Operating Massive MIMO in Unlicensed Bands for Enhanced Coexistence and Spatial Reuse
Giovanni Geraci, Adrian Garcia-Rodriguez, David López-Pérez, Andrea Bonfante, Lorenzo Galati Giordano, Holger Claussen
aa r X i v : . [ c s . I T ] F e b Operating Massive MIMO in Unlicensed Bands forEnhanced Coexistence and Spatial Reuse
Giovanni Geraci, Adrian Garcia-Rodriguez, David L´opez-P´erez, Andrea Bonfante,Lorenzo Galati Giordano, and Holger Claussen
Abstract —We propose to operate massive multiple-input mul-tiple output (MIMO) cellular base stations (BSs) in unlicensedbands. We denote such system as massive MIMO unlicensed(mMIMO-U). We design the key procedures required at a cellularBS to guarantee coexistence with nearby Wi-Fi devices operatingin the same band. In particular, spatial reuse is enhancedby actively suppressing interference towards neighboring Wi-Fidevices. Wi-Fi interference rejection is also performed duringan enhanced listen-before-talk (LBT) phase. These operationsenable Wi-Fi devices to access the channel as though no cellularBSs were transmitting, and vice versa. Under concurrent Wi-Fiand BS transmissions, the downlink rates attainable by cellularuser equipment (UEs) are degraded by the Wi-Fi-generatedinterference. To mitigate this effect, we select a suitable setof UEs to be served in the unlicensed band accounting for ameasure of the Wi-Fi/UE proximity. Our results show that theso-designed mMIMO-U allows simultaneous cellular and Wi-Fitransmissions by keeping their mutual interference below theregulatory threshold. Compared to a system without interferencesuppression, Wi-Fi devices enjoy a median interference powerreduction of between 3 dB with 16 antennas and 18 dB with 128antennas. With mMIMO-U, cellular BSs can also achieve largedata rates without significantly degrading the performance ofWi-Fi networks deployed within their coverage area.
Index Terms —Massive MIMO, 5G, unlicensed band, interfer-ence suppression, cellular/Wi-Fi coexistence.
I. I
NTRODUCTION
In view of the ever increasing mobile data demand, thewireless industry has turned its attention to unlicensed spec-trum bands, e.g., 5 GHz, to provide extra frequency resourcesfor the fifth generation (5G) cellular networks [2]–[5]. In5G communication systems, licensed-unlicensed integrationmay allow mobile operators to serve more users via trafficoffloading and/or to enhance their peak data rate throughcarrier aggregation. Besides, standalone unlicensed technolo-gies may unlock new vertical markets and their correspondingrevenues. On the other hand, harmonious coexistence withother technologies working in the unlicensed spectrum, suchas IEEE 802.11x (Wi-Fi), must be guaranteed [6]–[8]. Thisis because Wi-Fi systems rely on a contention-based accesswith a random backoff mechanism, i.e., carrier sensing mul-tiple access/collision avoidance (CSMA-CA) [9]. Therefore,cellular base stations (BSs) transmitting continuously overunlicensed bands would produce harmful interference andgenerate repeated backoffs at the Wi-Fi nodes.
The authors are with Bell Laboratories, Nokia, Dublin, Republic of Ireland(e-mail: [email protected]). The material in this paper will inpart be presented at the 2017 IEEE Int. Conf. on Comm. (ICC) [1]
A. Background and Motivation
Two main approaches are currently under consideration bynetwork operators to exploit the unlicensed band and guaranteecoexistence between cellular BSs and Wi-Fi devices. Bothaugment an existing licensed band interface with supplementalunlicensed band downlink transmissions.
1) Long Term Evolution unlicensed (LTE-U):
LTE-U usescarrier-sensing adaptive transmission (CSAT) and it is mainlytargeted at the United States market, where channel sensingoperations prior to transmission are not required [10]. WithCSAT, cellular BSs interleave their transmissions with idle in-tervals, which allow Wi-Fi devices to access the channel [11],[12]. For example, a cellular BS may access the channelat every other frame boundary, i.e., transmitting for a 10msframe, then leaving the channel idle for the next 10ms frame,etc., thus yielding a 50% on-off duty cycle. As a result, everychannel use gained by the cellular BS comes at the expenseof idle periods at the Wi-Fi devices.
2) Licensed Assisted Access (LAA):
In LAA, cellular BSssense the channel activity via energy detection, and theycommence a transmission in the unlicensed band only if thechannel is deemed free for a designated period of time [13],[14]. Such channel sensing operation, denoted as listen beforetalk (LBT), is mandatory in some regions, e.g., Europe andJapan [15], [16]. Similarly to the random access procedureused by Wi-Fi devices, LBT employs random backoff intervalsand a variable exponentially distributed contention windowsize. The latter is recommended by the 3GPP as the base-line approach for downlink transmissions to guarantee a fairsharing of time resources with Wi-Fi devices [17].While ensuring coexistence, both LTE-U/CSAT andLAA/LBT are based on discontinuous transmission, i.e., nei-ther allows simultaneous usage of the unlicensed spectrumby both cellular BSs and Wi-Fi devices when their coverageareas overlap. This may be a conservative approach in certainscenarios, mostly when multiple antennas are available. In fact,multiple antennas could be used by cellular BSs to increasespatial reuse and provide additional throughput without dimin-ishing the Wi-Fi data rates.
B. Approach and Contributions
We propose massive multiple-input multiple-output(MIMO) as a means to enhance coexistence, whilemaximizing spectrum reuse in the unlicensed band. MassiveMIMO has recently emerged as one of the potential disruptivetechnologies for the 5G wireless systems, where cellular
MIMO BSUE UE UEWi-Fi devices b e a m b ea m nu ll nu ll Fig. 1. Illustration of a mMIMO-U system: Each BS multiplexes UEs in the unlicensed band while suppressing interference at neighboring Wi-Fi devices.
BSs are envisioned to be equipped with a large number ofantennas [18]–[22]. In this paper, we consider a downlinkmassive MIMO system operating in the unlicensed band. Werefer to this system as massive MIMO unlicensed (mMIMO-U). In the proposed system, a subset of the spatial degreesof freedom (d.o.f.) provided by the large number of antennasare employed to suppress the mutual interference betweeneach massive MIMO BS and the Wi-Fi devices operatingin its neighborhood. This allows massive MIMO BSs andWi-Fi devices to access unlicensed bands simultaneously,thus increasing the network spatial reuse. The remainingspatial d.o.f. are used by the massive MIMO BS to multiplexmultiple data streams.The present work is expected to advance the understandingof 5G cellular networks operating in the unlicensed spectrum,where newly deployed massive MIMO and existing Wi-Fisystems may coexist. On the basis of the key principles of bothtechnologies, we identify the rich research opportunities andtackle the fundamental challenges that arise when operatingmassive MIMO in the unlicensed band. Our contributions canbe summarized as follows. • Scheduling:
We discuss the operations required for amassive MIMO cellular BS to: (i) acquire channel stateinformation from the neighboring Wi-Fi devices, (ii) allo-cate spatial resources for Wi-Fi interference suppressionand user equipment (UE) multiplexing, and (iii) select asuitable set of UEs to be served in the unlicensed band. • Transmission:
We devise the key transmission operationsof a mMIMO-U system, including (i) an enhanced LBTphase, (ii) procedures for UE pilot request and channel es-timation, and (iii) precoder calculation. In all of the abovephases, the large number of BS antennas is exploited tosuppress interference to/from neighboring Wi-Fi devices,so that cellular/Wi-Fi coexistence is improved. • Performance:
We evaluate the performance of the pro-posed mMIMO-U operations in scenarios of practicalinterest. We show that mMIMO-U significantly reducesmutual interference between massive MIMO cellular BSand Wi-Fi devices, while multiplexing a number of datastreams. As a result, large cellular data rates can be achieved without significantly degrading the performanceof Wi-Fi networks deployed within the coverage area ofa massive MIMO cellular BS.
