number of feedback bits. In this paper we investigate feedback optimization problems for the quantized feedback scheme via random vector quantization (RVQ) in a two-cell MIMO broadcast channel. Assuming each user knows its direct and interfering channel states perfectly, we address the following question: given a total number of feedback bits, how should a user allocate those bits to quantize its direct and cross channel information? We pose that question for different levels of BS cooperation, namely Network MIMO and Coordinated Beamforming (CBf). We focus on regularized zero-forcing (RZF) precoding structures and derive our results in the large system limit where the number of users and antennas per BS tend to infinity with their ratio being fixed. We show that for both cooperation schemes, each user should allocate more bits to quantize the cross channel as the latter's gain (ϵ) increases. We also show that, contrary to the full channel knowledge case, under this limited feedback scheme, for some values of (ϵ) no cooperation between the BSs is preferred.

This paper considers maximizing the network-wide minimum supported rate in the downlink of a two-cell system, where each base station (BS) is endowed with multiple antennas. This is done for different levels of cell cooperation. At one extreme, we consider single cell processing where the BS is oblivious to the interference it is creating at the other cell. At the other extreme, we consider full cooperative macroscopic beamforming. In between, we consider coordinated beamforming, which takes account of inter-cell interference, but does not require full cooperation between the BSs. We combine elements of Lagrangian duality and large system analysis to obtain limiting SINRs and bit-rates, allowing comparison between the considered schemes. The main contributions of the paper are theorems which provide concise formulas for optimal transmit power, beamforming vectors, and achieved signal to interference and noise ratio (SINR) for the considered schemes. The formulas obtained are valid for the limit in which the number of users per cell, K, and the number of antennas per base station, N, tend to infinity, with fixed ratio β = K/N. These theorems also provide expressions for the effective bandwidths occupied by users, and the effective interference caused in the adjacent cell, which allow direct comparisons between the considered schemes.

This paper considers base station (BS) cooperation in the form of coordinated beamforming, focusing on min-max fairness in the power usage subject to target SINR constraints. We show that the optimal beamforming strategies have an interesting nested zero-forcing structure. We then consider the asymptotic regime where the number of antennas at each BS and the number of users in each cell both grow large with their ratio tending to a finite constant. The limiting optimal beamformer structure is characterized in terms of the solution of a convex optimization problem. The dimensionality of this optimization problem is constant, as opposed to the problem of solving for the exactly optimal beamformer, and only knowledge of statistics is required to solve it. These asymptotic results provide insights into the average performance, as well as simple but efficient strategies for the finite system case. In particular, the optimal beamforming strategy from the large systems analysis only requires the base stations to have local instantaneous channel state information; the remaining parameters of the beamformer can be calculated using channel statistics which can easily be shared amongst the base stations.

We consider a multi-pair two-way relay channel (TWRC) where the single-antenna mobile terminals (MT) on each pair seek to communicate, and can do so, via a common multiple antenna relay station (RS). In the multi-pair TWRC, the main bottleneck on system performance is the interference seen by each MT due to the other communicating MT pairs. In this paper, we try to tackle this problem in the spatial domain by using multiple antennas at the RS. Considering Amplify-and-Forward (AF) and Quantize-and-Forward (QF) relaying strategies, different transmit/receive beamforming schemes at the RS are proposed. We compare our proposed schemes to each other and to the Decode-and-Forward (DF) relaying strategy with achievable sum rate taken as a performance metric and show that in a wide range of signal-to-noise ratio (SNR) our schemes outperform the DF relaying strategy.

In this letter, we address the problem of distributed multi-antenna cooperative transmission in a cellular system. Most research in this area has so far assumed that base stations not only have the data dedicated to all the users but also share the full channel state information (CSI). In what follows, we assume that each base station (BS) only has local CSI knowledge. We propose a suboptimal, yet efficient, way in which the multicell MISO precoders may be designed at each BS in a distributed manner, as a superposition of so-called virtual SINR maximizations: a virtual SINR maximizing transmission scheme yields Pareto optimal rates for the MISO Interference Channel (IC); its extension to the multicell MISO channel is shown to provide a distributed precoding scheme achieving a certain fairness optimality for the two link case. We illustrate the performance of our algorithm through Monte Carlo simulations.

This paper considers downlink multiantenna communication with base stations that perform cooperative precoding in a distributed fashion. Most previous work in the area has assumed that transmitters have common knowledge of both data symbols of all users and full or partial channel state information (CSI). Herein, we assume that each base station only has local CSI, either instantaneous or statistical. For the case of instantaneous CSI, a parametrization of the beamforming vectors used to achieve the outer boundary of the achievable rate region is obtained for two multi-antenna transmitters and two single-antenna receivers. Distributed generalizations of classical beamforming approaches that satisfy this parametrization are provided, and it is shown how the distributed precoding design can be improved using the so-called virtual SINR framework. Conceptually analog results for both the parametrization and the beamforming design are derived in the case of local statistical CSI. Heuristics on the distributed power allocation are provided in both cases, and the performance is illustrated numerically.

Coordination in a multi-cell/link environment has been attracting a lot of attention in the research community recently. In this paper, we consider the problem of coordinated beamforming where base stations (BS) equipped with multiple antennas attempt to serve a separate user each despite the interference generated by the other bases. We propose a framework for a distributed optimization of the beamformers at each base, where distributed is defined as using "local CSIT" only. We present and compare two distributed approaches (one iterative and another direct approach) which have in common the optimization of the beamformers as a combination of so-called egoistic and altruistic solutions for this problem. We provide the intuitions behind these approaches and some theoretical grounds for optimality in certain cases. Performance is finally illustrated through numerical simulations.

We consider a MIMO broadcast channel where the channel state information at the transmitter (CSIT), to be used for user scheduling and beamforming, is gained through a limited-rate feedback channel. In view of optimizing the overall spectral efficiency of the system, we propose an adaptive scheme in which the feedback rate is no longer constant but rather optimized as a function of the time-dependent channel quality seen at the user side. One key idea is that, under an average feedback rate constraint, a user ought to provide more feedback at moments when it is more likely to be scheduled.We provide the theoretical grounds for our approach then derive quasi-optimal feedback resource allocation schemes, the performance of which is illustrated through Monte Carlo simulations.

We consider the downlink of a multiuser MIMO channel, corresponding to a single cell with an Nt-antenna base station and K single-antenna mobile terminals (MTs). It is known that when full channel state information (CSI) is available at the transmitter (full CSIT) the capacity of the system scales as Ntlog(P/Nt- log K), under a total power constraint P [1], While, when the transmitter has no CSI, scaling reduces to that of a TDMA system. This paper examines the more realistic case of having an intermediate state of CSI. The key idea is based on a split of the allotted feedback between two stages: A first stage devoted to scheduling followed by a second stage for precoder design for the selected users. Based on an approximation of the achievable sum rate, we introduce a method for determining the splitting of the feedback rate so as to maximize performance and provide intuitions. We illustrate the gains of the 2-stage approach via Monte Carlo simulations.