Ubiquitous Cell-Free Massive MIMO Communications

Interdonato et al. REVIEW Ubiquitous cell-free Massive MIMO communications Giovanni Interdonato 1 * , Emil Bj¨ ornson 1 , Hien Quo c Ngo 3 , P ˚ al F renger 2 and Erik G La rsson 1 Abstract Since the first cellula r netw o rks w ere trialled in the 1970s, w e have witnessed an incredible wireless revolution. F rom 1G to 4G, the massive traffic growth has been managed by a combination of wider bandwidths, refined radio interfaces, and net wo rk densification, namely increasing the number of antennas p er site. Due its cost-efficiency , the latter has contributed the most. Massive MIMO (multiple-input multiple-output) is a key 5G technology that uses massive antenna a rrays to p rovide a very high beamforming gain and spatially multiplexing of users, and hence, increases the sp ectral and energy efficiency . It constitutes a centralized solution to densify a net wo rk, and its performance is limited b y the inter-cell interference inherent in its cell-centric design. Conversely , ubiquitous cell-free Massive MIMO refers to a distributed Massive MIMO system implementing coherent user-centric transmission to overcome the inter-cell interference limitation in cellula r netw o rks and p rovide additional macro-diversit y . These features, combined with the system scalability inherent in the Massive MIMO design, distinguishes ubiquitous cell-free Massive MIMO from prio r coordinated distributed wireless systems. In this a rticle, we investigate the eno rmous potential of this promising technology while addressing p ractical deployment issues to deal with the increased back/front-hauling overhead deriving from the signal co-p ro cessing. Keyw o rds: cell-free Massive MIMO; distributed p ro cessing; radio stripe system 1 Intro duction One of the primary w a ys to pro vide high per-user data rates-requiremen t for the creation of a 5G net w ork—is through net w ork densification, namely increasing the n um b er of an tennas per site and deploying smaller and smaller cells [ 1 ]. A comm unication technology that in v olv es base stations (BSs) with v ery large n um b er of transmitting/receiving an tennas is Mas- siv e MIMO [ 2 ], where MIMO stands for multiple-input m ultiple-output. This k ey 5G technology lev erages ag- gressiv e spatial m ultiplexing. In the uplink (UL), all the users transmit data to the BS in the same time- frequency resources. The BS exploits the massiv e n um- b er of channel observ ations to apply linear receiv e com- bining, whic h discriminates the desired signal from the in terfering signals. In the do wnlink (DL), the users are coheren tly serv ed by all the antennas, in the same time-frequency resources but separated in the spatial domain b y receiving very directiv e signals. By sup- p orting suc h a highly spatially-fo cused transmission (preco ding), Massive MIMO provides higher spectral * Correspondence: giovanni.interdonato@liu.se 1 Department of Electrical Engineering (ISY), Link¨ oping University , 581 83 Link¨ oping, Sweden Full list of autho r information is available at the end of the a rticle efficiency , and reduces the inter-cell in terference com- pared to existing mobile systems. The inter-cell interference is ho w ev er b ecoming the ma jor b ottlenec k as we densify the net w orks. It can- not be remov ed as long as w e rely on a net w ork-centric (cell-cen tric) implemen tation, since the inter-cell in- terference is inheren t to the cellular paradigm [ 3 ]. In a con v entional cellular netw ork, each user equipment (UE) is connected to the access p oin t (AP) in only one of the many cells (except during handov er). At a giv en time instance, the APs hav e different num bers of active UEs, causing in ter-cell interference (Fig. 1 , top-left). Cellular net w orks are sub optimal from a c han- nel capacit y viewp oin t b ecause higher sp ectral effi- ciency (SE) (bit/s/Hz/user) can b e ac hiev ed by co- pro cessing each signal at multiple APs [ 4 ]. The sig- nal co-pro cessing concept is presen t in [ 5 ], netw ork MIMO [ 6 , 7 ], coordinated m ultip oin t with join t trans- mission (CoMP-JT) [ 8 – 10 ], and m ulti-cell MIMO co- op erativ e netw orks [ 11 ]. It is conv en tionally imple- men ted in a netw ork-cen tric fashion, by dividing the APs in to disjoin t clusters as in Fig. 1 (top-right). The APs in a cluster transmit jointly to the UEs resid- ing in their joint co v erage area, thus it is equiv alen t Interdonato et al. Page 2 of 13 Single -an t enna AP UE M ulti-an t enna AP Single -an t enna AP UE AP M ulti-an t enna AP CPU CPU F r on thaul Back haul Subset of AP s ser ving UE 1 UE 1 Figure 1 Example of netwo rk deplo yments. T op-left: A conventional cellular netw ork where each UE is connected to only one AP . T op-right: A conventional netw o rk-centric implementation of CoMP-JT, where the APs in a cluster coop erate to serve the UEs residing in their joint coverage area. Bottom-left: A user-centric implementation of CoMP-JT, where each UE communicates with its closest APs. Bottom-right: A “cell-free” Massive MIMO netw o rk is a w a y to implement a user-centric netw o rk. to deploying a con v en tional cellular net w ork with dis- tributed an tennas in eac h cell. Despite the great theo- retical gains, the 3GPP L TE (3rd Generation Partner- ship Pro ject Long T erm Ev olution) standardization of CoMP-JT has not achiev ed muc h practical gains [ 12 ]. This fact do es not mean that the basic concept is fla w ed, but the net w ork-cen tric approach may not b e preferable. Con v ersely , when the co-pro cessing is implemented in a user-centric fashion, each user is served b y co- heren t join t transmission from its selected subset of APs ( user-sp e cific cluster ), while all the APs that af- fect the user take its interference in to consideration, as illustrated in Fig. 1 (b ottom-left). Hence, this ap- proac h eliminates the cell b oundaries resulting in no in ter-cell in terference. Suc h transmission design, gen- eralizable as user-sp e cific dynamic c o op er ation clus- ters [ 13 ], has b een considered in MIMO co operative net w orks [ 14 – 16 ], CoMP-JT [ 17 ], coop erativ e small cells ( c over-shifts ) [ 18 ], and C-RAN [ 19 , 20 ]. The com bination of time-division duplex (TDD) Massiv e MIMO op eration, dense distributed net w ork top ology , and user-cen tric transmission design creates a new concept, referred to as ubiquitous c el l-fr e e Mas- sive MIMO . T o a void preconceptions, we use the new “c el l-fr e e” c ommunic ation terminology from [ 21 , 22 ] instead of prior terminology . The word “cell-free” sig- nifies that, at least from a user p erspective, there are no cell b oundaries during data DL transmission, but all (or a subset of ) APs in the netw ork coop erate to join tly serve the users in a user-cen tric fashion. The APs are connected via front-haul connections to cen- tral pro cessing units (CPUs), which are resp onsible for the coordination. The CPUs are interconnected by bac k-haul (Fig. 1 , b ottom-righ t). In the