# HBF MU-MIMO with Interference-Aware Beam Pair Link Allocation for Beyond-5G
mm-Wave Networks

Aleksandar Ichkov1, Alexander Wietfeld2, Marina Petrova3 and Ljiljana Simić1
1Aleksandar Ichkov and Ljiljana Simić are with the Institute for Networked
Systems at RWTH Aachen University, Aachen 52072, Germany
(e-mail<EMAIL_ADDRESS>lsi@inets.rwth-aachen.de).  2Alexander
Wietfeld was with the Institute for Networked Systems at RWTH Aachen
University, Aachen, Germany. Now he is with the Chair of Communication
Networks at Technical University of Munich, Munich 80333, Germany (e-mail:
alexander.wietfeld@tum.de).  3Marina Petrova is with the Institute for
Networked Systems and the Mobile Communications and Computing Teaching and
Research Area at RWTH Aachen University, Aachen 52072, Germany
(e-mail: petrova@mcc.rwth-aachen.de).

###### Abstract

Hybrid beamforming (HBF) multi-user multiple-input multiple-output (MU-MIMO)
is a key technology for unlocking the directional millimeter-wave (mm-wave)
nature for spatial multiplexing beyond current codebook-based 5G-NR networks.
In order to suppress co-scheduled users’ interference, HBF MU-MIMO is
predicated on having sufficient radio frequency chains and accurate channel
state information (CSI), which can otherwise lead to performance losses due to
imperfect interference cancellation. In this work, we propose IABA, a 5G-NR
standard-compliant beam pair link (BPL) allocation scheme for mitigating
spatial interference in practical HBF MU-MIMO networks. IABA solves the
network sum throughput optimization via either a distributed or a centralized
BPL allocation using dedicated CSI reference signals for candidate BPL
monitoring. We present a comprehensive study of practical multi-cell mm-wave
networks and demonstrate that HBF MU-MIMO without interference-aware BPL
allocation experiences strong residual interference which limits the
achievable network performance. Our results show that IABA offers significant
performance gains over the default interference-agnostic 5G-NR BPL allocation,
and even allows HBF MU-MIMO to outperform the fully digital MU-MIMO baseline,
by facilitating allocation of secondary BPLs other than the strongest BPL
found during initial access. We further demonstrate the scalability of IABA
with increased gNB antennas and densification for beyond-5G mm-wave networks.

###### Index Terms:

Beyond-5G, millimeter-wave, HBF MU-MIMO, BPL allocation, interference
mitigation.

##  1 Introduction

The spectrum-rich millimeter-wave (mm-wave) bands are a key enabler for the
capacity enhancement of 5G and Beyond-5G cellular networks [1], with 3GPP
designating numerous bands in the frequency range 2 (FR2) between 24.5–71 GHz
for commercial deployments [2]. Overcoming the challenging propagation and
blockage-prone nature of the mm-wave channel necessitates large antennas and
beamforming at the next generation node B (gNB) and the users (UEs), and a new
type of beam management, in which the gNB and UE need to sweep their beam
candidates sequentially in order to establish connectivity via a directional
beam pair link (BPL) [3, 4].

The existing limited deployments of 5G-NR FR2 networks [5, 6] rely on
codebook-based analog beamforming (CBF), as a low complexity and cost-
effective solution, given that digital beamforming (DBF) is prohibitively
complex and costly for large antenna arrays requiring a dedicated radio
frequency (RF) chain per antenna element [7]. However, CBF limits the
transmission/reception to a single beam per time slot and RF chain over the
entire instantaneous bandwidth, i. e. constituting a time division multiple
access (TDMA) system [8], which limits the per-UE throughput in multi-UE
networks. To better utilize the large bandwidth and directional nature of mm-
wave links for beyond-5G deployments, 5G-NR also specifies the use of hybrid
beamforming (HBF) with multiple RF chains to simultaneously serve multiple UEs
via individual BPLs, i. e. spatial layers in a multi-user multiple input
multiple output (MU-MIMO) configuration [8]. This improves the spectral
efficiency as multiple UEs are served with spatial division multiple access
(SDMA) using the same time-frequency resources, and reduces latency as more
UEs can be served simultaneously instead of waiting for their TDMA time slot.

Unlocking the full potential of mm-wave networks by efficiently sharing the
network capacity via SDMA comes with many challenges in real network
deployments [9]. HBF MU-MIMO offers an attractive solution for mitigating the
co-scheduled UE beam interference via digital precoding for interference
cancellation. However, the efficiency of HBF MU-MIMO is predicated on: (i) the
antenna configuration having sufficient RF chains, (ii) the beam codebook
having sufficient steering resolution and (iii) resource scheduling being
dynamic and able to adapt to up-to-date channel state information (CSI). In
practice, the predefined gNB/UE codebooks play a key role in acquiring
accurate CSI. The mm-wave channel can only be observed through the codebook
entries which project the received RF signal to the baseband [10], and should
therefore be properly designed to provide sufficient gain and angular steering
resolution to estimate the full channel matrix. Prior mm-wave networking
studies on HBF MU-MIMO [11, 12, 13, 14, 15, 16, 17, 18] have typically focused
on designing the digital precoder for interference cancellation assuming
availability of perfect CSI at the gNB. In practice, CSI reporting is time
consuming and subject to the gNB/UE codebooks, network control signaling and
latency constraints [11, 12], which can lead to system performance degradation
of HBF MU-MIMO due to imperfect interference cancellation, e. g. [13, 16].
Moreover, [19] demonstrates that even under ideal digital precoding, there is
still a considerable amount of strong residual inter-cell interference, which
is highly dependent on the multi-UE BPL allocation for the network. A number
of mm-wave SDMA studies [20, 21, 22, 23, 24, 25, 26] have instead focused on
clustering co-scheduled UEs that can be served via spatially separated BPLs
for SDMA gains, using CBF with a sufficient number of individual antenna
arrays to serve all UEs. However, [25, 26] have shown that under realistic
antenna and channel models, CBF entails strong residual interference which
limits the extent of achievable BPL separation and SDMA gains. Interference
management in practical mm-wave SDMA networks should therefore jointly
consider the MU-MIMO interference cancellation and spatial BPL allocation.

Reference | Interference | Channel | Beamforming | Multi-cell | Intra-cell | Inter-cell
---|---|---|---|---|---|---
studies | management | model | model | network | interference | interference
[11, 12, 13, 14] | Interference cancellation | Geometric | HBF | ✗ | ✗ | Added-noise constant
[15, 16] | Interference cancellation | 3GPP, NYUSIM | HBF | ✓ | ✗ | Estimate
[17, 18] | Interference cancellation | Geometric | HBF | ✓ | ✗ | Added noise-constant
[20, 21] | Spatial BPL allocation | 3GPP, NYUSIM | Idealized | ✓ | ✗ | Estimate
[22, 23] | Spatial BPL allocation | Log-distance (LOS only) | Idealized | ✓ | ✗ | Estimate
[24, 25] | Spatial BPL allocation | 3GPP, NYUSIM | CBF | ✓ | Estimate | Estimate
[26] | Spatial BPL allocation | 3D ray-tracing | CBF | ✓ | ✓ | ✓
This paper | Both | 3D ray-tracing | HBF | ✓ | ✓ | ✓

TABLE I: Related work on interference management approaches for mm-wave SDMA
networks.

###  1.1 Related Work

The prior literature of these two main approaches for interference management
in mm-wave SDMA networks is summarized in Table I. The first approach relies
on designing a co-scheduled UE precoder for interference cancellation based on
CSI at the gNB using HBF MU-MIMO [11, 12, 13, 14, 15, 16, 17, 18]. The second
approach focuses on interference-aware and load-balancing multi-UE BPL
allocation using CBF serving UEs via individual antenna arrays [20, 21, 22,
23, 26, 24, 25].

Interference management for HBF MU-MIMO [11, 12, 13, 14, 15, 16, 17, 18]
typically treats the UE co-scheduling problem within a single cell [11, 12,
13, 14], or limited multi-cell scenarios [15, 16, 17, 18], designing the
digital baseband precoder, e. g. zero-forcing, under the assumption of a
sufficient number of RF chains and availability of perfect CSI at the gNB.
This is not always guaranteed in practice, which can lead to performance
degradation due to imperfect CSI and in turn only partial interference
cancellation [13]. Authors in [14] show the SDMA performance gains of HBF MU-
MIMO over CBF and study the end-to-end network implications. However, they
only consider a single gNB serving seven UEs, and still show that the network
suffers from significant control overhead and delay of acquiring full per-UE
CSI. Authors in [15, 16, 17, 18] consider HBF MU-MIMO in limited multi-cell
network scenarios. [15] proposes a HBF MU-MIMO framework based on full CSI and
multi-cell cooperation, showing that non-coordinated can outperform fully-
coordinated HBF MU-MIMO under availability of only quantized CSI [16]. Authors
in [17] propose a near interference-free UE scheduling (NIF), with [18]
further generalizing the NIF framework for different SDMA optimization
objectives, assuming perfect intra-cell interference cancellation and very
limited inter-cell interference. However, [17, 18] only assume interference as
an added noise constant, and UEs with only line-of-sight (LOS) links to their
serving gNB and non-LOS (NLOS) links to the other interfering gNBs.
Importantly, [15, 16, 17, 18] assume perfect coordination and synchronization
between the gNBs, and neglect the practical overhead and delay constraints of
obtaining full per-UE channel estimates, and thus only demonstrate HBF MU-MIMO
performance under idealized network conditions.