Notations:
Capital and lower-case bold letters denote matri-ces and vectors, respectively. The superscripts [ X ] ∗ , [ X ] T , and [ X ] H denote conjugate, transpose, and conjugate transpose,respectively. The notation b X denotes an approximation orestimate of X . The subspace spanned by the columns of X andits orthogonal subspace are denoted range { X } and null { X } ,respectively. Given a set X , card { X } denotes its cardinality.II. S YSTEM S ET -U P We now provide a general introduction to the networktopology and channel model used in this paper. More detailson the specific parameters used for our numerical studies willbe given in Section V.
A. Network Topology
We consider the downlink of a cellular network, as shownin Fig. 1, where massive MIMO cellular BSs are deployed tooperate in the unlicensed band in a synchronous manner, andcommunicate with their respective sets of connected cellularUEs, while multiple Wi-Fi devices, i.e., access points (APs)and stations (STAs), also operate in the same unlicensed band.It is important to note that even if cellular BSs may also haveaccess to a licensed band, this paper will focus on cellular BSoperations and transmissions in the unlicensed band.On the cellular side, we denote by I the sets of cellularBSs, and assume that all cellular BSs transmit with power P b .Cellular UEs associate to the cellular BS that provides thelargest average received power. Each BS i is equipped witha large number of antennas N , and it simultaneously serves K i of its associated UEs, K i ≤ N , on each time-frequencyresource block (RB) through spatial multiplexing. Each UEhas a single antenna. We denote K i the set of UEs served byBS i in the unlicensed band. It is important to note that whilethe total number of associated UEs is determined by the UEdensity and distribution as well as the nature of traffic, thevalue of K i can be chosen adaptively by BS i via schedulingoperations. ik [ m ] = p P b h H iik w ik s ik [ m ] + p P b X k ′ ∈ K i \ k h H iik w ik ′ s ik ′ [ m ] + p P b X i ′ ∈ I \ i X k ′ ∈ K i ′ h H i ′ ik w i ′ k ′ s i ′ k ′ [ m ]+ X ℓ ∈ L a p P ℓ q ℓik s ℓ [ m ]+ ǫ ik [ m ] (1) ν ik = P b | h H iik w ik | P b P k ′ ∈ K i \ k | h H iik w ik ′ | + P b P i ′ ∈ I \ i P k ′ ∈ K i ′ | h H i ′ ik w i ′ k ′ | + P ℓ ∈ L a P ℓ | q ℓik | + σ ǫ (2)On the Wi-Fi side, we denote by L AP , L STA , and L thesets of Wi-Fi APs, Wi-Fi stations, and all Wi-Fi devices,respectively, which are assumed to be invariant. Moreover,we denote by L a AP , L a STA , and L a the sets of active Wi-FiAPs, stations, and all Wi-Fi devices, respectively, which varyaccording to the Wi-Fi traffic profile [9], and assume that allWi-Fi devices ℓ transmit with power P ℓ . STAs associate tothe Wi-Fi AP that provides the largest average received power.Each AP is equipped with a single antenna, and serves oneSTA at the time. Each STA has a single antenna. B. Channel Model
All propagation channels are affected by slow fading(comprising antenna gain, path loss, and shadowing) andfast fading, as detailed in Section V. We adopt a block-fading propagation model, where the propagation channelsare assumed constant within their respective time/frequencycoherence intervals [23].Without loss of generality, and assuming a single antennafor all UEs and Wi-Fi devices, we define the followingvariables for a given time/frequency coherence interval: • h ijk = q ¯ h ijk ˜ h ijk ∈ C N × denotes the channel vectorbetween BS i and UE k in cell j ; • g iℓ = √ ¯ g iℓ ˜ g iℓ ∈ C N × denotes the channel vectorbetween BS i and Wi-Fi device ℓ ; • q ℓjk = √ ¯ q ℓjk ˜ q ℓjk ∈ C denotes the channel coefficientbetween Wi-Fi device ℓ and UE k in cell j .In the above, the coefficients ¯ h ijk ∈ R + , ¯ g iℓ ∈ R + , and ¯ q ℓjk ∈ R + represent the respective slow fading gains, whichare assumed constant. The coefficients ˜ h ijk ∈ C N × , ˜ g iℓ ∈ C N × , and ˜ q ℓjk ∈ C contain the respective fast fading, whichvaries at every time/frequency coherence interval.Without loss of generality, we also assume the same symbolduration for cellular and Wi-Fi transmissions. Thus, the signal y ik [ m ] ∈ C received by UE k in cell i at symbol interval m can be expressed as (1) at the top of this page, where (i) w ik ∈ C N × is the precoding vector from BS i to UE k incell i , (ii) s ik [ m ] ∈ C is the unit-variance signal intended forUE k in cell i , (iii) s ℓ [ m ] ∈ C is the unit-variance signaltransmitted by Wi-Fi device ℓ , and (iv) ǫ ik [ m ] ∼ CN (0 , σ ǫ ) is the thermal noise. The five terms on the right hand side of(1) respectively represent: useful signal, intra-cell interferencefrom the serving BS, inter-cell interference from other BSs,interference from Wi-Fi devices, and thermal noise.The resulting signal to interference plus noise ratio (SINR) ν ik at UE k in cell i is obtained via an expectation over allsymbols, and it is given by (2) at the top of this page. The corresponding interference power I : → ℓ [ m ] received atWi-Fi device ℓ due to cellular downlink operations is given by I : → ℓ [ m ] = P b X i ∈ I X k ∈ K i (cid:12)(cid:12) g H il w ik s ik [ m ] (cid:12)(cid:12) . (3)Each Wi-Fi device deems the channel as occupied and defersfrom transmission when the total received power, i.e., fromall cellular BSs and all other Wi-Fi devices, falls above theregulatory threshold γ LBT .III. M
ASSIVE
MIMO U
NLICENSED S CHEDULING
In this section, we discuss scheduling operations for theproposed mMIMO-U system. We first detail the necessaryprocedures for a BS to acquire channel state information (CSI)from the neighboring Wi-Fi devices. Then we discuss thespatial resource allocation, i.e., how to choose the number ofspatial d.o.f. to be allocated for Wi-Fi interference suppressionand for UE multiplexing, respectively. Finally, we devise a UEselection scheme for choosing the UEs to be served in theunlicensed band. The sequence of operations presented in thissection takes place at every Wi-Fi channel coherence interval,and is outlined in the three leftmost blocks of Fig. 2.