UL, data de- tection can b e p erformed lo cally at each AP , cen trally at the CPU or partially first at each AP and then at the CPU. The UL sp ectral efficiency of cell-free Mas- siv e MIMO under four different levels of receiver co- op eration are ev aluated in [ 23 ]. The full join t UL pro- cessing pro vides the best p erformance ov er an y full or partial lo cal pro cessing, assuming the MMSE (mini- m um mean square error) com bining is used. Ho wev er, the more the CPU is inv olv ed in the pro cessing, the higher the fron t-haul requirements are. W e stress that also in a “cell-free” net w ork, we migh t ha v e AP-specific sync hronization and reference signals, whic h are imp ortan t when accessing the net w ork. More sp ecifically , the UE initial access pro cedure in “cell- free” net w orks ma y follow the same principles as in L TE [ 24 ] or 5G-NR [ 25 ], whic h are based on the cel- lular architecture. An inactive UE first searches and Interdonato et al. Page 3 of 13 then selects the b est cell to camp on, by p erforming a so-called c el l se ar ch and sele ction procedure. By do- ing this, the UE acquires time and frequency sync hro- nization with the selected cell and detects the corre- sp onding Cel l ID as well as cell-sp ecific reference sig- nals, suc h as DMRS (demo dulation reference signal) and CQI (c hannel quality indicator). Hence, the cellu- lar architecture might be still underlying a “cell-free” net w ork, and b y the term “cell-free” w e just mean that there are no cell b oundaries created by the data trans- mission proto col in activ e mo de. 2 System op eration and resource allo cation Ubiquitous cell-free Massiv e MIMO enhances the con- v en tional (netw ork-cen tric) CoMP-JT by leveraging the b enefits of using Massiv e MIMO, i.e., high sp ec- tral efficiency , system scalability , and close-to-optimal linear pro cessing. T o give a first sense of the paradigm shift that cell-free Massiv e MIMO constitutes, Fig. 2 sho ws the user p erformance at differen t lo cations in an area with nine APs: left figure shows that the SEs in a cellular net w ork is p oor at the cell edges due to strong inter-cell in terference, while righ t figure sho ws that a cell-free netw ork can av oid interference by co- pro cessing ov er the APs and pro vide more uniform per- formance among the users. The SE is only limited b y signal propagation losses. 2.1 Ubiquitous Cell-F ree Massive MIMO: The Scalable W a y to Implement CoMP-JT The first challenge in implementing a cell-free Massive MIMO netw ork is to obtain sufficiently accurate chan- nel state information (CSI) so that the APs can simul- taneously transmit (receiv e) signals to (from) all UEs and cancel in terference in the spatial domain. The con- v en tional approac h of sending DL pilots and letting the UEs feed back c hannel estimates is unscalable since the feedbac k load is proportional to the num ber of APs. Hence, frequency-division duplex (FDD) op eration is not conv enien t, unless UL and DL c hannels are close enough in frequency to present similarities [ 26 ]. T o cir- cum v ent this issue, we note that each AP only requires lo cal CSI to p erform its tasks [ 27 ]. (Local CSI refers to the channel betw een the AP and to each of the UEs.) This lo cal CSI can b e estimated from UL pilots, thus there is no need of exchanging CSI b et w een the APs. Lo cal CSI is conv enien tly acquired in TDD op eration since, when a UE sends a pilot, each AP can simul- taneously estimate its channel to the UE. Hence, the o v erhead is independent of the n um ber of APs. By ex- ploiting c hannel recipro cit y , the UL channel estimates can b e also utilized as DL channel estimates, as in cel- lular Massive MIMO [ 2 ]. Just like Massive MIMO is the scalable wa y to implemen t multi-user MIMO [ 2 ], ubiquitous cell-free Massive MIMO is the scalable wa y to implemen t CoMP-JT. In cell-free net w orks there are L of geographically distributed APs that jointly serv e a relatively smaller n um b er K of UEs: L  K . Cell-free Massive MIMO can pro vide ten-fold impro v emen ts in 95%-lik ely SE for the UEs o v er a corresp onding cellular net work with small cells [ 21 , 28 ]. There are t w o key prop erties that explains this result. The first prop ert y is the increased macro-div ersit y . Fig. 3 (left) illustrates this with single-antenna APs deplo y ed on a square-grid with v arying inter-site dis- tance (ISD): 5, and 100 m. The figure sho ws the cum u- lativ e distribution function (CDF) of the channel gain for a UE at a random p osition with c hannel v ector h = [ h 1 . . . h L ] T ∈ C L , where h l is the channel from the l th AP . The channel gain is k h k 2 in cell-free Mas- siv e MIMO and max l | h l | 2 in a cellular netw ork. With a large ISD, the UEs with the b est c hannel conditions ha v e almost iden tical c hannel gains in b oth cases, but 1000 0 1000 2 800 Position [m] 4 500 Spectral Eciency [bit/s/Hz/user] 600 Position [m] 6 400 8 200 0 0 1000 0 1000 2 800 Position [m] 4 500 Spectral Eciency [bit/s/Hz/user] 600 Position [m] 6 400 8 200 0 0 Figure 2 Data coverage. Left: cellular netwo rk. Right: cell-free Massive MIMO netw ork. SE achieved b y UEs at different locations in an area covered by nine APs that a re deploy ed on a regular grid. Note that 8 bit/s/Hz was selected as the maximal SE, which corresponds to uncoded 256-QAM. Interdonato et al. Page 4 of 13 -110 -100 -90 -80 -70 -60 -50 -40 Cha nnel gain [d B] 0 0.2 0.4 0.6 0.8 1 CDF ISD : 1 00 m ISD : 5 m Cell-free Cellular -90 -80 -70 -60 -50 -40 -30 -20 -10 0 0.2 0.4 0.6 0.8 1 Figure 3 Macro-diversity and favorable p ropagation. Distribution of (left) the channel gain, and (right) the inner p roduct of channel vectors in cell-free Massive MIMO. The simulation setup considers 2500 single-antenna APs deploy ed on a square-grid with wrap-around and varying ISD. W e consider independent Rayleigh small-scale fading and three-slope path-loss mo del from [ 21 ]. the most unfortunate UEs gains 5 dB from cell-free pro cessing. With a small ISD of 5 m, which is reason- able for connected factory applications, all UEs obtain 5-20 dB higher channel gain b y the cell-free net w ork. The second property is favor able pr op agation , whic h means that the c hannel vectors h 1 , h 2 of any pair of UEs are nearly orthogonal, leading to little in ter-user in terference. The level of orthogonality can b e mea- sured b y the squared inner pro duct | h H 1 h 2 | 2 k h 1 k 2 k h 2 k 2 . A smaller v alue represents greater orthogonality . In a cellular netw ork with single-antenna APs, h 1 and h 2 are scalars and thus the measure is one. F av or- able propagation will, ho w ev er, app ear in cell-free Mas- siv e MIMO where h 1 , h 2 ∈ C L , since the combination of small-scale and large-scale fading makes the large- dimensional channel vectors pairwise nearly orthog- onal [ 29 ]. This is illustrated in Fig. 3 (righ t), which sho ws the CDF of the orthogonality measure for tw o randomly lo cated UEs. The inner product is very small for all the considered ISDs. Spatial correlated channels ma y hinder fav orable propagation. In this case, prop er user grouping and scheduling strategies can be imple- men ted to reduce users’ spatial correlation [ 30 ]. 