# Extended Reality over 3GPP 5G-Advanced New Radio: Link Adaptation
Enhancements

Pouria Paymard, Abolfazl Amiri, Troels E. Kolding, and Klaus I. Pedersen P.
Paymard and K.I. Pedersen are with the Department of Electronic Systems,
Technical Faculty of IT and Design; Aalborg University, Denmark; E-mail:
<EMAIL_ADDRESS>T. E. Kolding and K. I. Pedersen are with Nokia,
Aalborg, Denmark; E-mail: abolfazl.amiri@nokia.com,{klaus.pedersen,
<EMAIL_ADDRESS>
###### Abstract

One of the rapidly emerging services for fifth-generation (5G)-Advanced is
eXtended Reality (XR) which combines several immersive experiences and cloud
gaming services. Those services are demanding as they call for relatively high
data rates under tight latency constraints, sometimes also referred to as
dependable real-time applications. Supporting as many XR users per cell
requires highly efficient radio solutions. In this paper, we propose an
enhanced channel quality indicator (CQI) that results in a better link
adaptation to unleash the full performance potential of code block group (CBG)
based transmissions for XR cases. We present both an analytical analysis of
the related problems and solutions, as well as an extensive dynamic system-
level performance assessment in line with the 3rd generation partnership
project (3GPP)-defined advanced simulation methodologies. Our results show an
increased XR system capacity of 17% to 33% as compared to what can be
supported by current 5G systems with baseline CQI schemes. We also present
enhanced CQI complexity-reducing techniques based on derived closed-form
expressions that are attractive to the user equipment (UE) implementation.

##  I Introduction

Standardization of the fifth generation (5G) cellular, known as 5G New Radio
(NR), by the 3rd generation partnership project (3GPP) was first realized by
Release-15. Currently, 3GPP is working on Release-18 for 5G-Advanced, which
introduces several key enhancements and support for services, adopting
research findings from both industry and academia. One of the hot topics
considered is extended reality (XR) [1, 2, 3, 4, 5]. XR is an umbrella term
for three popular immersive applications i.e., virtual reality (VR), augmented
reality (AR), and mixed reality (MR) [1]. 5G-Advanced aims an offering
superior XR experience in public, consumer, and industrial sectors. XR
services are characterized by strict quality of service (QoS) requirements. As
an example, typical XR services call for data rates from 30 Mbps to 60 Mbps
with latency constraints from 5 ms to 15 ms for the radio access network part
and reliability targets on the order of 99% to 99.999% [1].

In fulfilling these requirements for as many XR users as possible per cell,
packet scheduling and link adaptation (LA) play a crucial role in assigning
the right amount of radio resources and modulation schemes to users to fulfill
the XR service requirements. LA assigns the modulation and the coding rate of
the error correction scheme based on the quality of the radio link. Two
fundamental components of the LA are the channel quality indicator (CQI) and
outer loop LA (OLLA) which work hand in hand to assess the quality of the
radio link and assign proper resources to satisfy a certain utility function
[6, 7, 8, 9, 10].

5G NR supports code block group (CBG)-based transmissions and associated
hybrid automatic repeat request (HARQ) operation which divides a transport
block (TB) into smaller groups of code blocks (CBs) to maximize the radio
resource usage efficiency in HARQ retransmissions. Basically, each CB has a
cyclic redundancy check (CRC). If one or more CBs in a CBG get failed, the
erroneous CBG should be retransmitted as HARQ acknowledgment (ACK) or
negative-acknowledgment (NACK) bits are provided per CBG in a TB. CBG-based
transmissions are essentially aligned with the transmission of huge payloads
such as XR cases. This can effectively reduce the retransmission payload size
and, accordingly, improve the resource efficiency [11, 12, 13, 14, 15].

###  I-A State of the Art

In the recent 3GPP Release-17 study item on XR over NR [1], the basic modeling
and system-level evaluation methodologies for XR were agreed, including the
definition of several XR-specific performance indicators (KPI). This study
item concluded that the current 5G network can support XR services, but also
identified several directions of possible enhancements to further boot the XR
capacity. A general overview of 3GPP XR research is also available in[2]. In
3GPP 5G-Advanced Release 18, 3GPP is now pursuing the introduction of further
XR enhancements as outlined in [3]. Among others, it includes capacity where
enhanced LA and enhanced CQI (eCQI) are under study.

The open literature is rich in LA studies, hence it would be too exhaustive to
list here. In the following, we therefore only summarize a representative
subset of those that are most relevant for this article. As an example, in [6]
the authors address CQI enhancements that entail biased interference filtering
of the collected channel quality measurements and so-called Worst-M CQI
reporting formats. The study in [7] proposes a machine learning-based approach
to address the CQI feedback delay problem. However, as will be discussed in
greater detail in this paper, currently known CQI designs are not designed to
take full advantage of CBG-based transmissions for XR use cases. OLLA schemes
that operate with traditional HARQ with a single bit ACK/NACK per transport
block are studied in [8, 9, 10]. The work in [8] introduces an algorithm to
improve the link robustness to the signal-to-interference-plus-noise ratio
(SINR) variability for a 5G centimeter-wave concept. Other OLLA approaches are
studied in [9]. The solution in [10] proposes a self-optimization algorithm to
adjust the OLLA initial offset.

There are also several studies of CBG-based transmissions in the literature.
As an example, the authors in [11] , and [12] propose CBG-based multi-bit
feedback approaches. The study in [13] presents new schemes which provide
improvements to the current CB/CBG HARQ feedback scheme. In [14], the authors
introduced a novel multi-level CBG-based HARQ scheme, which also offers
reduced overhead of HARQ feedback. In [15], we proposed two new low-complexity
OLLA algorithms tailored to CBG-based transmissions with multi-bit HARQ
feedback for the XR downlink. Contrary to traditional OLLA algorithms for
controlling the first transport block transmission error rate of 10%, we aimed
at controlling the desired CBG error rate for the first and the second
transmissions. Adopting such solutions was shown to help enhance the XR
capacity.

###  I-B Contributions

In this paper, we propose an eCQI scheme for XR use cases with CBG-based
transmissions. Our main contributions are:

  * •

We present an analytical analysis of the CBG-based transmissions to motivate
its potential advantages for the XR use cases and to determine the desired
block error rate operating point. This includes cases where errors on
individual CBGs are not always independent and identically distributed
(i.i.d.), but also cases with a correlation of different error levels.

  * •

We present a new eCQI scheme that guides the Next Generation NodeB (gNB) for
which modulation and coding scheme (MCS) to use, subject to the actual CBG-
based performance at the terminal.

  * •

Closed-form expressions for calculating eCQI in the terminal are derived that
are attractive for a low complexity implementation.

  * •

We assess the XR performance under realistic system-level conditions with
multiple users, multiple cells, dynamic XR traffic, and accurate modeling of
the major performance-determining radio access network functionalities in line
with [1]. The presented results confirm that there are promising benefits to
gain in terms of higher XR system capacity by adopting CBG-based HARQ schemes
with the proposed eCQI scheme.

###  I-C Structure of the Paper

The rest of this paper is organized as follows. Section II describes the
network model and XR traffic model. Section III states an analytical
assessment of the CBG-based HARQ retransmissions. In Section IV, we propose
the CBG-based. Section V discusses the computational complexity of enhanced
CQI reporting and closed-form expressions to reduce the added complexity.
Section VI includes the simulation setup and the performance evaluation.
Finally, Section VII concludes the paper.

##  II Setting The Scene

###  II-A Deployment Scenario and Frame Structure

We adopt the agreed 3GPP XR system model and related evaluation methodologies
in [1], assuming a time division duplex (TDD) 5G network with orthogonal
frequency-division multiple access (OFDMA). The considered scenario is the
indoor hotspot (InH) deployment with $B$ gNBs. We focus on the downlink (DL)
performance where we assume 100 MHz carrier bandwidth at 4 GHz, 30 kHz sub-
carrier spacing (SCS), and physical resource blocks (PRBs) consisting of 12
sub-carriers [16]. Each slot consists of 14 orthogonal frequency-division
multiplexing (OFDM) symbols. A fixed TDD radio frame configuration with a
DDDSU slot pattern with a 2.5 ms repetition period is assumed, where D, S, and
U denote Downlink-, Uplink-, and Special-slots.

