\underset{k\in\mathcal{K}}{\min}\
(\widehat{R}_{k}+\widehat{C}_{k}),&\textrm{MMF-rate}\\\
\frac{\sum_{k=1}^{K}(\widehat{R}_{k}+\widehat{C}_{k})}{\frac{1}{\eta}\text{tr}(\mathbf{P}\mathbf{P}^{H})+P_{\textrm{cir}}},&\textrm{EE}\\\
-\text{tr}(\mathbf{P}\mathbf{P}^{H}),&\textrm{sum-power}.\end{cases}$

Optimization algorithms adopted to solve $\mathcal{P}_{2}$ for different
utility functions are discussed in Section IV.A3.

Long-term precoder optimization: When the CSIT estimation error
$\widetilde{\mathbf{h}}_{k}$ is unbounded, for example, when the transmitter
only knows the Gaussian distribution of the CSIT estimation error, a worst-
case precoder optimization is not possible any more. Instead of designing
precoders for each instantaneous channel, in this case, long-term RSMA
precoder optimization over a long sequence of fading states is more commonly
used, see, e.g., [58, 77, 83, 90, 107, 109, 128, 135, 140, 87, 137]. By
defining $\mathbf{H}=[\mathbf{h}_{1},\ldots,\mathbf{h}_{K}]$,
$\widehat{\mathbf{H}}=[\widehat{\mathbf{h}}_{1},\ldots,\widehat{\mathbf{h}}_{K}]$,
and
$\widetilde{\mathbf{H}}=[\widetilde{\mathbf{h}}_{1},\ldots,\widetilde{\mathbf{h}}_{K}]$
respectively as the actual CSI, the estimated CSIT, and the corresponding
channel estimation errors of all users, we have
$\mathbf{H}=\widehat{\mathbf{H}}+\widetilde{\mathbf{H}}$. Assuming the fading
process to be ergodic and stationary, the ergodic rates (ER) characterizing
the long-term rate performance of the streams over all possible joint fading
states $\\{\mathbf{H},\widehat{\mathbf{H}}\\}$ are defined as

$\overline{R}_{\mathrm{c},k}=\mathbb{E}_{\\{\mathbf{H},\widehat{\mathbf{H}}\\}}\\{R_{c,k}\\}\quad\text{and}\quad\overline{R}_{k}=\mathbb{E}_{\\{\mathbf{H},\widehat{\mathbf{H}}\\}}\\{R_{k}\\}.$
(33)

Sending the common stream and the private stream of user-$k$ at respectively
ERs $\overline{R}_{\mathrm{c},k}$ and $\overline{R}_{k}$ increases the
robustness of the system. To further ensure that the common stream is
decodable at all users, the ER of the common stream cannot exceed
$\overline{R}_{\mathrm{c}}=\min\\{\overline{R}_{\mathrm{c},1},\ldots,\overline{R}_{\mathrm{c},K}\\}$
and the ergodic common rate allocated to user-$k$, $\overline{C}_{k}$, has to
satisfy $\sum_{k=1}^{K}\overline{C}_{k}=\overline{R}_{\mathrm{c}}$. The
resulting ergodic achievable rate of each user is
$\textrm{ER}_{k,tot}=\overline{R}_{k}+\overline{C}_{k}$. The corresponding
long-term precoder optimization problem $\mathcal{P}_{3}$ has a similar form
as $\mathcal{P}_{2}$, when $\widehat{R}_{\mathrm{c},k}$, $\widehat{R}_{k}$,
$\widehat{C}_{k}$ are simply replaced by $\overline{R}_{\mathrm{c},k}$,
$\overline{R}_{k}$, $\overline{C}_{k}$, respectively.

Figure 18: Relationship between the optimization problems for perfect and
imperfect CSIT, and relationship between the problems for RSMA and SDMA
(a.k.a. NoRS). RSMA for imperfect CSIT introduces a more general class of
problems for MIMO networks.

######  Remark 2.

When the strength of the channel estimation error is zero (i.e.,
$\|\mathbf{h}_{k}\|=0$), the CSIT becomes perfect (i.e.,
$\mathbf{h}_{k}=\widehat{\mathbf{h}}_{k}$). In this case, the worst-case
precoder optimization problem, $\mathcal{P}_{2}$, reduces to the problem for
perfect CSIT, $\mathcal{P}_{1}$, and the long-term precoder optimization
problem, $\mathcal{P}_{3}$, can be equivalently decomposed into a
$\mathcal{P}_{1}$ subproblem for each instantaneous channel realization.
Therefore, the problem to be solved for perfect CSIT is equivalent to the
problems to be solved for imperfect CSIT when the channel estimation error is
zero. Fig. 18 illustrates the relationship between the problems for perfect
and imperfect CSIT. The relation between the problems obtained for RSMA and
existing linearly precoded and non-linearly precoded strategies are also
illustrated. Since the simplest RSMA schemes (i.e., linearly precoded 1-layer
RS and 1-DPCRS) are more general than the conventional precoded schemes, RSMA
for imperfect CSIT further enlarges the optimization space. Therefore, RSMA
for imperfect CSIT introduces a more general class of optimization problems
for MIMO networks and the solutions to these problems lead to a more general
class of transmission strategies.

####  IV.A3 Optimization algorithms

Problems $\mathcal{P}_{1}$, $\mathcal{P}_{2}$, and $\mathcal{P}_{3}$ are
challenging to solve due to the non-convexity of the coupled rate expressions
(and the fractional objective function if EE is employed as utility function).
Following Remark 2, the algorithms proposed to solve $\mathcal{P}_{2}$ and
$\mathcal{P}_{3}$ can also be applied for solving $\mathcal{P}_{1}$. In
general, the precoder optimization algorithms proposed to solve
$\mathcal{P}_{1}$, $\mathcal{P}_{2}$, and $\mathcal{P}_{3}$ can be categorized
into globally optimal algorithms and suboptimal algorithms. In [84], a
globally optimal algorithm, namely, the successive incumbent transcending
(SIT) branch and bound (BB) algorithm was proposed to solve $\mathcal{P}_{1}$
optimally, when the WSR, EE, and sum-power objective functions were
considered. To reduce the computational complexity, a large number of works on
RSMA have focused on developing suboptimal algorithms to solve
$\mathcal{P}_{1}$, $\mathcal{P}_{2}$, and $\mathcal{P}_{3}$ with affordable
and tractable complexities, such as weighted minimum mean square error
(WMMSE)-based algorithms [58, 53, 99, 106, 119, 87, 137, 128, 109, 90, 83,
77], successive convex approximation (SCA)-based algorithms [74, 108, 96, 82,
122, 89, 100, 104, 115, 123, 135, 107, 116, 126, 127, 114, 102], alternating
direction method of multipliers (ADMM)-based algorithms [117, 139, 140], and
semidefinite relaxation (SDR)-based algorithms [125, 73, 105, 124, 86]. These
algorithms are able to converge to the Karush–Kuhn–Tucker (KKT) points of the
original problem. Numerical results in [84] show that the WSR performance
achieved by a WMMSE-based algorithm and the EE performance of a SCA-based
algorithm almost coincide with the corresponding globally optimal performance.

Though the computational complexity of the suboptimal algorithms is tractable,
it is still unfavorable for real-world applications. For example, SCA requires
solving a series of convex subproblems, and in each subproblem the non-convex
objective and constraints are approximated by locally tight lower bounds.

###  IV.B Low-Complexity Precoder Design

To further reduce the computational complexity, another line of RSMA research
focuses on closed-form and low-complexity precoder designs [71, 57, 88, 72,
76, 81, 80, 92, 93, 97, 113, 134], which is summarized in this subsection.