Interference management in CBF mm-wave SDMA networks focuses on spatial BPL
allocation for clustering co-scheduled UEs that can be sufficiently spatially
separated, e. g. [20, 21, 22, 23, 26, 24, 25]. Authors in [20, 21, 22]
demonstrate SDMA gains when sufficient BPL separation can be maintained to
effectively eliminate intra-cell interference, whereas [23] models the
interference in the angular domain but considers LOS links only. However, the
studies in [20, 21, 22, 23] rely on statistical channel models and idealized
sector antennas, that neglect the spatial distribution of feasible BPLs and
the resulting interference implications. Authors in [24] propose a CBF
approach using codebooks with low inter-beam overlap, and show that it can
outperform HBF MU-MIMO assuming quantized CSI feedback. However, [24] only
considers a single gNB serving UEs based on sum-rate clustering and only
estimates the interference as added noise. The authors in [25] propose a load-
balancing UE association which swaps the worst gNB-UE connection (WCS) at each
iteration considering the per-slot interference estimate. In [26] we show that
under realistic channel considerations, the non-negligible sidelobes of
realistic arrays result in significant intra-cell interference which strongly
limits the SDMA gains. Additionally, [26] proposes an interference-aware BPL
allocation for CBF SDMA networks which outperforms the WCS benchmark [25]. In
particular, [26] demonstrates the benefits of spatial BPL allocation by using
secondary BPLs for interference mitigation, going beyond the default 5G-NR
association to the strongest BPL found during initial access typically
considered in the literature, e.g. [13, 14, 15, 16, 17, 18, 24, 25].

###  1.2 Contributions

In this paper, we extend beyond the prior literature (_cf._ Table. I) and
propose an interference-aware BPL allocation (IABA) for practical mm-wave HBF
MU-MIMO networks that goes beyond the default 5G-NR association to the
strongest BPL found during initial access. We are thus the first to jointly
consider MU-MIMO interference cancellation and spatial BPL allocation for
interference management in practical mm-wave HBF MU-MIMO networks. The main
contributions of this work are as follows:

  * •

We present an extensive study of multi-cell mm-wave HBF MU-MIMO networks based
on site-specific channel data obtained via 3D ray-tracing with realistic
building and antenna models, the accuracy of which we have validated against
real-world phased antenna arrays measurements [27, 28], and network
configuration following 3GPP specifications for multi-sector antennas, initial
access and channel estimation [29].

  * •

We therefore characterize the residual intra- and inter-cell interference in
practical mm-wave HBF MU-MIMO networks, given the spatial distribution of
feasible BPLs and 5G-NR CSI signaling, showing that interference becomes the
main limiting factor of HBF MU-MIMO performance, which is in contrast to prior
studies assuming limited to no-interference operation [15, 16, 17, 18].

  * •

We propose IABA, a 5G-NR-compliant BPL allocation, as a solution for
mitigating the spatial interference in practical mm-wave HBF MU-MIMO networks.
We solve the network sum throughput optimization objective via either a
distributed or a centralized BPL allocation using dedicated channel state
information-reference signal (CSI-RS) resources for candidate BPL monitoring.

  * •

Our results show that IABA offers significant network performance gains over
default 5G-NR, by facilitating allocation of secondary BPLs other than the
strongest BPL found during initial access. We further demonstrate that under
realistic CSI signaling constraints, IABA allows HBF MU-MIMO to outperform the
interference-agnostic DBF MU-MIMO baseline.

###  1.3 Organization of the paper

The rest of this paper is organized as follows. Sec. 2 details the system
model considerations, including channel and multi-panel antenna models,
beamforming, channel estimation and multi-UE interference cancellation, and
presents key performance evaluation metrics. Sec. 3 presents the BPL
allocation problem and our IABA algorithm and 5G-NR-compliant operation. Sec.
4.1 presents the simulation model, and Sec. 4.2 presents the results. Sec. 5
concludes the paper.

##  2 System Model

###  2.1 mm-Wave Channel Model

We model the 3D directional mm-wave channel between the gNB and the UE as a
set of $K$ LOS and NLOS propagation paths using the geometric channel model
[30]. Assuming a gNB as the transmitter with $N_{\text{t}}$ antenna elements
and a UE as the receiver with $N_{\text{r}}$ antenna elements, we define the
geometric $N_{\text{r}}\times N_{\text{t}}$ channel matrix $\mathbf{H}$ as

$\mathbf{H}=\sqrt{\frac{N_{\text{r}}N_{\text{t}}}{K}}\sum_{k=1}^{K}\alpha_{k}\mathbf{a}_{\mathrm{r}}\left(\phi_{k}^{\text{r}},\theta_{k}^{\text{r}}\right)\mathbf{a}_{\mathrm{t}}^{H}\left(\phi_{k}^{\text{t}},\theta_{k}^{\text{t}}\right),$
(1)

where $\alpha_{k}$ denotes the complex channel gain of the $k^{\text{th}}$
path, and $\\{\phi_{k}^{\mathrm{t}},\theta_{k}^{\mathrm{t}}\\}$ and
$\\{\phi_{k}^{\mathrm{r}},\theta_{k}^{\mathrm{r}}\\}$ denote the angle of
departure (AoD) and angle of arrival (AoA) in azimuth and elevation,
respectively. The transmit and receive antennas are described by their
steering vectors $\mathbf{a}_{\mathrm{t}}$ and $\mathbf{a}_{\mathrm{r}}$,
which are identical to the phase-shifting weights applied to steer the antenna
arrays towards the AoD and AoA, respectively [10].

For the special case of an $N$ element uniform linear array (ULA) positioned
along the $y$-axis and steered towards angle $\phi$ in azimuth, the array
steering vector is given as

$\mathbf{a}_{\mathrm{ULA}}(\phi)=\frac{1}{\sqrt{N}}\left[1\;e^{j2\pi\frac{d}{\lambda}\sin(\phi)}\cdots
e^{j(N-1)2\pi\frac{d}{\lambda}\sin(\phi)}\right]^{T}.$

(2)

We generalize it to a uniform rectangular array (URA) in the $y$-$z$ plane,
with the array steering response given as

$\mathbf{a}_{\text{URA}}(\theta,\phi)=\mathrm{a}_{\text{h,
ULA}}(\phi)\otimes\mathrm{a}_{\text{v, ULA}}(\theta),$ (3)

where $\otimes$ denotes the Kronecker product of the horizontal steering
vector determining the azimuth response $\mathrm{a}_{\text{h, ULA}}(\phi)$ and
the vertical steering vector for the elevation response $\mathrm{a}_{\text{v,
ULA}}(\theta)$ of a same sized ULA (2).

Finally, we express the downlink received signal $\mathbf{y}$ as

$\mathbf{y}=\mathbf{w}_{\text{c}}^{\text{H}}\mathbf{H}\mathbf{W}_{\text{p}}\mathbf{s}+\mathbf{w}_{\text{c}}^{\text{H}}\mathbf{n},$
(4)

where $\mathbf{w}_{\text{c}}^{\text{H}}$ denotes the Hermitian of the
combining vector, $\mathbf{W}_{\text{p}}$ denotes the precoding matrix,
$\mathbf{s}$ denotes the data stream vector, and $\mathbf{n}$ denotes the
noise vector.

We use an open-source mm-wave ray-tracing tool to obtain site-specific
directional channel data based on real 3D building and antenna models [27,
28]. We perform dedicated ray-tracing runs for each gNB position in our multi-
cell network (_cf._ Sec. 4.1), considering free-space propagation and strong
reflections (up to two-bounces) as dominant propagation mechanisms;
diffraction is neglected due to its limited role at mm-wave [31]. The ray-
tracing output is used to reconstruct the channel matrix as per (1).

Figure 1: Example codebook with 16 beams for a sector antenna covering the
steering range of $\phi\in(-45^{\circ},~{}45^{\circ})$. Figure 2: Illustration
of a mm-wave network, with an example scenario of a gNB simultaneously serving
$N_{u}=6$ UEs. The gNB is using a fully-connected HBF architecture with
$N_{sec}=4$ sector panels each equipped with $N_{t}$ antenna elements and
$N^{g}_{RF,sec}=4$ RF chains, i. e. the gNB can simultaneously serve up to
$N^{g}_{RF}=16$ UEs . For clarity, we only illustrate two out of the four gNB
sector panels, with four UEs being served by sector #$1$ and two UEs served by
sector #$2$. The UEs use a CBF architecture with $N_{sec}=4$ sector panels,
each equipped with $N_{r}$ antenna elements, and $N^{u}_{RF}=1$ RF chain.

###  2.2 Multi-Panel Antenna & Beamforming Model

For the transmit/receive antennas, we employ the multi-panel antenna model
[29], where the gNB/UE is equipped with $N_{sec}=4$ sector antenna panels,
each covering one sector/quadrant of the angular space. We assume that the
gNB/UE has unified control over all its multi-panel antennas, which have a
fixed initial orientation. To steer the individual beams, we assume predefined
codebooks for each sector antenna panel, $\mathcal{C}^{g}_{sec}$ at the gNB
and $\mathcal{C}^{u}_{sec}$ at the UE of size $n_{q}$ bits, which consist of
$2^{n_{q}}$ beams covering the angular steering range of $\pm 45^{\circ}$,
following 3GPP’s specifications in Table. 7.3-1 in [29]. An example of such a
sector antenna codebook consisting of 16 beams is shown in Fig. 1.

