Beam Alignment for the Cell-Free
mmWave Massive MU-MIMO Uplink
Jannik Brun, Victoria Palhares, Gian Marti, and Christoph Studer

arXiv:2207.09879v1 [cs.IT] 20 Jul 2022

Department of Information Technology and Electrical Engineering, ETH Zurich, Zurich, Switzerlande-mail: brunj@student.ethz.ch, vmenescal@ethz.ch, gimarti@ethz.ch, and studer@ethz.ch

Abstract—Millimeter-wave (mmWave) cell-free massive multiuser (MU) multiple-input multiple-output (MIMO) systems combine the large bandwidths available at mmWave frequencies with
the improved coverage of cell-free systems. However, to combat
the high path loss at mmWave frequencies, user equipments (UEs)must form beams in meaningful directions, i.e., to a nearby accesspoint (AP). At the same time, multiple UEs should avoid transmitting to the same AP to reduce MU interference. We propose
an interference-aware method for beam alignment (BA) in thecell-free mmWave massive MU-MIMO uplink. In the consideredscenario, the APs perform full digital receive beamforming while
the UEs perform analog transmit beamforming. We evaluate ourmethod using realistic mmWave channels from a commercial
ray-tracer, showing the superiority of the proposed method overomnidirectional transmission as well as over methods that do nottake MU interference into account.

direction in which a UE should transmit is exacerbated by thefact that multiple UEs should avoid transmitting to the same(few-antenna) AP to mitigate multi-user (MU) interference.
A. Contributions

We consider the problem of beam alignment (BA) in the
uplink of cell-free mmWave massive MU-MIMO systems.
In the considered scenario, the UEs are able to perform
analog beamforming and the APs of the cell-free system areable to perform digital beamforming. In contrast to what iscustomary in the cell-free literature, we do not assume that the
number of APs is much larger than the number of UEs served[17], as such an assumption depends on a high pervasiveness ofwireless infrastructure. We propose a multi-user interferenceI. I NTRODUCTION
aware method for BA in the uplink of cell-free mmWave
Millimeter-wave (mmWave) cell-free massive multi-user massive MU-MIMO. The proposed method is complemented(MU) multiple-input multiple-output (MIMO) is expected to with an efficient block-sparse channel estimation (CHEST)
be a key to reliable high-throughput wireless connectivity: method and a centralized linear minimum mean square error
mmWave frequencies provide large portions of contiguous band- (LMMSE) data detector. The resulting scheme is evaluatedwidth [1] and cell-free systems promise improved coverage even using realistic mmWave channels from a commercial ray-tracer
under the notoriously challenging propagation characteristics [18], and with realistic transmit powers and noise figures. Ourat mmWave frequencies [2]. However, these advantages come results show that omnidirectional transmission at the UEs leads
at the prize of formidable engineering challenges. mmWave to inferior performance compared to the proposed scheme.
communication has thus been an active research topic for a In ablation studies we show that the limited capabilities ofnumber of years [1], [3], [4] and recently found its way into the UEs compared to fully digital beamforming seem to becommercial products [5]. While cell-free massive MU-MIMO of little importance, whereas the interference-awareness of
has also been an area of active research [6]–[8], the bulk of the BA algorithm contributes significantly to performance.
studies has been devoted to sub-6-GHz communication and These findings suggest that the problem of BA in dense celltypically assumes single-antenna transceivers both for the user free mmWave networks should be considered from a global
equipments (UEs) as well as for the access points (APs) [6]–[8]. perspective while the precise radio-frequency (RF) architecture
Even in the mmWave cell-free literature, the UEs are often of the UEs is comparably less important.
assumed to have a single antenna only [9]–[14], or, if they
B. Relevant Prior Art
have multiple antennas, they do not perform any kind of
Although there exists a substantial amount of literature
beamforming with these [2], [15] (with the exception of [16]).
However, the high path loss at mmWave frequencies is expected on cell-free systems with mmWave frequencies [2], [9]–[16],to require UE-side beamforming even in cell-free systems: most of these works do either not consider beamforming at
Rather than aimlessly transmitting the uplink signal in all all [9], or they consider beamforming only at the APs [2],directions, a UE should form a beam that is aligned to a [10]–[15]. References [11]–[14] consider APs with different
nearby AP. The challenge of determining the optimal beam variants of hybrid beamforming and single-antenna UEs, while[10] considers APs with analog beamforming and singleThe work of VP, GM, and CS was supported in part by an ETH Researchantenna UEs. References [2], [15] assume APs with hybrid
Grant. The work of CS was supported in part by ComSenTer, one of six centers
in JUMP, a SRC program sponsored by DARPA. The work of CS was supported beamforming and multi-antenna UEs, but the UEs do not use
in part by the U.S. NSF under grants CNS-1717559 and ECCS-1824379.
beamforming (the multiple antennas are only used for increased

RF
DSP

+

...