The precoder $\mathbf{p}_{i}$ for stream-$i$ can be written as
$\mathbf{p}_{i}=\sqrt{P_{i}}\bar{\mathbf{p}}_{i}$, where
$\bar{\mathbf{p}}_{i}=\frac{\mathbf{p}_{i}}{\|\mathbf{p}_{i}\|}$ is the
direction of the precoder for stream-$i$ and $P_{i}=\|\mathbf{p}_{i}\|^{2}$ is
the power allocated to that precoder. Different from precoder optimization,
where the precoders $\mathbf{p}_{i},\forall i$, (including their direction and
power) of all streams are jointly optimized at the transmitter, for low-
complexity precoder designs, usually the design of the precoder directions
$\bar{\mathbf{p}}_{i},\forall i$, and the optimization of power $P_{i},\forall
i$, are separated. For 1-layer RS, there are $K+1$ streams indexed by
$i\in\\{c,1,\ldots,K\\}$. The common stream $s_{c}$ is required to be decoded
by all users and its precoder direction $\bar{\mathbf{p}}_{c}$ is usually
designed in a multicast manner based on the following typical methods:

  * •

Random precoding [71, 57, 88, 72]: Random precoding, such as setting
$\mathbf{p}_{c}=\mathbf{e}_{1}$ (where $\mathbf{e}_{1}$ is a null vector with
one entry 1 and all other entries 0), is commonly used in the literature of
RSMA for DoF analysis. Using such random precoding for the common stream is
sufficient for RSMA to achieve the entire DoF region, but is not efficient in
terms of improving the SE performance.

  * •

Weighted matched beamforming (MBF) [92, 93, 97, 113, 134, 72, 76, 81]: The
precoder direction $\bar{\mathbf{p}}_{c}$ is designed to maximize the
achievable rate of the common stream, which can be formulated as follows

$\displaystyle\quad\max_{\bar{\mathbf{p}}_{c}}\,\min_{k}\,\,$
$\displaystyle\omega_{k}|{\mathbf{h}}_{k}^{H}\bar{\mathbf{p}}_{c}|^{2}$ (34a)
s.t. $\displaystyle\text{tr}(\bar{\mathbf{p}}_{c}\bar{\mathbf{p}}_{c}^{H})\leq
1.$ (34b)

The optimal precoder direction $\bar{\mathbf{p}}_{c}^{*}$ to solve (34) is the
weighted MBF, which is given by

$\bar{\mathbf{p}}_{c}=\sum_{k\in\mathcal{K}}\varpi_{k}\mathbf{h}_{k},$ (35)

where the optimal weight $\varpi_{k}$ for the two-user case is obtained in
[76], and the asymptotically optimal weight $\varpi_{k}$ as
$M\rightarrow\infty$ is obtained in [92, 93]. In both cases, $\varpi_{k}$ is a
function of $\omega_{k}$. To obtain a more tractable precoder design, equal
weighted MBF with $\varpi_{k}=\frac{1}{\sqrt{MK}}$ is commonly employed [92,
72].

  * •

Singular value decomposition (SVD) [58, 134]: SVD based designs choose the
dominant left singular vector of
$\mathbf{H}=[\mathbf{h}_{1},\ldots,\mathbf{h}_{K}]$ for
$\bar{\mathbf{p}}_{c}$. Such approach is also used to initialize the precoder
of the common stream for the WMMSE and SCA algorithms in [58].

The private stream $s_{k}$ is only decoded by user-$k$ and is treated as noise
by the other users. Therefore, popular linear precoding methods such as ZFBF,
RZF/MMSE, and block-diagonalization (BD) can be used to design the precoder
direction of the private streams:

  * •

ZFBF [71, 57, 88]: ZFBF steers the precoder direction of each user
$\bar{\mathbf{p}}_{k}$ to the space orthogonal to the space spanned by the
other users’ channel vectors, i.e.,
$\bar{\mathbf{p}}_{k}\in\mathrm{null}\left(\left[\mathbf{h}_{1},\ldots,\mathbf{h}_{k-1},\mathbf{h}_{k+1},\ldots,\mathbf{h}_{K}\right]^{H}\right)$.
It is therefore limited to the underloaded MISO BC, i.e., $M\geq K$.
Specifically, ZF designs
$\bar{\mathbf{P}}_{p}=[\bar{\mathbf{p}}_{1},\ldots,\bar{\mathbf{p}}_{K}]$ as

$\bar{\mathbf{P}}_{p}={{\left(\mathbf{H}\mathbf{H}^{H}\right)^{-1}}}\mathbf{H}.$
(36)

Such ZFBF for the private streams together with random beamforming for the
common stream achieves the optimal DoF region for the MISO BC with imperfect
CSIT [58, 57, 69].

  * •

RZF/MMSE [92, 93, 97, 72]: RZF precoding aims to tackle the ill-conditioned
behavior of the largest eigenvalue of
$\left(\mathbf{H}\mathbf{H}^{H}\right)^{-1}$ via a regularized form of channel
inversion. RZF designs the precoder direction $\bar{\mathbf{P}}_{p}$ as
follows

$\bar{\mathbf{P}}_{p}=\underset{\mathbf{F}}{\underbrace{\left(\mathbf{H}\mathbf{H}^{H}+\kappa\mathbf{I}\right)^{-1}}}\mathbf{H},$
(37)

where $\kappa=K\sigma_{n}^{2}$ is a regularization parameter (assuming the
noise power is the same at all users, i.e.,
$\sigma_{n}^{2}=\sigma_{n,k}^{2},\forall k\in\mathcal{K}$). RZF (37) reduces
to ZFBF (36) if $\kappa=0$.

  * •

(Regularized-)BD [80, 88]: (Regularized-)BD extends (Regularized-)ZFBF to the
MIMO BC with $Q\,(2\leq Q\leq M)$ receive antennas at each user. The precoder
direction $\bar{\mathbf{P}}_{k}\in\mathcal{C}^{M\times Q}$ based on
regularized-BD is designed as a cascade of two precoding matrices

$\bar{\mathbf{P}}_{k}=\bar{\mathbf{V}}_{k}\bar{\mathbf{W}}_{k},$ (38)

where the first filter $\bar{\mathbf{V}}_{k}$ is designed to partially remove
multi-user interference. Define
$\bar{\mathbf{H}}_{k}=[{\mathbf{H}}_{1},\ldots,{\mathbf{H}}_{k-1},{\mathbf{H}}_{k+1},\ldots,{\mathbf{H}}_{K}]$
as the channel matrix excluding ${\mathbf{H}}_{k}$. Applying SVD to
$\bar{\mathbf{H}}_{k}$, we have
$\bar{\mathbf{H}}_{k}={\mathbf{U}}_{k}{\mathbf{\Lambda}}_{k}{\mathbf{V}}_{k}$.
$\bar{\mathbf{V}}_{k}$ is chosen as
$\bar{\mathbf{V}}_{k}={\mathbf{V}}_{k}({\mathbf{\Lambda}}_{k}^{T}{\mathbf{\Lambda}}_{k}+Q\sigma_{n,k}^{2}\mathbf{I})^{-\frac{1}{2}}$.
The second filter $\bar{\mathbf{W}}_{k}$ is designed to enable parallel symbol
stream detection at user-$k$. Defining the effective channel matrix as
$\tilde{\mathbf{H}}_{k}=\mathbf{H}_{k}\bar{\mathbf{V}}_{k}^{H}$ and applying
SVD to $\tilde{\mathbf{H}}_{k}$, we have
$\tilde{\mathbf{H}}_{k}=\tilde{\mathbf{U}}_{k}\tilde{\mathbf{\Lambda}}_{k}\tilde{\mathbf{V}}_{k}^{H}$.
$\bar{\mathbf{W}}_{k}$ is designed as
$\bar{\mathbf{W}}_{k}=\tilde{\mathbf{V}}_{k}$. $\mathbf{U}_{k}^{H}$ is used to
design the receive filter at user-$k$.

Besides the precoder direction, the power allocation among the common and
private precoders, i.e., selecting the values of $P_{c},P_{1},\ldots,P_{K}$,
is also crucial for the performance of 1-layer RS, especially the division of
power between the common stream $P_{c}$ and the private streams
$P_{1}+\ldots+P_{K}$. Defining the fraction of the transmit power $P$
allocated to the private streams as $\tau\,(0\leq\tau\leq 1)$, we have
$P_{c}=(1-\tau)P$ as $P_{c}+P_{1}+\ldots+P_{K}=P$. Optimal closed-form
expressions for $\tau$ have been reported in [76] for perfect CSIT and in [92,
88] for imperfect CSIT. The powers allocated to the different private streams
can be chosen equal [88] or obtained via water-filling (WF) [76].

##  V RSMA PHY layer Design

The discussions on RSMA so far have been in terms of abstract message
definitions and Shannon capacity, which assumes Gaussian signalling and
infinite block length coding. A practical PHY layer architecture for RSMA has
been proposed in [79] including finite constellation modulation schemes,
finite length polar codes, and adaptive modulation and coding (AMC). This
architecture has been further extended in [88] to the MISO/MIMO BC with CSI
feedback delay and user mobility, in [90] to the MIMO BC employing a V-BLAST
receiver, and in [138] to satellite communications. In this section, we first
provide some toy examples to give an intuition about a practical PHY layer
architecture of RSMA. Then, we thoroughly delineate the PHY layer transmitter
and receiver architectures.