###  II-B XR-Specific 3GPP Traffic Model

Figure 1: The downlink XR traffic model according to Release 17 agreements in
[1].

The assumed downlink XR traffic modeling mimics a case where the XR
application server for view-port rendering or other session techniques is
performed. Then, the traffic is delivered to XR user equipment (UEs) via 5G
the radio access network part in close proximity to the users. XR video frames
are periodically generated at the application server based on a fixed rate of
$\lambda_{f}$ frames per second (fps). The arrival time of XR video frames to
gNB is quasi-periodic because of a random jitter that originates from
encoding, compressing, routing, etc. The random jitter is denoted by $J_{f}$,
which follows a truncated Gaussian distribution
$J_{f}\sim\mathcal{TN}(\mu_{j},\sigma_{j},a_{j},b_{j})$ with mean $\mu_{j}$,
variance $\sigma_{j}^{2}$, and non-zero interval $[a_{j},b_{j}],a_{j}\leq
b_{j}$. The arrival time of video frame $f$ is expressed as

$T_{f}=f\times\frac{1}{\lambda_{f}}\times 1000+J_{f}.$ (1)

The XR video frames have variable sizes due to the applied video compression
algorithms. The video frame size is modeled by a truncated Gaussian
distribution
$\Gamma_{f}\sim\mathcal{TN}(\mu_{\Gamma},\sigma_{\Gamma},a_{\Gamma},b_{\Gamma})$
with mean $\mu_{\Gamma}$, variance $\sigma_{\Gamma}^{2}$, and non-zero
interval $[a_{\Gamma},b_{\Gamma}],a_{\Gamma}\leq b_{\Gamma}$. Throughout the
rest of the paper, a video frame simply is denoted as a packet. The assumed XR
traffic is illustrated in Fig. 1.

###  II-C Radio Resource Scheduling

Scheduled transmissions are assumed, where each gNB dynamically schedules its
users whenever there are pending data in its buffer to be transmitted [17]. If
there are pending HARQ retransmissions, those are always prioritized over the
transmission of new data. Frequency domain multiplexing of users on PRB
resolution, using the well-known proportional-fair (PF) scheduler with the
following scheduling metric:

$u^{\ast}=\operatorname*{argmax}_{u}\left\\{\frac{\psi_{u,\chi}^{r}}{\bar{\psi}_{u}[t]}\right\\},$
(2)

where $t$ and $\chi$ are the transmission time interval (TTI) and PRB indices,
while $\bar{\psi}_{u}[t]$ is the average delivered throughput to UE $u$ in the
past. Moreover, $\psi_{u,\chi}^{r}$ is an estimate of the instantaneous
supported data rate of UE $u$ on PRB $\chi$ with the MCS index $r$. The value
of $\psi_{u,\chi}^{r}$ is obtained from the CQI sent by each UE. Notice here
that the baseline CQI expresses the highest data rate $\psi_{u,\chi}^{r}$ that
can be supported with a TBER less than $P_{\text{Target}}=10\%$. Finally,
Chase Combining HARQ re-transmissions [18] are assumed as the baseline.

For the cases with CBG-based transmissions, each scheduled transport block
(TB) is divided into multiple CBs that are separately encoded and have their
own CRC [19]. The maximum size of a CB is 8448 bits. These CBs are grouped
into CBGs. For each received TB, the receiver provides a multi-bit HARQ
feedback that indicates which CBGs are in error, and only the erroneously
received CBGs are thereafter retransmitted. A CBG is in error if one, or more,
of the CBs are erroneously decoded. The relationship between TB, CB, CBG, and
associated HARQ feedback bits for each CBG is illustrated in Fig. 2.

Figure 2: The construction of $M$ CBGs per TB, each consisting of $C$ CBs.

As defined in the 3GPP technical specification (TS) [19], if a UE is
configured to receive CBG-based transmissions, the UE obtains the number of
CBGs for a TB as $M=\min(F,C)$, where $F$ the maximum number of CBGs per TB is
configurable by radio resource control (RRC) as $F\in\left\\{2,4,6,8\right\\}$
for the physical downlink shared channel (PDSCH), and $C$ is the number of CBs
in the TB. For XR use cases with the described traffic model, we typically
have larger TB sizes with $8$ CBGs per scheduled transmission.

###  II-D Link Adaptation Mechanism

Figure 3: Simplified block diagram showing the link adaptation mechanism and
the partial feedback information from the UEs.

The overall framework for dynamic link adaptation (LA) is illustrated in Fig.
3. The gNB relies on the CQI feedback from the UEs to select the MCS for its
downlink transmissions. The currently standardized 5G NR CQI scheme
corresponds to the highest supported MCS index that the UE can decode with a
transport block error probability (TBEP) of less than a certain predefined
value (default is 10%). We refer to this as the baseline CQI. Note that the
baseline CQI is not having any explicit relation with CBG-based transmissions
as it was originally designed for the TB-based transmission with single-bit
HARQ feedback. The UE can be configured to report the CQI with a certain
periodicity over the number of frequency sub-bands
$\mathcal{S}=\\{1,\cdots,S\\}$. Reporting formats with wideband
($|\mathcal{S}|=1$) and sub-band($|\mathcal{S}|>1$)are supported [19, Table
5.2.2.1-1]. The UE obtains the CQI by performing measurements of the received
post-detection SINR. It uses the measured SINR to look up the highest
supported MCS with a maximum TBEP of less than 10%, assuming the UE has tables
with its TBEP performance versus SINR for different MCSs. See more details for
the 5G NR CQI reporting format in [19, Sec. 5.2].

As illustrated in Fig. 3, the control loop for link adaptation includes time-
variant radio channels, interference, and also delays in CQI reporting and
potential UE measurement imperfections for obtaining the CQI. Therefore, it is
common practice to also apply an OLLA scheme. The OLLA scheme is at the gNB
side, where it monitors the success of past downlink transmissions through the
HARQ feedback and imposes some additional offset on the received CQI before
applying it for MCS selection. Traditional OLLA for TB-based transmission with
Boolean (ACK or NACK) HARQ feedback is studied in [9], and many other
references. An enhanced OLLA (eOLLA) was recently explored in [15] that is
tailored to CBG-based transmissions where multi-bit HARQ feedback is coming
from the UE, i.e. ACK/NACK per CBG. As is described in these OLLA/eOLLA
references, the gNB is able to more accurately control the experienced
TBEP/CBGEP through proper parameterization of step-up and step-down sizes of
the so-called OLLA offset that is applied to the CQI before using it for MCS
selection.

###  II-E XR KPIs

We adopt the XR capacity definitions as earlier agreed by 3GPP in [1]. Here an
XR UE is marked as satisfied if the UE successfully receives more than X% of
the packets within a given packet delay budget (PDB). The XR Capacity is the
maximum number of XR users that can be supported per cell with at least Y% of
them being satisfied. It is assumed that X=99% and Y=90%. Our overall goal is
essentially to propose eCQI enhancements that lead to higher XR capacity as
compared to baseline cases with current CQI methods. In addition to the XR
user satisfaction and capacity, we also consider more generic radio KPIs in
our study. Those include the radio resource utilization that is measured by
monitoring the PRB utilization of the gNBs. The latter is a useful measure to
assess if our proposals result in higher radio resource efficiency for certain
offered traffic conditions. In addition, latency performance per XR packet and
error probabilities for HARQ transmissions are considered.

##  III Analytical Assessment of CBG-based Transmissions

In the following, the behavior of CBG-base transmissions is further analyzed
as the first step toward setting the scene for deriving eCQI schemes in such
cases. We examine the TB and CBG error probability behaviors for different
cases, including correlated and non-correlated error events.