UE

AP
sub-6-GHz
controlchannel

CPU

RF

...

array gain). To our knowledge, the only existing work thatconsiders the problem of beamforming or beam alignment on
the UE side is [16], which proposes a scheme in which the UEs
simultaneously estimate the direction of arrival (and departure)of the strongest beam. This paper also devises an algorithm
that partitions the APs into sets to minimize the interference
between APs which use non-orthogonal transmit patterns.
In stark contrast with previous work, we propose aninterference-aware UE BA method for the uplink of cellfree mmWave massive MU-MIMO systems, and taking into
account multi-antenna APs and UEs. Unlike other works, weconsider a scenario in which there are more UEs than APs
in the same time-frequency resource, which is of practicalimportance. Additionally, in opposition to the largely assumed
hybrid architectures, we study the situation where UEs rely on
analog beamforming and APs are fully digital [19].

CPU

RF

C. Notation
Fig. 1. Visualization of the considered cell-free scenario. The UEs use a
Upper case and lower case bold symbols denote matrices and single RF chain to load the antennas via phase shifters. The APs are fully
vectors, respectively. The N ×N identity matrix is given by IN . digital [19].
AT and AH are the transpose and conjugate transpose of A,
respectively; and Al,k is the matrix in the lth row block andnAP ×nUE
is the channel matrix from the `th AP
kth column block of the matrix A. diag(a1 , . . . , aN ) is a block- where H`,k ∈ C
to
the
kth
UE.
We
will
also use Hk = [HT1,k , . . . , HTL,k ]T ∈diagonal matrix whose diagonal blocks are a1 , . . . , aN . The
NR ×nUEto denote the kth column block of H. Any efEuclidean and Frobenius norms are k·k and k·kF , respectively. C
fects of power control are absorbed into the channel matrix.
II. S YSTEM M ODELThe UE beamforming matrix P is block-diagonal, P =We consider the uplink of a cell-free mmWave massive MU- diag(p1 , . . . , pK ), with diagonal blocks pk ∈ CnUE , k =MIMO system with L locally distributed access points (APs) 1, . . . , K. The block-diagonal structure reflects the fact thatthat are connected to a central processing unit (CPU) and jointly the UEs cannot transmit cooperatively. We assume UEs with aserve K UEs, see Fig. 1. Such a scenario could correspond single RF chain and analog phase shifters, so that the codebook
for instance to a shopping mall or a university campus. The of possible beams is
APs and UEs each have nAP and nUE antennas respectively,nso that the total number of receive and transmit antennas is P = p(φb ) = √ 1 [1, e−jπ cos φb , . . . , e−jπ cos φb (nUE −1) ]T ,nUE
NR = LnAP and NT = KnUE , respectively. The UEs aren π
B − 1 ooassumed to have a single radio-frequency (RF) chain and thusφb ∈ 0, , . . . ,π ,(3)rely on analog beamforming; the APs are assumed to be fullyBB
digital, i.e., every antenna is connected to its own RF chain.1
We assume a frequency-selective mmWave channel which is where |P| = B is the codebook size. Note that, since we use
divided into nsc frequency-flat subcarriers using orthogonal analog beamforming, the beamforming matrix P is identicalfrequency-division multiplexing (OFDM). The per-subcarrier for all subcarriers.
As in [16], we assume the existence of a sub-6-GHz control
input-output relation between all UEs and APs is expressed aschannel which can be used for control signaling from the CPU
y = HPs + n,(1) to the UEs. However, compared to [16], our scheme requires
where we omit the subcarrier index for ease of notation. Here, significantly less control signaling overhead: It only requiresy ∈ CNR is the receive vector, H ∈ CNR ×NT is the channel the CPU to communicate to each UE the codebook index of its
matrix, P ∈ CNT ×K is the UE beamforming matrix, s ∈ CK is selected beam, and requires no control signals from the UEs.
the vector of UE transmit symbols with per-symbol energy Es ,and n ∈ CNR is i.i.d. circularly-symmetric complex Gaussian
noise with variance N0 per complex entry. The channel matrix
has the following block structure,H1,1 · · · H1,K..  ,
H =  ...
(2)
. 
HL,1