###  V.A A Quick Introduction to RSMA PHY Layer

The examples in this section are based on the RSMA PHY layer architecture
described in [79]. In particular, we explain how the user messages are split
and combined at the transmitter based on the transmission rates and how the
received signals are processed by demonstrating the bit-level processing of
each user’s message.

We consider a scenario where a multi-antenna transmitter serves two single-
antenna receivers. The transmitter aims to send two independent messages to
the users, with each message being intended only for one user. According to
the RSMA framework, the transmitter forms one common message and two private
messages to transmit in such a setting.

(a) Example 1: $C_{1}=C_{2}=0.5$ bps/Hz, $R_{1}=R_{2}=1.0$ bps/Hz. The coding
rate is $1/2$ and the modulation scheme is QPSK for the common and private
streams, respectively.

(b) Example 2: $C_{1}=1.0$ bps/Hz, $C_{2}=0.5$ bps/Hz, $R_{1}=R_{2}=1.0$
bps/Hz. The coding rate is $3/4$ for the common stream and $1/2$ for the
private streams. The modulation scheme is QPSK for the common and private
streams, respectively.

(c) Example 3: $C_{1}=C_{2}=0.5$ bps/Hz, $R_{1}=2.5$ bps/Hz, $R_{2}=1.0$
bps/Hz. The coding rates is $1/2$ for the common stream and the private stream
of user-$2$, respectively, and $5/8$ for the private stream of user-$1$. The
modulation scheme is QPSK for the common stream and the private stream for
user-$2$, respectively, and 16-QAM for the private stream of user-$1$.

Figure 19: Examples for RSMA transmitters. Two separate messages are
transmitted to two users over $4$ consecutive symbols. The red bits represent
the message intended for user-$1$, the blue bits represent the message
intended for user-$2$, and the green bits represent the formed common message
after message splitting and combining. $R_{1}$ and $R_{2}$ denote the rates of
the private streams and $C_{1}$ and $C_{2}$ denote the portions of the rate of
the common stream allocated to user-$1$ and user-$2$, respectively.Appropriate
coding rates ($1/2$, $3/4$, $5/8$) and modulation schemes (QPSK, $16$-QAM) are
chosen to support the calculated transmission rates.

####  V.A1 RSMA transmitter operation

Fig. 19 illustrates the operations at the transmitter for different
transmission rates. In the figures, $R_{1}$ and $R_{2}$ denote the
transmission rates of the private streams and $C_{1}$ and $C_{2}$ denote the
portions of the rate of the common stream allocated to user-$1$ and user-$2$,
respectively. The transmission rate calculations for RSMA are explained in
detail in Section III. The rates can be calculated either at the transmitter
using the available CSIT, or obtained as a feedback from the users to be
served. In the following examples, we assume that the transmission rates
provided to the transmitter are achievable by means of finite blocklength
(FBL) coding and bit-interleaved coded modulation (BICM).

The transmission rates are input to the modules which perform message
splitting, message combining, modulation and coding; and they are used to
determine the number of message bits, the modulation scheme, and the channel
coding parameters. The transmitter is allocated $4$ consecutive symbols
(channel uses) to transmit two independent messages, each intended for only
one of the users. In the figures, the message intended for user-$1$ is
depicted in red color and the message for user-$2$ is depicted in blue. We
assume that the bits of the messages are independent. The transmission rates
dictate the number of message bits transmitted in one symbol. Thus, the number
of message bits that can be carried by the common and private streams is $4$
times the value of the corresponding transmission rates.

For Example 1 (Fig. 19(a)), the transmission rates for the common and private
streams are all $1$ bps/Hz. These rates allow $4$ message bits to be carried
over each stream. We consider the case where the modulation scheme for
transmission is chosen as QPSK and the coding rate is set as $1/2$. Next, we
check the portions of the common rate of the users, which are both equal to
$0.5$ bps/Hz. This implies that $2$ bits per user can be transmitted over the
common stream, which, together with the messages carried by the private
streams, sums up to $6$ message bits for each user. One can also verify that
the sum-rate for a single user is $C_{1}+R_{1}=1.5$ bps/Hz, which corresponds
to transmission of $6$ bits during $4$ channel uses. Next, we extract $6$
message bits from the message source buffer for each user. As the message bits
are independent, one can split the $6$ message bits of each user into the
common part of $2$ bits and the private part of $4$ bits by means of any
splitting pattern.

######  Remark 3.

In the considered example, the splitting operation is performed by assigning
the first $2$ bits to the common stream and the remaining bits to the private
stream. However, any other splitting pattern can be considered (such as,
selecting $2$ bits randomly for the common stream), as long as the message
bits are independent and a matching message desplitting operation is performed
at the receivers. The splitting pattern can also depend on the message
structure (for example, if the message bits from the message source are
concatenated messages for two separate applications, splitting can be
performed to separate these messages into common and private messages), the
protocols on the upper layers (MAC and above), or any other criterion imposed
by the system design.

After the message splitting is performed, we move to the process of message
combining to form the single common message to be transmitted over the common
stream. As the common parts of the messages from the two users are
independent, one can simply concatenate the $2$-bit common message parts to
form the $4$-bit common message by means of any concatenation pattern.

######  Remark 4.

In the considered example, the combining operation is performed by appending
the common message parts from the two users directly, with the common part
from user-$1$ representing the first $2$ bits of the new message and the part
from user-$2$ representing the last $2$ bits. However, any other combining
pattern can be employed as long as the message bits are independent and a
matching message decomposing operation is performed at the receivers. For
example, a comb-like combining operation can be performed, where each bit from
one user’s message is followed by a bit from the other user’s message, or a
1-1 mapping can be performed with a new message set consisting of all $4$-bit
messages.

After the message splitting and the message combining operations are
performed, the resulting $4$ bit messages are independently encoded by channel
codes of rates $1/2$ to obtain codewords of $8$-bits. The codewords are then
interleaved and modulated by QPSK modulation to obtain the $4$ symbols to be
transmitted.

######  Remark 5.

The channel coding applied on each stream can be performed over the same
codebook or different codebooks111111Here, the terminology codebook refers to
the set which contains all codewords of a channel code., as long as the
codebook for the common stream is known by both users and the codebooks for
the private streams are known by the corresponding users. Similarly, the
employed interleavers can be identical or different as long as the interleaver
for the common stream is known by both users and the interleavers for the
private streams are known by the corresponding users.

(a) Example 1.

(b) Example 2.

(c) Example 3.

Figure 20: Receiver operations for RSMA for the examples in Fig.19. Each
receiver performs message decomposing and desplitting to obtain the
transmitted message bits.

In Example 2 (Fig. 19(b)), the transmission rate of the common stream and the
portion of user-$1$ are increased compared to Example 1. Again, the
transmitter is allocated $4$ consecutive symbols for transmission and the
modulation scheme for transmission is chosen as QPSK. In this case, $4$ bits
can be transmitted over the common stream to user-$1$, while the number of
bits that can be transmitted to user-$2$ stays the same ($2$ bits).
Consequently, the total number of message bits intended for user-$1$ increases
to $8$ bits (this can be verified by multiplying the total sum-rate of
user-$1$, $C_{1}+R_{1}=2$ bps/Hz, by the number of transmit symbols).

Similar to the case in Example 1, the message splitting operation for user-$1$
is performed by assigning the first $4$ bits of the message of user-$1$ to the
common part, and the splitting operation for user-$2$ is performed in the
exact same fashion as in Example 1. The message combiner concatenates the
$4$-bit message that is the common message part of user-$1$ and the $2$-bit
message that is the common message part of user-$2$ by appending them,
resulting in a common message of $6$ bits. Since the transmission is performed
over $4$ QPSK symbols and a total of $8$ bits can be transmitted over a
stream, the coding rate is calculated as $3/4$ (which can also be calculated
by dividing the total common rate $C_{1}+C_{2}=1.5$ bps/Hz by the SE of QPSK
modulation). Finally, the encoding, interleaving, and modulation operations
are performed as done in Example 1.