For the beamforming, we assume a fully-connected HBF architecture at the gNB,
mapping all RF chain outputs per sector panel onto a common analog beamformer,
which applies a sum of all phase-shifting outputs to each of the $N_{t}$
elements of the sector antenna panel, as shown in Fig. 2. Each RF chain
controls a part of the overall sector antenna panel, with a total of
$N^{g}_{RF,sec}$ RF chains per panel. Thus, the maximum number of UEs that can
be served simultaneously at the gNB is constrained by the total number of RF
chains , i. e. $N_{u}\leq N^{g}_{RF}$, where
$N^{g}_{RF}=N_{sec}N^{g}_{RF,sec}$. At the UE, we assume a CBF architecture
following 5G-NR specifications in [29], such that each UE is equipped with
$N^{u}_{RF}=1$ RF chain controlling $N_{sec}=4$ sector antenna panels, each
consisting of $N_{r}$ antenna elements, as shown in Fig. 2.

###  2.3 Initial Access: Initial Serving BPL Selection

Steering the antenna beams to the correct orientation for establishing a mm-
wave BPL necessitates beam training [3]. A mm-wave BPL $l_{i,j}$ is defined by
the UE $i$, the serving gNB $j$, and the respective steering orientations at
the gNB $\\{\phi_{l_{i,j}}^{j},\theta_{l_{i,j}}^{j}\\}$ and the UE
$\\{\phi_{l_{i,j}}^{i},\theta_{l_{i,j}}^{i}\\}$. We follow the 5G-NR initial
access as our beam training procedure [3], and assume downlink control
operation based on an exhaustive beam sweep over the codebook entries of
$\mathcal{C}^{j}$ at gNB $j$ and $\mathcal{C}^{i}$ at UE $i$, where
$\mathcal{C}^{j}=\bigcup\limits_{sec=1}^{N_{sec}}\mathcal{C}^{j}_{sec}$ and
$\mathcal{C}^{i}=\bigcup\limits_{sec=1}^{N_{sec}}\mathcal{C}^{i}_{sec}$ denote
the complete gNB and UE codebooks consisting of all the entries for each
sector antenna codebook. The initial serving BPL $l_{i,j}$ for UE $i$ is then
selected out of the finite set of feasible BPLs found during initial access
over all gNBs,
$\mathbf{N}_{l,i}=\bigcup\limits_{j\in\mathbf{G}}\bigcup\limits_{n=1}^{|\mathcal{C}^{j}|}\bigcup\limits_{m=1}^{|\mathcal{C}^{i}|}{l}_{{i,j,n,m}}$
as the one which maximizes the synchronization signal block (SSB) reference
signal received power (RSRP), and is determined as

$l_{i,j}~{}\leftarrow~{}\underset{\begin{subarray}{c}l_{i,j}\in\mathbf{N}_{l,i}\\\
\forall\mathbf{w}_{\text{p},l_{i,j}}\in\mathcal{C}^{j}\\\
\forall\mathbf{w}_{\text{c},l_{i,j}}\in\mathcal{C}^{i}\end{subarray}}{\operatorname{argmax}}~{}P_{SSB}\left\|\mathbf{w}_{\text{c},l_{i,j}}^{\text{H}}\mathbf{H}_{i,j}\mathbf{w}_{\text{p},l_{i,j}}\right\|^{2},~{}~{}\forall
j\in\mathbf{G}$ (5)

where $P_{SSB}$ denotes the SSB transmit power, $\mathbf{G}$ denotes the set
of gNBs in the network, and $\mathbf{w}_{\text{p},l_{i,j}}$ and
$\mathbf{w}_{\text{c},l_{i,j}}$ denote the precoding and combining vectors
applied to steer the arrays towards the AoD and AoA of the BPL $l_{i,j}$,
respectively.

###  2.4 Channel Estimation

The exhaustive beam sweep of the finite gNB/UE codebooks determines the
steering orientations of the candidate BPLs that best correspond to the real
AoD/AoA of the $K$ LOS/NLOS channel propagation paths in (1), within the
margins of the codebook steering resolution. To accommodate for the inaccurate
angular information during channel estimation, we use the wide-angle steering
codebook which generates variable beamwidth patterns to fit a desired steering
resolution for a given antenna array [32], i. e. resulting in quantized
channel estimates due to use of codebooks with finite steering resolution.
Specifically, for both the gNB and the UE, we may define an azimuth steering
codebook $\mathcal{C}_{\phi}$ of size $n_{q}$ bits, which is able to
distinguish between $2^{n_{q}}$ angles over the range of $90^{\circ}$ for each
of the $N_{sec}=4$ antennas. Similarly, we may define an elevation steering
codebook $\mathcal{C}_{\theta}$ of size $n_{q}-1$ bits over the range of
$180^{\circ}$ for each of the $N_{sec}=4$ antennas. The finite channel
estimation resolution over the azimuth/elevation steering ranges is thus given
as

$\phi_{\mathrm{res}}=\frac{360^{\circ}}{N_{sec}\cdot
2^{n_{q}}},~{}~{}~{}\theta_{\mathrm{res}}=\frac{180^{\circ}}{N_{sec}\cdot
2^{n_{q}-1}}.$ (6)

The quantized angle estimates of the real AoD for the channel propagation
paths in (1) are defined as

$\hat{\phi}_{i,k}=\underset{\phi\in\mathcal{C}^{i}_{\phi}}{\operatorname{argmin}}\left\|\phi-\phi^{t}_{k}\right\|,~{}~{}\hat{\theta}_{i,k}=\underset{\theta\in\mathcal{C}^{i}_{\theta}}{\operatorname{argmin}}\left\|\theta-\theta^{t}_{k}\right\|,$
(7)

where the same principle holds equivalently for the AoD/AoA and each channel
propagation path $k$ in (1). We note that the use of finite resolution
codebooks results in an inability to distinguish individual channel paths with
the same quantized angles. In such cases, the channel estimation algorithm
reports a single path with quantized parameters, i. e. the individual paths
are merged into one known path and their complex gains are combined. Finally,
the estimated channel matrix $\hat{\text{H}}_{i}$ for UE $i$ is given as

$\hat{\text{H}}_{i}={\begin{pmatrix}\hat{\text{H}}_{1,1}&\cdots&\hat{\text{H}}_{1,4}\\\
\vdots&\ddots&\vdots\\\ \hat{\text{H}}_{4,1}&\cdots&\hat{\text{H}}_{4,4}\\\
\end{pmatrix}},$ (8)

where e. g. $\hat{\text{H}}_{1,4}\in\mathbb{C}^{N_{\text{r}}\times
N_{\text{t}}}$ denotes the estimated channel matrix between the first sector
antenna panel of UE $i$ and the fourth sector antenna panel at the serving gNB
$j$.

Following 3GPP’s specifications, we distinguish between gNB/UE codebooks used
for channel estimation and initial access, as well as reference signals used
for each procedure [33]. Assuming downlink operation using the same codebook
for channel estimation and initial access, the number of reference signals for
CSI reporting is limited to $64$, in line with 3GPP specifications for the
number of SSBs at FR2 [3]. In 5G-NR HBF MU-MIMO terms [33], this corresponds
to CSI reporting for Type-II codebooks with no oversampling and a sector
antenna codebook size of $n_{q}=4$ bits, i. e. 16 beams per each of the four
sector antennas and 64 beams in total. Type-II codebooks also support a more
detailed CSI-RS-based reporting [34], with an oversampling factor of up to
four for both azimuth and elevation, making a codebook size of $n_{q}=6$ bits
also feasible, i. e. 64 beams per each of the four sector antennas and a total
of 256 beams.

In Sec. 4.2 we vary the size of the gNB/UE codebooks used for channel
estimation, and study the corresponding accuracy of the estimated channel
matrix which is then used for designing the digital baseband precoder for
multi-UE interference cancellation (_cf._ Sec. 2.5). We additionally consider
as a reference the ideal case, where the channel estimates are acquired using
an infinite resolution codebook $n_{q}=\infty$, such that the channel path
angles and complex gains are assumed to be perfectly known, i. e.
$\hat{\text{H}}=\text{H}$.

###  2.5 Multi-User Interference Cancellation

The computation of the precoding weights for serving the multiple UEs at the
gNB is split into two stages, as per [13]. In the first stage, following the
initial exhaustive beam sweep, the codebook entries which maximize the RSRP
are selected to steer the arrays at the gNB $\mathbf{w}_{\text{p, RF},i}$, and
the UE $\mathbf{w}_{\text{c},i}$, towards the AoD/AoA of the serving BPL
$l_{i,j}$ (5).