###  III-A Identical and Independent CBGs Case

We start by defining the error probability of a TB, CB, and CBG as
$p^{r}_{\text{TB}}$, $p^{r}_{\text{CB}}$, and $p^{r}_{\text{CBG}}$,
respectively, for the special case of i.i.d. errors of CBs. Here $r$ is the
MCS index as defined in [19, Table 5.2.2.1-2-5]. A corresponding analysis
under such i.i.d. conditions is available in [11, 13, 12]. Therefore,
$p^{r}_{\text{CB},i}=p^{r}_{\text{CB},j}=p^{r}_{\text{CB}}$, $\forall
i,j\in\\{1,\cdots,C\\}$. In order to find the CBGEP, for each CBG $m$, we use
the error probability of the CBs within that CBG with the set of indices
$\mathcal{A}_{m}$, which leads to

$\displaystyle
p_{m}^{\text{CBG},r}=1-(1-p_{i}^{\text{CB},r})^{|\mathcal{A}_{m}|}.$ (3)

If all CBGs contain the same number of CBs, CBGEP will be the same for all
CBGs [20] and (3) can be rewritten as

$\displaystyle p^{r}_{\text{CBG}}=1-(1-p^{r}_{\text{CB}})^{C/M},$ (4)

where subscripts $m$ and $i$ are omitted due to identical properties of the
CBs and the CBGs. Finally, the TBEP can be expressed as

$p^{r}_{\text{TB}}=1-\left(1-p^{r}_{\text{CBG}}\right)^{M}=1-\left(1-p^{r}_{\text{CB}}\right)^{C}.$
(5)

Using simple substitutions, we rewrite the CBGEP as:

$p^{r}_{\text{CBG}}=1-\left(1-p^{r}_{\text{TB}}\right)^{\frac{1}{M}}.$ (6)

Assuming that $n_{e}$ denotes the number of failed CBGs in a TB, the
probability of having at most $N$ failed CBGs out of $M$ CBGs can be obtained
as [15]:

$\displaystyle P_{e}(r,n_{e}\leq
N)=\\!\\!\sum_{n_{e}=0}^{N}\\!\\!\binom{M}{n_{e}}\left(p^{r}_{\text{CBG}}\right)^{n_{e}}\left(1-p^{r}_{\text{CBG}}\right)^{M-n_{e}}.$
(7)

###  III-B Non-identical and Non-correlated Case

We next investigate the cases where the i.i.d. assumptions are no longer
enforced. That is, considering cases with correlated errors among CBs, and
also having different error probabilities per CB (and CBG). For such cases,
the CBGEP can be expressed as

$\displaystyle
p_{m}^{\text{CBG},r}=1-\bigcap_{i\in\mathcal{A}_{m}}(1-p_{i})^{\text{CB},r},$
(8)

that generalizes (3) for uneven CB error probabilities which can be a result
of variable effective SINR among the CBs of one CBG. For the sake of
simplicity, we now drop the superscript CBG and $p^{r}_{m}$ will refer to
CBGEP of CBG $m$ at MCS index $r$. The probability of only one CBG failing
i.e, $N=1$, is expressed:

$\displaystyle
P_{e}(r,1)=\sum_{m\in\mathcal{M}}p^{r}_{m}\bigcap_{j\in\mathcal{M}\setminus
m}(1-p^{r}_{j}),$ (9)

where $\mathcal{M}=\\{1,\cdots,M\\}$ and $\mathcal{M}\setminus m$ refers to
set exclusion where element $m$ is discarded from $\mathcal{M}$. Extending
this expression for a general value for $N$ results in:

$\displaystyle P_{e}(r,N)$
$\displaystyle=\frac{1}{N!}\underbrace{\sum_{m_{1}\in\mathcal{M}^{(0)}}p^{r}_{m_{1}}\cdots\sum_{m_{N}\in\mathcal{M}^{(N-1)}}p^{r}_{m_{N}}}_{N\text{times}}\quad$
(10)
$\displaystyle\times\bigcap_{m_{N+1}\in\mathcal{M}^{(N)}}(1-p^{r}_{m_{N+1}}),$

which is the direct extension of Binomial distribution in (7). Here,
$\mathcal{M}^{(t)}$ is set $\mathcal{M}$ with the exclusion of $t$ elements
where this exclusion is done after each of the inner summations and product
operators (for (9) $\mathcal{M}\\!\setminus\\!m$ is equivalent to the case
$t=1$). As can be seen from (10), as $N$ grows, these calculations become
tedious to evaluate. We return to this issue in V-A and propose some methods
for complexity reduction.

###  III-C Correlated Case

So far, we assumed independence between $p_{m}$s which may not always be the
case in reality. So here we study the correlated scenario for identical
$p_{m}$s. Assume a probability distribution of $Y=W_{1}+\cdots+W_{M}$, where
$W_{m}$, $m=1,\cdots,M$ are binary variables (i.e. CBG CRC checks) with mean
value and variance of $E(W_{m})=p_{m}$ and $\text{Var}(W_{m})=p_{m}(1-p_{m})$,
respectively. Additionally, there is a correlation coefficient of
$\text{Corr}(W_{m},W_{n})=\rho$, $m\neq n$. In our model, $0\leq\rho\leq 1$ is
a function of similarities between the assigned PRBs to each of the CBGs. The
probability distribution of $Y$ is found by the mixture of the distributions
of two variables [21]: a binomial distribution, $B(N,p)$, where
$p=p_{1}=\cdots=p_{m}$ is CBGEP, with a mixing coefficient of $(1-\rho)$ and a
modified Bernoulli distribution, $MBern(p)$111This distribution is taking
values $0$ or $n$ [22], rather than the conventional values 0 or 1. with a
mixing probability of $\rho$. Thus, the probability distribution of $Y$ is
given by

$\displaystyle\tilde{P}_{e}(r,N,\rho,M)$
$\displaystyle=\\!\\!{\binom{M}{N}}\\!(p^{r})^{N}(1\\!-\\!p^{r})^{M-N}(1\\!-\\!\rho)\delta_{A_{1}}\\!(\\!N)$
(11)
$\displaystyle+p^{r,\frac{N}{M}}(1-p^{r})^{\frac{M-N}{M}}\rho\delta_{A_{2}}(N)$

where $p^{r}=p_{1}^{r}=\cdots=p^{r}_{m}$ is CBGEP for all CBGs for MCS $r$,
$A_{1}=\\{0,1,\cdots,M\\}$, $A_{2}=\\{0,M\\}$ and $\delta_{\mathcal{X}}(x)$ is
the Delta function that is equal to $1$ if $x\in\mathcal{X}$ and is $0$
otherwise. It is worth mentioning that we do not study the case of correlated
and non-identical probability function, i.e. generalized form of (10), as it
is very complex to derive a closed-form function.

Figure 4: The probability of having at most $N$ failed CBGs for identical and
non-identical cases when there are $8$ CBGs in a TB.

In Fig. 4, we show the probability of having at most $k$ failed CBGs in a TB
for different identical, correlated, and non-identical cases. For correlated
cases, we assumed a correlation coefficient of 70% which is considered to be a
strong correlation between CBGEPs. As can be seen, the probability of having
two or less failed CBGs is roughly close to 1 for i.i.d cases (as an example,
the ratio is $99.8\text{\,}\mathrm{\char 37\relax}$ if
$P_{e_{\text{TB}}}=$10\text{\,}\mathrm{\char 37\relax}$$.). It is observed
that even for the correlated or non-identical CBGEP cases there is a high
probability of 90% having two or fewer failed CBGs in a TB. The worst-case
scenario in the figure happens when CBGs experience non-identical random CBGEP
distributions between 0 to 1. As an example of the worst-case scenario, the
probability of having at most five failed CBGs is about 85%. The results also
clearly show that if using the current baseline CQI scheme with a fixed TB
error rate target of 10%, the CBG errors will vary significantly depending on
the assumptions. This is undesirable as we prefer a link adaption scheme where
we more accurately control the number of failed CBGs per TB transmission, and
the corresponding error probabilities. This is desirable, so we are able to
control the number of resources used on HARQ retransmissions as this is
important for maximizing the XR capacity.