In Example 3 (Fig. 19(c)), the transmission rate of the private stream for
user-$1$ is increased compared to the one in Example 1. Again, the transmitter
is allocated $4$ consecutive symbols for transmission. Contrary to the
previous examples, the transmission rate of the private stream of user-$1$
($2.5$ bps/Hz) is larger than the SE of QPSK modulation ($2.0$ bps/Hz).
Therefore, we choose 16-QAM modulation for transmission, which has a larger SE
than QPSK. The number of message bits that can be transmitted over the private
stream of user-$1$ is calculated as $10$ bits and the number of codeword bits
that can be transmitted using 16-QAM modulation is $16$ bits, resulting in a
coding rate of $5/8$ for the considered stream (again, the coding rate can
also be calculated by dividing $R_{1}=2.5$ bps/Hz by the SE of 16-QAM
modulation). The number of message bits that can be transmitted over the
common stream and the private stream of user-$2$ are the same as in Example 1,
yielding an additional $2$ bits to be transmitted to user-$1$ over the common
stream. Consequently, the total number of message bits intended for user-$1$
becomes $12$, while the total number of message bits intended for user-$2$ is
$6$.

The message splitting and message combining operations are performed in the
exact same fashion as in Example 1 (first, $2$ message bits are split for the
common parts, and then combined by appending them). Then, the resulting common
and private messages are encoded and interleaved separately. Note that, in
this case, the codebook for the channel code applied to the private stream of
user-$1$ cannot be the same as those for the common stream and the private
stream of user-$2$, as opposed to the cases in Examples 1 and 2. Similarly,
the interleaver should be longer for the private stream of user-$1$. After
interleaving, QPSK modulation is applied to the common stream and the private
stream of user-$2$ and 16-QAM modulation is applied for the private stream of
user-$1$, all resulting in $4$ symbols for transmission.

######  Remark 6.

It is worth noting that, for the considered two-user scenarios, removing the
message splitting operation of the considered transmitter structure would
result in the conventional transmitter architecture for other MA schemes, such
as SDMA and NOMA. More specifically, SDMA transmitters do not apply message
splitting and combining, and directly encode the data signals for the two
users into two separate private streams. Similarly, NOMA transmitters do not
apply message splitting and combining, and directly encode the data signal for
one user into the common stream and that for the other user into one private
stream (the reasoning behind using the common stream terminology here for NOMA
will become clearer after the receiver operations are described in the next
section).

####  V.A1 RSMA receiver operation

Next, we explain the operations performed at the receiver for the examples
considered above. Fig. 20 depicts the operations at the receivers for each
example. Each receiver starts by processing the common stream by performing
equalization, Log-Likelihood Ratio (LLR) calculation, deinterleaving, and
decoding. Assuming correct detection and decoding, the outputs of the decoders
at the users are the message bits carried over the common stream. For Examples
1 and 3 (Figs. 20(a) and 20(c), respectively), the outputs are the $4$-bit
common message and for Example 2 (Fig. 20(b)), the outputs are the $6$-bit
common message. The decoded common messages are then input to the message
decomposers, which reverse the operation done by the message combiner at the
transmitter. The resulting decomposed messages are the common parts of the
user messages. Each user proceeds with the corresponding common parts of their
messages and discards the other user’s common message part, as illustrated in
Fig. 20 (the green message is decomposed into the red and blue messages,
user-$1$ proceeds with the red message and discards the blue, while it is the
other way around for user-$2$).

After signal reconstruction and interference cancellation, the corresponding
private streams are processed at each user following the same steps as used
for decoding the common stream. Assuming correct detection and decoding, the
outputs of the decoders are the private message bits intended for the
corresponding users. For Examples 1 and 2 (Figs. 20(a) and 20(b),
respectively), the decoder outputs at each user are the $4$-bit private
messages and for Example 3 (Fig. 20(b)), the output is the $10$-bit private
message at user-$1$ and the $4$-bit private message at user-$2$.

######  Remark 7.

One can notice that processing the common stream at any user involves decoding
a portion of the message of the other user. As the multi-user interference at
one user stems from the message of the other user, such a process can be
interpreted as partially decoding the interference. On the other hand,
processing the private stream at any user is done by treating a portion of the
message of the other user as noise. As the multi-user interference at one user
stems from the message of the other user, such a process can be interpreted as
partially treating the interference as noise.

Finally, the decoded common and private messages at each user are input to the
message desplitters, which reverse the operation done by the message splitter
at the transmitter. The outputs of the message desplitters at each user are
the intended messages for the corresponding users.

######  Remark 8.

As a final note in this section, we would like to comment on the relation
between the receiver operations needed for RSMA, SDMA and NOMA. A conventional
SDMA receiver does not detect or decode a common stream, and performs
detection of its intended private signal only by treating all interference as
noise. On the other hand, a conventional NOMA receiver in a two-user scenario
performs decoding of the common stream (recall from Remark 4 that the common
stream in NOMA includes the full message of one user and no contributions from
the message of the other user). For the user whose message is carried in the
common stream, this can be interpreted as treating the interference as noise,
as it does not continue with any decoding operations after the common message.
For the other user (whose message is carried in one private stream), this can
be interpreted as fully decoding the interference, as it performs interference
cancellation to continue with decoding its own message. This underlines a key
feature of RSMA - the capability to bridge the extreme regimes of decoding
interference and treating it as a noise.

Figure 21: PHY layer transmitter and receiver structures of RSMA with finite
constellation modulation schemes, finite length polar codes, and adaptive
modulation and coding (AMC) [79].

###  V.B RSMA PHY Layer Architecture

Fig. 21 illustrates the two-user PHY layer transmitter and receiver
architecture of 1-layer RS for the two-user MISO BC including message
splitting, finite-alphabet modulation, finite-length polar coding, AMC, and
SIC. The architecture can be extended in a straightforward manner to the PHY
layer of the RSMA schemes discussed in Section III. In the following, the
transmitter and receiver structures are explained in detail.

####  V.B1 Transmitter

At the transmitter, message $W_{k}$ intended for user-$k$ is split into two
sub-messages $W_{c,k},W_{p,k},k\in\\{1,2\\}$. The two common sub-messages
$W_{c,1},W_{c,2}$ are combined into one common message $W_{c}$. The three
obtained messages $W_{c},W_{p,1},W_{p,2}$ contain $K_{c},K_{p,1},K_{p,2}$
information bits, respectively, which are assumed to be independently and
uniformly distributed in binary fields of dimensions $K_{c},K_{p,1},K_{p,2}$,
respectively. The three obtained messages $W_{c},W_{p,1},W_{p,2}$ are
independently encoded into codewords $\nu_{c},\nu_{p,1},\nu_{p,2}$ with code
blocklengths $N_{c},N_{p,1},N_{p,2}$, respectively.

Before passing the codewords to the modulators, the bits in
$\nu_{c},\nu_{p,1},\nu_{p,2}$ are interleaved based on the BICM concept in
order to further improve the coding performance especially for high-order
modulation [163]. The interleaved bit vectors
$\nu^{\prime}_{c},\nu^{\prime}_{p,1},\nu^{\prime}_{p,2}$ are respectively
modulated into common symbol stream $s_{c}$ and private symbol streams
$s_{1},s_{2}$. Aiming at enhancing the system throughput, an AMC algorithm
uses the rates $C_{1},C_{2},R_{1},R_{2}$ calculated based on the designed
precoders in Section IV and the Shannon bound in (5)–(7) as link quality
metrics to determine the corresponding modulation schemes and the coding rates
for the symbol streams. After modulation, the modulated symbol streams are
then mapped to transmit antennas via precoding matrix $\mathbf{P}$.

######  Remark 9.

The PHY layer transceiver architecture described in [79] employs polar codes
[164] for channel coding and the modulation formats 4-QAM, 16-QAM, 64-QAM and
256-QAM. However, any other types of coding and modulation techniques can be
applied in an RSMA transceiver. For example, Low-Density Parity-Check (LDPC)
codes and Phase-Shift Keying (PSK) modulation have been employed in the RSMA
transceiver architectures described in [78, 132].