In the second stage, we need to compute the effective channel for each UE $i$
based on the estimated channel $\mathbf{\hat{H}}_{i}$ (8). For this, we use
the precoding $\mathbf{w}_{\text{p, RF},i}$ and combining
$\mathbf{w}_{\text{c},i}$ vectors from the first stage, as

$\mathbf{\hat{H}}_{\text{eff},i}=\mathbf{w}_{\text{c},i}^{\text{H}}\mathbf{\hat{H}}_{i}\mathbf{W}_{\text{p,RF}},$
(9)

where
$\mathbf{W}_{\text{p,RF}}\leftarrow\left[\mathbf{w}_{\text{p,RF,1}}\cdots\mathbf{w}_{\text{p,RF},N_{u}}\right]$
denotes the aggregate RF precoding matrix for the $N_{u}$ UEs served by the
gNB. Each UE feeds this channel information back to the gNB, with the
effective channel vector reflecting a drastically reduced dimensionality, i.
e. $N_{u}\ll N_{sec}N_{t}$. We note that the accuracy of the effective channel
depends on the estimated channel matrix $\mathbf{\hat{H}}_{i}$, which is
dictated by the gNB/UE codebooks used for channel estimation (_cf._ Sec. 2.4).

The gNB then designs the digital baseband precoder based on the UE channel
feedback using zero-forcing for multi-UE interference cancellation as

$\mathbf{W}_{\text{p,BB}}=\mathbf{\bar{H}}\left(\mathbf{\bar{H}}^{\text{H}}\mathbf{\bar{H}}\right)^{-1},$
(10)

where
$\mathbf{\bar{H}}=\left[\mathbf{\hat{H}}_{\text{eff},1}^{\text{H}}\cdots\mathbf{\hat{H}}_{\text{eff},N_{u}}^{\text{H}}\right]$
represents the aggregated effective channels for the $N_{u}$ UEs. The
resulting baseband precoding vectors for each UE $i$ are then normalized to
fulfill the power constraint,
$\mathbf{w}_{\text{p,BB},i}=\frac{\mathbf{w}_{\text{p,BB},i}}{\|\mathbf{W}_{\text{p,RF}}\mathbf{w}_{\text{p,BB},i}\|_{F}}$,
where $\|~{}\|_{F}$ denotes the Frobenius norm.

Finally, the individual precoding vector $\mathbf{w}_{\text{p},i}$ for UE $i$
in (4) is generated by multiplying the RF and baseband precoding,

$\mathbf{w}_{\text{p},i}=\mathbf{W}_{\text{p,RF}}\mathbf{w}_{\text{p,BB,i}},$
(11)

with $\mathbf{W}_{\text{p,RF}}\in\mathbb{C}^{N_{sec}N_{t}\times N_{u}}$ and
$\mathbf{w}_{\text{p,BB,i}}\in\mathbb{C}^{N_{u}\times N_{u}}$.

Effectively, the gNB precoder in the case of HBF maps the $N_{u}$ UE streams
to the $N^{g}_{RF}$ RF chains, thus significantly reducing the complexity
compared to DBF.

###  2.6 Performance Evaluation Metrics

The signal-to-interference-plus-noise-ratio (SINR) for UE $i$ served by gNB
$j$ via the serving BPL $l_{i,j}$ is given as

$SINR_{i}=\frac{RSS_{i}}{I_{intra,i}+I_{inter,i}+N},$ (12)

where $N$ denotes the noise power, consisting of thermal noise over the system
bandwidth plus a noise figure, and the received signal strength (RSS) is given
by

$RSS_{i}=P_{\text{i}}\|\mathbf{w}_{\text{c},i}^{\text{H}}\mathbf{{H}}_{i,j}\mathbf{w}_{\text{p},i}\|^{2},$
(13)

where $P_{\text{i}}$ denotes the gNB transmit power allocated to UE $i$ with
the total transmit power $P_{max}$ equally shared among all allocated UEs at
the gNB, and the precoding $\mathbf{w}_{\text{p},i}$ and combining
$\mathbf{w}_{\text{c},i}$ vectors determined as in Sec. 2.5.

We define the intra-cell interference $I_{intra,i}$ and inter-cell
interference $I_{inter,i}$ for UE $i$ served by gNB $j$ as

$I_{\text{intra},i}=P_{\text{U}}\|\mathbf{w}_{\text{c},i}^{\text{H}}\mathbf{{H}}_{i,j}\mathbf{W}_{\text{p}}^{j}\|^{2},$
(14) $I_{\text{inter},i}=P_{\text{U}}\|\mathbf{w}_{\text{c},i}\sum_{g\neq
j}\mathbf{{H}}_{i,g}\mathbf{W}_{\text{p}}^{g}\|^{2},$ (15)

where $P_{\text{U}}$ denotes the gNB transmit power allocated to each UE and
$\mathbf{W}_{\text{p}}^{j}=\left[\mathbf{w}_{\text{p},1},\cdots,\mathbf{w}_{\text{p},N_{u}}\right]$
denotes the precoding matrix for the $N_{u}$ UEs served by the gNB.

Lastly, to map the $SINR_{i}$ to the achievable throughput $R_{i}$, we adopt
the wideband 5G-NR model [5] using an attenuated, truncated Shannon bound as

$\displaystyle\small R_{i}=\begin{cases}0&SINR_{i}<SINR_{min},\\\
R_{max}&SINR_{i}\geq SINR_{max},\\\ \alpha
B\log_{2}(1+SINR_{i})&\mbox{otherwise},\end{cases}$ (16)

where $\alpha=0.75$ represents the implementation losses, $B=400$ MHz denotes
the bandwidth, ${SINR}_{min}=-5$ dB denotes the coverage threshold and
${SINR}_{max}=20.05$ dB is the SINR required to get the maximum achievable
throughput of $R_{max}=2$ Gbps.

##  3 Multi-User BPL Allocation in HBF MU-MIMO mm-Wave Networks

###  3.1 BPL Allocation Problem

Assuming that a UE is only served by a single gNB via one BPL, we formulate
the multi-UE BPL allocation that maximizes the network sum throughput as

$\mathbf{L}=\operatorname*{argmax}_{\mathbf{L}\subset\mathbf{N}_{l}}\;\sum\limits_{i\in\mathbf{U}}R_{i},$
(17) $\text{s.t.}~{}SINR_{i}\geq SINR_{min},\forall i\in\mathbf{L}$ (18a)
$|\mathbf{L}_{j}|\leq N^{j}_{RF},\forall j\in\mathbf{G}$ (18b)
$~{}\sum\limits_{i\in\mathbf{L}_{j}}P_{i}\leq P_{max},\forall j\in\mathbf{G}$
(18c)

where $\mathbf{L}$ denotes the set of allocated BPLs and
$\mathbf{N}_{l}=\bigcup\limits_{i=1}^{N_{UE}}\mathbf{N}_{{l,i}}$ denotes the
set of candidate BPLs for all UEs. The constraint in (18a) denotes the
coverage threshold for BPL allocation. The constraint in (18b) denotes the
maximum number of UEs that can be served simultaneously on each gNB. The
constraint in (18c) denotes the gNB transmit power allocation, with the total
power equally split among the served UEs. We note that the combinatorial
allocation problem (17) can be solved by exhaustive search, but this is
computationally infeasible for all but very small networks.

###  3.2 IABA: Interference-Aware BPL Allocation

We propose IABA, an interference-aware BPL allocation scheme which aims to
mitigate spatial interference in HBF MU-MIMO mm-wave networks and maximize the
network sum throughput (17). IABA is fully 5G-NR-compliant, and relies on
monitoring candidate BPLs via a centralized CSI-RS allocation, i. e. cIABA, or
a distributed, per-gNB CSI-RS allocation, i. e. dIABA. The detailed step-by-
step operation of IABA is as follows (_cf._ Alg. 1).

Algorithm 1 Interference-Aware BPL Allocation (IABA)

1:$\mathbf{U}$, $\mathbf{G}$, L, $\mathcal{C}^{g}$, $\mathcal{C}^{u}$,
$N^{g}_{RF}$, $N^{u}_{RF}$, $N_{CSI-RS}$.

2:Step 1. Initial user association

3:for each UE $i$ in $\mathbf{U}$ do

4:
$\mathbf{N}_{l,i}=\bigcup\limits_{j\in\mathbf{G}}\bigcup\limits_{n=1}^{|\mathcal{C}^{j}|}\bigcup\limits_{m=1}^{|\mathcal{C}^{i}|}{l}_{{i,j,n,m}}$,
set of all candidate BPLs.

5:
$l_{i,c}~{}\leftarrow~{}\underset{l_{i,c}\in\mathbf{N}_{l,i}}{\operatorname{argmax}}~{}RSS_{i}$,
initial serving BPL on gNB $c$ (5).

6:Step 2. CSI-RS candidate BPL monitoring

7:for each UE $i$ in $\mathbf{U}$ do

8: if (distributed IABA) then

9:
$\textbf{C}_{l,i}\leftarrow\underset{RSS}{\text{sort}}~{}(\mathbf{N}_{l,i,c})$,
sorted set of candidate BPLs on the initial serving gNB $c$.

10: $|\textbf{C}_{l,i}|=N_{CSI-RS}$, limit number of monitored BPLs.

11: else (centralized IABA)

12:
$\textbf{C}_{l,i}\leftarrow\underset{RSS}{\text{sort}}~{}(\mathbf{N}_{l,i})$,
sorted set of all candidate BPLs.

13: $|\textbf{C}_{l,i}|=N_{CSI-RS}$, limit number of monitored BPLs.