##  IV eCQI for CBG-based transmissions

Our hypothesis is that we will be able to further boost the XR capacity by
introducing an eCQI scheme where we are able to more explicitly control the
CBG errors, as compared to using the current baseline CQI that aims for 10%
TBEP. What we propose is an eCQI scheme where at most $N$ out of $M$ CBGs in a
TB transmission are in error with probability $P$. This allows controlling the
radio resources used for HARQ retransmissions while using the highest possible
MCS under such constraints. Given this starting, we present an eCQI solution
for this, assuming that parameters $N$, $M$, and $P$ are configured by the
network for the UEs; may e.g. be realized by RRC signaling as part of the
channel state information (CSI)-ReportConfig information element as defined in
[23].

The proposed eCQI method is summarized in Alg. 1.

Result: Highest MCS index to satisfy a given condition

_Initialize:_ $M$, $N$, $P$, tables to convert SINR (or MMIB) to error
probability per each MCS index.

1\. Calculate the effective SINR of each CB $\gamma_{i}^{\text{CB}},\forall
i\in\\{1,...,C\\}$.

for  _$r\in\mathcal{R}$ _ do

2\. Calculate error probability of each CB $p_{i}^{\text{CB}},\forall
i\in\\{1,...,C\\}$ using curves for MCS index of $r$.

3\. Find CBG error probability $p_{m}^{r}$ and $m\in\\{1,...,M\\}$ using (8).

4\. Calculate $P_{e}(r,N)$ using (10).

if  _Stopping criterion is met (e.g. for eCQI $\hat{P_{e}}(r,N)>P$)_ then

5\. Break.

else

6\. Choose the next element in $\mathcal{R}$ for $r$.

end for

7\. report $r\\!-\\!1$ as the best MCS index.

Algorithm 1 Generic calculations for eCQI.

After the UE has performed measurements of its experienced SINR, the effective
SINR of each CB can be calculated. The effective SINR values are mapped to
error probability values for each MCS index $r$ employing tables in the UE
that are pre-configured [13]. This may also be conducted using the mean mutual
information per bit (MMIB) metric and then using corresponding tables to
determine error probabilities [24]. Thereafter, $p_{i}^{\text{CB},r}$s are
used to calculate CBGEP from (8) and $P_{e}(r,N)$ from (10). These steps are
repeated for the MCS indices $r\in\mathcal{R}$ until the stopping condition of
$\hat{P}_{e}(r,N)=\sum_{i=0}^{N}P_{e}(r^{\ast},i)>P$ is met. Finally,
$r^{\ast}-1$ is reported as the highest supported eCQI index. Similar to the
baseline CQI scheme, eCQI reporting may be periodical or event-based.

##  V Complexity reduction for eCQI calculation

The eCQI should be realized in the UE with as low complexity as possible. As
can be seen from (10), as $N$ grows, these calculations become tedious to
evaluate and the problem becomes more severe due to limited processing power.
In order to address this challenge, we derive closed-form expressions for
$P_{e}(r,N)$ to reduce the eCQI complexity. These include several attractive
searching techniques for the main loop in Alg. 1.

###  V-A Closed-form Solutions for Special Cases

Considering an arbitrary number of CBGs in one TB $M\leq 8$, we derive closed-
form expressions for the probability calculations in (10) for values of
$N\in\\{0,1,2,3\\}$. Expressions for $N>3$ are more complex and omitted for
this paper. However, the extension of the methods used for $N<4$ cases is
straightforward for any arbitrary $N$ and can be achieved by following the
same steps as the cases stated below. Before starting to derive the closed-
form solutions, we define the Odds ratio (OR) of a random variable which is
defined as

$\displaystyle O_{m}=\frac{p_{m}}{1-p_{m}}$ (12)

which shows the ratio between the success and failure probability of an event
for our Bernoulli random variables. Now, by rewriting (9), we have

$\displaystyle P_{e}(r,1)$
$\displaystyle=\sum_{m\in\mathcal{M}}p^{r}_{m}\bigcap_{j\in\mathcal{M}\setminus
m}(1-p^{r}_{j})$ (13)
$\displaystyle=\Pi\sum_{m\in\mathcal{M}}\frac{p^{r}_{m}}{1-p^{r}_{m}}=\Pi\sum_{m\in\mathcal{M}}O^{r}_{m}=\Pi
M\bar{O^{r}}$

where,
$\Pi=P_{e}(r,0)=\bigcap_{m\in\mathcal{M}}(1-p^{r}_{m})=\bigcap_{m\in\mathcal{M}}\frac{1}{1+O^{r}_{m}}$
and the bar operator in $\bar{X}$ stands for the average value of variable
$X$.

Extending this result for the case of $N=2$ is straightforward. Using (10) for
$N=2$ leads to

$\displaystyle P_{e}(r,2)$
$\displaystyle=\\!\frac{1}{2!}\\!\sum_{m_{1}\in\mathcal{M}^{(0)}}\\!\\!p^{r}_{m_{1}}\\!\\!\sum_{m_{2}\in\mathcal{M}^{(1)}}\\!\\!\\!p^{r}_{m_{2}}\quad\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\bigcap_{m_{3}\in\mathcal{M}^{(2)}}\\!\\!\\!\Bigl{(}1-p^{r}_{m_{3}}\Bigr{)}$
(14) $\displaystyle=\frac{\Pi
M^{2}}{2}\Bigl{(}2\bar{O^{r}}^{2}-\text{Var}\bigl{(}O^{r}\bigr{)}\Bigr{)}$

where $\text{Var}(\cdot)$ is the variance operator.

###### Proof.

Please see Appendix A. ∎

Finally, extending the solutions for the case with $N=3$ with a similar
approach is given by.

$\displaystyle
P_{e}(r,3)=\frac{\Pi}{3!}\\!\\!\\!\sum_{m_{1}\in\mathcal{M}}\\!\\!\\!O^{r}_{m_{1}}\\!\\!\\!\sum_{m_{2}\in\mathcal{M}\setminus
m_{1}}\\!\\!\\!O^{r}_{m_{2}}\\!\\!\\!\sum_{m_{3}\in\mathcal{M}\setminus
m_{1},m_{2}}\\!\\!\\!\\!\\!\\!O^{r}_{m_{3}}$ (15)
$\displaystyle=\frac{M^{3}\Pi}{6}\Biggl{[}-2\Bigl{(}\bar{O^{r}}\Bigr{)}^{3}\\!-\\!3\bar{O^{r}}\text{Var}\Bigl{(}O^{r}\Bigr{)}\\!+\\!2\\!\\!\sum_{m\in\mathcal{M}}\\!\\!\Bigl{(}O^{r}_{m}\Bigr{)}^{3}\Biggr{]}$

###### Proof.

Please see Appendix B. ∎

Note that the last term in (15) can be calculated using the 3rd derivation of
the moment generating function of the random variable $O^{r}$. Further cases
for $N>3$ closed-form solutions can be obtained by similar approaches used so
far. The key point is to start from (10) and convert the expressions to be a
function of the OR. Then, by factorizing similar summations, low complexity
expressions can be found directly.

If the eCQI is configured in a way that it ensures having exactly $N$ failed
CBGs out of $M$ CBGs with probability $P$, then the expressions derived in
(13), (14), and (15) can be used directly. For instance, if the configuration
notifies at exactly $2$ failed CBGs, then the threshold comparison should be
done with $P_{e}(r,2)$.

###  V-B CQI Index Searching Schemes

Another main component in controlling the complexity of the eCQI is the
searching method of different MCS indices. In other words, if the MCS index
list $\mathcal{R}$ is ordered in a smart way, a proper eCQI (or CQI) index can
be obtained faster with fewer computations. Therefore, we analyze and propose
different methods to optimize the searching space size to adjust the
accuracy/complexity trade-off to find the best MCS index.

####  V-B1 Descending / Ascending Order

This linear search method (LSM) is the default way of iterating Alg. 1 over
different MCSs. For the case of descending order, the ordered list is made as
the following $\mathcal{R}=\\{r_{1},\cdots,r_{I}|r_{i}>r_{i+1}\\}$ with $I$ as
the total number of MCS indices. Similarly, for the case of ascending order,
we have $\mathcal{R}=\\{r_{1},\cdots,r_{I}|r_{i}<r_{i+1}\\}$. The benefit of
this type of listing is that they have almost no overhead complexity for
generation at the receiver. On the other hand, they are not optimal and may
result in added processing time since Alg. 1 may require iterating over many
elements before reaching the right index. In the following, we present several
alternative searching methods to speed up the eCQI calculations.