A. Wi-Fi Channel Covariance Estimation
In order to suppress interference to/from Wi-Fi devices, eachBS i requires information about the BS-to-Wi-Fi channels. Inour proposed mMIMO-U system, BS i periodically obtainsthe channel subspace occupied by neighboring Wi-Fi devicesthrough a channel covariance estimation procedure, presentedin the following.Throughout the channel covariance estimation procedure, allBSs remain silent, and thus each BS i receives the signal z i [ m ] = X ℓ ∈ L a p P ℓ g iℓ s ℓ [ m ] + η i [ m ] , (4)which consists of all transmissions from active Wi-Fi devicesand a noise term η i [ m ] ∼ CN ( , σ η I ) . Let us now denote by Z i ∈ C N × N the covariance of z i [ m ] ,which can be defined as Z i = E (cid:2) z i z H i (cid:3) , (5)where the expectation is taken with respect to L a , s , and η .Then, BS i can obtain an estimate b Z i of Z i via a simpleaverage over M c symbol intervals as [24] b Z i = 1 M c M c X m =1 z i [ m ] z H i [ m ] , (6) In the case of other cellular operators using the same unlicensed band, (4)would include their transmitted signals, and the mMIMO-U operations wouldensure coexistence with these operators as well as with Wi-Fi devices. i-Fi covariance estimation
BSs remain silent
Spatial resourceallocation i) Number of spatial nullsii) Number of scheduled UEs
Userselection EnhancedListen Before Talk(e-LBT) Request tosend pilots(RTSP)
Broadcast signalorthogonal to strongest Wi-Fi interfering directions
Pilot reception and CSI estimation
BS filters spatially with nulls towardsWi-Fi devices
Massive MIMO unlicensed transmission
BS maintains spatial filters towardsWi-Fi devices
Massive MIMO unlicensed scheduling
Precodeddata transmission
Spatial filtersto prevent interferencetowards Wi-Fi devices Selection of UEsto be served in theunlicensed band
Fig. 2. Flow chart of the proposed mMIMO-U procedures: Operations to the left (resp. right) are detailed in Section III (resp. Section IV). where the value of M c must be sufficiently large to ensurethat all neighboring Wi-Fi devices were active. Other possibleapproaches to channel covariance matrix estimation are dis-cussed in [25] and references therein. It is obvious that theoperation in (6) incurs an overhead, and an inherent trade-offexists between improving the quality of the estimate in (6) andreducing the overhead.Given the estimate b Z i , BS i applies a spectral decomposi-tion, obtaining b Z i = b U i b Λ i b U H i , (7)where the columns of b U i = [ b u i , . . . , b u iN ] form an orthonor-mal basis, and b Λ i = diag (cid:16)b λ i , . . . , b λ iN (cid:17) (8)contains a set of eigenvalues, such that b λ i ≥ b λ i . . . ≥ b λ iN .Then, with the proposed mMIMO-U operations, BS i canallocate a certain number of spatial d.o.f., denoted as D i , tosuppress interference to/from the dominant directions of theWi-Fi channel subspace. As it will be shown in Section V,a sufficiently large value of D i is required in order to ensurecoexistence. Note that a different unlicensed frequency channelcan be selected when the presence of a Wi-Fi device is detectedtoo close to the cellular BS.In order to allow such d.o.f. allocation procedure, let us nowdefine the matrix b Σ i , [ b u i , . . . , b u iD i ] , (9)whose columns contain the D i dominant eigenvectors of b Z i .For a sufficiently large D i , range { b Σ i } represents the channelsubspace on which BS i receives most of the Wi-Fi-transmittedpower. Since Wi-Fi uplink/downlink and BS downlink trans-missions share the same frequency band, channel reciprocityholds. Therefore, the power transmitted by BS i on range { b Σ i } represents the major source of interference for one or moreWi-Fi devices. B. Spatial Resource Allocation
From the Wi-Fi covariance estimate in (6), each BS per-forms spatial resource allocation. In particular, each BS cal-culates the number of UEs K i to spatially multiplex in theunlicensed band and the number of spatial d.o.f. D i to beallocated to suppress interference to/from neighboring Wi-Fidevices. To this end, a variety of criteria can be employed toselect the pair ( K i , D i ) , which must satisfy D i ≤ min { N − K i , M c } . (10) The inequality in (10) indicates that D i + K i should not exceedthe available spatial d.o.f. N at the BS, and that D i shouldbe upper bounded by the rank M c of b Z i defined in (6). Intuitively, the value of D i controls the number of excessd.o.f. used for interference suppression, and it is chosen bycompromising beamforming gain at the UEs for enhancedinterference suppression to/from Wi-Fi devices. For instance, D i could be set as the number of dominant eigenvectors of b Z i , i.e., those containing a given percentage of received Wi-Fisignal power. We refer the reader to [22] for a relevant studyon the choice of K i . C. UE Selection
Power emissions in the unlicensed band are strictly regu-lated. In some countries, the maximum allowed transmit powerdecreases with the number of antenna elements, if these areused to focus energy in a particular direction [27]. This meansthat the coverage area of mMIMO-U BSs may be limited, andonly UEs sufficiently close to the BS should be scheduled inthe unlicensed band. Moreover, when cellular BSs and Wi-Fi devices simultaneously operate in the unlicensed band, theWi-Fi-to-UE interference may degrade the cellular downlinkrates. Therefore, a mMIMO-U BS should select UEs that arenot in the proximity of a Wi-Fi device.In light of the above, and based on information availablefrom protocols currently implemented, we propose for each BS i to rank the associated cellular UEs according to the followingmetric µ ik = P b ¯ h iik P b P i ′ ∈ I \ i ¯ h i ′ ik + P ℓ ∈ L AP P ℓ ¯ q ℓik . (11)Intuitively, µ ik represents a measure of the average SINRreceived at UE k in cell i during a non-precoded broadcastsignal transmission. The metric in (11) accounts for theaverage channel gain between the UE and: the serving BS,other BSs, and Wi-Fi APs. In practical implementations, µ ik can be obtained via the two following steps. • An accurate estimation of ¯ h iik can be obtained at theUE through downlink measurements on the cell referencesignal (CRS), by subtracting the reference signal power(signaled by the BS) from the reference signal receivedpower (RSRP) [28], [29]. The fast fading component ˜ h iik is removed by filtering the measurements over a timewindow [30]. Applying the same procedure on the CRStransmitted by other BSs yields the terms ¯ h i ′ ik , i ′ ∈ I \ i . Note that for sparse communication channels, the number of availablespatial d.o.f. may be lower than the number of antennas N [26]. The value of ¯ q ℓik can be obtained through the automaticneighbor relations (ANR) function, where BS i requestsUE k to report Wi-Fi measurements that contain thereceived signal strength indicator (RSSI) from Wi-Fi AP ℓ [31]. Typically, few dominant terms ¯ q ℓik are sufficientto estimate µ ik , as the UE is unlikely to be close to amultitude of Wi-Fi APs at the same time.The above measurements can be fed back by the UE to theBS on a licensed control signaling interface [17]. The BS thenselects the K i UEs with the highest metric µ ik for transmissionin the unlicensed band. UEs that are not selected, e.g., becausethey are co-located with a WiFi device, may be scheduledfor transmission in the licensed band, or may wait to be re-scheduled when their channel conditions have varied, e.g.,because the UE or Wi-Fi are not transmitting or their positionshave changed.The advantage of using the proposed metric µ ik instead ofinstantaneous CSI for scheduling purposes lies in the fact that µ ik varies on a slow scale. Thus, feedback from the UEs doesnot need to be requested at every BS-UE channel coherenceinterval, and the resulting overhead is lower.IV. M ASSIVE
MIMO U
NLICENSED T RANSMISSION
The main operations we propose to perform at the mMIMO-U BSs for data transmission are: enhanced LBT, UE pilotrequest and channel estimation, and precoder calculation, asoutlined in the four rightmost blocks of Fig. 2. In all ofthe above operations, the large number of transmit antennasavailable at the BSs is exploited to suppress interferenceto/from neighboring Wi-Fi devices, so that both cellular BSsand Wi-Fi devices can simultaneously use the unlicensed band.