14:Step 3. Multi-UE BPL allocation

15:for each UE $i$ in $\mathbf{U}$ do

16: $\mathbf{C}_{SINR_{i}}$ = {}, provisional BPL allocation set for UE $i$.

17: for each $l_{i,j}$ in $\textbf{C}_{l,i}$ do

18: Compute precoding/combining weights (9)–(11):

19:
$\\{\mathbf{w}_{\text{p,}k}\\}_{k=1}^{|\mathbf{L}_{j}|+1},\\{\mathbf{w}_{\text{c,}k}\\}_{k=1}^{|\mathbf{L}_{j}|+1}$,
$\forall k\in\\{\textbf{L},l_{i,j}\\}$.

20: Update metrics of allocated BPLs (12):

21: if (distributed IABA) then

22: $SINR_{k}$, $\forall k\in\\{\textbf{L}_{j},l_{i,j}\\}$.

23: else (centralized IABA)

24: $SINR_{k}$, $\forall k\in\\{\textbf{L},l_{i,j}\\}$.

25: Provisional BPL allocation:

26: if $(SINR_{k}\geq SINR_{min}$ & $|\mathbf{L}_{j}|\leq N^{j}_{RF}$),
$\forall k\in\textbf{L}$ then

27: $\mathbf{C}_{{SINR_{i}}}=\\{\mathbf{C}_{{SINR_{i}}},l_{i,j}\\}$.

28: else

29: continue

30: if $\textbf{empty}(\mathbf{C}_{{SINR_{i}}})$ then

31: drop UE $i$ from network.

32: else

33:
$l_{i,j}\leftarrow\underset{l_{i,j}\in\mathbf{C}_{SINR_{i}}}{\operatorname{argmax}}SINR_{i}$,
$\mathbf{L}\leftarrow l_{i,j}$.

34:L, final BPL allocation set.

In the first step, the set of candidate BPLs $\mathbf{N}_{l,i}$ for each UE
$i$ is established following the exhaustive beam sweep of the gNB/UE codebooks
during initial access. The UE is initially associated to the gNB which
provides the strongest BPL as per (5). In the second step, the network sets up
the monitoring of candidate BPLs by allocating dedicated CSI-RS resources.
Each UE can monitor up to $N_{CSI-RS}$ BPLs, either solely on the serving gNB
using dIABA or over the complete network using cIABA. In the third step, the
multi-UE BPL allocation is executed by selecting among the $N_{CSI-RS}$
monitored BPLs using CSI-RS measurement reporting. The precoding/combining
weights are computed for each new candidate BPL using (9)–(11), taking into
account all previously allocated BPLs on the serving gNB. Following this, the
network updates the $SINR$ of the co-allocated BPLs, i. e. solely on the
serving gNB for dIABA or across all gNBs for cIABA. The decision on whether
the candidate BPL is allocated is then made in an interference-aware manner,
as follows. If none of the previously allocated BPLs are degraded below the
coverage threshold (18a), and the gNB has enough physical resources to serve
all allocated UEs (18b), the candidate BPL is provisionally allocated to
$\mathbf{C}_{{SINR_{i}}}$. Otherwise, the candidate BPL is discarded. Once the
$N_{CSI-RS}$ candidate BPLs for the UE have been checked, the candidate BPL in
$\mathbf{C}_{{SINR_{i}}}$ providing the highest $SINR$ is allocated to the
final BPL allocation set $\mathbf{L}$. If none of the candidate BPLs are
eligible for allocation, the UE is dropped.

In Sec. 4.2, we evaluate the proposed IABA against the default interference-
agnostic 5G-NR baseline, where each UE is allocated its strongest BPL as found
during initial access (Step 1 of Alg. 1), such that new allocations can lead
to previously allocated BPLs being dropped from the network due to excessive
interference.

Complexity Analysis: Considering closely the multi-UE BPL allocation in Step 3
in Alg. 1, line 21/23 have the highest cost due to the computation of the
updated $SINR$ for all co-allocated BPLs. This involves the multiplication of
the updated combining, channel, and precoding matrices as per (12), which is
of complexity order $\mathcal{O}(N_{t}^{2})$ [11]. We note that the selection
of the serving BPL for each UE $i$ is then done in line 32 in Alg. 1 by
finding the maximum SINR BPL in the provisional allocation set
$\mathbf{C}_{{SINR_{i}}}$, which requires
$|\mathbf{C}_{{SINR_{i}}}|\text{log}(|\mathbf{C}_{{SINR_{i}}}|)$ computations.

dIABA runs independently on each gNB, having
$|\mathbf{C}_{l,i}|N_{UE}/N_{gNB}$ iterations on average, where
$N_{UE}=|\mathbf{U}|$ and $N_{gNB}=|\mathbf{G}|$. In each iteration, the
candidate BPLs for each associated UE are checked, in total
$|\mathbf{C}_{l,i}|\leq K$, where $K$ denotes the number of channel
propagation paths between UE $i$ and its serving gNB $j$ in (1). We note that
the exact number of candidate BPLs between a UE and its serving BS depends on
their relative positions, site-specific channel and codebook considerations.
The computational complexity of dIABA is thus given as
$\mathcal{O}\left(K\frac{N_{UE}^{2}}{N_{gNB}}N_{t}^{2}\right).$

cIABA runs a single loop with $N_{\text{UE}}$ iterations, considering
potentially all candidate BPLs over the complete network, which constitutes
$|\mathbf{C}_{l,i}|N_{gNB}\leq KN_{gNB}$ repetitions of SINR calculations. The
computational complexity of cIABA is thus given as
$\mathcal{O}\left(KN_{gNB}N_{UE}^{2}N_{t}^{2}\right).$

This shows that with network densification, the computational complexity of
the centralized allocation cIABA scales with $\mathcal{O}(N_{UE}^{2}N_{gNB})$,
whereas for dIABA it scales with $\mathcal{O}(N_{UE}^{2}/N_{gNB})$.

For the default 5G-NR BPL allocation, the calculation for each UE involves
$N_{UE}/N_{gNB}$ calculations on the serving gNB, as we need to calculate the
SINR for all allocated BPLs including the new one, but only for the per-UE
best RSS BPL found during initial access; this is done for every gNB so in
total $N_{gNB}$ iterations. Thus, the computational complexity of default
5G-NR is given as
$\mathcal{O}\left(\frac{N_{UE}^{2}}{N_{gNB}}N_{t}^{2}\right).$

###  3.3 5G-NR-Compliant IABA Operation

The proposed IABA is fully compliant with the 5G-NR standard, and relies
solely on standardized reference signals for dedicated channel measurements
(CM) and interference measurements (IM) [35]. The detailed step-by-step 5G-NR
standard-compliant operation of IABA is illustrated in Fig. 3.

For initial access, we follow the downlink control operation where the gNBs
transmit SSB reference signals, such that each SSB corresponds to a different
beam index (ID) in the gNB codebook (_cf._ Step 1 in Fig. 3). Following 3GPP’s
specifications, the SSBs are allocated in the first 5 ms of an SS burst, which
is transmitted with a periodicity of $T_{SS}=20$ ms. We note that 3GPP limits
the maximum number of SSBs $N_{SSB}$ up to 64 for FR2 [3]. During the
transmission of an SS burst, the UE keeps its beam fixed, and continues to
sweep all of its beams over consecutive SS bursts, as illustrated in Fig. 3. A
complete beam sweep of the gNB/UE codebooks thus takes $MT_{SS}$, where
$M=|\mathcal{C}^{u}|$ denotes the number of beam entries in the UE codebook.
The UE sends back a measurement report of the beam sweep, including the SSB-
RSRP, SSB-ID and UE beam ID of the best $N_{CSI-RS}$ candidate BPLs, as shown
in Fig. 3. The UE is consequently initially associated to the gNB which
provides the strongest BPL in terms of SSB-RSRP (_cf._ Sec. 2.3).

Following the initial access, the network sets up the monitoring of candidate
BPLs (_cf._ Step. 2 in Fig. 3). For this, IABA uses dedicated non-zero power
(NZP) CSI-RS resources to monitor the best $N_{CSI-RS}$ candidate BPLs found
during initial access for each UE, with $N_{CSI-RS}\leq 4$ for FR2 [3]. After
selecting the per-UE $N_{CSI-RS}$ BPLs for active monitoring, the network
schedules the NZP CSI-RS CM/IM resources following the 5G-NR standardized
methodology [36]. During the multi-UE BPL allocation, the network utilizes NZP
CSI-RS CM resources for measuring the precoded RSRP/SINR, i. e. using the same
precoding as for potential data transmission on the candidate BPL. Dedicated
NZP CSI-RS IM resources are used to estimate the interference from other
concurrent transmissions via interference-aware CSI-RS scheduling. NZP CSI-RSs
can be transmitted in any orthogonal frequency-division multiplex (OFDM)
symbols as configured by the radio resource control, and take fewer radio
resources, e. g. one OFDM symbol, and are transmitted with lower periodicity
compared to SSBs [3]. Step. 3 in Fig. 3 shows an example MU-MIMO scenario with
three UEs, where one UE receives its NZP CSI-RS for CM while the other two
conduct IM at the same time. IABA uses the dedicated NZP CSI-RS CM/IM to
compute the precoding/combining before each BPL allocation (Step 3 of Alg. 1).
At the UE, this corresponds to the beam entry used to steer the array towards
the candidate BPL. At the gNB, this is reflected as using a different
precoding matrix index for Type II codebooks, which provide multi-beam support
suitable for interference cancellation in HBF MU-MIMO configurations with up
to four spatial layers, as defined in Sec. 5.2.2.2.1–5 in TS 38.214 [33] and
detailed in Sec. 2.4–2.5.

