## 1 Introduction  
The global annual wireless data traffic continues to grow rapidly. Devices are growing at a compound annual growth rate (CAGR) of approximately 10%, approaching 30 billion devices by 2023 [1]. To support the massive data traffic and connectivity in the future, new technologies will be discussed and compared in the development of sixth generation (6G) standards to surpass existing wireless communication systems. Since cell-free massive multiple-input multiple-output (MIMO) was proposed, it has been widely investigated by the academic community, and it is considered a key technology of future 6G [2, 3]. Cell-free massive MIMO systems, in which users are simultaneously served by many access points (APs), can provide uniform quality of service (QoS) to users in a wide area, ensuring the same experience for all users [4]. All APs are connected to a central processing unit (CPU) and cooperate to cover a designated area. Because the system has no cell boundaries, cell-free massive MIMO can overcome the handover problem in traditional cellular communication systems. In addition, cell-free massive MIMO has the advantages of high coverage probability, substantial spectral efficiency, and high energy efficiency [5, 6]. Cell-free massive MIMO, allowing a user-centric approach, deploys many APs to serve a small number of users simultaneously in a specific area. The distance between users and APs is shortened to reduce path loss, which reduces the impact of large-scale fading. The flexible deployment of low-cost APs allows flexible deployment in space-constrained scenarios, such as roadside facilities and building walls. The cell-free architecture avoids handover in cellular networks and reduces delays and network outages caused by handover [7]. The spectral efficiency of cell-free massive MIMO systems with conjugate beamforming (CB) and matched filter (MF) receivers shows a 5-10 times improvement in throughput per user compared to small cells and is not affected by correlated shadow fading [8]. The zero forcing (ZF) precoder reduces interuser interference and further improves the average user throughput, and the energy efficiency of the ZF precoder is shown to be significantly improved over conventional centralized massive MIMO systems [9]. Moreover, cell-free achieves high energy efficiency under different path loss models [10]. Benefiting from the channel hardening phenomenon, massive MIMO uses linear processing to achieve excellent performance and eliminate small-scale fading effects [11]. In time division duplex (TDD)-based centralized massive MIMO systems, due to the channel hardening effect, downlink channel estimation is not required, and the channel state information (CSI) of uplink channel estimation is directly precoded in downlink transmission [12]. Relying on the channel hardening properties inherited from massive MIMO, all cell-free massive MIMO systems adopt simple precoding and combining schemes [8; 13]. Performance analysis approaches related to centralized massive MIMO are widely applied. Many works use statistical CSI for cell-free massive MIMO power control [8; 13; 14; 15]. The advantage of this approach is that large-scale fading tends to change slowly, so statistical information can reduce the amount of calculation. When the channel hardening phenomenon is evident, power control within statistical CSI is almost identical to instant information. According to the literature [16], cell-free massive MIMO with single-antenna APs experiences a weaker channel hardening effect. In this case, if power control uses the statistical channel information, then the result will be far from optimal. Unlike TDD cell-free MIMO, the frequencies of uplink and downlink channels are different in frequency division duplex (FDD) systems. There is no reciprocity between uplink and downlink channels [17; 18]. Downlink training is required to obtain downlink CSI.