···

HL,K

1 This is not unrealistic since the APs consist of only few (e.g., four) antennas.

A. Communication Scheme
Multi-user interference-aware BA requires knowledge of thechannel matrix in (2) or some surrogate thereof. Knowledgeof the channel matrix in wireless systems is typically acquired
through the transmission of pilots, which leads to a chicken-oregg problem: On one hand, if the UEs transmit pilot symbols
without using appropriate beamforming vectors, the APs will
only pick up a very weak signal which does not allow reliable

CHEST.2 On the other hand, some knowledge of the channel
matrix is necessary for the UEs to select appropriate beams.
We solve this conundrum using a two-stage scheme: In thefirst stage, the UEs transmit non-orthogonal pilots in different
directions to ensure sufficient receive signal strength for at least
some of the directions. Based on these pilots, the CPU thenperforms a coarse estimate of the channel matrix which it thenuses for BA. Note that this estimate of the channel matrix only
needs to be accurate enough to determine the angles of strong
receptivity. In the second stage, the UEs fix their beamformers
to the selected beams, which are communicated to them via
the available sub-6-GHz control channel. The UEs transmit
orthogonal pilot sequences used by the CPU to perform ahigh-quality estimate of the compound of the channel matrix
and the beamforming matrix HP. This estimate is then used
for data detection, which in this paper we do using centralized
LMMSE equalization ŝ = WH y with

−1
N0
.
(4)
W = HP (HP)H HP +IK
Es
Many other detection methods, including decentralized ones,
would of course be possible and are left for future work.
We will now first describe the BA procedure before explaining the pre-beam-alignment (pre-BA) and post-beam-alignment(post-BA) CHEST steps that precede and follow it, respectively.
III. B EAM A LIGNMENT
As stated in Section II-A, BA requires knowledge of thechannel matrix (or some suitable surrogate thereof). It is
important to remember that here we consider frequencyselective mmWave channels that can be divided into frequencyflat subcarriers. Ideally, BA would be applied to each of thesubcarriers independently. However, since the UEs use analog
beamforming, they can only form a single beam, which isthen used for all subcarriers. We therefore perform BA basedon the strongest subcarrier channel matrices per UE and AP,
i.e., based on a surrogate matrix H̄ ∈ CNR ×NT consisting of2
the blocks H̄`,k = arg maxv=1,...,nsc Hv`,k F , where v is thesubcarrier index.
Even when using such a frequency-flat surrogate, optimal BA
is typically not practical for common optimization objectives
such as achievable sum-rate or max-min achievable rate since it
requires the optimization over a combinatorial set. For instance,
for max-min achievable rate optimal BA, we would be required
to solve the following optimization problem:max(p1 ,...,pK )∈P K

mink=1,...,K

SINRk (p1 , . . . , pK ),(5)

where SINRk (p1 , . . . , pK ) is the post-equalization signal-tointerference-plus-noise ratio (SINR) of the kth UE given the
beamforming vectors p1 , . . . , pK :SINRk (p1 , . . . , pK ) = P|wkH Hk pk |2

2,
H
0
0 2
k0 6=k |wk Hk pk | + N0 kwk k2(6)

with wk being the kth column of (4). Solving this optimization
problem through an exhaustive search for K = 32 UEs anda codebook size of B = 16 would amount to B K ≈ 1038
evaluations of the objective in (6). Clearly, this is not feasible
in practice. We therefore now outline some more practicalmethods for BA.
A. Interference-Unaware Digital Beam Alignment
We start by discussing the well-known eigenbeamforming
method [20], which in our case is not applicable because
it would require digital beamforming, but which we will
later use as an evaluation baseline. If multi-user interference
were negligible (and the UEs could perform full digital
beamforming), one could simply optimize the (pre-equalization)
signal-to-noise ratio (SNR) for every user, by solving
Es kHk pk2
s.t. kpk = 1, k = 1, . . . , K,
(7)
p
NR N0
which yields the leading (= belonging to the largest singularvalue) right-singular vector of the per-UE channel matrix Hk .
max