Figure 3: 5G-NR-compliant operation for IABA: (i) SSB-based initial beam sweep
for BPL selection, (ii) scheduling of NZP CSI-RS for BPL monitoring, (iii) NZP
CSI-RS scheduling for MU-MIMO channel/interference measurements.

##  4 Performance Evaluation

###  4.1 Simulation Model

We consider a realistic urban area in Seoul, with the mm-wave network
consisting of gNBs and UEs deployed within a central $500$ m $\times$
$500~{}\text{m}$ network area, as shown in Fig. 4. The gNB deployment follows
a regular distribution on a uniform grid, where the gNB locations are mapped
to the closest building corner near the actual grid position. We consider gNB
deployment densities of $\lambda_{gNB}=\\{64,196\\}$ $\text{gNBs/km}^{2}$. The
sparse deployments are a representative of early mm-wave networks deployed as
a hot-spot capacity extension, whereas the dense deployments correspond to
future mm-wave networks. The UEs are randomly deployed following a Poisson
point process (PPP) with a density of $\lambda_{UE}=1000$ $\text{UEs/km}^{2}$.

We assume an operating carrier frequency of $f_{c}=28$ GHz and a system
bandwidth of $B=400$ MHz, corresponding to 5G-NR FR2 network deployments [2].
We consider saturated downlink traffic, and assume a maximum gNB transmit
power of $P_{max}=30$ dBm and a noise power of $N=-78$ dBm, consisting of
thermal noise over the system bandwidth plus a noise figure of 10 dB. We model
the gNB antenna as per 3GPP’s specifications with a size of up to $N_{t}=1024$
elements and $N^{g}_{RF}=4$ RF chains per sector panel [29], deployed at a
height of 6 m. Each gNB is thus equipped with a total of
$N^{g}_{RF}=N_{sec}N^{g}_{RF,sec}=16$ RF chains. We assume a CBF architecture
at the UE and a multi-sector antenna with $N_{r}=16$ elements per sector
panel, deployed at a height of 1.5 m. The UEs are equipped with $N^{u}_{RF}=1$
RF chain, as per 5G-NR specifications [29]. Throughout, the results represent
Monte Carlo simulations with 20 network realizations of random UE deployments.
Table II summarizes the studied cellular network parameters.

Figure 4: Illustration of the urban site in Seoul, showing the building layout and an example gNB ($\bullet$) and UE ($\times$) deployment over the network study area (green box); $\lambda_{gNB}=64$ $\text{gNBs/km}^{2}$ and $\lambda_{UE}=1000$ $\text{UEs/km}^{2}$. Parameter | Value
---|---
Network area size |  $500$ m $\times$ $500~{}\text{m}$
gNB distribution | uniform grid
gNB density $\lambda_{gNB}$ |  $\\{64,196\\}$ $\text{gNBs/km}^{2}$
gNB height |  $6$ m
UE distribution | PPP
UE density $\lambda_{UE}$ |  $1000$ $\text{UEs/km}^{2}$
UE height |  $1.5$ m
# sector antenna panels $N_{sec}$ | 4
# RF chains per gNB sector $N^{g}_{RF,sec}$ | 4
# RF chains per gNB $N^{g}_{RF}$ | 16
# RF chains per UE $N^{u}_{RF}$ | 1
gNB sector antenna size $N_{t}$ | {256, 1024} elements
UE sector antenna size $N_{r}$ | 16 elements
# bits for steering codebook $n_{q}$ |  {2, 4, 6, 8, 10, $\infty$}
# SSBs $N_{SSB}$ | 64
# monitored CSI-RS $N_{CSI-RS}$ |  {2, 4, $\infty$}
Carrier frequency $f_{c}$ |  $28$ GHz
System bandwidth $B$ |  $400$ MHz
Max. gNB transmit power $P_{max}$ |  $30$ dBm
Noise power $N$ |  $-78$ dBm
Coverage threshold $SINR_{min}$ |  $-5$ dB
Max. achievable throughput $R_{max}$ | 2 Gbps
TABLE II: Studied cellular network parameters.

###  4.2 Results

In the following, we present the results of our extensive study of mm-wave HBF
MU-MIMO performance and the evaluation of IABA under practical network
constraints. In Sec. 4.2.1, we study the baseline performance of IABA and
compare it against default 5G-NR111In [26], we show that IABA outperforms WCS,
as a literature benchmark [25] for spatial BPL allocation in CBF mm-wave SDMA
networks. We expect the same performance trends to hold, and do not include an
explicit comparison against WCS for HBF MU-MIMO in this work. We note that, as
far as we are aware of, there are no other mm-wave networking studies on HBF
MU-MIMO (_cf._ Table. I) that consider multi-UE interference cancellation and
spatial BPL allocation jointly. We therefore select HBF MU-MIMO with default
5G-NR UE association to the strongest gNB and BPL found during initial access
(_cf._ Sec. 2.3) as our main performance evaluation benchmark. for the ideal
case of $n_{q}=\infty$ and $N_{CSI-RS}=\infty$. In Sec. 4.2.2 we study the
effect of candidate BPL monitoring in IABA, and show that IABA significantly
outperforms default 5G-NR under realistic CSI-RS signaling, i. e. $N_{CSI-
RS}\leq 4$. In Sec. 4.2.3 we analyze the effect of quantized CSI feedback, i.
e. $n_{q}<\infty$, on the HBF MU-MIMO performance, showing the benefits of
IABA and performance gains over the default interference-agnostic 5G-NR.
Finally, in Sec. 4.2.4 we study the practical performance trade-offs in terms
of CSI-RS BPL monitoring $N_{CSI-RS}$ and quantized CSI feedback $n_{q}$, and
show that IABA allows HBF MU-MIMO to even outperform the DBF MU-MIMO baseline,
with further benefits of increased gNB antennas and densification in beyond-5G
networks.

####  4.2.1 Beyond 5G-NR Baseline Performance

(a) SINR

(b) INR

(c) SNR

Figure 5: SINR, INR and SNR distribution for the different BPL allocation
approaches, assuming $n_{q}=\infty$, $N_{CSI-RS}=\infty$, i. e. ideal channel
estimation and CSI-RS BPL monitoring, and our baseline network of
$\lambda_{gNB}=64$ BSs/km2, $\lambda_{UE}=1000$ UEs/km2, $N_{t}=256/N_{r}=16$
elements.

(a) Allocated BPL index

(b) Allocated BPL type

Figure 6: Index and type of the allocated BPLs, assuming $n_{q}=\infty$,
$N_{CSI-RS}=\infty$, $\lambda_{gNB}=64$ BSs/km2, $\lambda_{UE}=1000$ UEs/km2,
and $N_{t}=256/N_{r}=16$ elements.

Let us being by studying the performance of IABA, and compare it against the
interference-agnostic, default 5G-NR BPL allocation (referred to as 5G-NR) for
our baseline network deployment of $\lambda_{gNB}=64$ BSs/km2,
$\lambda_{UE}=1000$ UEs/km2, and $N_{t}=256/N_{r}=16$ elements. We
additionally assume ideal channel estimation and CSI-RS BPL monitoring, i. e.
$n_{q}=\infty$ and $N_{CSI-RS}=\infty$. Fig. 5 presents the resulting SINR,
interference-to-noise-ratio (INR) and signal-to-noise-ratio (SNR)
distributions and Fig. 6 illustrates the network BPL allocation, i.e.
index/type of allocated BPLs, for the different BPL allocation schemes.

Fig. 5a shows that the proposed IABA significantly improves both the coverage
and achieved SINR over the 5G-NR baseline. The centralized approach cIABA
improves the coverage by 20 percentage points (pp), and the median SINR by 10
dB over 5G-NR. The distributed approach dIABA also outperforms 5G-NR by 4 pp
in terms of coverage and over 4 dB in the median SINR. Interestingly, while
Fig. 5b confirms that zero-forcing in HBF MU-MIMO fully cancels the intra-cell
interference, there is a significant portion of allocated UEs that are still
affected by strong residual inter-cell interference, i. e. 60% of the UEs for
cIABA and over 45% for dIABA/5G-NR experience inter-cell interference above
the noise floor ($INR>0$). We emphasize that this result is in contrast to
assumptions made in prior mm-wave studies, which typically assume limited to
no-interference due to simplified antenna/channel models, e.g. [24, 25, 19,
17, 18].