####  V-B2 Binary Search Method (BSM)

This method focuses on the order of steps in which the MCS index is checked in
Alg.1. Therefore, a simple index list, such as the one described in subsection
V-B1, can be used to begin with. Then, $r=I/2$ can be used for the initial
value. After calculating $P_{e}(r,N)$, depending on its comparative logic to
$P$, the next $r$ will be decided using a simple BSM. In other words, starting
with $r_{\frac{I}{2}}$ and for each $r$, if $P_{e}(r,N)>P$, then the next
index should be in the lower half of the MCS list. Thus, the next $r$ is
$r_{\frac{I}{2}-\frac{I}{4}}=r_{\frac{I}{4}}$. Likewise if $P_{e}(r,N)<P$,
then the next index should be in the upper half of the MCS list and
$r_{\frac{3I}{4}}$. This mechanism continues until for some $r_{i}$, we have
$P_{e}(r_{i},N)<P$ and $P_{e}(r_{i+1},N)>P$. A flowchart of embedded BSM in
the eCQI index determination is shown in Fig. 5. As illustrated there, for
each entry in the CQI table, the UE calculates (10) using one of the closed-
form solutions provided in the previous section. Depending on the outcome of
$P_{e}(r,N)\overset{?}{<}P$, the next index is determined via the BSM. The
process continues until the highest index that satisfies the target
probability condition is found.

Figure 5: The flowchart of embedded BSM in the eCQI index determination.

####  V-B3 Relaxed Decision Criterion

This method is an alternative to the argument in the ‘if’ condition in Alg.1,
where instead of having a firm decision boundary at $P$, a small tolerance
factor is included in the condition. This can be done with
$|P_{e}(r,N)-\delta_{p}|\overset{?}{<}P$, where $\delta_{p}$ allows a small
room for the error probability variation. This condition can be used in two
ways: 1) any $r$ satisfying it is reported or 2) the next $r$ in $\mathcal{R}$
is reported without going into the steps of Alg.1 to avoid additional
calculations.

In order to choose a proper searching method, we evaluate the complexity of
each method in the next subsection.

###  V-C Complexity Analysis

We compare the computational complexity of the direct calculations of (10) and
the closed-form solutions for the eCQI technique in terms of the number of
multiplications. We focus on two main parts which are the execution of (10)
and the size of the CQI index search space $|\mathcal{R}|$. The reason for
this choice is that these two are the main components of controlling the
complexity of Alg.1, as the former one is repeated $1\leq t\leq|\mathcal{R}|$
times until the algorithm finds the proper CQI index. It is true that there
are several other steps in Alg.1 that require processing resources, yet for
the sake of comparison, we ignore those since they have the same complexity no
matter which method is used for probability derivations.

####  V-C1 Complexity for the Execution of (10)

As a baseline method, we assume direct calculations of (10), where a series of
multiplications are done sequentially until all cases of failed CBGs are
covered based on a given $N$. Starting from the simplest case of $N=1$ in (9),
the complexity is equal to $M(M-1)=M^{2}-M=\mathcal{O}(M^{2})$
multiplications. For $P_{e}(r,2)$ the result is
$M(M-1)M/2=\mathcal{O}(\frac{1}{2}M^{3})$. With a straightforward extension
for any arbitrary $N$, the complexity for the execution of (10) is given by

$\displaystyle
C_{\text{Direct}}=M\binom{M}{N}=\frac{MM!}{(M-N)!N!}=\mathcal{O}(\frac{1}{N!}M^{N+1}).$
(16)

With a similar approach, we try to derive the complexity of our proposed
method to calculate (10). It is worth mentioning that the proposed expressions
are in form of functions of the OR $O^{r}$ and thus, it is expected that
calculating $O^{r}$ is done directly from SINR values. This can be done
utilizing a set of new curves that map SINR to $O^{r}$ and can be generated
using the SINR to TBEP curves and transformation in (12). For the case of
$N=1$ in (13), the only term containing multiplications is $\Pi$ that requires
$M=\mathcal{O}(M)$ multiplications. Similarly, for $N=2$ in (14) we have
$M+M+1=2M+1=\mathcal{O}(2M)$ multiplications which is from calculating $\Pi$,
$\sum_{m_{1}\in\mathcal{M}}(O^{r}_{m_{1}})^{2}$ and
$(\sum_{m_{1}\in\mathcal{M}}O^{r}_{m_{1}})^{2}$, respectively. Likewise, for
$N=3$ in (15) there are $3M+3=\mathcal{O}(3M)$ multiplications. Thus, by
extending these results, for a general $N$ value we have

$\displaystyle C_{\text{Closed}}=\mathcal{O}(NM).$ (17)

As can be seen from the complexity expressions, our proposed method has a
better behavior concerning $M$ and $N$, i.e.
$C_{\text{Direct}}>C_{\text{Closed}}$. The lower complexity is a result of
factorizing the repeated operations and doing them only once instead of
calculating long summation loops.

####  V-C2 CQI Index Searching Space Size

Another main component in determining the complexity of Alg.1 is the number of
iterations after step 1 that scales the number of total multiplications
linearly. For the baseline case of descending/ascending order, the size of the
search space is $|\mathcal{R}|$ in the worst-case scenario and is equal to
$\frac{|\mathcal{R}|}{2}$ on average. This is due to the fact that the UE will
start checking all indices from the beginning to the end of the CQI tables of
[19, Table 5.2.2.1-2-5] and on average it may end up searching half of the
entries. On the other hand, the complexity of the BSM is much lower and is
$\log_{2}(|\mathcal{R}|)$ due to the step-wise halving of the search space.
Finally, for the relaxed decision scheme, the search space size could be
realized as $\alpha\log_{2}(|\mathcal{R}|)$ with $0<\alpha=f(\delta_{p})\leq
1$, where the complexity can be scaled as a function of $\delta_{p}$. However,
there is an inverse relation between $\alpha$ and TBEP, as for a more relaxed
decision criterion, the resulting error rate will increase.

Figure 6: Complexity comparison between the proposed and baseline methods in
terms of number of multiplications in logarithmic scale.

Figure 6 shows a comparison of the complexity of different combinations of
eCQI determination and searching methods. As can be seen, the lowest
computational load and our preferred solution can be achieved by choice of the
closed form type solution and a BSM for the CQI index selection part.

##  VI Numerical Evaluations

###  VI-A 3GPP-Specific Simulation Methodology

To evaluate the performance of the proposed methods, we use highly realistic
dynamic system-level simulations, where the performance-determining parts of
radio access network mechanisms such as dynamic packet scheduling, link
adaptation, HARQ, as well as time- and frequency-varying inter-cell
interference are accurately accounted for. We adopt the simulation methodology
and modeling for 5G NR, as agreed in the 3GPP technical report [1], and also
used in the following studies [2, 15]. We chose system-level simulations as
our methodology here to obtain results with a high degree of realism in highly
dynamic multi-cell and multi-user settings as deriving the performance in
terms of achievable XR capacity is not analytically traceable. All simulations
are carried out using the Monte Carlo approach with long simulation runs to
obtain statistically reliable results.

