A cell-free massive multiple-input multiple-output 1 system is considered using a max-min approach to maximize 2 the minimum user rate with per-user power constraints. First, 3 an approximated uplink user rate is derived based on channel 4 statistics. Then, the original max-min signal-to-interference-5 plus-noise ratio problem is formulated for the optimization of 6 receiver filter coefficients at a central processing unit and user 7 power allocation. To solve this max-min non-convex problem, 8 we decouple the original problem into two sub-problems, namely, 9 receiver filter coefficient design and power allocation. The 10 receiver filter coefficient design is formulated as a generalized 11 Eigenvalue problem, whereas the geometric programming (GP) 12 is used to solve the user power allocation problem. Based on 13 these two sub-problems, an iterative algorithm is proposed, 14 in which both problems are alternately solved while one of 15 the design variables is fixed. This iterative algorithm obtains 16 a globally optimum solution, whose optimality is proved through 17 establishing an uplink-downlink duality. Moreover, we present a 18 novel sub-optimal scheme which provides a GP formulation to 19 efficiently and globally maximize the minimum uplink user rate. 20 The numerical results demonstrate that the proposed scheme 21 substantially outperforms the existing schemes in the literature. 22 Index Terms-Cell-free massive MIMO, max-min resource 23 allocation, geometric programming, uplink-downlink duality, 24 convex optimization, generalized eigenvalue problem.

Cell-free Massive multiple-input multiple-output (MIMO) is considered, where distributed access points (APs) multiply the received signal by the conjugate of the estimated channel, and send back a quantized version of this weighted signal to a central processing unit (CPU). For the first time, we present a performance comparison between the case of perfect fronthaul links, the case when the quantized version of the estimated channel and the quantized signal are available at the CPU, and the case when only the quantized weighted signal is available at the CPU. The Bussgang decomposition is used to model the effect of quantization. The max-min problem is studied, where the minimum rate is maximized with the power and fronthaul capacity constraints. To deal with the non-convex problem, the original problem is decomposed into two sub-problems (referred to as receiver filter design and power allocation). Geometric programming (GP) is exploited to solve the power allocation problem whereas a generalized eigenvalue problem is solved to design the receiver filter. An iterative scheme is developed and the optimality of the proposed algorithm is proved through uplink-downlink duality. A user assignment algorithm is proposed which significantly improves the performance. Numerical results demonstrate the superiority of the proposed schemes.

A cell-free Massive multiple-input multiple-output (MIMO) uplink is considered, where the access points (APs) are connected to a central processing unit (CPU) through limited-capacity wireless microwave links. The quantized version of the weighted signals are available at the CPU, by exploiting the Bussgang decomposition to model the effect of quantization. A closed-form expression for spectral efficiency is derived taking into account the effects of channel estimation error and quantization distortion. The energy efficiency maximization problem is considered with per-user power, backhaul capacity and throughput requirement constraints. To solve this non-convex problem, we decouple the original problem into two sub-problems, namely, receiver filter coefficient design and power allocation. The receiver filter coefficient design is formulated as a generalized eigenvalue problem whereas a successive convex approximation (SCA) and a heuristic sub-optimal scheme are exploited to convert the power allocation problem into a standard geometric programming (GP) problem. An iterative algorithm is proposed to alternately solve each sub-problem. Complexity analysis and convergence of the proposed schemes are investigated. Numerical results indicate the superiority of the proposed algorithms over the case of equal power allocation.

We consider a cell-free Massive multiple-input multiple-output (MIMO) system and investigate the system performance for the case when the quantized version of the estimated channel and the quantized received signal are available at the central processing unit (CPU), and the case when only the quantized version of the combined signal with maximum ratio combining (MRC) detector is available at the CPU. Next, we study the max-min optimization problem, where the minimum user uplink rate is maximized with backhaul capacity constraints. To deal with the max-min non-convex problem, we propose to decompose the original problem into two sub-problems. Based on these sub-problems, we develop an iterative scheme which solves the original max-min user uplink rate. Moreover, we present a user assignment algorithm to further improve the performance of cell-free Massive MIMO with limited backhaul links. aaKeywords: Cell-free Massive MIMO, geometric programming, generalized eigenvalue problem, limited backhaul.

A cell-free massive multiple-input multiple-output (MIMO) uplink is considered, where quantize-and-forward (QF) refers to the case where both the channel estimates and the received signals are quantized at the access points (APs) and forwarded to a central processing unit (CPU) whereas in combinequantize-and-forward (CQF), the APs send the quantized version of the combined signal to the CPU. To solve the non-convex sum rate maximization problem, a heuristic sub-optimal scheme is exploited to convert the power allocation problem into a standard geometric programme (GP). We exploit the knowledge of the channel statistics to design the power elements. Employing largescale-fading (LSF) with a deep convolutional neural network (DCNN) enables us to determine a mapping from the LSF coefficients and the optimal power through solving the sum rate maximization problem using the quantized channel. Four possible power control schemes are studied, which we refer to as i) small-scale fading (SSF)-based QF; ii) LSF-based CQF; iii) LSF use-and-then-forget (UatF)-based QF; and iv) LSF deep learning (DL)-based QF, according to where channel estimation is performed and exploited and how the optimization problem is solved. Numerical results show that for the same fronthaul rate, the throughput significantly increases thanks to the mapping obtained using DCNN.