2.2 TDD Proto col The TDD protocol recommended for cell-free Massiv e MIMO is illustrated in Fig. 4 . Eac h AP estimates the UL channel from each UE by measurements on UL pi- lots. By virtue of recipro cit y , these estimates are also v alid for the DL channels. Hence, the pilot resource requiremen t is independent of the num ber of AP an- tennas and no UL feedbac k is needed. After applying precoding, each UE sees an effective scalar c hannel. The UE needs to estimate the gain of this c hannel to deco de its data. Note that in cellular Massiv e MIMO, owing to channel har dening , the UE ma y rely on knowledge of the a v erage channel gain for deco ding [ 2 ]. In cell-free Massiv e MIMO, in contrast, there is less hardening and DL effectiv e gain estimation is desirable at the user [ 29 , 31 ]. This estimate can ei- ther be obtained from DL pilots sen t by the AP during a DL training phase [ 31 ] (Fig. 4 , left) or, p oten tially , blindly from the DL data transmission if there are no DL pilots (Fig. 4 , righ t). Fig. 4 shows t wo possible TDD frame configurations, with and without DL pilot transmission. The configu- UL pilo ts 𝜏 u , p UL da ta 𝜏 u , d DL da ta 𝜏 d , d 𝑇 c 𝐵 𝑐 𝜏 UL pilo ts 𝜏 u , p UL da ta 𝜏 u , d DL da ta 𝜏 d , d DL pilo ts 𝜏 d , p 𝑇 c 𝐵 𝑐 𝜏 Figure 4 TDD frame structure. The TDD frame with no pilot-based DL training (right) is used in cellular Massive MIMO, which can rely on channel hardening, while b oth options a re on the table fo r cell-free Massive MIMO. Note that, guard intervals are not depicted since deducted from the coherence time interval. Interdonato et al. Page 5 of 13 ration including the pilot-based DL training, depicted on the left in Fig. 4 , consists of four phases: ( i ) UL training; ( ii ) UL data transmission; ( iii ) Pilot-based DL training; and ( iv ) DL data transmission. Fig. 4 , on the righ t, illustrates the TDD frame without DL pi- lot transmission. This implies that, for data deco ding, the UEs either rely on channel hardening or blindly estimate the DL c hannel from the data. The channel c oher enc e interval is defined as the time-frequency in terv al during which the channel can b e appro ximately considered as static. It is deter- mined by the propagation en vironment, UE mobility , and carrier frequency [ 2 ]. The frequency-selectivity of the c hannel can b e tackled by using OFDM (orthog- onal frequency-division multiplexing), whic h trans- forms the wideband channel in to many parallel nar- ro wband flat-fading channels [ 2 ]. Alternativ ely , single- carrier mo dulation sc hemes can b e used with similar p erformance [ 32 , 33 ]. In regard to handling channel frequency-selectivit y , there is no conceptual difference b et ween cellular and cell-free Massiv e MIMO. The TDD frame should be equal or shorter than the smallest coherence time among the active UEs. F or simplicit y , w e 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 num ber of samples p er frame sp en t on transmission of UL pi- lots, UL data, DL pilots and DL data, resp ectiv ely . Imp ortan tly , τ can b e adjusted o v er time (by v ary- ing the v alues of τ u , p , τ d , p , τ d , d , τ u , d ) to accommo date the coherence interv al v ariation and the traffic load c hange. Ho w ever, suc h frame reconfiguration should o ccur slowly to limit the amoun t of con trol signaling required b y the resource re-allo cation. The maxim um n um b er of mutually orthogonal pi- lots is upper-b ounded b y τ . Hence, allocating a unique orthogonal pilot per user is physically imp ossible in net w orks with K ≥ τ , and either non-orthogonal pi- lots or pilot reuse are necessary . UEs that send non- orthogonal pilots (or share the same pilot) cause m u- tual interference that make the resp ectiv e channel es- timates correlated, a phenomenon kno wn as pilot c on- tamination . 2.3 Uplink Pilot Assignment T o limit pilot con tamination, efficien t pilot assignmen t is imp ortan t. W e herein fo cus on uplink pilot assign- men t, but similar arguments are v alid for downlink pilot assignmen t to o [ 34 ]. Uplink pilot assignment is determined either lo cally at eac h AP , or cen trally at the CPU. In the latter case, a message mapping the UE identifier to the pilot in- dex is communicated to all the APs which forw ard it to the UEs. This UE-to-pilot mapping can b e trans- mitted either in the broadcast control c hannel within the system information acquisition process or in the random access c hannel during the random access pro- cedure. Pilot assignmen t can b e done in sev eral w a ys: • Random pilot assignment: Each UE is randomly assigned one of the τ u , p m utually orthogonal pi- lots. This method requires no co ordination, but there is a substantial probability that closely lo- cated UEs use the same pilot, leading to bad p er- formance. • Brute-force optimal assignmen t: A search ov er all p ossible pilot sequences can b e performed to max- imize a utility of c hoice, suc h as the max-min rate or sum rate. This metho d is optimal but its com- plexit y grows exponentially with K . • Greedy pilot assignmen t [ 21 ] The K UEs are first assigned pilot sequences at random. Then this as- signmen t is iteratively improv ed by p erforming small c hanges that increase the utility . • Structured/Clustering pilot assignment [ 35 , 36 ]: regular pilot reuse structures are adopted to guar- an tee that users sharing the same pilot are enough spatially separated, and ensure a marginal pilot con tamination. 2.4 P o wer Control P o wer con trol is imp ortan t to handle the near-far ef- fect, and protect UEs from strong interference. The p o wer control can b e go v erned b y the CPU, whic h tells the APs and UEs which p o wer-con trol co efficien ts to use. By using closed-form capacit y b ounds that only dep end on the large-scale fading, the pow er con trol can b e w ell optimized and infrequen tly updated, e.g., a few times p er second. When maximum-ratio (MR) preco ding is used, at AP l , the symbol in tended for UE k , q k , is first w eigh ted by ˆ g ∗ lk and √ ρ lk , where ˆ g lk is the estimate of the c hannel from AP l to UE k and ρ lk is the p o wer-con trol co efficien t. The w eighted sym bols of all K UEs will b e then com bined and transmitted to the UEs. In the UL, at UE k , the corresp onding symbol q k is weigh ted b y a pow er-con trol co efficien t √ ρ k b e- fore transmission to the APs. The blo c k diagram that depicts the signal pro cessing in the DL and the UL is sho wn in Fig. 5 . In general, the p o w er-con trol co efficien ts should b e selected to maximize a given p erformance ob jective. This ob jectiv e ma y , for example, b e the max-min rate or sum rate: • Max-Min F airness Po wer Control: The goal of this p o wer-con trol p olicy is to deliver the same rate to all UEs and maximizing that rate. In a large