####  V.B2 Receiver

At user-$k$, MMSE equalizer $g_{c,k}^{\textrm{MMSE}}$ is first employed to
detect the common symbol stream $s_{c}$. The MMSE equalizer is calculated by
minimizing mean square error (MSE) metric
$\mathbb{E}\\{|g_{c,k}y_{k}-s_{c}|^{2}\\}$, and obtained as follows

$g_{c,k}^{\textrm{MMSE}}=\frac{\mathbf{p}_{c}^{H}\mathbf{h}_{k}}{\left|\mathbf{{h}}_{k}^{H}\mathbf{{p}}_{c}\right|^{2}+\sum_{l=1}^{K}\left|\mathbf{{h}}_{k}^{H}\mathbf{{p}}_{l}\right|^{2}+\sigma_{n,k}^{2}}.$
(39)

Log-likelihood ratios (LLRs) are then calculated for soft decision (SD)
decoding from the equalized symbols. The bit LLRs are sent to the bit
deinterleaver and then to the channel decoder to obtain common message bits
$\widehat{W}_{c}$. Finally, the intended common part $\widehat{W}_{c,k}$ is
extracted from $\widehat{W}_{c}$. After obtaining $\widehat{W}_{c}$, user-$k$
employs hard decision (HD) SIC to reconstruct $s_{c}$ from $\widehat{W}_{c}$
by replicating the operations at the transmitter. $s_{c}$ is then removed from
the received signal as
$y^{\prime}_{k}=y_{k}-\mathbf{h}_{k}^{H}\mathbf{p}_{c}s_{c}$. MMSE equalizer
$g_{k}^{\textrm{MMSE}}$ is employed to detect the private symbol stream
$s_{k}$. The MMSE equalizer is calculated by minimizing MSE
$\mathbb{E}\\{|g_{k}y^{\prime}_{k}-s_{k}|^{2}\\}$, and obtained as follows

$g_{k}^{\textrm{MMSE}}=\frac{\mathbf{p}_{k}^{H}\mathbf{h}_{k}}{\sum_{\begin{subarray}{c}l=1,\\\
l\neq
k\end{subarray}}^{K}\left|\mathbf{{h}}_{k}^{H}\mathbf{{p}}_{l}\right|^{2}+\sigma_{n,k}^{2}}.$
(40)

Following the same decoding procedure, $\widehat{W}_{c}$ and
$\widehat{W}_{p,k}$ are obtained. By merging $\widehat{W}_{p,k}$ and
$\widehat{W}_{c,k}$, $\widehat{W}_{k}$ is recovered.

Figure 22: Comparison of linearly precoded MA schemes for $K$-user downlink transmission. TABLE IX: Comparison of different MA schemes. Multiple Access |  OMA |  SDMA | NOMA | RSMA
---|---|---|---|---
Strategy |  LP |  MU–LP |  Multi-antenna NOMA ($G=1$) |  Multi-antenna NOMA ($G>1$) | All forms of RS
Design principle |  Orthogonal resource allocation to avoid interference |  Fully treat interference as noise |  Fully decode interference |  Fully decode interference in each group and treat interference between groups as noise |  Partially decode interference and partially treat interference as noise
Decoder architecture |  Treat interference as noise |  Treat interference as noise |  SIC at receivers |  SIC at receivers |  SIC at receivers
Ideal user deployment scenario |  Any angle between user channels and any disparity in channel strengths |  Users channels are (semi-) orthogonal with similar channel strengths. |  Users experience aligned channel directions and a large disparity in channel strengths. |  Users in the same group experience aligned channel directions and a large disparity in channel strengths. Users in different groups experience orthogonal channels. |  Any angle between channels and any disparity in channel strengths
Network load |  Only one active user (in each radio resource) |  Better suited for underloaded network |  Better suited for overloaded network |  Better suited for underloaded network |  Suited to any network load

##  VI Comparison of Multiple Access Schemes

In this section, we comprehensively compare downlink RSMA with existing MA
schemes in terms of their design principles and frameworks, DoF performance,
SE performance, LLS performance, and their complexities. The advantages and
disadvantages of RSMA are summarized at the end of this section.

###  VI.A Framework Comparison

Fig. 22 illustrates the relationship between linearly precoded MA schemes
including multicasting, SDMA, OMA, NOMA, and four linearly precoded RSMA
schemes, namely, generalized RS, 2-layer RS, 1-layer RS, and RS–CMD.

Generalized RS is a universal linearly precoded scheme that comprises all
other schemes except RS-CMD as sub-schemes. By allocating non-zero power to
the $K$-order stream, $|\mathcal{K}_{i}|$-order streams, and $1$-order streams
while turning off all other streams, generalized RS reduces to 2-layer HRS.
2-layer HRS reduces to 1-layer RS when the $|\mathcal{K}_{i}|$-order streams
of 2-layer HRS are turned off (with zero transmit power allocated to them).
RS-CMD is not a special instance of other RSMA schemes as RS-CMD does not
combine and jointly encode user messages. Though the common streams in RS-CMD
are decoded by all or at least several users, each stream is intended only for
a single user.

SDMA illustrated in Fig. 1(b) is a sub-scheme of all linearly precoded RSMA
schemes. By turning off the power allocated to all common streams, RSMA
reduces to SDMA. In contrast, NOMA based on SC-SIC in Fig. 1(b) or SC-SIC per
group in Fig. 2 utilizes each common stream to fully encode the entire message
of a single user. It is a sub-scheme of generalized RS. By optimizing the
group of users to decode each common stream, RS-CMD can be made more general
than NOMA. Therefore, NOMA is shown as a special case of RS-CMD in Fig. 22.
For OMA, illustrated in Fig. 1(a), in each time-frequency resource block, only
a single user can be active, i.e., the transmit power is fully allocated to a
single private stream. It is the simplest MA scheme and is therefore a sub-
scheme of all other MA schemes except for PHY layer multicasting. PHY layer
multicasting allows the transmitter to serve multiple users simultaneously by
jointly encoding the messages intended for different users into one common
stream decoded by all users. In other words, multicasting is a sub-scheme of
1-layer RS/2-layer RS/generalized RS when the transmit power is fully
allocated to the $K$-order common stream.

Table IX summarizes the comparison of the different MA schemes in terms of
their design principles as well as the user deployment scenarios and network
loads they are best suited for. Apparently, the most important characteristic
that makes RSMA distinct from the other MA schemes lies in its flexible
interference management policy of partially decoding interference and
partially treating residual interference as noise, which allows RSMA to
generalize and encompass multi-antenna NOMA, SDMA, OMA, and multicasting as
sub-schemes. Most importantly, RSMA smoothly bridges different sub-schemes
without hard switching between them.

In the simple two-user case, 1-layer RS (see Fig. 4) becomes a super-set of
not only OMA (see Fig. 1(a)), SDMA (see Fig. 1(b)), and multicasting, but also
NOMA (see Fig. 1(c)). As illustrated in Table X, OMA, SDMA, NOMA, and
multicasting are particular instances of 1-layer RS. Specifically, SDMA is a
special case of 1-layer RS by forcing $\left\|\mathbf{p}_{c}\right\|^{2}=0$.
In this way, $W_{k}$ is directly encoded into $s_{k}$. By encoding message
$W_{2}$ entirely into $s_{c}$ (i.e., $W_{c}=W_{2}$) and $W_{1}$ into $s_{1}$
while turning off $s_{2}$ ($\left\|\mathbf{p}_{2}\right\|^{2}=0$), we obtain
NOMA. When only user-1 is scheduled (i.e.,
$\left\|\mathbf{p}_{c}\right\|^{2}=\left\|\mathbf{p}_{2}\right\|^{2}=0$), we
obtain OMA. When messages $W_{1},W_{2}$ are both encoded into $s_{c}$ (i.e.,
$W_{c}=\\{W_{1},W_{2}\\}$) and the private streams are turned off
($\left\|\mathbf{p}_{1}\right\|^{2}=\left\|\mathbf{p}_{2}\right\|^{2}=0$), we
obtain multicasting. Note that the multicasting specified in Table X is from a
perspective of PHY layer transmission regardless of the content that $s_{c}$
conveys, as discussed in Remark 1.

TABLE X: Messages-to-streams mapping in the two-user MISO BC [76]. | $s_{1}$ | $s_{2}$ | $s_{c}$
---|---|---|---
SDMA | $\,\,\quad\quad W_{1}\quad\quad\,\,$ | $W_{2}$ | –
NOMA | $W_{1}$ | – | $W_{2}$
OMA | $W_{1}$ | – | –
Multicasting | – | – | $W_{1},W_{2}$
1-layer RS | $W_{p,1}$ | $W_{p,2}$ | $W_{c,1},W_{c,2}$
| decoded by its intended user and | decoded by
| treated as noise by the other user |  both users

###  VI.B Complexity Comparison

The complexity of different linearly precoded strategies are qualitatively
compared in Table XI in terms of their encoder complexity, scheduler
complexity, and receiver complexity.

