In this paper, we propose an opportunistic downlink interference alignment (ODIA) for interferencelimited cellular downlink, which intelligently combines user scheduling and downlink IA techniques. The proposed ODIA not only efficiently reduces the effect of inter-cell interference from other-cell base stations (BSs) but also eliminates intra-cell interference among spatial streams in the same cell. We show that the minimum number of users required to achieve a target degrees-of-freedom (DoF) can be fundamentally reduced, i.e., the fundamental user scaling law can be improved by using the ODIA, compared with the existing downlink IA schemes. In addition, we adopt a limited feedback strategy in the ODIA framework, and then analyze the required number of feedback bits leading to the same performance as that of the ODIA assuming perfect feedback. We also modify the original ODIA in order to further improve sum-rate, which achieves the optimal multiuser diversity gain, i.e., log log N , per spatial stream even in the presence of downlink inter-cell interference, where N denotes the number of users in a cell. Simulation results show that the ODIA significantly outperforms existing interference management techniques in terms of sum-rate in realistic cellular environments. Note that the ODIA operates in a distributed and decoupled manner, while requiring no information exchange among BSs and no iterative beamformer optimization between BSs and users, thus leading to an easier implementation. Inter-cell interference, interference alignment, degrees-of-freedom (DoF), transmit & receive beamforming, limited feedback, multiuser diversity, user scheduling. [5] for cellular uplink and downlink networks, also known as the interfering multiple-access channel (IMAC) or interfering broadcast channel (IBC), respectively, have received much attention. The existing IA framework for cellular networks, however, still has several practical challenges: the scheme proposed in [5] requires arbitrarily large frequency/time-domain dimension extension, and the scheme proposed in [4] is based on iterative optimization of processing matrices and cannot be optimally extended to an arbitrary downlink cellular network in terms of achievable DoF. In the literature, there are some results on the usefulness of fading in single-cell downlink broadcast channels, where one can obtain multiuser diversity gain along with user scheduling as the number of users is sufficiently large: opportunistic scheduling [6], opportunistic beamforming [7] , and random beamforming [8] . Scenarios exploiting multiuser diversity gain have been studied also in ad hoc networks [9], cognitive radio networks [10] , and cellular networks [11] . Recently, the concept of opportunistic IA (OIA) was introduced in [12]-[14] for the K-cell uplink network (i,e., IMAC model), where there are one M-antenna base station (BS) and N users in each cell. The OIA scheme incorporates user scheduling into the classical IA framework by opportunistically selecting S (S ≤ M) users amongst the N users in each cell in the sense that inter-cell interference is aligned at a pre-defined interference space. It was shown in [13] , [14] that one can asymptotically achieve the optimal DoF if the number of users in a cell is beyond a certain value, i.e., if a certain user scaling condition is guaranteed. For the K-cell downlink network (i.e., IBC model) assuming one M-antenna base station (BS) and N per-cell users, studies on the OIA have been conducted in [15]-[20]. More specifically, the user scaling condition for obtaining the optimal DoF was characterized for the K-cell multiple-input single-output (MISO) IBC [15] , and then such an analysis of the DoF achievability was extended to the K-cell MIMO IBC with L receive antennas at each user [16]-[20]-full DoF can be achieved asymptotically, provided that N scales faster than SNR KM −L , for the K-cell MIMO IBC using OIA [19] , [20] , where SNR denotes the received signal-to-noise ratio. In this paper, we propose an opportunistic downlink IA (ODIA) framework as a promising interference management technique for K-cell downlink networks, where each cell consists of one BS with M antennas and N users having L antennas each. The proposed ODIA jointly takes into account user scheduling and downlink IA issues. In particular, inspired by the precoder design in [4], we use two cascaded beamforming matrices to construct our precoder at each BS. To design the first transmit beamforming matrix, we use a user-specific beamforming, which conducts a linear zero-forcing (ZF) filtering and thus eliminates intra-cell interference among spatial streams in the same cell. To design the second transmit beamforming matrix,
The work of REF reduces the number of users to achieve the optimal DoF at the expense of increased feedback information from each user.
Opportunistic Downlink Interference Alignment
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