net- w ork, some UEs may hav e v ery bad c hannels to all Interdonato et al. Page 6 of 13                                 Figure 5 Po w er control. Pro cessed signals at the l th AP (left) and the k th UE (right) with maximum ratio p recoding/combining. APs, thus it is necessary to drop them from ser- vice before applying this policy , otherwise the ser- vice will b e bad for every one. As in cellular Mas- siv e MIMO, the max-min fairness p o w er-control co efficien ts can b e obtained efficien tly by means of linear and second-order cone optimization [ 21 , Section IV-B]. • P o wer Con trol with User Prioritization: The rate requiremen ts are typically different among the UEs, which can b e taken into account in the p o wer-con trol p olicy . F or instance, UEs that use real-time services or hav e more exp ensiv e sub- scriptions hav e higher priority . The max-min fair- ness pow er control can b e extended to consider w eigh ted rates, where the individual weigh ts rep- resen t the priorities. Minim um rate constraints can b e also included. • P o wer Control with AP Selection: Due to the path-loss, APs far aw a y from a giv en UE will mo d- estly contribute to its p erformance. AP selection is implemen ted by setting non-zero pow er-con trol co efficien ts to the APs designed to serv e that UE. Optimal p o w er control is performed at the CPU. Cen tralized p o w er-con trol strategies might jeopardize the system scalabilit y and latency as the num ber of APs and UEs grows significantly . Simpler, scalable and distributed pow er-con trol p olicies, but providing de- creased p erformance, are proposed in [ 21 , 28 , 37 ]. T o achiev e go od netw ork p erformance, pilot assign- men t and p o w er con trol can be p erformed join tly . 3 Practical Deplo yment Issues The cost and complexit y of deplo yment, limited capac- it y of bac k/fron t-haul connections, and netw ork syn- c hronization are three ma jor issues that need to b e solv ed in a practical deploymen t. 3.1 Radio Strip es System The cabling and internal comm unication b et w een APs is c hallenging in practical cell-free Massiv e MIMO de- plo ymen ts. An appropriate, cost-efficien t architecture is the r adio strip e system [ 38 ], presen ted next. In a radio strip e system, the antennas and the as- so ciated an tenna pro cessing units (APUs) are serially lo cated inside the same cable, whic h also provides syn- c hronization, data transfer, and p o w er supply via a shared bus; see Fig. 6 . More sp ecifically , the actual APs consist of antenna elements and circuit-mounted c hips (including p ow er amplifiers, phase shifters, fil- ters, mo dulators, A/D and D/A con v erters) inside the protectiv e casing of a cable or a strip e. Each radio strip e is then connected to one or m ultiple CPUs. A radio stripe em b eds multiple an tenna elements, where eac h antenna elemen t effectiv ely is an AP . These APs could in turn coop erate phase-coheren tly . Hence, ef- fectiv ely a radio strip e constitutes a multiple-an tenna AP . Moreov er, dep ending on the carrier frequency , the m ultiple antennas can either b e co-lo cated (at higher frequencies the antenna elements are smaller) or dis- tributed on the radio strip e. Since the total num ber of an tennas is assumed to b e large, the transmit p o w er of each an tenna can b e v ery lo w, resulting in low heat- dissipation, small volume and w eigh t, and low cost. Small low-gain an tennas are used. F or example, if the carrier frequency is 5.2 GHz then the antenna size is 2.8 cm, thus, the an tennas and pro cessing hardware can b e easily fitted in a cable or a stripe. The receive/transmit processing of an antenna is p erformed right next to itself. On the transmitter side, eac h APU receiv es up to K streams of input data (e.g., one stream p er UE, one UE with K streams, or some other UE-stream allo cation) from the previous APU Interdonato et al. Page 7 of 13 APU Pr ot ec t i ng ma t er i al I n t er na l c onnect or (po w er , f r on t ha ul , clock ) APU CPU CPU D/A D/A A/D A/D DSP AP U Q I D/A D/A A/D A/D An t enna eleme n t s Q I Q I Q I Figure 6 Radio strip e system design. Each radio strip e sends/receives data to/from one or multiple CPUs through a shared bus (or internal connector), which also provides synchronization and pow er supply to each APU. via the shared bus. In eac h an tenna, the input data streams are scaled with the pre-calculated preco ding v ector and the sum-signal is transmitted ov er the radio c hannel to the receiv er(s). By exploiting channel reci- pro cit y , the preco ding vector may b e a function of the estimated UL c hannels. F or example, if the conjugate of the estimated UL c hannel is used, MR precoding is obtained. This precoding requires no CSI sharing b et ween the an tennas. On the receiver side, the received radio signal is m ultiplied with the combining vector previously cal- culated in the UL pilot phase. The output gives K data streams. The pro cessed streams are then com- bined with the data streams received from the shared bus and sen t again on the shared bus to the next APU. More sp ecifically , the m th APU sums its received data streams to the input streams from APU m − 1 con- sisting of combined signals from APUs 1 , . . . , m − 1, for one or more UEs. This cum ulativ e signal is then outputted to APU m + 1. The combination of signals is a simple p er-stream addition operation. The radio strip e system facilitates a flexible and c heap cell-free Massive MIMO deplo yment. Cheapness comes from man y aspects: ( i ) deplo ymen t do es not re- quire highly qualified p ersonnel. Theoretically , a radio strip e needs only one (plug and pla y) connection ei- ther to the front-haul netw ork or directly to the CPU; ( ii ) a conv en tional distributed Massive MIMO deploy- men t requires a star top ology , i.e., a separate cable b et ween each APs and a CPU, whic h may b e econom- ically infeasible. Con versely , radio strip e installation complexit y is unaffected by the n um b er of an tenna el- emen ts, thanks to its compute-and-forward architec- ture. Hence, cabling b ecomes m uch c heaper. The star top ology might b e preferable from a p erformance p er- sp ectiv e, but the cost of deploymen t of the front-haul net w ork migh t be very high or ev en prohibitiv e. A w a y to efficiently use the long front-haul cables is to em- b ed antenna elements in to them, turning the cables Interdonato et al. Page 8 of 13 in to radio strip es. As a result, a star topology but with man y radio strip es is obtained and the cov erage impro v ed; ( iii ) maintenance costs are cut down as a radio strip e system offers increased robustness and re- silience: highly distributed functionality offer limited o v erall impact on the net w ork when few strip es be- ing defected; ( iv ) lo w heat-dissipation makes co oling systems simpler and c heap er. While cellular APs are bulky , radio strip es enable in- visible installation in existing construction elemen ts as exemplified in Fig. 7 . Moreo v er, a radio strip e