# Cell-Free Massive MIMO Power Consumption with Serial Front-Hauls
## 1 Introduction  
MIMO technology has revolutionized wireless communications by enabling the use of multiple antennas at both the transmitter and receiver to improve data rates and spectral efficiency [1]. Building on the success of MIMO, massive MIMO, which employs hundreds of antennas to serve multiple users simultaneously, has become a key enabler for next-generation networks, providing substantial gains in capacity, reliability, and energy efficiency [2]. Recently, cell-free massive MIMO has emerged as a promising solution to extend these benefits beyond traditional cellular architectures. Unlike conventional MIMO systems that rely on centralized base stations, cell-free massive MIMO considers a single Central Processing Unit (CPU) connected to a large number of remote radio transmission/ reception points, better known as APs, that coherently serve a much smaller number of User Equipments (UEs), offering seamless connectivity and enhanced performance not only for sub-6 GHz frequencies but also for the Millimeter Wave (mmW) band [3, 4]. In this architecture, the UEs are not allocated to different serving cells, since all of them are served by all the APs, thus the name cell-free. In cell-free massive MIMO, and when considering time division duplex schemes, the typical transmission/ reception process can be described as follows. Firstly, in an uplink training phase, the channel state is estimated at the APs through pilot signals sent by the UEs. Then, the estimated channel information is transmitted from the APs to the CPU via the front-haul network, which can consist of different topologies such as dedicated, serial, or tree structures. At the CPU, a set of precoding coefficients is determined, which are mathematical weights applied to the transmitted signals to optimize beamformingand minimize interference [5]. These coefficients are then shared with all APs, ensuring coherent transmission and improving system performance. Secondly, in the downlink transmission, the complex coefficient and the payload data of all UEs are transmitted from the CPU to all AP. Note that the coefficients are different for each AP but the data are the same since all APs are transmitting to all UEs at the same time. Finally, the uplink transmission takes place. It is worth mentioning that the APs are assumed to be equipped with multiplexers/demultiplexers, analog/digital and digital/analog converters, and a base-band (BB) unit, allowing the signal to be transmitted digitally through the front-haul. The cell-free massive MIMO system's fundamentals have been deeply explained, e.g., in [3, 6, 7, 8]. Energy efficiency in massive MIMO systems [3] has been a significant concern for both the academic community and industry. This issue has been explored in numerous publications [9, 10, 11, 12, 13, 14]. In [9], an optimal power allocation algorithm is proposed to maximize overall energy efficiency. Ref. [10] presents a zero-forcing precoding design aimed at achieving the same goal. In [11], energy efficiency is maximized using a user-centric approach, optimizing power coefficients by considering that each UE communicates only with neighboring APs. Ref. [12] introduces energy-efficient AP sleep-mode techniques for cell-free millimeter-wave massive MIMO networks based on spatial traffic distribution in realistic wireless environments. Ref. [13] proposes a new transmission scheme for cell-free massive MIMO designed to maximize energy efficiency while considering front-haul capacity and power constraints, AP power constraints, and user power and spectral efficiency constraints. Finally, in [14], an energy efficiency maximization problem is formulated, where user-AP association, hybrid beamforming, and AP selection are jointly optimized. The power consumption models of the previously mentioned publications are designed for networks with front-haults where there is a dedicated link between the CPU and each one of the distributed elements. However, the front-haul could be shared among multiple APs in serial deployments.