A. Enhanced Listen Before Talk
In order to comply with the regulations in the unlicensedband, each BS must perform LBT before any data transmis-sion [15]. In current coexistence approaches, such as LAA, atransmission opportunity is gained by BS i if the sum powerreceived from all devices using the same band falls below theregulatory threshold for a designated time interval, i.e., I i ← : [ m ] = k z i [ m ] k < γ LBT , m = 1 , . . . , M
LBT , (12)where z i [ m ] is given in (4), and the duration M LBT is given bya distributed inter-frame space (DIFS) interval plus a randomnumber of backoff time slots [9]. The process in (12) isalso known as energy detection. LBT may be sometimesconservative allowing for the transmission of either a singleBS or a Wi-Fi device within a certain coverage area, thuspreventing spatial reuse of the same unlicensed band.In the proposed mMIMO-U system, the LBT phase isenhanced as follows. When BS i listens to the transmissionscurrently taking place in the unlicensed band, it filters thereceived signal z i [ m ] with the D i spatial nulls defined in (9).Let us define the following matrices b Π i = b Σ i b Σ H i , (13)which projects a vector onto the subspace range { b Σ i } , and b Π ⊥ i = I − b Π i = I − b Σ i b Σ H i , (14) R T SP p i l o t R T SP n o p i l o t mMIMOBS UE Wi-FidevicesSIFSSIFS N AV
Fig. 3. A UE responds to RTSP messages with omnidirectional pilot signals,unless a network allocation vector message is received from a Wi-Fi device. which projects a vector onto null { b Σ i } . A transmission oppor-tunity is then gained by BS i if the condition I i ← : [ m ] = (cid:13)(cid:13)(cid:13) b Π ⊥ i z i [ m ] (cid:13)(cid:13)(cid:13) < γ LBT , m = 1 , . . . , M
LBT , (15)holds for M LBT symbols.In other words, since the channel subspace range { b Σ i } isoccupied by neighboring Wi-Fi devices, BS i may transmitdownlink signals on the channel subspace null { b Σ i } only, andit must ensure that no concurrent transmissions are detected on null { b Σ i } . This is accomplished by measuring the aggregatepower of the received signal filtered through the projection b Π ⊥ i . Provided that a sufficient number of d.o.f. D i have beenallocated for interference suppression, the condition in (15)is met. Therefore, unlike conventional LBT operations, theenhanced LBT (e-LBT) phase allows both mMIMO-U BSs andWi-Fi devices to simultaneously access the unlicensed band. B. UE Channel Estimation
Once the LBT procedure has succeeded, in order to spatiallymultiplex the K i selected UEs, BS i requires knowledge oftheir channels h iik , k ∈ K i . UE CSI may be obtained viapilot signals transmitted during a training phase at every BS-UE channel coherence interval, where coexistence betweenuplink pilots sent by UEs and Wi-Fi transmissions must beguaranteed. In the proposed UE channel estimation phase, BS i addresses the selected UEs with a request to send pilots(RTSP) message, as shown in Fig. 3. The RTSP message istransmitted on the subspace null { b Σ i } , such that interferencegenerated at neighboring Wi-Fi devices is suppressed. Theaddressed UEs respond by simultaneously transmitting backomnidirectional pilot signals after a short inter-frame space(SIFS) time interval [9]. Let the pilot signals span M p symbols on each coherenceinterval. The pilot transmitted by UE k in cell i is denoted UEs may receive RTSP messages superimposed with concurrent Wi-Fitransmissions. However, this is unlikely to occur thanks to the UE selectionmetric in (11), which tends to schedule UEs that are far from Wi-Fi APs. The UE selection metric in (11) also ensures that pilots do no createsignificant interference at Wi-Fi devices. Moreover, a UE may be informedof ongoing nearby Wi-Fi transmissions via network allocation vector (NAV)messages and thus decide to refrain from transmitting its pilot [9]. y v i ik ∈ C M p , where i ik is the index in the pilot codebook,and all pilots form an orthonormal basis [32], [33]. Each pilotsignal received at the BS suffers contamination due to pilotreuse across mMIMO-U cells and due to concurrent Wi-Fitransmissions. The collective received signal at BS i is denotedas Y i ∈ C N × M p and given by Y i = X j ∈ I X k ∈ K j p P jk h ijk v T i jk + X ℓ ∈ L a p P ℓ g iℓ s T ℓ + N i , (16)where s ℓ = [ s ℓ [1] , . . . , s ℓ [ M p ]] , N i contains additive noise atBS i during pilot signaling, and P jk is the power transmittedby UE k in cell j . We assume fractional uplink power controlas follows [34], [35] P jk = min (cid:8) P max , P · ¯ h αjjk (cid:9) , (17)where P max is the maximum UE transmit power, P is a cell-specific parameter, α is a path loss compensation factor, and ¯ h jjk is the slow fading measured at UE k in cell j based onthe RSRP [28], [29]. The aim of (17) is to compensate onlyfor a fraction α of the path loss, up to a limit imposed by P max .The received signal Y i in (16) is processed at BS i by (i) correlating it with the known pilot signal v i ik , and (ii) projecting it onto null { b Σ i } . The above operations respectivelyreject interference from (i) orthogonal pilots, and (ii) neigh-boring Wi-Fi transmissions. BS i thus obtains the followingCSI estimate for UE k in cell i [36] b h iik = b Π ⊥ i Y i v ∗ i ik = p P ik b Π ⊥ i h iik + b Π ⊥ i (cid:16) X j ∈ I \ i X k ∈ K j p P jk h ijk v T i jk + X ℓ ∈ L a p P ℓ g iℓ s T + N i (cid:17) v ∗ i ik (18)where intra-cell pilot contamination is not present since BS i allocates different pilots for different UEs in cell i . C. Precoder Calculation and Data Transmission