Let us further analyze the nature of the residual spatial interference in HBF
MU-MIMO mm-wave networks to gain insight into how IABA achieves its
performance gains over the 5G-NR baseline in Fig. 5a. Zero-forcing cancels
intra-cell interference by projecting the UE’s channel vector on a precoding
vector that is orthogonal to other UEs’ channel vectors (10). The penalty for
this depends on the mutual channel correlation, and is reflected as a loss in
the RSS if the channels are highly correlated, known as the zero-forcing
penalty [12]. The mm-wave channel is sparse, and the effective UE channel
depends on the choice of the beam codebook entries which maximize the RSS of
the candidate BPLs found during initial access. In practice, the chosen beams
amplify certain channel paths and attenuate others, so that the allocated BPLs
in the 5G-NR baseline typically share common strong paths, e. g. for nearby
co-located UEs, which results in high channel correlation. In such cases, the
zero-forcing penalty incurs significant losses in order to fully cancel intra-
cell interference, due to its inability to compensate for the low angular
separation of the allocated BPLs. Namely, always selecting the best RSS BPLs
at initial access for serving all UEs as in 5G-NR results in a high zero-
forcing penalty and thus poor SNR after zero-forcing precoding, as shown in
Fig. 5c. By contrast, the proposed IABA is able to significantly improve the
SNR in Fig. 5c by effectively increasing the angular separation of the
allocated BPLs after zero-forcing via selection of the
$n^{\text{th}}$-strongest BPLs at initial access, as shown in Fig. 6a. By
allocating secondary BPLs to increase the angular BPL separation, i. e. $n>1$,
IABA reduces the zero-forcing penalty and mitigates strong interference that
would otherwise result by only allocating the best RSS BPL, i. e. $n=1$. For
example, 20% of the UEs for dIABA and 57% for cIABA are allocated BPLs other
than the best RSS BPL, as shown in Fig. 6a. Moreover, Fig. 6b shows that 45%
of the UEs are allocated NLOS BPLs for cIABA, compared to 27% for dIABA and
only 19% for 5G-NR. cIABA further improves the overall network performance by
allowing handovers for 21% of the UEs in Fig. 6b, thus having the benefit of
load-balancing and outperforming the other BPL allocation approaches.

In summary, the results in Figs. 5-6 demonstrate the significant benefit of
interference-aware BPL allocation to manage the residual spatial interference
in HBF MU-MIMO mm-wave networks that cannot be mitigated by zero-forcing alone
even under ideal channel estimation ($n_{q}=\infty$).

####  4.2.2 CSI-RS BPL Monitoring for IABA

(a) SINR

(b) Allocated BPL index

(c) Allocated BPL type

Figure 7: SINR distribution and allocated BPL index/type for varying $N_{CSI-
RS}$, assuming ideal channel estimation $n_{q}=\infty$, $\lambda_{gNB}=64$
BSs/km2, $\lambda_{UE}=1000$ UEs/km2, and $N_{t}=256/N_{r}=16$ elements.

Let us next focus on how IABA achieves network-wide performance gains in
practice for our baseline network deployment. Fig. 7 shows the SINR
distribution and the allocated BPL index/type for varying $N_{CSI-
RS}=\\{2,4,\infty\\}$ under ideal channel estimation ($n_{q}=\infty$). Fig. 7a
shows that constraining $N_{CSI-RS}$ has only a limited impact on the achieved
SINR for dIABA. This is because the ideal allocation ($N_{CSI-RS}=\infty$) of
the per-UE BPLs for dIABA picks at most the second best BPL for 88% of UEs,
and 98% up to the fourth best BPL, as shown in Fig. 7b. Limiting $N_{CSI-RS}$
to four thus results in no significant impact of the achievable network
performance for dIABA in Fig. 7a.

In contrast, Fig. 7b shows that cIABA allocates the fifth or higher BPL index
for 19% of the UEs for $N_{CSI-RS}=\infty$. Importantly, only 45% of the UEs
are allocated the best RSS BPL for $N_{CSI-RS}=\infty$, compared to 50% for
$N_{CSI-RS}=4$ and 68% for $N_{CSI-RS}=2$. Thus, limiting $N_{CSI-RS}$ for
cIABA has a more significant impact in terms of SINR degradation in Fig. 7a
than for dIABA. Reducing $N_{CSI-RS}$ also limits the use of secondary NLOS
BPLs for interference mitigation in cIABA, and increases the primary use of
LOS BPLs, e. g. from 37% for $N_{CSI-RS}=\infty$ up to 46% for $N_{CSI-RS}=2$
in Fig. 7c. In addition, the load-balancing rate via handovers drops from 21%
down to 5% for $N_{CSI-RS}=2$ in Fig. 7c. Consequently, Fig. 7a shows that
cIABA with $N_{CSI-RS}=2$ achieves 15 pp lower coverage than cIABA with
$N_{CSI-RS}=\infty$, with its overall SINR performance being comparable to
dIABA with $N_{CSI-RS}=\infty$.

Our results in Fig. 7 thus highlight that CSI-RS BPL monitoring improves both
coverage and achievable SINR, and is particularly important for cIABA.
Limiting the number of monitored candidate BPLs inherently limits the load-
balancing opportunities for cIABA, considering that the best candidate BPLs
found during initial access are provided by the initial serving gNB.
Nonetheless, cIABA monitoring up to the $N_{CSI-RS}=4$ best candidate BPLs –
in line with 3GPP’s specifications for FR2 [3] – is able to reap the benefits
of IABA’s CSI-RS BPL monitoring and significantly outperform 5G-NR in Fig. 7a,
by allocating secondary BPLs to over 50% of the UEs (_cf._ Fig. 7b). This
result demonstrates the practical feasibility of IABA for network-wide,
interference-aware BPL allocation in HBF MU-MIMO networks.

####  4.2.3 CSI Reporting & Channel Feedback Quantization

(a) SINR

(b) $I_{intra}$NR

(c) $I_{inter}$NR

Figure 8: SINR and INR distribution using quantized channel feedback from
varying codebook sizes $n_{q}=\\{4,6,\infty\\}$, assuming $N_{CSI-RS}=4$,
$\lambda_{gNB}=64$ BSs/km2, $\lambda_{UE}=1000$ UEs/km2, and
$N_{t}=256/N_{r}=16$ elements.

(a) Angular misalignment $\Delta\phi$

(b) Gain loss $\Delta G$

Figure 9: Distribution of angular misalignment between the steering
orientation of the codebook main lobe and the ideal BPL orientation
$\Delta\phi$, and the incurred gain loss due to misalignment $\Delta G$,
assuming codebook sizes of $n_{q}=\\{4,6,\infty\\}$ for our baseline network
deployment.

Next, we analyze the performance of IABA assuming quantized channel feedback
for our baseline HBF MU-MIMO network deployment. We set $N_{CSI-RS}=4$ as per
Sec. 4.2.2, and vary the size of the codebooks used for channel estimation,
$n_{q}=\\{4,6,\infty\\}$, as discussed in detail in Sec. 2.4.

Fig. 8 shows the resulting SINR and INR distributions using quantized channel
feedback from varying codebook sizes. Fig. 8a shows that finite codebooks can
achieve good coverage, but lead to significant performance degradation, i. e.
over 10 dB loss in the median SINR for the smallest $n_{q}=4$ codebook
compared to the ideal $n_{q}=\infty$ codebook. Fig. 8a shows that a codebook
of size $n_{q}=6$ bits still suffers from significant SINR loss compared to
the ideal $n_{q}=\infty$ codebook, due to the inability to perform ideal zero-
forcing given the quantized channel estimates. We emphasize that this is
despite the fact that a codebook of size $n_{q}=\\{4,6\\}$ bits does not incur
significant angular misalignment between the steering orientation of the main
lobe for the used codebook entry and the ideal BPL orientation corresponding
to the true channel propagation path, i. e. the misalignment is within the
half-power beamwidth (HPBW) in Fig. 9a. In particular, Fig. 9b shows that a
codebook of size $n_{q}=6$ bits already performs very close to the ideal in
terms of incurred gain loss due to misalignment. Instead the detrimental
effect of the quantized codebook comes from poor intra-cell interference
suppression due to inaccurate channel estimates.

Fig. 8b confirms that, unlike the ideal case of $n_{q}=\infty$, the HBF MU-
MIMO network is unable to fully cancel the intra-cell interference using a
finite resolution codebook, and there is strong residual intra-cell
interference affecting over 60% of UEs for $n_{q}=\\{4,6\\}$, regardless of
the BPL allocation approach. On the other hand, Fig. 8c shows that the extent
of inter-cell interference is not strongly affected as long as the codebook
steering resolution covers the HPBW, as is the case for both codebooks of
$n_{q}=\\{4,6\\}$. Fig. 8b thus highlights that practical limitations on the
channel estimation codebook size and resulting accuracy of channel estimates
strongly limit the extent to which spatial interference in HBF MU-MIMO
networks can be mitigated by interference cancellation techniques such as
zero-forcing. This emphasizes the even greater importance in practical
networks of additional interference mitigation via spatial separation of BPL
allocation for beyond-5G deployments. Fig. 8 shows these benefits of
interference-aware BPL allocation for practical deployments: IABA
significantly improves coverage and SINR over 5G-NR under quantized CSI
feedback $n_{q}=\\{4,6\\}$ and realistic CSI-RS BPL monitoring $N_{CSI-RS}=4$.

