We introduce an opportunistic interference mitigation (OIM) protocol, where a user scheduling strategy is utilized in K-cell uplink networks with time-invariant channel coefficients and base stations (BSs) having M antennas. Each BS opportunistically selects a set of users who generate the minimum interference to the other BSs. Two OIM protocols are shown according to the number S of simultaneously transmitting users per cell: opportunistic interference nulling (OIN) and opportunistic interference alignment (OIA). Then, their performance is analyzed in terms of degrees-of-freedom (DoFs). As our main result, it is shown that KM DoFs are achievable under the OIN protocol with M selected users per cell, if the total number N of users in a cell scales at least as SNR (K−1)M . Similarly, it turns out that the OIA scheme with S(< M ) selected users achieves KS DoFs, if N scales faster than SNR (K−1)S . These results indicate that there exists a trade-off between the achievable DoFs and the minimum required N . By deriving the corresponding upper bound on the DoFs, it is shown that the OIN scheme is DoF-optimal. Finally, numerical evaluation, a two-step scheduling method, and the extension to multi-carrier scenarios are shown. Index TermsBase station (BS), channel state information, cellular network, degrees-of-freedom (DoFs), interference, opportunistic interference alignment (OIA), opportunistic interference mitigation (OIM), opportunistic interference nulling (OIN), uplink, user scheduling. Recently, as an alternative approach to show Shannon-theoretic limits, interference alignment (IA) was proposed by fundamentally solving the interference problem when there are two communication pairs [7]. It was shown in [8] that the IA scheme can achieve the optimal degrees-of-freedom (DoFs), which are equal to K/2, in the K-user interference channel with time-varying channel coefficients. The basic idea of the scheme is to confine all the undesired interference from other communication links into a pre-defined subspace, whose dimension approaches that of the desired signal space. Hence, it is possible for all users to achieve one half of the DoFs that we could achieve in the absence of interference. Since then, interference management schemes based on IA have been further developed and analyzed in various wireless network environments: multiple-input multiple-output (MIMO) interference network [9] [16]. These constraints need to be relaxed in order to apply IA to more practical systems. In [9], a distributed IA scheme was constructed for the MIMO interference channel with time-invariant coefficients. It requires only local CSI at each node that can be acquired from all received channel links via pilot signaling, and thus is more feasible to implement than the original one [8]. However, a great number of iterations should be performed until designed transmit/receive beamforming (BF) vectors converge prior to data transmission. Now we would like to consider practical wireless uplink networks with K-cells, each of which h...
A rank-r matrix X ∈ R m×n can be written as a product U V , where U ∈ R m×r and V ∈ R n×r . One could exploit this observation in optimization: e.g., consider the minimization of a convex function f (X) over rank-r matrices, where the set of rank-r matrices is modeled via the factorization U V . Though such parameterization reduces the number of variables, and is more computationally efficient (of particular interest is the case r min{m, n}), it comes at a cost: f (U V ) becomes a non-convex function w.r.t. U and V .We study such parameterization for optimization of generic convex objectives f , and focus on first-order, gradient descent algorithmic solutions. We propose the Bi-Factored Gradient Descent (BFGD) algorithm, an efficient first-order method that operates on the U, V factors. We show that when f is (restricted) smooth, BFGD has local sublinear convergence, and linear convergence when f is both (restricted) smooth and (restricted) strongly convex. For several key applications, we provide simple and efficient initialization schemes that provide approximate solutions good enough for the above convergence results to hold.
We consider the non-square matrix sensing problem, under restricted isometry property (RIP) assumptions. We focus on the non-convex formulation, where any rank-r matrix X ∈ R m×n is represented as U V ⊤ , where U ∈ R m×r and V ∈ R n×r . In this paper, we complement recent findings on the nonconvex geometry of the analogous PSD setting [5], and show that matrix factorization does not introduce any spurious local minima, under RIP.
We introduce a distributed opportunistic scheduling (DOS) strategy, based on two pre-determined thresholds, for uplink K-cell networks with time-invariant channel coefficients. Each base station (BS) opportunistically selects a mobile station (MS) who has a large signal strength of the desired channel link among a set of MSs generating a sufficiently small interference to other BSs. Then, performance on the achievable throughput scaling law is analyzed. As our main result, it is shown that the achievable sum-rate scales as K log(SNR log N ) in a high signal-to-noise ratio (SNR) regime, if the total number of users in a cell, N , scales faster than SNR K−1 1−ǫ for a constant ǫ ∈ (0, 1). This result indicates that the proposed scheme achieves the multiuser diversity gain as well as the degrees-offreedom gain even under multi-cell environments. Simulation results show that the DOS provides a better sum-rate throughput over conventional schemes. Index TermsWireless scheduling, inter-cell interference, cellular uplink, degrees-of-freedom, multi-user diversity. Now we would like to consider realistic uplink networks with K cells, each of which has one base station (BS) and N mobile stations (MSs). IA for such uplink K-cell networks was first proposed in [7], but has practical challenges including a dimension expansion to achieve the optimal degrees-of-freedom.In the literature, there are some results on the usefulness of fading in single-cell broadcast channels, where one can exploit a multiuser diversity gain: opportunistic scheduling [13], opportunistic beamforming [14], and random beamforming [15]. In single-cell downlink systems, the impact of partial channel knowledge at the transmitter has also been studied by showing whether the multiuser diversity gain can be achieved through opportunistic scheduling schemes based on limited feedback [16], [17]. Moreover, scenarios obtaining the multiuser diversity have been studied in cooperative networks by applying an opportunistic two-hop relaying protocol [18] and an opportunistic routing [19], and in cognitive radio networks with opportunistic scheduling [20]. Such opportunism can also be utilized in downlink multicell networks through a simple extension of [15]. In a decentralized manner, it however remains open how to design a constructive algorithm that can achieve the multiuser diversity gain in uplink multi-cell networks, which are fundamentally different from downlink environments since for uplink, there exists a mismatch between the amount of generating interference at each MS and the amount of interference suffered by each BS from multiple MSs, thus yielding the difficulty of user scheduling design.In this paper, we introduce a distributed opportunistic scheduling (DOS) protocol, so as to show that full multiuser diversity gain can indeed be achieved in time-division duplexing (TDD) uplink K-cell networks with time-invariant channel coefficients. To our knowledge, such an attempt for the network model has never been conducted before. The channel reciproc...
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