deploy- men t may integrate for example temp erature sensors, microphones/sp eak ers, or vibration sensors, and pro- vide additional features such as fire alarms, burglar alarms, earthquake warning, indo or p ositioning, and climate monitoring and con trol. 3.2 F ront-haul and Back-haul Capacity While there is no need to share CSI betw een an ten- nas, the CPUs m ust provide eac h APU with the data streams. The data is deliv ered from the core netw ork via the bac k-haul and then forw arded to the APU o v er the front-haul; see Fig. 6 . Similarly , the CPU receiv es the cumulativ e signals from its radio stripes ov er the fron t-haul and deco des them. The data will then be deliv ered to the core netw ork ov er the bac k-haul. The required front-haul capacit y of a radio strip e is prop ortional to the num ber of sim ultaneous data streams that it supports at maxim um netw ork load. The required bac k-haul capacit y of a CPU corresponds to the sum rate of the data streams that its ra- dio stripes will transmit/receive at maxim um net work load. The w a y to limit these capacity requirements is to constrain the num b er of UEs that can be served p er AP (e.g., radio strip e) and CPU. T o av oid creat- ing cell boundaries, a user-cen tric p erspective must b e used when selecting which subset of APs that serve a particular UE [ 21 , 39 , 40 ], as illustrated on the b ottom- left in Fig. 1 . Supp ose a UE is alone in the net w ork and all APs transmit to it with full p o w er. Since the path-loss de- ca ys rapidly with the propagation distance, 95% of the receiv ed p o wer will originate from a subset of the APs, called the 95%-subset . When the ISD is large, as in a con v entional cellular netw ork, the 95%-subset migh t only contain a handful of APs. As the ISD reduces (i.e., the num ber of APs p er km 2 gro ws), the 95%- subset is larger. This prop ert y can be used to limit the back-haul signaling. F or example, it is sho wn in [ 21 ] that only 10-20% of the APs in the 1 km 2 area surrounding a UE b elongs to the 95%-subset. 3.3 Synchronization T o serv e a UE b y coherent joint transmission from m ul- tiple APs, the net w ork infrastructure needs to b e syn- c hronized. The net work might hav e an absolute time (phase) reference, but the APs are unsync hronized. This means that, effectively , the transmitter and re- ceiv er circuits of each AP hav e their own time ref- erences. The difference in time reference b et w een the Figure 7 Potential applications and deployment concepts. Radio stripes, here illustrated in white, enable invisible installation in existing construction elements. Interdonato et al. Page 9 of 13 transmitter and receiv er in a given AP represents the recipro cit y calibration error. The difference in, say , transmitter time reference, b et ween an y pair of APs represen ts the synchronization error betw een these t w o APs. T o limit the recipro cit y and sync hronization er- rors, a synchronization process needs to b e applied at regular in terv als. Supp ose the transmitter of AP i has a clo c k bias of t i (i.e., its local time reference clo c k sho ws zero at abso- lute time t i ) and the receiv er has a clo c k bias of r i (i.e., its clo c k shows zero at absolute time r i ). W e prop ose a simple synchronization proto col that w orks as follo ws: 1 A t lo cal time zero (absolute time t 1 ), AP 1 trans- mits a known pulse. AP 2 receiv es this pulse at time t 1 − r 2 , according to its clo c k, and timestamps it with δ 12 = t 1 − r 2 . Similarly , AP 3 timestamps the pulse with δ 13 = t 1 − r 3 . 2 A t its lo cal time zero, AP 2 transmits a known pulse. AP 1 timestamps the received pulse with its lo cal reception time δ 21 = t 2 − r 1 . AP 3 timestamps it with δ 23 = t 2 − r 3 . 3 Finally , at its lo cal time zero, AP 3 transmits a kno wn pulse. AP 1 timestamps this received pulse with δ 31 = t 3 − r 1 . AP 2 timestamps it with δ 32 = t 3 − r 2 . The quan tities δ ij are kno wn from the measuremen ts, but t 1 , r 1 , t 2 , r 2 , t 3 , r 3 cannot b e obtained from δ ij since the corresp onding linear equation system is sin- gular. Ho w ev er, the recipro cit y and sync hronization er- rors are easily reco vered: t 1 − r 1 = δ 12 + δ 31 − δ 32 , t 2 − r 2 = δ 21 + δ 32 − δ 31 , t 3 − r 3 = δ 31 + δ 23 − δ 21 , t 1 − t 2 = δ 13 − δ 23 , t 1 − t 3 = δ 12 − δ 32 , t 2 − t 3 = δ 21 − δ 31 . This enables sync hronization b et w een the three APs. This synchronization metho d can b e applied in a differen tial manner. Consider measurements δ ij tak en at a first p oin t in time at whic h the biases are t 1 , r 1 , t 2 , r 2 , t 3 , r 3 , and then measuremen ts δ 0 ij tak en at a sec- ond point in time at which the biases are t 0 1 , r 0 1 , t 0 2 , r 0 2 , t 0 3 , r 0 3 . The application of the abov e method to δ 0 ij − δ ij yields the evolution of clo c k biases, up to a drift that is common to the whole group. Extension to sync hronization b et ween t w o groups is straigh tforw ard. Consider tw o groups A and B, eac h group comprising three APs. The recipro cit y and syn- c hronization errors within each group may be cali- brated through the ab o v e-described pro cedure. Eac h group will, ho w ev er, ha v e an unknown remaining clock bias. Let δ A,B ij , t A i − r B j the time discrepancy mea- sured at AP j in group B, follo wing the known pulse transmission by AP i in group A. The in ter-group syn- c hronization error can b e easily obtained by t A i − t B j = δ A,B ik − δ B,B j k . Extensions to synchronization b et w een more than t w o groups follo ws the same metho dology as ab o v e. Note that, in a radio strip e system, groups of APs are sequen tial. Hence, synchronization is only required b et ween a group and its neigh b or. 4 P erfo rmance of Ubiquitous Cell-Free Massive MIMO W e will analyze the an ticipated p erformance, in terms of DL SE (bit/s/Hz/user), in t wo case studies of prac- tical in terest: ( i ) an industrial indo or scenario, and ( ii ) an outdo or piazza scenario. F or b oth the cases w e as- sume that the antenna elemen ts, embedded in the ra- dio strip es, implement MR preco ding lo cally and no CSI is exchanged. Hence, eac h an tenna element effec- tiv ely acts as a single-an tenna AP . T o ev aluate the DL p er-user SE, w e use the closed-form expression for the DL capacit y lo w er b ound given in [ 21 , Section I II-B], whic h is v alid for single-antenna APs implemen ting MR preco ding and UEs relying on knowledge of the a v erage channel gain for deco ding. This closed-form expression is obtained under the assumption of inde- p enden t Rayleigh fading channels, and accounts for c hannel estimation errors and in terference from pilot con tamination. The tw o case studies differ in terms of propaga- tion channel model, path-loss mo del, carrier frequency (whic h affects the antenna geometry), cov erage re- quiremen ts, and radio strip es la y out deplo ymen t. 4.1 Industrial Indo o r Scenario Ubiquitous cov erage, low latency , ultra-reliable com- m unication, and resilience are key for wireless