TABLE I: Summary of System-level Evaluation Parameters Parameter | Setting | Parameter | Setting
---|---|---|---
Simulation time | 10 seconds (20,000 slots) | Simulation runs | 10 runs per result
Deployment | InH (120m$\times$50m) | Layout | 12 cells
Inter-site Distance | 20 m | TDD Frame structure | DDDSU
TTI length | 14 OFDM symbols | Carrier frequency | 4 GHz
System Bandwidth | 100 MHz | SCS | 30 kHz
MIMO scheme | SU-MIMO with rank 1 | Modulation | QPSK up to 256QAM
gNB height | 3 m | gNB power | 31 dBm
gNB Tx processing delay | 2.75 OFDM symbols | gNB antenna | 1 panel with 32 elements
|  | (4 × 4 and 2 polarization)
UE Rx processing delay | 6 OFDM symbols | UE height | 1.5 m
UE speed | 3 km/h | UE antenna | 4 omni-directional antennas
|  | (2 × 1 and 2 polarization)
Jitter distribution |  $\mathcal{TN}(0,2,-4,4)$ ms | Frame size (30Mbps) |  $\mathcal{TN}(62,6,31,93)$ kB
Frame size (45Mbps) |  $\mathcal{TN}(93,10,46,140)$ kB | Frame rate | 60 fps
Source data rate | 30 Mbps, 45 Mbps | Packet delay budget | 10 ms, 15 ms
HARQ scheme | Chase combining | HARQ retransmissions | Up to 3 retransmissions
CSI | Periodic CQI every 2 ms | Initial OLLA Offset | 0 dB
Upper limit of OLLA Offset | 15 dB | Lower limit of OLLA Offset | -25 dB

Simulation assumptions/parameters are summarized in Table I. We simulate an
InH scenario as described in [1], where the 3D radio channel propagation model
is calibrated against alike results published in 3GPP. The scenario is
composed of 12 gNBs. XR UEs are randomly distributed in the network according
to a spatial uniform distribution. Serving cell selection is based on the
strongest reference signal received power (RSRP) criteria. TDD mode is
adopted, where we assume a DDDSU slot pattern. Each slot is having a duration
of 0.5 ms and is composed of 14 OFDM symbols where the first symbol of each
slot is always carrying control overhead such as scheduling grants on the
physical downlink control channel (PDCCH). In the special slot, the first ten
symbols are allocated for downlink, two symbols are for a gap, and the last
two symbols are for uplink. Simulations are conducted at the symbol level
(time-domain) and sub-carrier resolution (frequency-domain).

For LA purposes, UEs report the CQI index periodically in the uplink slot. We
assume CQI reporting every 2 ms with a CQI reporting delay of 2 ms. The
scheduler is PF. Asynchronous adaptive HARQ with Chase Combining for failed
transmissions is assumed, where the post-processing SINR equals the linear sum
of SINRs of the different HARQ transmissions (first transmission and
subsequent retransmissions) [25]. Error-free ACK/NACK feedback is assumed from
UEs. The maximum number of HARQ retransmissions is set to three. For every TTI
the effective SINR for each scheduled user is calculated per resource element
(RE). Based on those SINR samples per RE for each scheduled UE, the effective
SINR is applied for link-to-system-level mapping to determine MMIB [24]. The
MMIB is calculated as

$\displaystyle\text{MMIB}=\frac{1}{N_{\text{CBS}}}\sum_{b_{i}\in
N_{\text{CBS}}}1-H\left(\frac{1}{1+\exp(|\text{LLR}_{b_{i}}|)}\right),$ (18)

where, $N_{\text{CBS}}$ is the number of bits per each CB, $H(\cdot)$ is the
mutual information operator and $\text{LLR}_{b_{i}}$ is the Log Likelihood
Ratio (LLR) of bit $b_{i}$. Results from link simulations are used to convert
the MMIB metric to an error probability to determine if the transmission is
successfully decoded or failed [26].

###  VI-B Performance Results

In the following we present results from the dynamic system-level simulations
for the following cases:

  1. 1.

Baseline CQI with TB-based Tx, TBER target=10%: Corresponding to a selection
of the highest MCS while not exceeding the 10% TBER target with TB-based
transmission and single-bit HARQ feedback is per TB. Traditional OLLA with 10%
TBER target is assumed.

  2. 2.

Baseline CQI with CBG-based Tx, TBER target=10%: Corresponding to the
selection of the highest MCS while not exceeding 10% TBER target for the TB
while assuming CBG-based transmissions and multi-bit HARQ feedback so only
failed CBGs are retransmitted. Traditional OLLA with 10% TBER target is
assumed.

  3. 3.

eCQI with CBG-based Tx and eOLLA: Using the proposed eCQI scheme and the eOLLA
scheme from [15] is to control the CBG error probability.

The setting of parameters $N$ and $P$ are selected based on a series of
simulations to use the setting that results in the best performance in terms
of XR capacity. For the considered XR cases with large TBs typically
containing $M=8$ CBGs, we find that a reasonable default setting is $N=4$ and
$P=50\%$, meaning that the eCQI corresponds to the maximum supported MCS with
at most out of 8 eight failed CBGs with 50% probability.

(a) Experienced CB SINR

(b) Experienced CBG SINR

Figure 7: The experienced CB/CBG SINR values for a certain TB of a UE in the
network.

Fig 7(a) shows the experienced CB SINRs (in dB) for the multiple TBs in the
first transmissions for a certain UE in the network. As can be seen, there is
a correlation among CB SINR values. In addition, the CBs in a TB experience
uneven SINR values which result in non-identical CB and CBG error probability.
This confirms that we cannot assume i.i.d. errors of the individual CBs (and
hence also CBGs), and hence must take correlations and different values of
error probabilities for the CBs (and CBGs) into account as expressed in
Section III.

Figure 8: Empirical CDF of MCS index selection when the minimum required data
rate is 45 Mbps and there are 5 UEs per cell.

Fig. 8 shows the empirical cumulative distribution function (CDF) of MCS
selection for different schemes, assuming an offered load of 5 XR users per
cell with 45 Mbps application layer throughput. As can be seen, the proposed
eCQI method selects higher MCS indices than the baseline cases, resulting in
higher radio resource efficiency. For example, eCQI with $N=4$ selects the
highest MCS index 80% of the time, while the baseline with CBG transmissions
chooses the highest MCS index 40% of the time. This confirms the desired
behavior, where gNB selects higher MCS indices for the CBG-based transmissions
as this can be afforded, given that still only a fraction of the CBGs will
fail in the first transmission, resulting in more resource-efficient
transmissions.

Fig. 9 shows the empirical CDF of the PRB utilization in the network for
offered load levels of 3 and 5 XR users per cell. For the low load scenario,
there PRB utilization is displaying only marginal differences, while more
significant gains in PRB utilization are observed for the high load scenario,
where the eCQI scheme outperforms the baseline cases. The proposed eCQI scheme
with $N=4$ improves the resource utilization by 17% at the 50th percentile as
compared to the baseline. This resource efficiency gain originates from
partial CBG retransmissions and higher MCS selection as shown in Fig. 4 and
Fig. 8, respectively.

(a) Data rate=45 Mbps, 3 UEs per cell

(b) Data rate=45 Mbps, 5 UEs per cell

Figure 9: Empirical CDF of PRB utilization for the different XR QoS
requirements and loads in the network.

(a) Data rate=45 Mbps, 3 UEs per cell

(b) Data rate=45 Mbps, 5 UEs per cell

Figure 10: 99th percentile of the empirical CDF of application layer delay for
the different XR QoS requirements and loads in the network.

Fig. 10 shows the 99th percentile of the empirical CDF of the application
layer packet delay for the different load levels with an XR data rate of
45Mbps. It is observed that the delay performance is roughly the same in the
low load case, while clear gains are observed for the high load case. This is
because temporal variations of queuing at the gNB occur for the high load case
especially for the baseline CQI cases, while this happens less often for the
eCQI cases as users are served more efficiently on the radio interface.

(a) QoS requirement: data rate=30 Mbps, PDB=10ms

(b) QoS requirement: data rate=30 Mbps, PDB=15ms

(c) QoS requirement: data rate=45 Mbps, PDB=10ms

(d) QoS requirement: data rate=45 Mbps, PDB=15ms

Figure 11: System capacity: the supported number of UEs per cell when at least
$90\text{\,}\mathrm{\char 37\relax}$ of them are marked as satisfied UEs. A
satisfied UE should successfully receive more than $99\text{\,}\mathrm{\char
37\relax}$ of its own packets within the PDB [1].