Thanks to the plurality of transmit antennas, BS i is ableto spatially multiplex K i UEs, while forcing D i nulls on thechannel subspace range { b Σ i } occupied by the neighboring Wi-Fi devices, as depicted in Fig. 1.Let us define the estimated fast-fading channel matrix b H i ∈ C N × K i as b H i = " b h ii ¯ h ii , . . . , b h iiK i ¯ h iiK i , (19)obtained at BS i normalizing the estimates b h iik in (18) by theslow fading channel component. Employing the normalizedestimates in the precoder generally guarantees uniform UEaverage power allocation. The precoding matrix W ik = [ w i , . . . , w iK i ] between BS i and its served UEs is thenobtained at every coherence interval as [37]–[39] W i = 1 √ ζ i b H i (cid:16) b H H i b H i (cid:17) − , (20)where the constant ζ i is chosen to normalize the averagetransmit power such that X k ∈ K i k w ik k = 1 . (21)The precoder in (20) employs the estimated channels obtainedin (18) via projection on null { b Σ i } , and thus forces D i nullson the channel subspace occupied by the neighboring Wi-Fi devices. We note that from a mathematical perspective,the projection onto null { b Σ i } is equivalent to employing avirtual array with N − D i antennas. Due to the projection on null { b Σ i } , the matrix b H i has rank at most min { K i , N − D i } .Therefore, the condition D i ≤ N − K i must hold for theinverse in (20) to exist. Such condition is guaranteed by theinequality in (10).The achievable rate at cellular UE k in cell i is given by R ik = A i · log (1 + ν ik ) (22)where the SINR ν ik is given by (2) using (20) as the precoder,the notation denotes the indicator function, and A i is theevent of successful e-LBT operation defined in (15). To avoidloss of generality by considering channel-specific parameters,in (22), we have omitted a multiplicative factor accounting forthe overhead incurred by Wi-Fi channel covariance estimation,UE CSI acquisition, and e-LBT. The expected cellular rate perBS ¯ R CELL is then obtained as ¯ R CELL = E (cid:2)P i ∈ I P k ∈ K i R ik (cid:3) card { I } (23)where the expectation is taken with respect to all channelrealizations and Wi-Fi traffic dynamics.V. N UMERICAL R ESULTS
In this section, we evaluate the performance of the proposedmMIMO-U operations. We perform system-level simulationsaccording to the scenario and methodologies described inTable I, unless otherwise specified. We first demonstrate thecoexistence enhancement provided by mMIMO-U with respectto a conventional approach without Wi-Fi interference rejec-tion. Then, we quantify the cellular data rates achievable inthe unlicensed band. We also reveal the effect of an imperfectWi-Fi channel covariance estimation. Finally, we discuss howthe mMIMO-U spatial resources should be allocated as atrade-off between Wi-Fi interference suppression and cellularbeamforming gain. Note that zero forcing (ZF) precoding as used above has been shown tooutperform maximum ratio transmission in terms of per-cell sum rate [22], andit can be extended to the case of multi-antenna UEs by considering block diag-onalization [37]. When the system dimensions make the ZF matrix inversionin (20) computationally expensive, a simpler truncated polynomial expansioncan be employed with similar performance [40]. Further improvements maybe achieved by regularizing the inversion in (20) [41]–[43], or via interferencealignment schemes [44]–[46].ABLE IS
IMULATION PARAMETERS
Parameter Description
Cellular layout Hexagonal with wrap-around, 19 sites,3 sectors each, 1 BS per sectorInter-site distance 500m [48]UEs distribution Random (P.P.P.), 32 UEs deployed per sectoron averageUE association Based on slow fading gainUE pilot allocation Random with reuse 1 ( M p = 8 )UE channel estimation Least-squares estimatorWi-Fi hotspots 2 outdoor hotspots per sector, radius: 20 m Wi-Fi devices 8 devices per hotspot: 1 AP and 7 STAsCarrier frequency 5.15 GHz (U-NII-1) [49]System bandwidth 20 MHz with 100 resource blocks [48], [49]Wi-Fi throughput 65 Mbps per cluster [9]LBT regulations Threshold γ LBT = − dBm [9]d.o.f. allocation K i = 8 and D i = 0 . N − K i ) BS precoder As in (20)BS antennas Downtilt: ◦ , height: m [48]BS antenna array Uniform linear, element spacing: d = 0 . λ BS antenna pattern Antennas with 3 dB beamwidth of ◦ and 8dBi max. [50]BS tx power 30 dBm [49]Wi-Fi tx power APs: 24 dBm, STAs: 18 dBm [27]UE tx power Fractional uplink power control with P = − dBm and α = 0 . [34]UE noise figure 9 dB [51]UE rx sensitivity -94 dBm [52]Fast fading Ricean, distance-dependent K factor [53]Lognormal shadowing BS to UE as per [48], UE to UE as per [54]Path loss 3GPP UMa [48] and 3GPP D2D [54]Thermal noise -174 dBm/Hz spectral density A. Enhanced Coexistence
Figures 4 and 5 show coexistence in the unlicensed bandfrom the perspective of Wi-Fi devices and cellular BSs,respectively, comparing the proposed mMIMO-U to a con-ventional approach, where no Wi-Fi interference suppressionis performed. The Wi-Fi channel covariance is computed via(5), and the behavior of both schemes is evaluated with anidentical number of BS antennas.Figure 4 shows coexistence in the unlicensed band from theperspective of Wi-Fi devices (both APs and STAs), assumingthat cellular BSs have gained access to the unlicensed medium.The figure shows the cumulative distribution function (CDF)of the aggregate interference received by a Wi-Fi device,obtained from (3). With mMIMO-U, Wi-Fi devices are ableto access the unlicensed band while BSs are transmitting.In fact, for N ≥ , the aggregate interference is alwaysbelow the regulatory threshold γ LBT = − dBm. On theother hand, with a conventional approach, Wi-Fi devices mightnot have access to the channel because the interference theyreceive is above γ LBT . Moreover, Fig. 4 shows that even whenbelow the threshold, the aggregate interference received witha conventional approach is 50% of the time above − dBm,which may affect the quality of Wi-Fi transmissions due to thenon-negligible interference generated [47]. This phenomenonis not observed with mMIMO-U, as long as a sufficient numberof antennas N is available. We consider outdoor Wi-Fi devices since this case involves no wallpenetration losses, making coexistence with cellular BSs more challenging. -100 -90 -80 -70 -60 -50 -40
Interference power at Wi-Fi devices [dBm] C D F N = 16 N = 32 N = 128 LBTmMIMO-U γ LBT
Fig. 4. Coexistence in the unlicensed band as seen by Wi-Fi devices. -90 -80 -70 -60 -50 -40 -30
Interference power at cellular BSs [dBm] C D F N = 16 N = 32 N = 128 LBTmMIMO-U γ LBT
Fig. 5. Coexistence in the unlicensed band as seen by cellular BSs.
