Dohyung Park

Opportunistic Interference Mitigation Achieves Optimal Degrees-of-Freedom in Wireless Multi-Cell Uplink Networks

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 of simultaneously transmitting users per cell, S: 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 of users in a cell, N, 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.

Can One Achieve Multiuser Diversity in Uplink Multi-Cell Networks?

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 SNRK-1/1-ε for a constant ε∈(0,1). This result indicates that the proposed scheme achieves the multiuser diversity gain as well as the degrees-of-freedom gain even under multi-cell environments. Simulation results show that the DOS provides a better sum-rate throughput over conventional schemes.

Finding low-rank solutions to smooth convex problems via the Burer-Monteiro approach

A rank-r matrix X ∈ ℝ^m×n can be written as a product UV ^⊤, 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 ƒ(X) over rank-r matrices, where the set of rank-r matrices is modeled via the factorization in U and V variables. Such heuristic has been widely used before for problem instances, where the solution is (approximately) low-rank. Though such parameterization reduces the number of variables and is more efficient w.r.t. computational and memory requirements (of particular interest is the case r ≪ min{m, n}), it comes at a cost: ƒ(UV ^⊤) becomes a non-convex function w.r.t. U and V. In this paper, we study such parameterization in optimizing generic smooth convex ƒ, that has Lipschitz continuous gradients, 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 ƒ is smooth and BFGD is initialized properly, it has local sublinear convergence to a globally optimum point. As a test case, we consider the 1-bit matrix completion problem: We compare BFGD with state-of-the-art approaches and show that it has at least competitive test error performance on real dataset experiments, while being faster in execution, as compared to the rest of the algorithms. We conclude this work with some remarks and open questions for further investigations.

On the multiuser diversity in SIMO interfering multiple access channels: Distributed user scheduling framework

Due to the difficulty of coordination in the cellular uplink, it is a practical challenge how to achieve the optimal throughput scaling with distributed scheduling. In this paper, we propose a distributed and opportunistic user scheduling (DOUS) that achieves the optimal throughput scaling in a single-input multiple-output interfering multiple-access channel, i.e., a multi-cell uplink network, with M antennas at each base station (BS) and N users in a cell. In a distributed fashion, each BS adopts M random receive beamforming vectors and then selects M users such that both sufficiently large desired signal power and sufficiently small generating interference are guaranteed. As a main result, it is proved that full multiuser diversity gain can be achieved in each cell when a sufficiently large number of users exist. Numerical evaluation confirms that in a practical setting of the multi-cell network, the proposed DOUS outperforms the existing distributed user scheduling algorithms in terms of sum-rate.