TABLE XI: Qualitative comparison of the complexity of different MA schemes. Multiple Access |  OMA |  SDMA | NOMA | RSMA
---|---|---|---|---
Strategy |  LP |  MU–LP |  Multi-antenna NOMA ($G=1$) |  Multi-antenna NOMA ($G>1$) |  1-layer RS |  2-layer HRS |  Generalized RS | RS-CMD
Encoder complexity |  Encode $K$ streams |  Encode $K$ streams |  Encode $K$ streams |  Encode $K$ streams |  Encode $K+1$ streams |  Encode $K+G+1$ streams |  Encode $2^{K}-1$ streams |  Encode $2K$ streams
Scheduler complexity |  Complex as OMA requires sub-carrier/time-slot allocation for all users. |  Complex as MU–LP requires to pair semi-orthogonal users with similar channel gains. |  Very complex as it requires finding aligned users and decide between $K!$ user orderings. |  Very complex as it requires to divide users into orthogonal groups, with aligned users in each group. Decide between $\sum_{k=1}^{K}S(K,k)$ grouping method and at most $K!$ decoding orders for each grouping method. |  Simple user scheduling as it can cope with any user deployment scenario, and does not rely on user grouping or user ordering. |  Decide between $\sum_{k=1}^{K}S(K,k)$ groupings without decoding order. |  Decide between $\prod_{k=2}^{K-1}\binom{K}{k}!$ decoding orders. |  Decide upon $\sum_{k=1}^{K}S(K,k)$ grouping methods and at most $(K!)^{K}$ decoding orders.
Receiver complexity |  Does not require SIC. |  Does not require SIC. |  Requires $K-1$ layers of SIC at each user. Sensitive to error propagation. |  Requires $|\mathcal{K}_{i}|-1$ layers of SIC at each user in group-$g$. Sensitive to error propagation. |  Requires 1 layer of SIC at each user. Less sensitive to error propagation (compared to NOMA, and other more complex RS schemes). |  Requires 2 layers of SIC at each user. Less sensitive to error propagation (compared to NOMA, and other more complex RS schemes). |  Requires $2^{K-1}-1$ layers of SIC at each user. Sensitive to error propagation. |  Requires $K$ layers of SIC at each user. Sensitive to error propagation.

####  VI.B1 Encoder complexity

Due to the use of message splitting, more streams need to be encoded at the
RSMA transmitter. The encoder complexity of RSMA is therefore higher than
those of other MA schemes. Among the linearly precoded RSMA schemes, 1-layer
RS has the lowest encoding complexity with only one additional stream
(compared to the SDMA and NOMA baselines where $K$ messages are encoded into
$K$ streams) encoded at the transmitter in the $K$-user case. For 2-layer HRS,
as there is one group-specific common stream for each user group, in total $G$
additional common streams are encoded at the transmitter besides the common
stream for all users. Therefore, the encoder complexity difference between
1-layer RS/2-layer HRS and SDMA/NOMA121212Here, the encoder complexity is
measured in terms of the number of encoded streams. is invariant to the number
of users $K$ while the encoder complexity difference between RS-
CMD/generalized RS and SDMA/NOMA increases with $K$ due to the large number of
sub-messages split from each message, as illustrated in Table VIII.

####  VI.B2 Scheduler complexity

Even though SDMA has the lowest encoder and receiver complexities, it entails
a relatively high scheduler complexity due to the requirement of pairing users
with semi-orthogonal channels and similar channel strengths to achieve high
performance. Fig. 29 in Section VI.C further shows that SDMA is mainly
beneficial when the users’ channels are sufficiently orthogonal. Moreover, as
discussed in Section I-A, well-designed user scheduling requires accurate CSIT
and leads to high signaling overhead and latency. The SIC receivers used in
NOMA and RSMA introduce additional scheduler complexity compared with OMA and
SDMA. Two additional aspects have to be considered at the transmitter due to
the use of SIC, namely, the decoding order and the user grouping. The coupled
nature of user grouping, decoding order, precoders, and user selection
requires a joint optimization at the transmitter [165]. Among all strategies
using SIC, multi-antenna NOMA ($G>1$), 2-layer HRS, and RS-CMD bear the
highest user grouping complexity. As discussed in [53], the total number of
possible user groupings for these three schemes is $\sum_{k=1}^{K}S(K,k)$,
where $S(K,k)=\frac{1}{k!}\sum_{i=0}^{k}(-1)^{i}\binom{k}{i}(k-i)^{K}$ is a
Stirling set number [166] representing the total number of partitions of a set
of $K$ elements into $k$ non-empty sets.

In terms of the decoding order, multi-antenna NOMA, generalized RS, and RS-CMD
all entail inevitably high decoding order complexity. For multi-antenna NOMA
($G=1$), all users employ the same decoding order to decode the user messages
and the transmitter should select between $K!$ possible decoding orders for
the $K$ streams. Note that for multi-antenna NOMA ($G=1$), it is advantageous
for the scheduler to select users with aligned channels and significant
channel strength differences, which however increases the scheduler
complexity. For multi-antenna NOMA ($G>1$), as the user grouping is jointly
optimized with the decoding order, at most $K!$ decoding orders have to be
considered in each user group. For generalized RS, though the decoding order
starts from the $K$-order streams downwards to the $1$-order streams (see
Section III.B5), there are $\binom{K}{k}$ $k$-order streams for $2\leq k\leq
K-1$, which results in $\binom{K}{k}!$ possible decoding orders. Therefore,
the transmitter has to select between $\prod_{k=2}^{K-1}\binom{K}{k}!$
possible decoding orders for users to decode all intended streams [53]. For
RS-CMD, if it is assumed that the $K$ common streams are decoded at all users
as in Section III.B6, in total $(K!)^{K}$ decoding orders need to be
considered at the transmitter without the issue of user grouping. Otherwise,
the transmitter has to jointly decide the decoding order and the group of
common streams decoded at each user.

In summary, both multi-antenna NOMA ($G>1$) and RS-CMD have relatively the
highest scheduler complexity since the decoding order and user grouping have
to be jointly decided. For multi-antenna NOMA ($G>1$), users with semi-
orthogonal channels should be assigned to different user groups and the user
channels within the same user group should be aligned. In contrast, 1-layer RS
has relatively the lowest scheduler complexity among all aforementioned MA
schemes (including OMA, SDMA, NOMA, and all RSMA schemes) as it does not
require grouping and ordering, and is less sensitive to user pairing. Hence,
1-layer RS does not require complex user scheduling and pairing. Generally,
all RSMA schemes including 1-layer RS, 2-layer HRS, generalized RS, and RS-CMD
are suited for users with any channel strength disparity and channel
directions. As per Fig. 13 in [107], surprisingly generalized RS and 1-layer
RS without user scheduling outperform SDMA with user scheduling when the CSIT
is sufficiently inaccurate.

####  VI.B3 Receiver complexity

Both OMA and SDMA have comparatively the lowest receiver complexity as they do
not need SIC. Among the schemes using SIC (including NOMA and all RSMA
schemes), 1-layer RS and 2-layer HRS entail the lowest receiver complexity. In
the $K$-user scenario, the number of SIC operations required at each user is
$1$ for 1-layer RS and $2$ for 2-layer HRS, which is relatively low and
independent of the number of users $K$. Hence, both 1-layer RS and 2-layer HRS
are not severely affected by error propagation. All remaining schemes,
including NOMA (for a fixed user group $G$), generalized RS, and RS-CMD,
require several SIC operations depending on $K$, which not only leads to an
increased transceiver complexity but also increases the susceptibility to SIC
error propagation. Specifically, each user requires $K-1$ layers of SIC in
multi-antenna NOMA ($G=1$) while each user from user group-$i$ requires
$|\mathcal{K}_{i}|-1$ layers of SIC in multi-antenna NOMA ($G>1$)131313For a
certain decoding order, the number of SIC layers used at different users for
decoding the data streams of other users is different. However, as the
decoding order depends on the users’ instantaneous CSI, all users are required
to implement the maximum number of SIC layers as each of them may have to
decode the streams of all other users (in the same user group) for some
channel conditions., where $|\mathcal{K}_{i}|\leq K$ is the number of users in
group-$i$141414Readers are referred to [13] for more details on the system
model of multi-antenna NOMA.. The receivers for RS-CMD and generalized RS are
both complex as $K$ and $2^{K-1}-1$ layers of SIC are required, respectively.
Though generalized RS provides a higher flexibility in interference management
compared with the other schemes, it also entails a higher receiver complexity.
In view of the high transmitter and receiver complexities of RS-CMD and
generalized RS, attempts towards low-complexity versions have been made [82,
103, 100, 128] by controlling the number of common streams decoded at each
user and simplifying the decoding order design. Moreover, readers are reminded
that there are two motivations for introducing generalized RS, one is to
explore the best achievable performance at the expense of a higher complexity
at the transceivers, and the other one is to identify which common stream(s)
lead(s) to the highest performance gains, and from there identify which
stream(s) could be turned off so as to reduce the encoding and decoding
complexities.