Figure 5 evaluates coexistence from the cellular BSs’ stand-point, with mMIMO-U and with a conventional approach.It is assumed that Wi-Fi devices have gained access to theunlicensed medium, and the CDF of the interference receivedby cellular BSs is shown, obtained as the expectation of(15) with respect to the symbols. Cellular BSs implementingthe proposed mMIMO-U are generally able to access theunlicensed band, while Wi-Fi devices are transmitting. With N = 16 and N = 32 antennas, the aggregate interferencereceived by the BSs is and of the time belowthe threshold γ LBT , respectively. On the other hand, BSsthat perform conventional operations incur repeated backoffs,since their received interference is and of thetime above γ LBT , respectively. Increasing the value of N with the conventional approach yields a larger interference atthese BSs, because more aggregate power is received. Instead,the proposed mMIMO-U drastically reduces such interferencefor increasing N , since an increasing number of d.o.f. areallocated for interference suppression. Number of BS antennas, N Su m r a t e p e r s ec t o r [ M bp s ] Cellular rates (upper bound)Cellular rates (mMIMO-U)Wi-Fi rates (upper bound)Wi-Fi rates (mMIMO-U)
Fig. 6. Cellular and Wi-Fi data rates with proposed mMIMO-U versus numberof BS antennas. Upper bounds on both rates are also shown, obtained inthe ideal case of exclusive cellular and Wi-Fi use of the unlicensed band,respectively.
B. Achievable Data Rates
Figures 6 and 7 show the data rates per cellular sector,obtained as in (23). In Fig. 6, perfect knowledge of thechannel covariance in (5) is assumed, whereas Fig. 7 capturesthe effects of an imperfect covariance estimation. Moreover,note that Wi-Fi inter-cluster interference and collisions areneglected, Wi-Fi devices in a cluster are assumed active oneat a time, and all rates provided by Wi-Fi APs are assumedequal to 65 Mbps when they gain access to the channel [9]. Figure 6 shows four curves: (i) the Wi-Fi rates achiev-able with mMIMO-U; (ii) the cellular rates achievable withmMIMO-U; (iii) the Wi-Fi rates achievable when no cellulartransmissions take place; and (iv) the cellular rates achievablewhen no Wi-Fi transmissions take place. Note that (iii) and (iv) can be regarded as upper bounds for (i) and (ii) , respectively.The following observations can be made from Fig. 6. First,for N ≥ , the Wi-Fi rates achieved by mMIMO-U areconstant across all values of N and equal to the maximumvalue of 130 Mbps per sector. This reflects the fact that devicesfrom both Wi-Fi clusters in the sector can access the medium100% of the time, since the received interference is alwaysbelow γ LBT as shown in Fig. 4. Second, cellular rates withmMIMO-U are affected by the number of BS antennas N .For example, while 270 Mbps are achieved with N = 16 ,cellular rates above 600 Mbps and 800 Mbps can be obtainedby increasing N to 48 and 112, respectively. In fact, as shownin Fig. 4, a larger number of antennas also allows to suppressmore interference to/from Wi-Fi devices, while leaving morespatial d.o.f. to multiplex cellular UEs with a larger array gain.Third, as the number of antennas N grows, the gap betweenthe cellular rates and the upper bound does not vanish sinceit is also due to the Wi-Fi-to-UE interference. As discussed in Section VI, a more accurate characterization of Wi-Firates in the presence of mMIMO-U transmissions requires higher-layer trafficmodels, e.g., those accounting for medium access control (MAC) protocols.
Number of symbols, M c Su m r a t e s p e r s ec t o r [ M bp s ] -85-80-75-70-65-60-55 % - w o r s t i n t e rf e r e n ce a t W i - F i [ d B m ] Rates ( N = 64)Rates ( N = 128)Interference ( N = 64)Interference ( N = 128) Fig. 7. Cellular mMIMO-U rates and interference generated at Wi-Fi devicesversus number of symbols used for Wi-Fi covariance estimation.
Figure 7 draws the attention to two effects caused by inaccu-racies in the Wi-Fi channel covariance estimate: degradationof the cellular rates and increased interference generated atWi-Fi devices. To illustrate these phenomena, we show theachievable cellular rates and the 5th-percentile of I : → ℓ in(3), i.e., the 5%-worst interference received by Wi-Fi devicesduring mMIMO-U operations. Both quantities are plottedversus the number of Wi-Fi samples M c used to computethe estimate in (6). The figure shows that as the number ofsamples M c increases, the following occurs: the cellular ratesgrow, because the success rate of the e-LBT phase increases;and the interference at Wi-Fi devices diminishes, because theaccuracy of the nulls increases. The value of M c required toachieve large rates grows with N . Therefore, the Wi-Fi channelcoherence interval poses a physical limitation to the numberof BS antennas that can be effectively exploited [24]. C. Spatial Resource Allocation
Figures 8 and 9 illustrate the inherent trade-off between al-locating more spatial d.o.f. for Wi-Fi interference suppressionand employing them to augment cellular beamforming gain. Inthese figures, N = 64 BS antennas and K i = 8 selected UEsper sector are considered. The number of spatial d.o.f. D i al-located for Wi-Fi interference suppression is varied to observeits impact. Three scenarios are considered, corresponding toone, two, and four Wi-Fi clusters per sector, respectively, with8 Wi-Fi devices per cluster.Figure 8 shows the data rates per cellular sector as a functionof D i . Four observations are due: (i) as D i increases from lowvalues up to an optimal point, the rates increase because thee-LBT phase in (15) is more likely to be successful; (ii) as D i keeps increasing beyond the optimal value, the rates decreasebecause fewer d.o.f. are available for cellular beamforminggain; (iii) the optimal value of D i increases with the numberof Wi-Fi clusters per sector, because more nulls are requiredto suppress Wi-Fi interference; and (iv) more Wi-Fi clusterscorrespond to lower cellular rates, because a larger Wi-Fi-to-UE interference is received. Number of spatial nulls, D i Su m r a t e p e r s ec t o r [ M bp s ] Fig. 8. Cellular mMIMO-U rates versus number of spatial nulls D i in thepresence of one, two, and four Wi-Fi clusters per sector. Number of spatial nulls, D i -95-90-85-80-75-70-65 % - w o r s t i n t e r f e r e n ce a t W i - F i[ d B m ] Fig. 9. Cellular-to-Wi-Fi interference versus number of spatial nulls D i inthe presence of one, two, and four Wi-Fi clusters per sector. Figure 9 shows the 5%-worst interference received by Wi-Fidevices. Similar observations can be made: (i) as D i increasesfrom low values up to a worst point, interference increasesbecause more cellular BSs activate after successful e-LBT, thusmore transmissions are generated; (ii) as D i keeps increasingbeyond the worst value, the interference decreases becausemore d.o.f. are employed to suppress it; (iii) the optimal valueof D i increases with the number of Wi-Fi clusters per sector,because more nulls should be employed to suppress Wi-Fiinterference; and (iv) for a given D i , more Wi-Fi clusterscorrespond to larger interference, because Wi-Fi devices tendto occupy more spatial dimensions, out of which only D i canbe nulled. VI. C ONCLUSION
A. Summary of Results
We considered a mMIMO-U network, where massiveMIMO cellular BSs and Wi-Fi devices operate in the same unlicensed band. We designed the main mMIMO-U schedulingand transmission operations to be performed at the BSs to en-hance cellular/Wi-Fi coexistence. The scheduling procedurescan be executed in a distributed fashion and include acquiringchannel state information from the neighboring Wi-Fi devices,allocating spatial resources for Wi-Fi interference suppressionand UE multiplexing, and selecting a suitable set of UEsto be served in the unlicensed band. For the transmissionphase, we proposed to perform enhanced listen before talk,followed by UE pilot request, UE channel estimation, andprecoder calculation. All along the mMIMO-U operations,the large number of BS antennas is exploited to suppressinterference to/from neighboring Wi-Fi devices. As a result,Wi-Fi devices may access the unlicensed band as though nocellular transmissions were taking place, and vice versa. Thisenhances spatial reuse.We evaluated the performance of mMIMO-U through simu-lations. Our results demonstrated the coexistence enhancementprovided by mMIMO-U with respect to a conventional LAA-like approach. In fact, provided that cellular BSs are equippedwith a sufficient number of antennas, mMIMO-U ensuresthat the mutual interference between cellular BSs and Wi-Fidevices falls below the regulatory threshold. We showed thatlarge cellular data rates can be achieved without significantlydegrading the performance of Wi-Fi networks deployed withinthe coverage area of a cellular BS. We finally discussed howthe spatial resources made available by mMIMO-U should beallocated by compromising Wi-Fi interference suppression forcellular beamforming gain.