B. Interference-Unaware Analog Beam Alignment
In the considered scenario, the UEs can only form beams
from the finite set (3) and so in general will be unable tobeamform the leading right-singular vector of Hk . However,
if multi-user interference is negligible or ignored, we canstill solve (7) to maximize the (pre-equalization) SNR for
every UE, except that we now optimize over the codebook of
possible beams P instead of the set {p : kpk = 1}. Since thisoptimization problem can be solved individually per UE, we
can solve it using an exhaustive search over KB possibilities.
C. Interference-Aware Analog Beam Alignment
As we will see in the Section V, ignoring MU interference
results in suboptimal performance. For this reason, our proposed
BA algorithm takes MU interference into account. We havealready seen that maximizing joint optimization objectives,
such as max-min-optimal achievable rate is impractical. For
this reason, we use an algorithm in which the UEs greedily
optimize their individual post-equalization SINR, given thecurrently selected beams of the other UEs. Such an algorithm
can be succinctly motivated by a German idiom:3 “Wheneveryone thinks of themselves, everyone is taken care of.” Themethod operates as follows: First, we perform a singular value
decomposition (SVD) for each per-UE channel matrix Hk ,k = 1, . . . , K. We then sort the UEs in descending orderaccording to the largest singular value σk of their per-UE
channel matrix Hk . Assume now that the UEs are orderedin this way, i.e., σk > σi for i > k. Starting from an empty
set of UEs, we then iteratively select the beam for the kth
UE which maximizes the post-equalization SINR, where theinterference-term only takes into account the interference of
those UEs whose beams have already been selected:
pk = arg max Pp̃k

2 Because of channel reciprocity, the same would also hold if the pilots weretransmitted by the APs instead of the UEs.

|vkH Hk p̃k |2

2,
H
0
0 2
k0 <k |vk Hk pk | + N0 kvk k2

3 “Wenn jeder an sich denkt, ist an alle gedacht.”(8)

for k = 1, . . . , K. In (8), vk is the kth column of the LMMSE
equalization matrix as in (4), but restricted to only the first kUEs, i.e., to those UEs whose beam has already been selected
or is currently being selected. This means that vk is a functionof p1 , . . . , pk−1 and p̃k , as well as H1 , . . . , Hk .
Then, in a second round, we use a coordinate descentapproach where every UE has the chance to re-adjust its beams
to adapt to the beams of the UEs that were selected later bytaking into account the interference of all UEs according totheir curently selected beams. This round iterates in reverse
order, k = K, . . . , 1,
|vkH Hk p̃k |2
2,
H
0
0 2
k0 6=k |vk Hk pk | + N0 kvk k2

pk = arg max P
p̃k

(9)

where vk now denotes the kth column of the LMMSE
equalization matrix (4) considering all UEs, i.e., vk is now afunction of p1 , . . . , p̃k , . . . , pK , as well as H1 , . . . , HK .
IV. C HANNEL E STIMATION
The previous section on BA assumed that the channel matrix
H is known for every subcarrier. We now describe our proposed
method to estimate the channel with sufficient accuracy for the
BA procedure.
A. Pre-Beam-Alignment Channel Estimation (Pre-BA CHEST)
To perform BA based on the strongest subcarrier, we would
in principle have to estimate the channel matrix for every
subcarrier individually. However, to keep complexity at bay, andsince large-scale fading properties do not change dramaticallybetween adjacent subcarriers, we only estimate the channel
matrix for a subset of subcarriers which are spaced uniformly
over the total number of used subcarriers.
We now describe the CHEST in per-subcarrier fashion, where
we again omit the subcarrier index for brevity. We estimate
the channel matrix at the APs using pilot signals transmitted
at the UEs for npilot time slots, i.e., we observe
Y = HB + N,

(10)

B can become very tall, which results in degenerate estimatesof the channel matrix H. Conversely, if only one UE at atime transmits its pilot beams, CHEST is much easier but thescheme becomes time consuming, with npilot = BK time slots.
To develop a scheme which is both sufficiently accurate
and efficient, we use a clustering scheme, where the K UEs
are randomly clustered into C equisized clusters: All UEs
belonging to the same cluster transmit their pilot beams
simultaneously, while the different clusters transmit their pilot
beams sequentially, resulting in npilot = BC.
We also use an informative prior that exploits the blocksparsity of the channel matrix H which results from the
distributed nature of the APs and the UEs in combination
with the high directivity of mmWave channels [1]. Specifically,
we estimate H by solving the convex optimization problem
Ĥ = arg min
H∈CNR ×NT

1
2
kY − HBkF + µ kHkBS ,2(11)where µ is a regularization parameter and we use the blocksparsity promoting prior [21]kHkBS =L X
K
X

kH`,k kF .