###  VI.C Performance Comparison

Next, we evaluate the performance of the considered MA schemes in terms of
their DoF region, rate region, operational region, user fairness, and LLS
performance.

####  VI.C1 DoF region

The degrees-of-freedom (DoF) (a.k.a. multiplexing gain) of user-$k$ achieved
by communication scheme $j,j\in\\{\textrm{N, M, R}\\}$, (N, M, R respectively
stand for NOMA, MU–LP, RSMA) are defined as follows

$d_{k}^{(j)}=\lim_{P\rightarrow\infty}\frac{R_{k}^{(j)}(P)}{\log_{2}(P)},$
(41)

where $R_{k}^{(j)}(P)$ is the rate of user-$k$ for scheme $j$ under transmit
power constraint $P$. Mathematically, DoF $d_{k}^{(j)}$ is the first-order
approximation of the rate of user-$k$ at high SNR and is therefore the pre-log
factor of $R_{k}^{(j)}(P)$ at high SNR. It can be also interpreted as the
number or fraction of interference-free streams that can be simultaneously
transmitted from the transmitter to user-$k$ using scheme $j$. The larger
$d_{k}^{(j)}$ is, the faster the rate of user-$k$ increases with SNR.

Figure 23: The DoF region for the two-user MISO BC with imperfect CSIT, $\alpha=0.6$ [15]. TABLE XII: Comparison of sum-DoF and MMF-DoF of different MA schemes for perfect and imperfect CSIT [13]. Scheme |  Sum/MMF DoF |  Perfect CSIT |  Imperfect CSIT
---|---|---|---
NOMA |  $d_{\textnormal{s}}^{(\textnormal{N})}$ |  $\min\left(M,G\right)$ |  $\max\left(1,\min\left(M,G\right)\alpha\right)$
|  $d_{\textnormal{mmf}}^{(\textnormal{N})}$ |  | $\left\\{\begin{matrix}\frac{1}{g},&M\geq K-g+1\\\ \\\ 0,&M<K-g+1\end{matrix}\right.$
---
| $\left\\{\begin{matrix}\frac{\alpha}{g},&G>1\>\textnormal{and}\>M\geq
K-g+1\\\ 0,&G>1\>\textnormal{and}\>M<K-g+1\\\
\frac{1}{K},&G=1\end{matrix}\right.$
---
SDMA |  $d_{\textnormal{s}}^{(\textnormal{M})}$ |  $\min\left(M,K\right)$ |  $\max\left(1,\min\left(M,K\right)\alpha\right)$
|  $d_{\textnormal{mmf}}^{(\textnormal{M})}$ |  | $\left\\{\begin{matrix}1,&M\geq K\\\ \\\ 0,&M<K\end{matrix}\right.$
---
| $\left\\{\begin{matrix}\alpha,&M\geq K\\\ \\\ 0,&M<K\end{matrix}\right.$
---
RSMA |  $d_{\textnormal{s}}^{(\textnormal{R})}$ |  $\min\left(M,K\right)$ |  $1+\left(\min\left(M,K\right)-1\right)\alpha$
|  $d_{\textnormal{mmf}}^{(\textnormal{R})}$ |  | $\left\\{\begin{matrix}1,&M\geq K\\\ \\\ \frac{1}{1+K-M},&M<K\end{matrix}\right.$
---
$\left\\{\begin{matrix}\frac{1+(K-1)\alpha}{K},&M\geq K\\\
\frac{1+(M-1)\alpha}{K},&M<K\>\textnormal{and}\>\alpha\leq\frac{1}{1+K-M}\\\
\frac{1}{1+K-M},&M<K\>\textnormal{and}\>\alpha>\frac{1}{1+K-M}\end{matrix}\right.$

A DoF region is defined as the enclosure of all possible DoF tuples
($d_{1}^{(j)},\ldots,d_{K}^{(j)}$). We recall here that 1-layer RS, which is
the simplest RSMA scheme, already achieves the optimal DoF region in the
multi-antenna BC with imperfect CSIT [69, 167, 61, 70]. All other MA
strategies therefore can only achieve the same or worse DoF compared to RSMA.
The DoF region illustrated in Fig. 23 for the two-user MISO BC confirms the
explicit DoF gain achieved by RSMA. Each DoF point in Fig. 23 is calculated
based on the imperfect CSIT model in (29), where the estimated channel of
user-$k$ at the transmitter $\widehat{\mathbf{h}}_{k}$ and the corresponding
channel estimation error $\widetilde{\mathbf{h}}_{k}$ have i.i.d. complex
Gaussian entries following distributions $\mathcal{CN}(0,\sigma_{k}^{2})$ and
$\mathcal{CN}(0,\sigma_{e,k}^{2})$, respectively. The error variance scales
with SNR as $\sigma_{e,k}^{2}\sim\mathcal{O}(P^{-\alpha})$, where
$\alpha\in[0,\infty)$ is the CSIT scaling factor representing the quality of
the CSIT in the high SNR regime [68, 16, 168, 55, 58]. In limited feedback
systems, where users send quantized versions of their channels back to the BS,
$\alpha$ can be interpreted in terms of the number of feedback bits.
$\alpha=0$ represents partial CSIT with finite precision, i.e., a constant
number of feedback bits, while $\alpha=\infty$ represents perfect CSIT.
Normally, we choose $\alpha\in[0,1]$ since $\alpha=1$ corresponds to perfect
CSIT in the DoF sense [55].

Figure 24: Sum/MMF-DoF vs. number of SIC layers for MISO BC with imperfect
CSIT, $M=4$, $K=6$, $\alpha=0.5$ [13].

(a) Sum-DoF vs. number of users $K$

(b) MMF-DoF vs. number of users $K$

Figure 25: Sum/MMF-DoF vs. number of users $K$ for MISO BC with imperfect
CSIT, $\alpha=0.5$, $M=6$ [13].

In Fig. 23, $\alpha=0.6$ is considered. In such imperfect CSIT scenarios, SDMA
can only achieve a DoF of $\alpha$ for each user. In comparison, 1-layer RS
leverages the common stream to achieve an extra DoF of $1-\alpha$ while
keeping an achievable DoF of $2\alpha$ for the two private streams. By
respectively allocating the entire common stream to transmit the sub-messages
of user-$1$ and user-$2$, the corner points of $(1,\alpha)$ and $(\alpha,1)$
of 1-layer RS are achieved. The line segment between the two corner points can
be achieved by adjusting the amount of the common stream allocated to transmit
the sub-messages of the two users.

Besides the DoF region, sum-DoF and MMF-DoF have been used in the MIMO
literature to assess the capability of a strategy to exploit multiple
antennas. These performance metrics are defined as follows

$d_{\textnormal{s}}^{(j)}=\lim_{P\rightarrow\infty}\frac{R_{\textnormal{s}}^{(j)}(P)}{\log_{2}(P)}=\sum_{k=1}^{K}d_{k}^{(j)},$
(42)
$d_{\textnormal{mmf}}^{(j)}=\lim_{P\rightarrow\infty}\frac{R_{\textnormal{mmf}}^{(j)}(P)}{\log_{2}(P)}=\min_{k=1,...,K}d_{k}^{(j)},$
(43)

where $R_{\textnormal{s}}^{(j)}=\sum_{k=1}^{K}R_{k}^{(j)}$ is the sum-rate and
$R_{\textnormal{mmf}}^{(j)}=\min_{k}\\{R_{k}^{(j)}|k\in\mathcal{K}\\}$ is the
MMF rate. Sum-DoF $d_{\textnormal{s}}^{(j)}$ is the total number of
interference-free data streams that can be transmitted to all users by
employing scheme $j$. MMF-DoF $d_{\textnormal{mmf}}^{(j)}$ (a.k.a. symmetric
DoF) are the DoF that can be simultaneously achieved by all users. The sum-DoF
and MMF-DoF of NOMA, SDMA, and RSMA for the MISO BC with perfect and imperfect
CSIT have been calculated in [13] and are summarized in Table XII for
convenience. Without loss of generality, we assume the numbers of users in
different user groups are all equal to $g=|\mathcal{K}_{i}|,i\in\mathcal{G}$,
for SC-SIC per group.