commu- nications in a factory en vironmen t. The flexible dis- tributed cell-free arc hitecture, with its macro-diversit y gain and inheren t abilit y to suppress interference, is suitable to cop e with the requiremen ts of this scenario. W e consider the industrial indo or environmen t de- scrib ed in [ 41 ]: a 7-8 m high building with metal ceiling and concrete floors and w alls. The industrial in ven tory mainly consists of metal machinery . The radio strip es are deplo y ed in an area of 100 × 100 meters in such a w a y that 400 APs shap e a 20 × 20 regular grid, as sho wn in Fig. 8 (left). The end-most antennas are 5 m apart. They are placed at 6 m ab o ve ground level, while the UE antenna height is 2 m. The carrier frequency that w e consider is 5200 MHz, whic h is within the frequency band 5150-5825 MHz adopted for application of indoor industrial wireless comm unications. Hence, a λ/ 2 an- tenna element (where λ denotes the wa v elength) has size 2.8 cm. Interdonato et al. Page 10 of 13 1 2 3 4 5 Spectr al E ffi c ienc y [bit/ s/H z/u ser] 0 0.2 0.4 0.6 0.8 1 CD F CD-FP T MMF-C QB AP select ion MMF-R PB AP select ion MMF 0 20 40 60 80 100 m 0 20 40 60 80 100 m Figure 8 Industrial indo o r scenario. Left figure illustrates the grid APs deployment. On the right, the CDF fo r the p er-user SE, as defined in [ 21 , Section II I-B]. In these simulations, w e use the one-slop e path-loss mo del defined in [ 41 ], with reference distance d 0 = 15 m, path-loss at reference distance PL( d 0 ) = 70 . 28 , path-loss exponent n = 2 . 59 , and log-no rmal shadowing standard deviation σ = 6 . 09 . We choose L = 400 , K = 20 , bandwidth B = 20 MHz, and max per-AP radiated p o w er 200 mW. The small-scale fading follows i.i.d. Rayleigh distribution. W e implement a wrap-around technique to simulate no cell b ounda ries. The DL p er-user SE and the impact of pow er con- trol is sho wn in Fig. 8 (righ t). W e consider K = 20 uniformly distributed UEs, m utually orthogonal UL pilots ( τ u , p = K ), no DL training ( τ d , p = 0), TDD frame length τ = 200 samples, and four different DL p o wer control settings, assuming a maximum p er-AP radiated p o wer of 200 mW: 1 CD-FPT: Channel-dep enden t full p o w er trans- mission. All APs transmit with full p o w er and the pow er-con trol coefficients for a giv en AP l are the same for all k = 1 , . . . , K . The p o w er- con trol co efficien t b et w een AP l and UE k is ρ lk =  P K k 0 =1 γ lk 0  − 1 , where γ lk 0 is the v ariance of the corresp onding c hannel estimate ˆ g lk 0 ; 2 MMF: Max-min fairness p o wer control. All the APs are inv olv ed in coherently serving a giv en UE. The p o wer control co efficien ts are chosen to maximize the minimum sp ectral efficiency of the net w ork, as describ ed in detail in [ 21 , Section IV- B]. 3 MMF-RPB AP selection [ 40 ]: Max-min fairness p o wer con trol with received-pow er-based AP se- lection. Only a subset of APs serves a given UE k . The subset consists of the APs that contribute at least α % (e.g., 95%, as describ ed b efore) of the p o wer assigned to UE k . Mathematically , |A k | X l =1 % lk P L j =1 √ ρ j k γ j k ≥ α % , where |A k | is the cardinality of the user- k -sp ecific AP subset, and { % 1 k , . . . , % Lk } is the set of the co- efficien ts % lk , √ ρ lk γ lk sorted in descending or- der. 4 MMF-CQB AP selection [ 40 ]: Max-min fairness p o wer control with channel-qualit y-based AP se- lection. This method selects the APs with the best c hannel qualit y (largest large-scale fading co effi- cien t) tow ards UE k as follows |A k | X l =1 ¯ β lk P L j =1 β j k ≥ α % , where β j k is the large-scale fading co efficien t of the c hannel b et ween the j th AP and the k th UE, and { ¯ β 1 k , . . . , ¯ β Lk } is the set of the large-scale fad- ing co efficien ts sorted in desc ending order. The AP selection in [ 40 ] is p erformed cen trally at the CPU as full information on the channel large-scale fad- ing co efficien ts to all users is needed. An alternative, distributed scheme is prop osed in [ 42 ], where eac h AP autonomously decides whether to participate in the service of a giv en user based on lo cal pilot observ a- tions. Max-min fairness p o w er con trol doubles the 95%- lik ely SE compared to the baseline CD-FPT case. Thanks to optimal p o w er control, the radio stripe sys- tem can guaran tee to eac h UE almost 4.5 bit/s/Hz. The p erformance with AP selection is also ev aluated (dashed and dashed dotted lines). W e can see that the Interdonato et al. Page 11 of 13 SE reduction is minor if the RPB AP selection strat- egy is used, while the CQB criterion leads to a 20% reduction. The performance gap is attributable to the cardinalit y of the corresp onding AP subsets; on a v er- age, CQB uses 17% of the APs and RPB uses 42% of the APs. 4.2 Outdo o r Piazza Scenario Installations causing a big visual impact on the en- vironmen t can b e prohibited in areas lik e piazzas and historic places. In suc h a scenario, a radio strip e system can pro vide all the adv antages previously describ ed with an unobtrusiv e deploymen t. W e consider a ra- dio stripe system that cov ers a 300 × 300 meters square. The radio stripes are placed along the perimeter of the square at 9 m height, for example, on building facades. There are 400 APs in total, as sho wn in Fig. 9 (left). W e consider K = 20 uniformly distributed UEs, mu- tually orthogonal UL pilots ( τ u , p = K ), no DL train- ing ( τ d , p = 0), TDD frame length τ = 200 samples, and the same p o w er-control p olicies as b efore. T o deal with the large co verage area, w e set the maxim um per- APs radiated p ow er to 400 mW, and use the carrier frequency 2000 MHz, which giv es a λ/ 2 antenna ele- men t 7.5 cm long. There is actually no need for m uc h higher transmit p o w er in outdo or scenarios. The ra- diated p o wer can b e further low ered by adding more APs while guaranteeing the same cov erage and perfor- mance. The n umerical results are sho wn in Fig. 9 (right). With max-min p o w er control, w e can pro vide a SE around 4.5 bit/s/Hz/user, doubling the 95%-lik ely SE compared to the baseline CD-FPT. Due to the AP deplo ymen t symmetry , the AP selection strategies p er- form almost equally w ell; CQB and RPB select around 1 / 3 of the APs on a v erage. The p erformance gap with resp ect the case with no AP selection is negligible, th us 2 / 3 of the APs can b e left out in the transmission to- w ards a given UE. 5 Conclusion: Where there’s a will, there’s a wa y Cell-free Massiv e MIMO brings the best of t w o w orlds: the macro-diversit y from distributing man y APs and the interference cancellation from cellular Massive MIMO. The TDD operation ensures system scalability and distributed processing as the c hannel estimation and preco ding o ccur at eac h AP , th us no instan taneous CSI is exc hanged ov er the fron t-haul. The user-cen tric data transmission suppresses the inter-cell in terference and also con tributes to reduce the fron t-haul o v erhead. Thanks to all these