(12)`=1 k=1

The optimization problem (11) can be efficiently solved using
forward-backward-splitting (FBS) [22].
B. Post-Beam-Alignment Channel Estimation (Post-BA CHEST)
Using the estimates Ĥ in (11) of the channel matrices forthe different subcarriers, the CPU then performs BA as detailedin Section III and communicates the selected beams to theUEs using the sub-6-GHz control channels. The UEs then
fix their beams accordingly in the form of the beamforming
matrix P. With these beams now being fixed, we effectively
have a compound channel matrix HP ∈ CNR ×K for every
subcarrier. Since the beams P have been appropriately selected,
we can estimate this compound channel (for every subcarrier)with high accuracy for reliable data detection. We do this byletting the UEs transmit pilot sequences which together form
a Hadamard matrix. The APs then estimate HP using leastsquares estimation.

where the matrix B ∈ CNT ×npilot is the compound of the UE
transmit symbols and the beams they form while transmitting
them. Assuming that the matrix B (which we call the beamV. N UMERICAL R ESULTS
pilot matrix) is known, the APs estimate H ∈ CNT ×NR based
We now evaluate the performance of our proposed scheme
on Y ∈ CNR ×npilot . Note that, since this happens before the BAincomparison with a number of baselines.
phase, the beams which can be used by the UEs in B need to
be predetermined. To explore the channels’ characteristics as A. Simulation Setup
fully as possible, and to make sure that we get adequate signal
We simulate a local cell-free communication scenario inreceive power at least during some of the time slots of Y, thewhich
K = 32 UEs, each with nUE = 8 antennas, communicate
UEs essentially sweep through the beam codebook. The kth
withL= 16 APs, each with nAP = 4 antennas. We use a carriernUE ×npilot
UE transmits the per-UE beam-pilot matrix B(k,·) ∈ C,
frequencyof 28 GHz and a bandwidth of 1 GHz divided into
which is the kth row block of B, and whose columns containn=2048
orthogonal subcarriers. For the pre-BA CHEST4
sc
all beams p ∈ P. If all of the UEs would transmit their beamprocedure,
weestimate the channels of the subcarrier indicespilots simultaneously, we would have the most efficient CHEST
v
∈
{1,
229,
456,
684, 911, 1139, 1366, 1594, 1821, 2048}
scheme with npilot = B. However, depending on the number
andconsideringC= 8 equisized clusters. The BA step isof UEs K and the size of the beam codebook B, the matrix
performed based on the strongest subcarrier channel matrices
4 This means that the UE pilot symbols for the pre-BA CHEST all equal 1.
per UE and AP, as detailed in Section III. The UEs use aFig. 2. Simulated scenario with 1336 possible UE locations (red), each with
nUE = 8 antennas, and L = 16 APs (green), each with nAP = 4 antennas.