B. Future Work and Discussion
This work is suitable for several extensions from the systemmodel, design, and deployment perspectives: • Model:
Accurate traffic models are desirable for Wi-Fidevices and multiple operators sharing the same unli-censed band to evaluate how well BSs can estimate thechannel covariance in (5). The rate computation at Wi-Fi devices should also account for these traffic models,since even when the received interference falls below theregulatory threshold, it may still affect the data rates [47]. • Design:
While in the current paper we focused on cellulardownlink, appropriate procedures for mMIMO-U uplinkshould be defined. Coexistence between UE-to-BS trans-missions and Wi-Fi transmissions must be guaranteed.One possible way to accomplish this would be to haveBSs obtain access to the medium, and reserve it for theirUEs to send uplink data in a synchronous manner. • Deployment:
An alternative strategy to the mMIMO-U scenario considered in this paper could consist ofa more dense deployment of smaller low-power BSs,equipped with fewer antennas, covering smaller areas,and thus having to coexist with fewer Wi-Fi devices. Suchdeployment could allow, e.g., enterprise owners to roll-out high-performing indoor coverage without purchasinglicensed spectrum from mobile network operators.A final remark is due on emission regulations in unlicensedbands. Currently, in some countries, the maximum transmitower must be reduced for an increasing number of antennas,if the corresponding d.o.f. are used to focus energy in aparticular direction [27]. The scheme considered in this paperemploys a large number of d.o.f. for UE multiplexing andWi-Fi interference suppression, which led us not to accountfor the above guidance. Indeed, we expect future regulationsto contemplate this aspect and consider adjustments to theguidance. A
CKNOWLEDGMENT
The authors would like to thank Dr. Thomas L. Marzettafor his insightful comments.R
EFERENCES[1] G. Geraci, A. Garcia Rodriguez, D. L´opez-P´erez, A. Bonfante, L. GalatiGiordano, and H. Claussen, “Enhancing coexistence in the unlicensedband with massive MIMO,” in
Proc. IEEE Int. Conf. on Comm. (ICC) ,May 2017, accepted for publication.[2] 3GPP RP-131723, “Discussion paper on unlicensed spectrum integrationto IMT systems,” Dec. 2013.[3] Qualcomm News, “Introducing MulteFire: LTE-like performance withWi-Fi-like simplicity,” June 2015.[4] Nokia Executive Summary, “The MulteFire opportunity for unlicensedspectrum,” 2015.[5] R. Zhang, M. Wang, L. X. Cai, Z. Zheng, X. Shen, and L. L. Xie, “LTE-unlicensed: The future of spectrum aggregation for cellular networks,”
IEEE Wireless Communications , vol. 22, no. 3, pp. 150–159, June 2015.[6] H. Zhang, X. Chu, W. Guo, and S. Wang, “Coexistence of Wi-Fi andheterogeneous small cell networks sharing unlicensed spectrum,”
IEEEComms. Mag. , vol. 53, no. 3, pp. 158–164, Mar. 2015.[7] A. Mukherjee, J. F. Cheng, S. Falahati, L. Falconetti, A. Furusk¨ar,B. Godana, D. H. Kang, H. Koorapaty, D. Larsson, and Y. Yang, “Systemarchitecture and coexistence evaluation of licensed-assisted access LTEwith IEEE 802.11,” in
Proc. IEEE Int. Conf. on Comm. Workshop(ICCW) , June 2015, pp. 2350–2355.[8] M. Bennis, M. Simsek, A. Czylwik, W. Saad, S. Valentin, and M. Deb-bah, “When cellular meets WiFi in wireless small cell networks,”
IEEECommun. Mag. , vol. 51, no. 6, pp. 44–50, June 2013.[9] E. Perahia and R. Stacey,
Next Generation Wireless LANs: 802.11n and802.11ac . Cambridge University Press, June 2013.[10] LTE-U Forum, “Coexistence study for LTE-U SDL V1.0,”
LTE-UTechnical Report , Feb. 2015.[11] M. I. Rahman, A. Behravant, H. Koorapaty, J. Sachs, and K. Bal-achandran, “License-exempt LTE systems for secondary spectrum usage:Scenarios and first assessment,” in
Proc. IEEE Sym. New Frontiers inDynamic Spectrum Access Networks (DySPAN) , May 2011, pp. 349–358.[12] Qualcomm Research, “LTE in unlicensed spectrum: Harmonious coex-istence with Wi-Fi,” June 2014.[13] 3GPP Technical Report 36.889, “Feasibility study on licensed-assistedaccess to unlicensed spectrum (Release 13),” Jan. 2015.[14] R. Ratasuk, N. Mangalvedhe, and A. Ghosh, “LTE in unlicensed spec-trum using licensed-assisted access,” in
Proc. IEEE Global Telecomm.Conf. Workshops , Dec. 2014, pp. 746–751.[15] 3GPP RP-140808, “Review of regulatory requirements for unlicensedspectrum,” June 2014.[16] Nokia, “Nokia LTE for unlicensed spectrum,” white paper , June 2014.[17] C. Cano, D. Lopez-Perez, H. Claussen, and D. J. Leith, “Using LTEin unlicensed bands: Potential benefits and co-existence issues,”
IEEECommun. Mag. , vol. 54, no. 12, pp. 116–123, Dec. 2016.[18] T. L. Marzetta, “Noncooperative cellular wireless with unlimited num-bers of base station antennas,”
IEEE Trans. Wireless Commun. , vol. 9,no. 11, pp. 3590–3600, Nov. 2010.[19] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta,O. Edfors, and F. Tufvesson, “Scaling up MIMO: Opportunities andchallenges with very large arrays,”
IEEE Signal Process. Mag. , vol. 30,no. 1, pp. 40–60, Oct. 2013.[20] L. Lu, G. Y. Li, A. L. Swindlehurst, A. Ashikhmin, and R. Zhang,“An overview of massive MIMO: Benefits and challenges,”
IEEE J. Sel.Topics Signal Process. , vol. 8, no. 5, pp. 742–758, Oct. 2014. [21] E. G. Larsson, O. Edfors, F. Tufvesson, and T. L. Marzetta, “MassiveMIMO for next generation wireless systems,”
IEEE Commun. Mag. ,vol. 52, no. 2, pp. 186–195, Feb. 2014.[22] E. Bj¨ornson, E. G. Larsson, and M. Debbah, “Massive MIMO formaximal spectral efficiency: How many users and pilots should beallocated?”