features, cell-free Massive MIMO succeeds where all the prior co ordinated distributed wireless systems failed. While this article has outlined the basic pro cessing and implemen tation concepts, many op en issues re- main, ranging from comm unication theory to measure- men ts and engineering efforts: • P o w er control: While (weigh ted) max-min pow er- con trol is computationally tractable and pro vides uniform qualit y of service, it do es not take actual traffic patterns in to account. New p o w er con trol algorithms are needed to balance fairness, latency , and netw ork throughput, while p ermitting a dis- tributed implemen tation. • Distributed signal pro cessing: MR preco d- ing/detection and sync hronization can b e dis- 0 50 100 150 200 250 300 m 0 50 100 150 200 250 300 m AP 1 2 3 4 5 6 Sp ectral E ffi ciency [bit /s/Hz/user] 0 0.2 0.4 0.6 0.8 1 CDF CD-F PT MMF -CQB AP selecti on MMF -RPB AP selecti on MMF Figure 9 Outdo o r piazza scenario. Left figure illustrates the APs deploy ed along the perimeter of the piazza. On the right, the CDF for the p er-user SE, as defined in [ 21 , Section II I-B]. In these simulations the la rge-scale fading is modeled as in [ 21 ], assuming uncorrelated shadow fading. W e choose L = 400 , K = 20 , bandwidth B = 20 MHz, and max per-AP radiated p o wer 400 mW. The small-scale fading follows i.i.d. Rayleigh distribution. Interdonato et al. Page 12 of 13 tributed, as describ ed earlier, but the data enco d- ing/deco ding must b e carried out at one or mul- tiple CPUs. The distribution of such signal pro- cessing tasks o v er the net w ork is non-trivial, when lo oking for a go od tradeoff betw een high rates and limited bac k-haul signaling. • Resource allo cation and broadcasting : Schedul- ing, paging, pilot allo cation, system information broadcast, and random access are basic function- alities that traditionally rely on a cellular arc hi- tecture. New algorithms and proto cols are needed for these tasks in cell-free net works. • Channel modeling: The performance analysis of cell-free net works hav e primarily considered Ra yleigh fading channels. Practical c hannels are lik ely to contain a mix of line-of-sight and non- line-of-sigh t paths, and will likely differ substan- tially dep ending on the carrier frequency . Dedi- cated channel measurements follo w ed by refined c hannel mo deling are necessary to b etter under- stand the channel c haracteristics and fine-tune re- source allo cation algorithms. • DL channel estimation: Recent works [ 29 , 34 ] sho w that cell-free net w orks pro vide a lo w de- gree of c hannel hardening. DL channel estimates, needed for data deco ding, can either b e obtained from DL pilots, whic h increases the pilot ov er- head, or b y blind estimation tec hniques that uses the DL data. Dedicated algorithms for this esti- mation are needed. • Compliance with existing standards: The 5G standard is intended to b e forward-compatible and only relies on cell-iden tities for the basic func- tionalities. It is likely that cell-free data transmis- sion can be implemented in 5G, but further work in standardization and conceptual dev elopmen t is needed. • Protot yp e dev elopmen t: The step from a promising commu nication concept to a practi- cal netw ork requires substan tial prototyping. The first working cell-free protot yp e ma y b e pCell, where [ 43 ] describ es a setup with 32 APs serving 16 UEs. Since e v ery AP in a cell-free net w ork has lo w cost and fo otprin t, protot yping can b e car- ried out using rather simple components. One can b egin by demonstrating the synchronization and join t pro cessing capabilities with a small n umber of APs in a limited area, and then contin ue with more APs and larger co verage area. Abbreviations 3GPP: 3rd generation partnership project; AP: access point; APU: ante nna processing unit; BS: base station; CD-FPT: channel-dependent full p o wer transmission; CDF: cumulative distribution function; CoMP-JT: coordinated multip oint with joint transmission; CPU: central processing unit; CQI: channel quality indicator; CSI: channel state information; DL: downlink; DMRS: demodulation reference signal; FDD: frequency-division duplex; ISD: inter-site distance; L TE: long term evolution; MIMO: multiple-input multiple-output; MMF: max-min fairness pow er control; MMF-RPB: MMF with received-p o wer-based AP selection; MMF-CQB: MMF with channel-quality-based AP selection; MMSE: minimum mean square erro r; MR: maximum-ratio; NR: new radio; OFDM: o rthogonal frequency-division multiplexing; SE: sp ectral efficiency; TDD: time-division duplex; UE: user equipment; UL: uplink. Authors’ contributions All authors have contributed to this research w ork, read and approved the final manuscript. Authors’ info rmation This wo rk was conducted when Giovanni Interdonato was with Ericsson Research (Ericsson AB), Link¨ oping, Sw eden. Funding This pap er was supp o rted b y the Europ ean Union’s Ho rizon 2020 research and innovation programme under grant agreement No 641985 (5Gwireless), and ELLI IT. Availability of data and materials Data sharing is not applicable to this article as no datasets were generated or analysed during the current study . Competing interests The authors decla re that they have no comp eting interests. Author details 1 Department of Electrical Engineering (ISY), Link¨ oping University , 581 83 Link¨ oping, Sweden. 2 Ericsson Research, Ericsson AB, 583 30 Link¨ oping, Sweden. 3 Electrical Engineering and Computer Science (EEECS), Queen’s University Belfast, BT3 9DT Belfast, U.K.. References 1. J.G. Andrews, X. Zhang, G.D. Durgin, A.K. Gupta, Are we approaching the fundamental limits of wireless netw ork densification?, IEEE Commun. Mag. 54 (10), pp. 184–190 (2016) 2. T.L. Marzetta, E.G. La rsson, H. Y ang, H.Q. Ngo, Fundamentals of Massive MIMO (Cambridge Universit y Press, Cambridge, 2016) 3. A. Lozano, R.W. Heath, J.G. Andrews, F undamental limits of coop eration, IEEE T rans. Inf. Theory 59 (9), pp. 5213–5226 (2013) 4. S. Shamai, B.M. Zaidel, Enhancing the cellula r downlink capacit y via co-processing at the transmitting end, in Proc. IEEE Vehicular T echnology Conference (VTC-Spring), pp. 1745–1749 (2001) 5. S. Zhou, M. Zhao, X. Xu, J. W ang, Y. Y ao, Distributed wireless communication system: A new architecture for future public wireless access, IEEE Commun. Mag. 41 (3), pp. 108–113 (2003) 6. S. V enkatesan, A. Lozano, R. V alenzuela, Net wo rk MIMO: Overcoming intercell interference in indo o r wireless systems, in Pro c. Asiloma r Conf. Signals, Syst., Comput., pp. 83–87 (2007) 7. G. Caire, S. Ramprashad, H. Papadopoulos, Rethinking netw ork MIMO: Cost of CSIT, p erfo rmance analysis, and architecture comparisons, in Proc. Information Theory and Applications W orkshop (IT A), pp. 1–10 (2010) 8. M. Boldi, A. T¨ olli, M. Olsson, E. Ha rdouin, T. Svensson, F. Bo cca rdi, L. Thiele, V. Jungnickel, Coordinated multip oint (CoMP) systems, in Mobile and Wireless Communications for IMT-Advanced and Beyond, ed. by A. Osseiran, J. Monserrat, W. Mohr (Wiley , 2011), pp. 121–155 9. P . Marsch, S. Br¨ uck, A. Garavaglia, M. Schulist, R. Weber, A. Dek o rsy , Clustering, in Co o rdinated multi-point in mobile communications: From theo ry to practice, ed. b y P . Ma rsch, G. Fett w eis (Cambridge University Press, Ney Y ork, 2011), pp. 139–159 10. R. Irmer, H. Droste, P . Ma rsch, M. Grieger, G. Fettw eis, S. Brueck, H.P . Mayer, L. Thiele, V. Jungnickel, Co o rdinated multip oint: Concepts, p erfo rmance, and field trial results, IEEE Commun. Mag. 49 (2), pp. 102–111 (2011) 11. D. Gesb ert, S. Hanly , H. Huang, S. Shamai, O. Simeone, W. Y u, Multi-cell MIMO co operative netw orks: A new look at interference, IEEE J. Sel. Areas Commun. 