Ubiquitous cellfree Massive MIMO enhances the conventional (networkcentric) CoMPJT by leveraging the benefits of using Massive MIMO, i.e., high spectral efficiency, system scalability, and closetooptimal linear processing. To give a first sense of the paradigm shift that cellfree Massive MIMO constitutes, Fig. 2 shows the user performance at different locations in an area with nine APs: the left figure shows that the SEs in a cellular network are poor at the cell edges due to strong intercell interference, while the right figure shows that a cellfree network can avoid interference by coprocessing over the APs and provide more uniform performance among the users. The SE is only limited by signal propagation losses.
Ubiquitous cellfree Massive MIMO: the scalable way to implement CoMPJT
The first challenge in implementing a cellfree Massive MIMO network is to obtain sufficiently accurate channel state information (CSI) so that the APs can simultaneously transmit (receive) signals to (from) all UEs and cancel interference in the spatial domain. The conventional approach of sending DL pilots and letting the UE feed back channel estimates is unscalable since the feedback load is proportional to the number of APs. Hence, frequency division duplex (FDD) operation is not convenient, unless UL and DL channels are close enough in frequency to present similarities [26]. To circumvent this issue, we note that each AP only requires local CSI to perform its tasks [27]. (Local CSI refers to the channel between the AP and to each of the UEs.) This local CSI can be estimated from UL pilots; thus, there is no need of exchanging CSI between the APs. Local CSI is conveniently acquired in TDD operation since, when a UE sends a pilot, each AP can simultaneously estimate its channel to the UE. Hence, the overhead is independent of the number of APs. By exploiting channel reciprocity, the UL channel estimates can be also utilized as DL channel estimates, as in cellular Massive MIMO [2]. Just like Massive MIMO is the scalable way to implement multiuser MIMO [2], ubiquitous cellfree Massive MIMO is the scalable way to implement CoMPJT.
In cellfree networks, there are L of geographically distributed APs that jointly serve a relatively smaller number K of UEs: L≫K. Cellfree Massive MIMO can provide tenfold improvements in 95% likely SE for the UEs over a corresponding cellular network with small cells [21, 28]. There are two key properties that explains this result.
The first property is the increased macrodiversity. Figure 3 (left) illustrates this with singleantenna APs deployed on a square grid with varying intersite distance (ISD): 5 and 100 m. The figure shows the cumulative distribution function (CDF) of the channel gain for a UE at a random position with channel vector \(\mathbf {h} =[\!h_{1} \, \ldots \, h_{L}]^{T} \in \mathbb {C}^{L}\), where h_{l} is the channel from the lth AP. The channel gain is ∥h∥^{2} in cellfree Massive MIMO and maxlh_{l}^{2} in a cellular network. With a large ISD, the UEs with the best channel conditions have almost identical channel gains in both cases, but the most unfortunate UEs gain 5 dB from cellfree processing. With a small ISD of 5 m, which is reasonable for connected factory applications, all UEs obtain 5–20 dB higher channel gain by the cellfree network.
The second property is favorable propagation, which means that the channel vectors h_{1},h_{2} of any pair of UEs are nearly orthogonal, leading to little interuser interference. The level of orthogonality can be measured by the squared inner product
$$\frac{\mathbf{h}_{1}^{H}\mathbf{h}_{2}^{2}}{\ \mathbf{h}_{1} \^{2} \ \mathbf{h}_{2} \^{2}}.$$
A smaller value represents greater orthogonality. In a cellular network with singleantenna APs, h_{1} and h_{2} are scalars, and, thus the measure is one. Favorable propagation will, however, appear in cellfree Massive MIMO where \(\mathbf {h}_{1},\mathbf {h}_{2} \in \mathbb {C}^{L}\), since the combination of smallscale and largescale fading makes the largedimensional channel vectors pairwise nearly orthogonal [29]. This is illustrated in Fig. 3 (right), which shows the CDF of the orthogonality measure for two randomly located UEs. The inner product is very small for all the considered ISDs. Spatial correlated channels may hinder favorable propagation. In this case, proper user grouping and scheduling strategies can be implemented to reduce users’ spatial correlation [30].
TDD protocol
The TDD protocol recommended for cellfree Massive MIMO is illustrated in Fig. 4. Each AP estimates the UL channel from each UE by measurements on UL pilots. By virtue of reciprocity, these estimates are also valid for the DL channels. Hence, the pilot resource requirement is independent of the number of AP antennas and no UL feedback is needed.
After applying precoding, each UE sees an effective scalar channel. The UE needs to estimate the gain of this channel to decode its data. Note that in cellular Massive MIMO, owing to channel hardening, the UE may rely on knowledge of the average channel gain for decoding [2]. In cellfree Massive MIMO, in contrast, there is less hardening and DL effective gain estimation is desirable at the user [29, 31]. This estimate can be obtained either from DL pilots sent by the AP during a DL training phase [31] (Fig. 4, left) or, potentially, blindly from the DL data transmission if there are no DL pilots (Fig. 4, right).
Figure 4 shows two possible TDD frame configurations, with and without DL pilot transmission. The configuration including the pilotbased DL training, depicted on the left in Fig. 4, consists of four phases: (i) UL training, (ii) UL data transmission, (iii) pilotbased DL training, and (iv) DL data transmission. Figure 4, on the right, illustrates the TDD frame without DL pilot transmission. This implies that for data decoding, the UEs either rely on channel hardening or blindly estimate the DL channel from the data.
The channel coherence interval is defined as the timefrequency interval during which the channel can be approximately considered as static. It is determined by the propagation environment, UE mobility, and carrier frequency [2]. The frequency selectivity of the channel can be tackled by using OFDM (orthogonal frequencydivision multiplexing), which transforms the wideband channel into many parallel narrowband flatfading channels [2]. Alternatively, singlecarrier modulation schemes can be used with similar performance [32, 33]. In regard to handling channel frequency selectivity, there is no conceptual difference between cellular and cellfree Massive MIMO.
The TDD frame should be equal or shorter than the smallest coherence time among the active UEs. For simplicity, we herein assume it is equal. Let τ=T_{c}B_{c} the length of TDD frame in samples, where B_{c} is the coherence bandwidth and T_{c} indicates the coherence time. It is partitioned as τ=τ_{u,p}+τ_{u,d}+τ_{d,p}+τ_{d,d}, where τ_{u,p},τ_{u,d},τ_{d,p}, and τ_{d,d} denote the total number of samples per frame spent on transmission of UL pilots, UL data, DL pilots, and DL data, respectively. Importantly, τ can be adjusted over time (by varying the values of τ_{u,p},τ_{d,p},τ_{d,d}, and τ_{u,d}) to accommodate the coherence interval variation and the traffic load change. However, such frame reconfiguration should occur slowly to limit the amount of control signaling required by the resource reallocation.
The maximum number of mutually orthogonal pilots is upper bounded by τ. Hence, allocating a unique orthogonal pilot per user is physically impossible in networks with K≥τ, and either nonorthogonal pilots or pilot reuse is necessary. UEs that send nonorthogonal pilots (or share the same pilot) cause mutual interference that make the respective channel estimates correlated, a phenomenon known as pilot contamination.
Uplink pilot assignment
To limit pilot contamination, efficient pilot assignment is important. We herein focus on uplink pilot assignment, but similar arguments are valid for downlink pilot assignment too [34].
Uplink pilot assignment is determined either locally at each AP or centrally at the CPU. In the latter case, a message mapping the UE identifier to the pilot index is communicated to all the APs which forward it to the UEs. This UEtopilot mapping can be transmitted either in the broadcast control channel within the system information acquisition process or in the random access channel during the random access procedure. Pilot assignment can be done in several ways:

Random pilot assignment: Each UE is randomly assigned one of the τ_{u,p} mutually orthogonal pilots. This method requires no coordination, but there is a substantial probability that closely located UEs use the same pilot, leading to bad performance.

Bruteforce optimal assignment: A search over all possible pilot sequences can be performed to maximize a utility of choice, such as the maxmin rate or sum rate. This method is optimal, but its complexity grows exponentially with K.

Greedy pilot assignment [21]: The K UEs are first assigned pilot sequences at random. Then, this assignment is iteratively improved by performing small changes that increase the utility.

Structured/clustering pilot assignment [35, 36]: regular pilot reuse structures are adopted to guarantee that users sharing the same pilot are enough spatially separated, and ensure a marginal pilot contamination.
Power control
Power control is important to handle the nearfar effect and protect UEs from strong interference. The power control can be governed by the CPU, which tells the APs and UEs which power control coefficients to use. By using closedform capacity bounds that only depend on the largescale fading, the power control can be well optimized and infrequently updated, e.g., a few times per second.
When maximumratio (MR) precoding is used at AP l, the symbol intended for UE k, q_{k}, is first weighted by \(\hat {g}_{lk}^{\ast }\) and \(\sqrt {\rho _{lk}}\), where \(\hat {g}_{lk}\) is the estimate of the channel from AP l to UE k and ρ_{lk} is the power control coefficient. The weighted symbols of all K UEs will be then combined and transmitted to the UEs. In the UL, at UE k, the corresponding symbol q_{k} is weighted by a power control coefficient \(\sqrt {\rho _{k}}\) before transmission to the APs. The block diagram that depicts the signal processing in the DL and the UL is shown in Fig. 5.
In general, the power control coefficients should be selected to maximize a given performance objective. This objective may, for example, be the maxmin rate or sum rate:

Maxmin fairness power control: The goal of this power control policy is to deliver the same rate to all UEs and to maximize that rate. In a large network, some UEs may have very bad channels to all APs; thus, it is necessary to drop them from service before applying this policy, otherwise the service will be bad for everyone. As in cellular Massive MIMO, the maxmin fairness power control coefficients can be obtained efficiently by means of linear and secondorder cone optimization [21, Section IVB].

Power control with user prioritization: The rate requirements are typically different among the UEs, which can be taken into account in the power control policy. For instance, UEs that use realtime services or have more expensive subscriptions have higher priority. The maxmin fairness power control can be extended to consider weighted rates, where the individual weights represent the priorities. Minimum rate constraints can be also included.

Power control with AP selection: Due to the path loss, APs far away from a given UE will modestly contribute to its performance. AP selection is implemented by setting nonzero power control coefficients to the APs designed to serve that UE.
Optimal power control is performed at the CPU. Centralized power control strategies might jeopardize the system scalability and latency as the number of APs and UEs grows significantly. Simpler, scalable, and distributed power control policies, but providing decreased performance, are proposed in [21, 28, 37].
To achieve good network performance, pilot assignment and power control can be performed jointly.