####  4.2.4 Towards Practical Interference-aware BPL Allocation for Beyond-5G

Finally, let us analyze the practical performance trade-offs in terms of
channel estimation, CSI availability, and BPL monitoring, towards the
feasibility of interference-aware BPL allocation as the proposed IABA for
beyond-5G mm-wave networks. We consider codebook sizes of $n_{q}=\\{4,6\\}$
bits as per Sec. 4.2.3, and set the number of monitored CSI-RS BPLs $N_{CSI-
RS}=4$ as per Sec. 4.2.2. We then compare HBF MU-MIMO with different BPL
allocation approaches against two reference mm-wave candidate architectures,
both with default 5G-NR BPL allocation:

  1. _(i)_

DBF MU-MIMO: UEs are served via SDMA using DBF and zero-forcing for multi-UE
interference cancellation, following the same system model considerations as
for HBF MU-MIMO in Sec. 2.2–2.4,

  2. _(ii)_

CBF SU-MIMO: UEs are served via TDMA using CBF, corresponding to current 5G-NR
FR2 networks.

(a) SINR ($n_{q}=\infty,N_{CSI-RS}=\infty$)

(b) SINR ($n_{q}=6,N_{CSI-RS}=4$)

(c) Throughput ($n_{q}=6,N_{CSI-RS}=4$)

Figure 10: SINR and throughput distribution for different beyond-5G network
configurations and practical channel estimation and CSI-RS reporting
($\lambda_{gNB}=64$ BSs/km2, $\lambda_{UE}=1000$ UEs/km2, and
$N_{t}=256/N_{r}=16$ elements).

We start with the reference network performance under ideal conditions
($n_{q}=\infty$, $N_{CSI-RS}=\infty$) for our baseline network with
$\lambda_{BS}=64$ BSs/km2, $\lambda_{UE}=1000$ UEs/km2, and
$N_{t}=256/N_{r}=16$ elements. Fig. 10a presents the SINR distribution,
confirming that DBF MU-MIMO performs the best, whereas CBF SU-MIMO is able to
provide high SINR at the cost of reduced coverage. Fig. 10a also shows that
HBF MU-MIMO with default 5G-NR BPL allocation performs the worst, with the
proposed IABA enabling HBF MU-MIMO to close the gap to the DBF MU-MIMO
baseline. In particular, Fig. 10a shows that HBF MU-MIMO with cIABA performs
within 3.5 dB of the DBF MU-MIMO baseline for the median SINR, and
significantly outperforms the default 5G-NR HBF MU-MIMO, e. g. 8.5 dB gain for
the median SINR case.

Let us now move to the more practical network deployments, with Fig. 10b
showing the SINR distribution for the case of $n_{q}=6$ bits and $N_{CSI-
RS}=4$. Comparing Figs. 10a and 10b confirms that both HBF and DBF MU-MIMO
suffer from significant performance degradation due to imperfect interference
cancellation using quantized channel estimates, whereas CBF SU-MIMO
performance is robust since the misalignment loss of the steering codebook is
negligible (_cf._ Fig. 9). Importantly, Fig. 10b shows that HBF MU-MIMO
benefits strongly from the proposed IABA, and is able to outperform DBF over
the complete SINR range. This is also because DBF is particularly affected
under quantized CSI feedback, since the accuracy of the estimated channel
matrix is significantly degraded due to the higher dimensionality
requirements, degrading the multi-UE interference cancellation performance.
Namely, HBF MU-MIMO is affected by a quantized codebook to a lesser extent
than DBF, due its lower requirements on the effective UE channel estimates. To
better understand the network performance, Fig. 10c maps using (16) the SINR
in Fig. 10b to the achievable per-UE throughput for the different
configurations. Fig. 10c shows that HBF MU-MIMO with cIABA outperforms all
other configurations, and achieves a median throughput of $1.35$ Gbps, which
is 35% higher than that of the DBF MU-MIMO baseline. Fig. 10c also shows that
current 5G-NR deployments relying on CBF SU-MIMO are only able to achieve
limited per-UE throughput when a large number of UEs are served on each gNB,
due to the time resource sharing of TDMA. Furthermore, Fig. 10c shows that HBF
MU-MIMO utilizing dIABA achieves better performance for over half of the UEs
compared to the DBF MU-MIMO baseline, though at a cost of somewhat reduced
coverage; this makes the less computationally demanding dIABA particularly
suitable for dense mm-wave SDMA deployments.

(a) Varying $N_{t}$ ($\lambda_{gNB}=64$ gNBs/km2).

(b) Varying $\lambda_{gNB}$ ($N_{t}=256$ elements).

Figure 11: Throughput distribution for the different BPL allocation
approaches, assuming HBF MU-MIMO with varying gNB antenna $N_{t}$ and
deployment density $\lambda_{gNB}$ ($\lambda_{UE}=1000$ BS/km2, $N_{r}=16$
elements).

Our results in Fig. 10 thus highlight that the move towards fully-scaled SDMA
necessitates interference-aware BPL allocation in order to unlock the full
potential of mm-wave for beyond-5G networks. With the envisioned antenna size
increase and network densification, we lastly look at the scalability of IABA
in practical mm-wave HBF MU-MIMO networks. In Fig. 11 we consider the case
when UEs are equipped $N_{r}=16$ elements per sector antenna, and present the
throughput distribution for a larger gNB sector antenna of $N_{t}=1024$
elements and a higher gNB density of $\lambda_{gNB}=196$ gNBs/km2, alongside
our baseline network deployment of $N_{t}=256/\lambda_{gNB}=64$ as shown in
Fig. 10c.

Fig. 11a highlights a strong benefit from increased gNB sector antenna for all
BPL allocation approaches. The proposed IABA yields significant performance
gains when moving from a 256- to 1024-element sector antenna: a two-fold
increase in the median throughput for dIABA from 950 Mbps to 1.88 Gbps, and a
similar increase for cIABA from 1.3 Gbps to 2 Gbps, as show in Fig. 11a. The
increased gNB antenna directionality makes more candidate BPLs feasible for
allocation, thus increasing the gNB’s ability to spatially distinguish nearby
UEs and thus increase the co-scheduled UE BPL separation. For example, more
than half of the UEs get the maximum achievable throughput of 2 Gbps with HBF
MU-MIMO using cIABA, amounting to a 10 pp increase over the interference-
agnostic 5G-NR baseline. Fig. 11a thus shows that large antenna arrays in fact
benefit more from interference-aware BPL allocation, further highlighting the
limiting factor of spatial interference in realistic mm-wave SDMA deployments.

Fig. 11b presents the effect of network densification as another crucial
aspect towards improving the wide-area mm-wave coverage and achievable
performance, assuming $N_{t}=256$ elements per gNB sector. The denser
deployment increases the ability of dIABA and cIABA to mitigate interference,
and in particular, improves the load-balancing effect of cIABA. Fig. 11b shows
that the three-fold increase in gNB deployment density results in a
significant increase in the per-UE achievable throughput – over 60% of UEs get
the maximum achievable throughput using cIABA, compared to the 35% for the
sparse deployment. Similar trends are observed for both dIABA and 5G-NR.
Importantly, Fig. 11b also shows that cIABA achieves full network-wide
coverage for the dense deployment, and a 10 pp improvement in coverage
compared to the 5G-NR baseline. This highlights the primary importance of
interference-aware BPL allocation for mm-wave SDMA in dense network
deployments, thus validating the design strategy of the proposed IABA for
practical beyond-5G HBF MU-MIMO networks.

##  5 Conclusions

We proposed IABA, a 5G-NR standard-compliant BPL allocation scheme, for
mitigating residual spatial interference in practical mm-wave HBF MU-MIMO
networks. IABA solves the network sum throughput optimization via either a
distributed or a centralized BPL allocation using dedicated CSI-RS resources
for candidate BPL monitoring. We presented a comprehensive study of practical
multi-cell mm-wave HBF MU-MIMO networks, and showed that spatial interference
becomes the main limiting factor of HBF MU-MIMO performance, which is in
contrast to prior mm-wave networking studies assuming simplified channel and
antenna models and perfect CSI at the gNB. Our results showed that IABA offers
significant performance gains over default 5G-NR, by facilitating allocation
of secondary BPLs other than the strongest BPL found during initial access.
Importantly, we demonstrated that IABA allows HBF MU-MIMO to outperform the
interference-agnostic DBF MU-MIMO baseline, with further benefits of increased
gNB antennas and densification for beyond-5G mm-wave networks. Our ongoing
work is focused on low-complexity BPL allocation schemes using site-specific
codebooks for adaptive CSI acquisition and further spatial multiplexing gains
in diverse network configuration deployments.

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  *[FR2]: frequency range 2
  *[gNB]: next generation node B
  *[UEs]: users
  *[BPL]: beam pair link
  *[CBF]: codebook-based analog beamforming
  *[DBF]: digital beamforming
  *[RF]: radio frequency
  *[TDMA]: time division multiple access
  *[HBF]: hybrid beamforming
  *[MU-MIMO]: multi-user multiple input multiple output
  *[SDMA]: spatial division multiple access
  *[CSI]: channel state information
  *[LOS]: line-of-sight
  *[NLOS]: non-LOS
  *[CSI-RS]: channel state information-reference signal
  *[URA]: uniform rectangular array
  *[SSB]: synchronization signal block
  *[RSRP]: reference signal received power
  *[SINR]: signal-to-interference-plus-noise-ratio
  *[RSS]: received signal strength
  *[OFDM]: orthogonal frequency-division multiplex
  *[INR]: interference-to-noise-ratio
  *[SNR]: signal-to-noise-ratio
  *[HPBW]: half-power beamwidth