The main results related to XR capacity assessment are displayed in Fig. 11
where the fraction of satisfied users is plotted. The results are shown for
different numbers of UEs per cell for four different XR QoS requirements with
XR source data rates of 30Mbps and 45Mbps, and PDB values of 10ms and 15 ms.
Recall that the XR capacity is defined as the maximum number of supported
users per cell, while at least 90% of those are satisfied. The case 30Mbps
corresponds to the so-called ”single eye” video streaming, while the 45Mbps
case is representing “dual eye” applications. As expected, the higher data
rate cases consume more radio resources so less number of UEs can be satisfied
per cell. Overall, the proposed eCQI scheme outperforms the baseline cases in
all the scenarios. It can be observed that eCQI with $N=4$ supports one more
XR UE per cell as compared to the CQI baseline cases. This is equivalent to a
system capacity gain of 17% to 33% for the different XR scenarios. This is a
result of being more resource-efficient when using the eCQI scheme as also
pictured in Fig. 9. It is furthermore observed that the XR capacity decreases
with few users when the PDB is tightened from 15ms (typical value for cloud
gaming applications) to 10ms (typical value for AR and VR cases). The relative
XR capacity of using eCQI over baseline CQI is typically higher for the higher
XR data rates and lower PDB values, i.e. in the range where there is the most
need for improving the otherwise modest XR capacity.

##  VII Conclusions

This paper has introduced an eCQI scheme for 5G-Advanced XR use cases to
unleash the full performance potential of CBG-based transmissions. The eCQI
provides valuable feedback to the gNB that enables it to conduct more accurate
link adaptation, where only up to $N$ out of $M$ CBGs are in error with
probability $P$. This complements the recently published eOLLA scheme for also
controlling the CBG error rate.

Our analytical assessment of the CBG-based transmission performance shows
significant differences depending on whether individual CBs (and CBGs) have
i.i.d. errors, or whether they are correlated and potentially have different
error probabilities. Our results from the dynamic system-level simulations
show that the i.i.d. assumption is not valid under realistic conditions as we
typically observe some correlation and also different error probabilities per
CB/CBG as a result of time-frequency variations of the experienced
interference per CB/CBG at the receiver. Our XR system-level capacity
assessments show attractive gains of 17-33% from using the eCQI scheme as
compared to baseline CQI. The gains are often larger for the more challenging
XR use cases with higher application source data rates and tighter PDB. The
obtained gains confirm the eCQI benefits of being able to more accurately
guide the gNB for proper selection of the MCS, capturing the UE experienced
CBG performance characteristics. The complexity at the UE for calculating the
eCQI feedback based on radio channel SINR measurements is also assessed. For
this purpose, we derived linear closed-form expressions that are easy to
implement in the UE for a low complexity eCQI realization.

##  Appendix A proof of closed-form for (14)

$\displaystyle
P_{e}(r,2)=\\!\frac{1}{2!}\\!\\!\sum_{m_{1}\in\mathcal{M}^{(0)}}\\!\\!\\!\\!p^{r}_{m_{1}}\\!\\!\\!\\!\sum_{m_{2}\in\mathcal{M}^{(1)}}\\!\\!\\!\\!p^{r}_{m_{2}}\quad\\!\\!\\!\\!\\!\\!\\!\\!\bigcap_{m_{3}\in\mathcal{M}^{(2)}}\\!\\!\Bigl{(}1-p^{r}_{m_{3}}\Bigr{)}=\frac{\Pi}{2}\\!\\!\sum_{m_{1}\in\mathcal{M}}O^{r}_{m_{1}}\\!\\!\sum_{m_{2}\in\mathcal{M}\setminus
m_{1}}O^{r}_{m_{2}}$ (19)
$\displaystyle={\Pi}\\!\\!\sum_{m_{1}\in\mathcal{M}}O^{r}_{m_{1}}\Biggl{(}\sum_{m_{2}\in\mathcal{M}\setminus
m_{1}}\\!\\!\\!\\!O^{r}_{m_{2}}\\!+\\!O^{r}_{m_{1}}\\!-\\!O^{r}_{m_{1}}\\!\\!\Biggr{)}=\frac{\Pi}{2}\sum_{m_{1}\in\mathcal{M}}O^{r}_{m_{1}}\left(\sum_{m_{2}\in\mathcal{M}}O^{r}_{m_{2}}-O^{r}_{m_{1}}\right)$
$\displaystyle=\frac{\Pi}{2}\Biggl{[}\Bigl{(}\sum_{m_{1}\in\mathcal{M}}O^{r}_{m_{1}}\Bigr{)}^{2}-\sum_{m_{1}\in\mathcal{M}}\Bigl{(}O^{r}_{m_{1}}\Bigr{)}^{2}\Biggr{]}=\frac{\Pi}{2}\Biggl{[}\Bigl{(}M\bar{O^{r}}\Bigr{)}^{2}\\!-\\!M^{2}\text{Var}\Bigl{(}O^{r}\Bigr{)}\\!+\\!\Bigl{(}M\bar{O^{r}}\Bigr{)}^{2}\Biggl{]}$
$\displaystyle=\frac{\Pi
M^{2}}{2}\Bigl{(}2\bar{O^{r}}^{2}-\text{Var}\bigl{(}O^{r}\bigr{)}\Bigr{)}.$

##  Appendix B proof of closed-form for (15)

$\displaystyle
P_{e}(r,3)=\frac{\Pi}{3!}\\!\\!\sum_{m_{1}\in\mathcal{M}}\\!\\!\\!\\!O^{r}_{m_{1}}\sum_{m_{2}\in\mathcal{M}\setminus
m_{1}}O^{r}_{m_{2}}\\!\\!\\!\\!\sum_{m_{3}\in\mathcal{M}\setminus
m_{1},m_{2}}\\!\\!\\!\\!O^{r}_{m_{3}}$ (20)
$\displaystyle=\\!\frac{\Pi}{6}\\!\\!\sum_{m_{1}\in\mathcal{M}}\\!\\!\\!O^{r}_{m_{1}}\\!\Biggl{[}\sum_{m_{2}\in\mathcal{M}\setminus
m_{1}}\\!\\!\\!\\!\\!\\!O^{r}_{m_{2}}\\!\Biggl{(}\sum_{m_{3}\in\mathcal{M}\setminus
m_{1}}\\!\\!\\!\\!\\!\\!O^{r}_{m_{3}}\\!\\!-\\!O^{r}_{m_{2}}\\!\Biggr{)}\\!\Biggr{]}$
$\displaystyle=\frac{\Pi}{6}\\!\\!\sum_{m_{1}\in\mathcal{M}}\\!\\!\\!O^{r}_{m_{1}}\\!\Biggl{[}\\!\Biggl{(}\sum_{m_{2}\in\mathcal{M}\setminus
m_{1}}\\!\\!\\!\\!O^{r}_{m_{2}}\\!\Biggr{)}^{2}\\!\\!-\\!\\!\\!\\!\\!\sum_{m_{2}\in\mathcal{M}\setminus
m_{1}}\\!\\!\Bigl{(}\\!O^{r}_{m_{2}}\\!\Bigr{)}^{2}\\!\Biggr{]}$
$\displaystyle=\frac{\Pi}{6}\\!\\!\sum_{m_{1}\in\mathcal{M}}\\!\\!\\!O^{r}_{m_{1}}\\!\Biggl{[}\\!\Biggl{(}\sum_{m_{2}\in\mathcal{M}}\\!\\!\\!O^{r}_{m_{2}}\\!-\\!O^{r}_{m_{1}}\\!\Biggr{)}^{2}\\!\\!\\!-\\!\\!\\!\\!\\!\sum_{m_{2}\in\mathcal{M}}\Bigl{(}O^{r}_{m_{2}}\Bigr{)}^{2}+\\!\bigl{(}\\!O^{r}_{m_{1}}\\!\bigr{)}^{2}\Biggr{]}\\!\\!$
$\displaystyle=\\!\frac{\Pi}{6}\\!\\!\\!\sum_{m_{1}\in\mathcal{M}}\\!\\!\\!\\!O^{r}_{m_{1}}\\!\Biggl{[}\\!\Bigl{(}\\!\\!\sum_{m_{2}\in\mathcal{M}}\\!\\!\\!O^{r}_{m_{2}}\\!\Bigr{)}^{2}\\!\\!-\\!\\!\\!\\!\sum_{m_{2}\in\mathcal{M}}\\!\\!\\!\\!O^{r}_{m_{2}}O^{r}_{m_{1}}+\\!\bigl{(}O^{r}_{m_{1}}\bigr{)}^{2}\\!-\\!\\!\\!\sum_{m_{2}\in\mathcal{M}}\\!\\!\Bigl{(}\\!O^{r}_{m_{2}}\\!\Bigr{)}^{2}\\!+\\!\Bigl{(}\\!O^{r}_{m_{1}}\\!\Bigr{)}^{2}\Biggr{]}$
$\displaystyle=\\!\frac{\Pi}{6}\Biggl{[}\\!\Bigl{(}\\!\sum_{m\in\mathcal{M}}\\!\\!O^{r}_{m}\\!\Bigr{)}^{3}-3\Bigl{(}\sum_{m\in\mathcal{M}}O^{r}_{m}\Bigr{)}\Biggl{(}\sum_{m\in\mathcal{M}}\Bigl{(}O^{r}_{m}\Bigr{)}^{2}\Biggr{)}+2\sum_{m\in\mathcal{M}}\Bigl{(}O^{r}_{m}\Bigr{)}^{3}\Biggr{]}$
$\displaystyle=\frac{\Pi}{6}\Biggl{[}\\!\Bigl{(}M\bar{O^{r}}\Bigr{)}^{3}\\!\\!-3M\bar{O^{r}}\Bigl{(}M^{2}\Bigl{(}\bar{O^{r}}^{2}\\!+\\!\text{Var}\bigl{(}\\!O^{r}\\!\bigl{)}\\!\Bigr{)}\\!\biggr{)}+2\\!\\!\sum_{m\in\mathcal{M}}\\!\\!\Bigl{(}\\!O^{r}_{m}\\!\Bigr{)}\\!^{3}\\!\Biggr{]}$
$\displaystyle=\frac{M^{3}\Pi}{6}\Biggl{[}-2\Bigl{(}\bar{O^{r}}\Bigr{)}^{3}\\!\\!-3\bar{O^{r}}\text{Var}\Bigl{(}\\!O^{r}\\!\Bigr{)}\\!+\\!2\\!\\!\sum_{m\in\mathcal{M}}\Bigl{(}\\!O^{r}_{m}\\!\Bigr{)}^{3}\Biggr{]}.$

