Fairness Scheduling in User-Centric Cell-Free Massive MIMO Wireless Networks
Fabian Göttsch, Noboru Osawa, Issei Kanno, Takeo Ohseki, Giuseppe Caire
Abstract
We consider a user-centric cell-free massive MIMO wireless network with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> remote radio units, each with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> antennas, serving <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> single-antenna user devices (UEs). Most of the current literature considers the regime <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LM</i> ≫ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> , where the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> UEs are active on each time-frequency slot, and evaluates the system performance in terms of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ergodic rates</i> . In this paper, we take a quite different viewpoint. We observe that the regime of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LM</i> ≫ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> corresponds to a lightly loaded system with low sum spectral efficiency (SE). In contrast, in most relevant scenarios, the number of UEs is much larger than the total number of antennas (think of a sport event with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> ~ 10, 000 users and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ML</i> ~ 200 antennas). To achieve high sum SE and handle <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> ≫ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ML</i> , users must be scheduled over the time-frequency resource. The number of active users <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">act</sub> ⩽ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> must be carefully chosen such that: 1) the network operates close to its maximum SE; 2) the active user set must be chosen dynamically over time in order to enforce fairness in terms of per-user time-averaged <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">throughput rates</i> . The fairness scheduling problem is canonically formulated as the maximization of a suitable concave componentwise non-decreasing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">network utility function</i> of the per-user rates. The intermitted user transmission due to scheduling imposes slot-by-slot coding/decoding, which in turn prevents the achievability of ergodic rates. Hence, we model the per-slot service rates using information outage probability. In order to obtain a tractable problem, we make a “decoupling” assumption on the CDF of the instantaneous mutual information seen at each UE <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> receiver. We approximately enforce this condition by introducing a conflict graph that prevents the simultaneous scheduling of users with large pilot contamination conflict and propose an adaptive scheme for instantaneous service rate scheduling based on locally estimating the mutual information CDF at each UE. Overall, the proposed dynamic scheduling is the first to address such system dimensions with tens of thousand users in a scalable way, is robust to system model uncertainties, and can be easily implemented in practice.