IEEE Trans. Wireless Commun. , vol. 15, no. 2, pp. 1293–1308, Feb. 2016.[23] M. Medard and D. N. C. Tse, “Spreading in block-fading channels,” in
Proc. Asilomar Conf. on Signals, Systems, and Computers , vol. 2, Oct.2000, pp. 1598–1602.[24] J. Hoydis, K. Hosseini, S. T. Brink, and M. Debbah, “Making smart useof excess antennas: Massive MIMO, small cells, and TDD,”
Bell LabsTech. J. , vol. 18, no. 2, pp. 5–21, Sept. 2013.[25] E. Bj¨ornson, L. Sanguinetti, and M. Debbah, “Massive MIMO withimperfect channel covariance information,” in
Proc. Asilomar Conf. onSignals, Systems, and Computers , Nov. 2016, to appear. Available as:https://arxiv.org/pdf/1612.04128.pdf.[26] D.-S. Shiu, G. J. Foschini, M. J. Gans, and J. M. Kahn, “Fadingcorrelation and its effect on the capacity of multielement antennasystems,”
IEEE Trans. Commun. , vol. 48, no. 3, pp. 502–513, Mar. 2000.[27] FCC 662911, “Emissions testing of transmitters with multiple outputsin the same band,” Oct. 2013.[28] 3GPP Technical Specification 36.201, “LTE; Evolved universal terres-trial radio access (E-UTRA); LTE physical layer (Release 10),” June2011.[29] 3GPP Technical Specification 36.213, “LTE; Evolved universal terres-trial radio access (E-UTRA); Physical layer procedures (Release 10),”June 2011.[30] J. Zhang, P. Soldati, Y. Liang, L. Zhang, and K. Chen, “Pathlossdetermination of uplink power control for UL CoMP in heterogeneousnetwork,” in
Proc. IEEE Global Telecomm. Conf. Workshops , Dec. 2012,pp. 250–254.[31] 3GPP Technical Report 36.300, “Evolved universal terrestrial radioaccess (E-UTRA) and evolved universal terrestrial radio access network(E-UTRAN); Overall description (Release 14),” Sept. 2016.[32] J. Jose, A. Ashikhmin, T. L. Marzetta, and S. Vishwanath, “Pilotcontamination and precoding in multi-cell TDD systems,”
IEEE Trans.Wireless Commun. , vol. 10, no. 8, pp. 2640–2651, Aug. 2011.[33] H. Q. Ngo, E. G. Larsson, and T. L. Marzetta, “The multicell multiuserMIMO uplink with very large antenna arrays and a finite-dimensionalchannel,”
IEEE Trans. Commun. , vol. 61, no. 6, pp. 2350–2361, June2013.[34] C. U. Castellanos, D. L. Villa, C. Rosa, K. I. Pedersen, F. D. Calabrese,P. H. Michaelsen, and J. Michel, “Performance of uplink fractionalpower control in UTRAN LTE,” in
Proc. IEEE Veh. Tech. Conference(VTC) , May 2008, pp. 2517–2521.[35] R1-073224, “Way forward on power control of PUSCH,” in , June 2007.[36] M. Kay,
Fundamentals of Statistical Signal Processing: Detection The-ory , P. H. PTR, Ed., 1998.[37] Q. H. Spencer, A. L. Swindlehurst, and M. Haardt, “Zero-forcing meth-ods for downlink spatial multiplexing in multiuser MIMO channels,”
IEEE Trans. Signal Process. , vol. 52, no. 2, pp. 461–471, Feb. 2004.[38] G. Geraci, R. Couillet, J. Yuan, M. Debbah, and I. B. Collings, “Largesystem analysis of linear precoding in MISO broadcast channels withconfidential messages,”
IEEE J. Sel. Areas Commun. , vol. 31, no. 9, pp.1660–1671, Sept. 2013.[39] H. H. Yang, G. Geraci, T. Q. S. Quek, and J. G. Andrews, “Cell-edge-aware precoding for downlink massive MIMO cellular net-works,” submitted to
IEEE Trans. Signal Process. , 2016, available asarXiv:1607.01896.[40] A. Kammoun, A. M¨uller, E. Bj¨ornson, and M. Debbah, “Linear pre-coding based on polynomial expansion: Large-scale multi-cell MIMOsystems,”
IEEE J. Sel. Topics Signal Process. , vol. 8, no. 5, pp. 861–875,Jan. 2014.[41] C. B. Peel, B. M. Hochwald, and A. L. Swindlehurst, “A vector-perturbation technique for near-capacity multiantenna multiuser com-munication - Part I: Channel inversion and regularization,”
IEEE Trans.Commun. , vol. 53, no. 1, pp. 195–202, Jan. 2005.[42] G. Geraci, M. Egan, J. Yuan, A. Razi, and I. B. Collings, “Secrecy sum-rates for multi-user MIMO regularized channel inversion precoding,”
IEEE Trans. Commun. , vol. 60, no. 11, pp. 3472–3482, Nov. 2012.[43] H. Tataria, P. J. Smith, L. J. Greenstein, P. A. Dmochowski, and M. Shafi,“Performance and analysis of downlink multiuser MIMO systems withregularized zero-forcing precoding in Ricean fading channels,” in
Proc.IEEE Int. Conf. on Comm. (ICC) , May 2016, pp. 1–7.44] V. R. Cadambe and S. A. Jafar, “Interference alignment and degrees offreedom of the K-user interference channel,”
IEEE Trans. Inf. Theory ,vol. 54, no. 8, pp. 3425–3441, Aug. 2008.[45] C. Suh, M. Ho, and D. N. C. Tse, “Downlink interference alignment,”
IEEE Trans. Commun. , vol. 59, no. 9, pp. 2616–2626, Sept. 2011.[46] R. F. Ustok, M. Shafi, P. A. Dmochowski, and P. J. Smith, “Interferencealignment with combined receivers for heterogeneous networks,” in
Proc. IEEE Int. Conf. on Comm. (ICC) , June 2014, pp. 5287–5292.[47] N. Jindal and D. Breslin, “LTE and Wi-Fi in unlicensed spectrum: Acoexistence study,”