Utility Maximization for Large-Scale Cell-Free Massive MIMO Downlink

Abstract

We consider utility maximization problems in the downlink cell-free massive multiple-input multiple-output (MIMO) whereby a large number of access points (APs) simultaneously serve a group of users. Four fundamental maximization objectives are of interest: (i) average spectral efficiency (SE), (ii) proportional fairness, (iii) harmonic-rate, and (iv) minimum SE of all users, subject to a sum power constraint at each AP. As considered problems are non-convex, existing solutions normally rely on successive convex approximation (SCA) and use off-the-shelf convex solvers, which implement an interior-point algorithm, to solve derived convex problems. The complexity of such methods scales quickly with the problem size. Therefore, we propose an accelerated projected gradient method to solve the considered problems. Particularly, each iteration of the proposed solution is given in a closed form and only requires the first order oracle of the objective, rather than the Hessian matrix as in known solutions, and thus is much more memory efficient. Numerical results demonstrate that our proposed solution achieves the same utility performance but with far less run-time, compared to the SCA method. Simulation results show that large-scale cell-free massive MIMO has the intrinsic user fairness, i.e. the four utility functions can deliver nearly uniformed services to all users.

Foundations of User-Centric Cell-Free Massive MIMO

“…The algorithms presented in this monograph can be extended to handle these cases as well. Moreover, there are utility functions that have a totally different structure, such as the geometric mean of the SEs (also known as proportional fairness) and the harmonic mean of the SEs [25], [64], [106]. However, apart from limiting the length of this monograph, there are two strong reasons for why we only covered the max-min fairness and sum SE utilities.…”

Mirror Prox Algorithm for Large-Scale Cell-Free Massive MIMO Uplink Power Control

“…Channel coefficients are generated using (1), in which the large-scale fading coefficient between the m-th AP and the l-th user is modeled as ζ ml = PL ml z ml , where PL ml is the corresponding path loss, and z ml represents the log-normal shadowing between the m-th AP and the l-th user with mean zero and standard deviation σ sh , respectively. In this paper, we adopt the threeslope path loss model and model parameters as in [8]. Noise figure is set to 9 dB.…”

“…Note that we also demonstrate the impact of introducing ω when reformulating (P 2 ) into (P 4 ). As can be observed clearly, a proper value Iteration index Average achievable rate (bps/Hz) optimal solution [1], [3], [4] APG & GDA [8], [13], [14] mirror prox with ω = 1 mirror prox with ω = M of ω can indeed speed up the convergence of Algorithm 1 very significantly. By extensive simulation settings, we find that ω = M yields a good convergence rate for Algorithm 1 overall, which is shown in Fig.…”

“…A common feature of all aforementioned studies is the use of LP or (more complex) GP by means of off-the-shelf convex solvers, and thus are suitable for small-scale scenarios. In particular, a low complexity first-order accelerated projected gradient (APG) algorithm was applied to the max-min fairness problem following Nesterov's smoothing technique [6] in both downlink [7], [8] and uplink [9] channels. However, this method can only produce an approximate solution whose accuracy is inversely proportional to the number of users, and hence, is not suitable for very large numbers of users.…”

UAV-Enabled Hardware-Impaired Cell-free Massive MIMO With Spatially-Correlated Rician Fading

“…The Algorithm 1, which computes optimal transmit power in a closed-form, has a trivial complexity. Also, the proposed closed-form MM approach in Algorithm 1 has the same complexity as that of [38] and [39], when applied for the system models therein.…”