The problem of interference management is considered in the context of a linear interference network that is subject to long term channel fluctuations due to shadow fading. The fading model used is one where each link in the network is subject independently to erasure with probability p. It is assumed that each receiver in the network is interested in one unique message, which is made available at M transmitters. Optimal schemes from a Degrees of Freedom (DoF) viewpoint are analyzed for the setting of no erasures, and new schemes are proposed with better average DoF performance at higher probabilities of erasure. Additionally, for M=1, the average per user DoF is characterized for every value of p, and optimal message assignments are identified. For M>1, it is first established that there is no strategy for assigning messages to transmitters in networks that is optimal for all values of p. The optimal cooperative zero-forcing scheme for M=2 is then identified, and shown to be information-theoretically optimal when the size of the largest subnetwork that contains no erased links is at most five.
One major obstacle toward a practical implementation of asymptotic interference alignment is that the achievable DoF is approached only with a very large number of signal dimensions. The feasibility of alignment with finite symbol extension is studied in @cite_5 and @cite_17 . All the presented coding schemes in this work do not require symbol extension.
@cite_5 @cite_17
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We explore the feasibility of linear interference alignment using finite signaling dimensions and symbol extensions. In the non-zero total intersection regime, we show that the number of sources is upperbounded by a function of channel diversity. The available diversity places a fundamental constraint on the number of signal spaces that can overlap at one destination (where they are undesired) while maintaining the resolvability of a subset of those signals (desired signals) at another destination. Specifically, the number of such signal spaces cannot be larger than the channel diversity. This is the diversity constraint that we identify in this paper. Not only is the proposed method applicable for X channels, interference channels, and their rank-deficient counterparts, it can also be used for both circular symmetric signaling (CSS) and asymmetric complex signaling (ACS) over a combination of frequency and MIMO channels with arbitrary symbol extensions. Recent results establish the optimality of interference alignment to approach the Shannon capacity of interference networks at high SNR. However, the extent to which interference can be aligned over a finite number of signalling dimensions remains unknown. Another important concern for interference alignment schemes is the requirement of global channel knowledge. In this work we provide examples of iterative algorithms that utilize the reciprocity of wireless networks to achieve interference alignment with only local channel knowledge at each node. These algorithms also provide numerical insights into the feasibility of interference alignment that are not yet available in theory.