28 (9), pp. 1380–1408 (2010) 12. R. Fantini, W. Zirw as, L. Thiele, D. Aziz, P . Baracca, Coordinated multi-point transmission in 5G, in 5G Mobile and Wireless Interdonato et al. Page 13 of 13 Communications T echnology , ed. b y A. Osseiran, J. Monserrat, P . Marsch (Cambridge Universit y Press, Cambridge, 2016), p. 248276 13. E. Bj¨ ornson, E. Jorswieck, Optimal resource allo cation in coordinated multi-cell systems, Foundations and T rends in Communications and Information Theo ry 9 (2-3), pp. 113–381 (2013) 14. A. T¨ olli, M. Co dreanu, M. Juntti, Coop erative MIMO-OFDM cellular system with soft handover b et ween distributed base station antennas, IEEE T rans. Wireless Commun. 7 (4), pp. 1428–1440 (2008) 15. I. Garcia, N. Kusashima, K. Sak aguchi, K. Araki, Dynamic co operation set clustering on base station coop eration cellular netw orks, in Proc. IEEE International Symposium on P ersonal, Indoor and Mobile Radio Communications (PIMRC), pp. 2127–2132 (2010) 16. S. Kaviani, O. Simeone, W. Krzymien, S. Shamai, Linear p recoding and equalization for net wo rk MIMO with partial coop eration, IEEE T rans. Veh. T echnol. 61 (5), pp. 2083–2095 (2012) 17. P . Baracca, F. Bo cca rdi, V. Braun, A dynamic joint clustering scheduling algorithm fo r downlink CoMP systems with limited CSI, in Proc. IEEE International Symposium on Wireless Commun. Systems (ISWCS), pp. 830–834 (2012) 18. V. Jungnickel, K. Manolakis, W. Zirwas, B. P anzner, V. Braun, M. Lossow, M. Sternad, R. Ap elfrojd, T. Svensson, The role of small cells, co o rdinated multipoint, and massive MIMO in 5G, IEEE Commun. Mag. 52 (5), pp. 44–51 (2014) 19. J. Y uan, S. Jin, W. Xu, W. T an, M. Matthaiou, K. W ong, User-centric netw o rking fo r dense C-RANs: High-SNR capacity analysis and antenna selection, IEEE T rans. Commun. 65 (11), pp. 5067–5080 (2017) 20. C. Pan, M. Elk ashlan, J. Wang, J. Y uan, L. Hanzo, User-centric C-RAN architecture fo r ultra-dense 5G netw orks: Challenges and methodologies, IEEE Commun. Mag. 56 (6), pp. 14–20 (2018) 21. H.Q. Ngo, A. Ashikhmin, H. Y ang, E.G. Larsson, T.L. Ma rzetta, Cell-free Massive MIMO versus small cells, IEEE T rans. Wireless Commun. 16 (3), pp. 1834–1850 (2017) 22. E. Nay ebi, A. Ashikhmin, T.L. Marzetta, H. Y ang, Cell-free Massive MIMO systems, in Pro c. Asiloma r Conf. Signals, Syst., Comput., pp. 695–699 (2015) 23. E. Bj¨ ornson, L. Sanguinetti, Making cell-free massive MIMO competitive with MMSE pr o cessing and centralized implementation, CoRR abs/1903.10611 (2019). Online: 24. E. Dahlman, S. Pa rkvall, J. Sk¨ old, 4G: L TE/L TE-Advanced for Mobile Broadband, 2nd edn. (Academic Press, Oxfo rd, 2013) 25. E. Dahlman, S. Pa rkvall, J. Sk¨ old, 5G NR: The Next Generation Wireless Access T echnology , 1st edn. (Academic Press, London, 2018) 26. S. Kim, B. Shim, FDD-based cell-free massive MIMO systems, in Proc. IEEE International Wo rkshop on Signal Processing Advances in Wireless Communications (SP A WC), pp. 1–5 (2018) 27. E. Bj¨ ornson, R. Zakhour, D. Gesb ert, B. Ottersten, Co operative multicell precoding: Rate region characterization and distributed strategies with instantaneous and statistical CSI, IEEE T rans. Signal Process. 58 (8), pp. 4298–4310 (2010) 28. E. Nay ebi, A. Ashikhmin, T.L. Marzetta, H. Y ang, B.D. Rao, Precoding and pow er optimization in cell-free Massive MIMO systems, IEEE T rans. Wireless Commun. 16 (7), pp. 4445–4459 (2017) 29. Z. Chen, E. Bj¨ ornson, Channel hardening and favorable p ropagation in cell-free Massive MIMO with sto chastic geometry , IEEE T rans. Commun. 66 (11), pp. 5205–5219 (2018) 30. S.E. Hajri, J. Denis, M. Assaad, Enhancing favo rable propagation in cell-free massive MIMO through spatial user grouping, in Proc. IEEE International Wo rkshop on Signal Pro cessing Advances in Wireless Communications (SP A WC), pp. 1–5 (2018) 31. G. Interdonato, H.Q. Ngo, E.G. L a rsson, P . Frenger, Ho w much do downlink pilots imp rove cell-free Massive MIMO?, in Pro c. IEEE Global Commun. Conf. (GLOBECOM), pp. 1–7 (2016) 32. A. Pitarok oilis, S.K. Mohammed, E.G. Larsson, On the optimality of single-carrier transmission in la rge-scale antenna systems, IEEE Wireless Commun. Lett. 1 (4), pp. 276–279 (2012) 33. J.C. Marinello Filho, C. Panazio, T. Ab r˜ ao, Uplink p erfo rmance of single-carrier receiver in massive MIMO with pilot contamination, IEEE Access 5 , pp. 8669–8681 (2017) 34. G. Interdonato, H.Q. Ngo, P . F renger, E.G. Larsson, Downlink training in cell-free massive MIMO: A blessing in disguise, CoRR abs/1903.10046 (2019). Online: 35. M. Atta rifa r, A. Abbasfar, A. Lozano, Random vs structured pilot assignment in cell-free massive MIMO wireless netw orks, in Pro c. IEEE International Conference on Communications Workshops (ICC Wo rkshops), pp. 1–6 (2018) 36. R. Sabbagh, C. P an, J. W ang, Pilot allocation and sum-rate analysis in cell-free massive MIMO systems, in Proc. IEEE International Conference on Communications (ICC), pp. 1–6 (2018) 37. G. Interdonato, P . F renger, E.G. Larsson, Scalabilit y aspects of cell-free massive MIMO, in Pro c. IEEE International Conference on Communications (ICC), pp. 1–6 (2019) 38. P . Frenger, J. Hederen, M. Hessler, G. Interdonato. Imp roved antenna arrangement fo r distributed massive MIMO (2017). Patent application WO2018103897. Online: patentscope.wipo.int/search/en/WO2018103897 39. S. Buzzi, C. D’Andrea, Cell-free massive MIMO: User-centric approach, IEEE Wireless Commun. Lett. 6 (6), pp. 706–709 (2017) 40. H.Q. Ngo, L.N. T ran, T.Q. Duong, M. Matthaiou, E.G. Larsson, On the total energy efficiency of cell-free Massive MIMO, IEEE T rans. Green Commun. Netw., 2 (1), pp. 25–39 (2018) 41. E. T anghe, W. Joseph, L. Verloock, L. Ma rtens, H. Cap oen, K.V. Herwegen, W. V antomme, The industrial indo o r channel: Large-scale and temp o ral fading at 900, 2400, and 5200 MHz, IEEE T rans. Wireless Commun. 7 (7), pp. 2740–2751 (2008) 42. O.Y. Bursalioglu, G. Caire, R.K. Mungara, H.C. Papadopoulos, C. Wang, F og massive MIMO: A user-centric seamless hot-spot architecture, IEEE T rans. Wireless Commun. 18 (1), pp. 559–574 (2019) 43. A. Fo renza, S. P erlman, F. Saibi, M.D. Dio, R. van der Laan, G. Caire, Achieving large multiplexing gain in distributed antenna systems via coop eration with pCell technology , in Proc. Asilomar Conf. Signals, Syst., Comput., pp. 286–293 (2015)