## References

  * [1] 3GPP TR 38.838 V17.0.0, “Study on XR (Extended Reality) Evaluations for NR (Release 17),” , Tech. Rep., Dec., 2021.
  * [2] V. Petrov _et al._ , “Standardization of Extended Reality (XR) over 5G and 5G-Advanced 3GPP New Radio,” 2022. [Online]. Available: https://arxiv.org/abs/2203.02242
  * [3] 3GPP Work Item Description, “Study on XR Enhancements for NR on RP-213587,” , Tech. Rep., Dec., 2021.
  * [4] E. Chen _et al._ , “Frame-Level Integrated Transmission for Extended Reality over 5G and Beyond,” in _2021 IEEE Global Communications Conference (GLOBECOM)_. IEEE, Dec., 2021, pp. 1–6.
  * [5] M. Huang and X. Zhang, “MAC Scheduling for Multiuser Wireless Virtual Reality in 5G MIMO-OFDM Systems,” in _2018 IEEE Int. Conf. Commun. Workshops (ICC Workshops)_ , May, 2018.
  * [6] G. Pocovi, A. A. Esswie, and K. I. Pedersen, “Channel Quality Feedback Enhancements for Accurate URLLC Link Adaptation in 5G Systems,” in _2020 IEEE 91st Veh. Technol. Conf. (VTC2020-Spring)_ , May, 2020.
  * [7] A. Balieiro, K. Dias, and P. Guarda, “A Machine Learning Approach for CQI Feedback Delay in 5G and Beyond 5G Networks,” in _2021 30th Wireless and Optical Communications Conference (WOCC)_ , Oct., 2021, pp. 26–30.
  * [8] M. G. Sarret _et al._ , “Dynamic outer loop link adaptation for the 5G centimeter-wave concept,” in _Proceedings of European Wireless 2015; 21th European Wireless Conf._ VDE, May, 2015.
  * [9] F. Blanquez-Casado _et al._ , “eOLLA: an enhanced outer loop link adaptation for cellular networks,” _Eurasip J. Wirel. Commun. Netw._ , vol. 2016, no. 1, pp. 1–16, Jan., 2016.
  * [10] A. Duran _et al._ , “Self-optimization algorithm for outer loop link adaptation in LTE,” _IEEE Commun. Lett._ , vol. 19, no. 11, pp. 2005–2008, Sep., 2015.
  * [11] S. R. Khosravirad, L. Mudolo, and K. I. Pedersen, “Flexible multi-bit feedback design for HARQ operation of large-size data packets in 5G,” in _2017 IEEE 85th Veh. Technol. Conf. (VTC Spring)_ , June, 2017.
  * [12] J. Yeo _et al._ , “Partial retransmission scheme for HARQ enhancement in 5G wireless communications,” in _2017 IEEE Globecom Workshops (GC Wkshps)_ , Dec., 2017.
  * [13] B. Göktepe _et al._ , “Reduced CBG HARQ feedback for efficient multimedia transmissions in 5G for coexistence with URLLC traffic,” in _2018 IEEE Int. Symp. Broadband Multimed. Syst. Broadcast. (BMSB)_ , June, 2018.
  * [14] J. Wu, “Multilevel Code-block Group based HARQ-ACK Control Channel Design,” in _2018 Int. Conf. Comput. Netw. Commun. (ICNC)_. IEEE, Mar., 2018, pp. 264–268.
  * [15] P. Paymard _et al._ , “Enhanced Link Adaptation for Extended Reality Code Block Group based HARQ Transmission,” 2022. [Online]. Available: https://arxiv.org/abs/2208.11950
  * [16] 3GPP TS 38.211 V17.1.0, “NR; Physical channels and modulation (Release 17),” Tech. Spec., Mar., 2022.
  * [17] K. Pedersen _et al._ , “Agile 5G Scheduler for Improved E2E Performance and Flexibility for Different Network Implementations,” _IEEE Communications Magazine_ , vol. 56, no. 3, pp. 210–217, 2018.
  * [18] H. Holma, A. Toskala, and T. Nakamura, _5G technology: 3GPP new radio_. John Wiley & Sons, 2020.
  * [19] 3GPP TS 38.214 V17.1.0, “NR; Physical layer procedures for data (Release 17),” Tech. Spec., Mar., 2022.
  * [20] K. I. Pedersen, G. Pocovi, and J. Steiner, “Preemptive scheduling of latency critical traffic and its impact on mobile broadband performance,” in _2018 IEEE 87th Veh. Technol. Conf (VTC Spring)_ , June, 2018.
  * [21] C. A. Diniz, M. H. Tutia, and J. G. Leite, “Bayesian analysis of a correlated binomial model,” _Brazilian Journal of Probability and Statistics_ , vol. 24, no. 1, pp. 68–77, 2010.
  * [22] J. Fu and R. Sproule, “A generalization of the binomial distribution,” _Communications in Statistics-Theory and Methods_ , vol. 24, no. 10, pp. 2645–2658, 1995.
  * [23] 3GPP TS 38.331 V17.0.0, “NR; Radio Resource Control (RRC) protocol specification (Release 17),” Tech. Spec., Mar., 2022.
  * [24] T. Tang, R. Doostnejad, and T. J. Lim, “Mean mutual information per coded bit based precoding in mimo-ofdm systems,” in _2010 IEEE 72nd Vehicular Technology Conference-Fall_. IEEE, 2010, pp. 1–5.
  * [25] D. Chase, “Code combining-a maximum-likelihood decoding approach for combining an arbitrary number of noisy packets,” _IEEE transactions on communications_ , vol. 33, no. 5, pp. 385–393, 1985.
  * [26] N. Varshney _et al._ , “Link-Level Abstraction of IEEE 802.11ay based on Quasi-Deterministic Channel Model from Measurements,” in _2020 IEEE 92nd Veh. Technol. Conf. (VTC2020-Fall)_ , Nov., 2020, pp. 1–7.