QPSK transmit constellation and transmit at a maximum powerof 20 dBm using ± 3dB power control. To model realistic RF
hardware, the APs have a noise figure of 7 dB [23].
The wireless channels are simulated using Wireless InSite
from Remcom [18]. The setup, which is depicted in Fig. 2,
consists of a 200 m × 280 m area and contains 1336 possible
UE locations (visualized in Fig. 2 as red squares) which
are arranged on a grid. To simulate random user orientations, we also consider four possible angles for each user:{0◦ , 45◦ , 90◦ , 135◦ }. The position and orientation of the APs
are fixed. The APs and UEs are at heights of 12 m and 1.65 m,
respectively. Both APs and UEs have uniform linear arrayswith omnidirectional antennas spaced by half a wavelength.
B. Performance Metrics and Baseline Methods
As performance metrics we consider the cumulative density
function (CDF) or complementary CDF (CCDF) of the rootmean-squared-symbol error (RMSSE) per UE, the SINR per
UE per subcarrier, and the spectral efficiency (SE) per UE(summed over all subcarriers), all considering an LMMSE
equalizer. The RMSSE for the kth UE is defined asv
u Pnsc PTD (tv)(tv) 2u− sk
v=1
t=1 ŝkt
RMSSEk =,(13)
Pnsc PTD (tv) 2
v=1
t=1 skis available and hence we estimate the channel as describedin Section IV. To prove the efficacy of our proposed preBA CHEST scheme from Section IV-A, Fig. 3 also contains
results where we combine pre-BA CHEST for BA with groundtruth channel knowledge for data equalization (dashed curves).
The fact that the results where we perform pre-BA CHEST
are virtually identical to the results where perfect channel
knowledge is available also during the BA step proves that our
pre-BA CHEST procedure solves its task nearly optimally. Any
performance deterioration from Fig. 3 to Fig. 4 is due to theloss incurred by the post-BA CHEST for data detection, where
we only used a plain vanilla least squares channel estimator.
The performance hierarchy between the methods is very
similar for all performance metrics, and regardless of whether
channel knowledge is available or has to be estimated. The“single-antenna” method has the worst performance among all
considered approaches. This shows that omnidirectional singleantenna UEs suffer from significant performance losses incell-free mmWave systems compared to beamforming-capable
UEs with adequately selected beams. The “digital IU” method
and its analog counterpart “analog IU” perform substantiallybetter. Notably, “analog IU” is almost as good as “digital IU,”
suggesting that the more limited expressiveness of the beams
that can be formed by the “analog IU” compared to “digital
IU” are not negatively affecting the performance. Finally, the“analog IA” achieves by far the best performance. The difference
between “analog IA” and the interference-unaware methods islarger for the weakest UEs. The spectral efficiency of the 10%
weakest UEs is essentially 1.3× better for the interferenceaware method as for the interference-unaware methods. Thisshows that optimal BA of dense cell-free mmWave networks
requires algorithms that select the beams for the UEs jointly
and take multi-user interference into account. Contrastingly, theprecise RF architecture and resulting beamforming expressivityof the UEs seem to be comparably less important.
VI. C ONCLUSIONS

We have proposed an interference-aware beam alignment
method together with a channel estimation scheme for cell-freemmWave massive MU-MIMO systems. Our results have shown
(tv)
(tv)
where TD is the number of time slots and ŝk and sk are that multi-user interference-aware beam alignment consistently
the estimated and transmitted symbols of the kth UE in the outperforms methods that do not take interference into account,
vth subcarrier in the tth time slot.
which in turn outclass omnidirectional transmission without
In our numerical results, we refer to the interference-unaware beamforming. We have also shown the efficacy of our proposed
analog BA from Section III-B as “analog IU” and to the pre-beam-alignment channel estimation method in comparison
interference-aware analog BA from Section III-C as “analog IA.” to a hypothetical scenario where ground truth channel knowlAs the first baseline method, we use “single antenna,” where edge is available. For future work we highlight the combinationeach UE has nUE = 1 antenna, i.e., no BA capabilities. For a of our methods with decentralized data detection schemes asfair comparison, the total transmit power of “single antenna” well as considering the UE beam alignment problem in theUEs is the same as in the other techniques. The second baseline mmWave cell-free downlink.
is the interference-unaware digital BA (Section III-A), which
we refer to as “digital IU.”
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0.6
0.4

single antenna
digital IU
analog IU
analog IA

0.2
0

0

10

no CHEST
pre-BA CHEST

0.8
CCDF

CDF

0.8

1

1

no CHEST
pre-BA CHEST

20
30
RMSSE per UE [%]

40

0.6
0.4

single antenna
digital IU
analog IU
analog IA

0.2
0

50

0

0.6
0.4

single antenna
digital IU
analog IU
analog IA

0.2

5
10
15
20
25
SINR per UE per subcarrier [dB](a)no CHEST
pre-BA CHEST

0.8
CCDF

1

30

0
4′ 000(b)6′ 000 8′ 000 10′ 000 12′ 000 14′ 000 16′ 000
SE per UE [bits/channel use]

(c)

1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

single antenna
digital IU
analog IU
analog IA

0.2
0

0

10

20
30
RMSSE per UE [%]

(a)

40

CCDF

1

CCDF

CDF

Fig. 3. Subfigures (a), (b), and (c) show the CDF or CCDF of the RMSSE per UE, the SINR per UE per subcarrier, and the SE per UE, respectively, forground truth channel knowledge (solid) or pre-BA CHEST in combination with perfect post-BA CHEST (dashed).

0.4

single antenna
digital IU
analog IU
analog IA

0.2

50

0

0

0.2

5
10
15
20
25
SINR per UE per subcarrier [dB]

(b)

0.4

30

0
4′ 000single antenna
digital IU
analog IU
analog IA
6′ 000 8′ 000 10′ 000 12′ 000 14′ 000 16′ 000
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