Computational framework for optimal robust beamforming in coordinated multicell systems

Abstract

Abstract-Coordinated beamforming can significantly improve the performance of cellular systems through joint interference management. Unfortunately, such beamforming optimization problems are typically NP-hard in multicell scenarios, making heuristic beamforming the only feasible choice in practice. This paper proposes a new branch-reduce-and-bound algorithm that solves such optimization problems globally, with a complexity suitable for benchmarking and analysis. Compared to prior work, the framework handles robustness to uncertain intercell interference and numerical analysis shows higher efficiency. I. INTRODUCTIONMost resource allocation problems in multiantenna multicell systems are non-convex and NP-hard [1], meaning that the optimal solution cannot be obtained in polynomial time. Thus, only heuristic suboptimal beamforming strategies can be applied in practice when trying to optimize, for example, the sum performance, proportional fairness, or harmonic mean. Still, it is very important to compute the optimal solution to use it as a benchmark and to study its properties.The key to solve non-convex resource allocation problems systematically is to find a suitable parameter space that represents all feasible and some infeasible strategies, and then apply some global optimization technique to iteratively reduce this space with guaranteed convergence to a global optimum In addition, all of these papers assume perfect channel state information (CSI) between all transmitters and all users in the system, which is almost impossible to achieve in practice.Herein, we propose a framework for computing optimal coordinated beamforming with robustness to CSI uncertainty. We use a new branch-reduce-and-bound (BRB) algorithm and operate in the space of the robust performance region. At each iteration, we solve a quasi-convex resource allocation problem that we call robust fairness-profile optimization (RFO). We show by simulations that the BRB algorithm is more efficient than the polyblock approximation algorithm.

Optimal Resource Allocation in Coordinated Multi-Cell Systems

“…If the design of these sets is explicitly included in the resource allocation (e.g., optimization with acceptable outage probabilities), it seems that conservative approximations 1 of each user's performance are required to achieve tractable problem formulations [50,241,289]. The alternative is to have fixed uncertainty sets and maximizing the worst-case performance, which is mathematically more convenient as it can provide convex problem formulations [17,26,242,257]. Therefore, this section describes a set of worst-case robustness approaches for multi-cell resource allocation.…”

“…The system cannot account for any error; the stochastic error vector˜ k could potentially cancel out the nominal vector as˜ k = − h k or be very large (the distribution is even unbounded for Rayleigh fading channels). This is often handled by only considering a subset of error vectors, the uncertainty set, that has high probability of containing the error [9,17,26,50,239,241,242,257,286,289,328]. If the design of these sets is explicitly included in the resource allocation (e.g., optimization with acceptable outage probabilities), it seems that conservative approximations 1 of each user's performance are required to achieve tractable problem formulations [50,241,289].…”

“…17 This line-search approach was suggested in [218,274,275] and utilized for multi-cell resource allocation with single-antenna interference channels in [206], coordinated MISO beamforming in [153,276], and general multi-cell MISO systems in [26]. Other types of curves r(τ ) can also be used to capture certain properties of f (·) -one should always try to utilize any structure that exists in the problem.…”

“…The two special cases when single-stream beamforming is provably optimal corresponds to the MISO interference channel and to coordinated beamforming with perfect intra-cell CSI (which might be a reasonable model as inter-cell CSI is harder to obtain [17]). In these cases it is possible to optimize the beamforming vectors v j k k directly (instead of optimizing S j k k which basically has N j k times more variables) and achieve convex problem formulations -which is generally not the case even when the final solution is known to be rank one.…”

“…The uncertainty originates from a variety of sources; for example, imperfect channel estimation, feedback quantization, inadequate channel reciprocity, and delays in CSI acquisition on fading channels. It is common to have an additive error model [9,17,26,50,239,241,242,257,286,289,328] with…”