In Fig. 24, the tradeoff between the sum/MMF-DoF and the number of SIC layers
for the MISO BC with $M=4$ and $K=6$ is illustrated. Imperfect CSIT is
considered and the CSIT scaling factor is $\alpha=0.5$. As can be observed,
multi-antenna NOMA ($G=3$) achieves better sum-DoF but worse MMF-DoF compared
to multi-antenna NOMA ($G=1$). 1-layer RS achieves the highest sum/MMF-DoF
among all schemes and entails a much lower complexity compared to NOMA.

Fig. 25 illustrates the sum- and MMF-DoF for the MISO BC with imperfect CSIT
versus the number of users $K$ when the number of transmit antennas is $M=6$
and the CSIT scaling factor is $\alpha=0.5$. 1-layer RS shows an explicit sum-
and MMF-DoF gain compared to all other schemes for all $K$. In Fig. 25(b), the
MMF-DoF of SDMA and multi-antenna NOMA ($G=1$) drops to 0 when $K>6$ and
$K>7$, respectively. This implies that the rate of the worst user does not
scale with the SNR and the rate saturates at high SNR. To maintain multiple
access and fairness among users, multi-antenna NOMA ($G=1$) is more suitable
when $K>M$ but it requires $K-1$ layers of SIC at each user. Taking 0.1 as the
MMF-DoF threshold for all users in Fig. 25(b), we observe that 1-layer RS can
serve around 15 users using 1 layer of SIC while multi-antenna NOMA ($G=1$)
can only serve 10 users at most using 9 layers of SIC. Hence, RSMA is
significantly more efficient than NOMA since RS with only one layer of SIC can
support a much larger number of users than NOMA with multiple layers of SIC.

(a) $\alpha=0.9,\sigma_{2}^{2}=1$

(b) $\alpha=0.9,\sigma_{2}^{2}=0.09$

(c) $\alpha=0.6,\sigma_{2}^{2}=1$

(d) $\alpha=0.6,\sigma_{2}^{2}=0.09$

Figure 26: Ergodic rate region comparison of different multiple access schemes
with imperfect CSIT, averaged over 100 random channel realizations, $K=2$, SNR
= 20 dB [77].

(a) $\sigma_{1}^{2}=\sigma_{2}^{2}=\sigma_{3}^{2}=1,M=4$

(b) $\sigma_{1}^{2}=\sigma_{2}^{2}=\sigma_{3}^{2}=1,M=2$

(c) $\sigma_{1}^{2}=\sigma_{2}^{2}=1,\sigma_{3}^{2}=0.09,M=2$

Figure 27: Ergodic sum rate versus CSIT quality comparison of different MA
schemes, averaged over 100 random channel realizations, $K=3$, SNR = 20 dB.

####  VI.C2 Rate region

Motivated by the DoF optimality of RSMA in the high SNR regime, attempts have
been made to explore the achievable rate (or SE) of RSMA in the finite SNR
regime [58, 77]. Fig. 26 evaluates the ergodic rate (ER) region of different
MA schemes averaged over 100 random channel realizations for the MISO BC with
imperfect CSIT. The BS has $M=2$ antennas and serves two single-antenna users.
The imperfect CSIT model follows (29) and the channel estimates of each user,
$\widehat{\mathbf{h}}_{k}$, have i.i.d. complex Gaussian entries following
distribution $\mathcal{CN}(0,\sigma_{k}^{2})$. The variance of
$\widehat{\mathbf{h}}_{1}$ is fixed to $\sigma_{1}^{2}=1$ while the variance
of $\widehat{\mathbf{h}}_{2}$ varies between $\sigma_{2}^{2}=1$ and
$\sigma_{2}^{2}=0.09$ representing equal channel strength and 10 dB channel
strength disparity between the two user channels, respectively. ER is defined
in the same way as in (33) and
$\textrm{ER}_{k,tot}=\overline{R}_{k}+\overline{C}_{k}$. Each rate pair
$\textrm{ER}_{1,tot},\textrm{ER}_{2,tot}$ at the boundary of the ER region is
obtained by solving $\mathcal{P}_{3}$ in Section IV.A for a certain weight
pair $u_{1},u_{2}$ with
$U_{n}(\mathbf{{P}},\overline{\mathbf{c}})=\sum_{k=1}^{K}u_{k}(\overline{R}_{k}+\overline{C}_{k})$
and $R_{k}^{th}=0$ bit/s/Hz. By changing the weight pair and optimizing the
rate pair accordingly, we obtain the entire ER region. The ER region of
DPC/DPCRS is the convex hull of the rate regions for all possible encoding
orders. Readers are referred to [77] for details on the optimization. In the
two-user case, M-DPCRS and generalized RS respectively reduce to 1-DPCRS and
1-layer RS. In Fig. 26, we use the terminology “DPCRS” to represent “M-DPCRS”
and “1-DPCRS”, and the terminology “RS” to represent “Generalized RS” and
“1-layer RS”, respectively.

From Fig. 26, we observe that DPCRS enlarges the ER region of all other
schemes and linearly precoded RS even outperforms DPC when the CSIT quality is
poor. DPC and SDMA (based on MU–LP) can be seen as two extreme schemes that
highly rely on accurate CSIT to fully manage interference at the transmitter
side, and both of them are therefore sensitive to CSIT inaccuracy. Hence, the
ER regions of DPC and SDMA (based on MU–LP) quickly shrink as the CSIT quality
decreases from $\alpha=0.9$ (in Fig. 26(c) and (d)) to $\alpha=0.6$ (in Fig.
26(a) and (b)). On the other hand, NOMA can be seen as an extreme scheme that
fully manages/cancels interference at the receiver side. However, it cannot
fully exploit the available DoF and results in poor performance [13]. DPCRS
and RS bridge the two extremes and use the common streams to smartly create a
mix of transmitter-side and receiver-side interference cancellation. By
adjusting the contribution of the common stream, it can dynamically decide the
level of interference that needs to be canceled at the transmitter or the
receiver side. Therefore, we conclude that in practical deployments with
partial CSIT, RSMA with a combination of transmitter-side and receiver-side
interference cancellation outperforms full transmitter-side interference
cancellation schemes such as SDMA (based on MU–LP or DPC) and full receiver-
side interference cancellation schemes such as NOMA (based on SC–SIC). RSMA is
more flexible, and hence, more robust to CSIT inaccuracies and everchanging
user deployments.

In Fig. 27, we further evaluate the ergodic sum rate (ESR) performance of
different linearly precoded schemes for a three-user MISO BC with imperfect
CSIT where generalized RS does not reduce to 1-layer RS. RS–CMD is also
considered where each user is required to decode three common streams
resulting in $6^{3}$ possible decoding orders to be considered at the
transmitter. To ease the computational burden, we only consider one decoding
order, namely, the ascending order of the users’ channel strengths. The
precoders of all schemes are designed to maximize the ESR (when users have
equal weights). In all figures, generalized RS outperforms all other schemes,
especially when the network is overloaded, see Fig. 27 (b) and (c).
Generalized RS achieves significant gains compared to the other MA schemes
when multi-user interference is strong and there is enough power allocated to
all common streams. The ESRs of multi-antenna NOMA ($G=1$) and SDMA drop
dramatically as $\alpha$ decreases from 1 to 0.2. Note that in the three-user
case, 1-layer RS yields an explicit performance gain over multi-antenna NOMA
($G=1$) and is robust to CSIT inaccuracies. Most importantly, 1-layer RS does
not require transmitter scheduling and only needs one layer of SIC at each
user, while multi-antenna NOMA ($G=1$) requires the transmitter to select from
6 decoding orders and each user has to be capable of performing two layers of
SIC. The joint transmitter-side and receiver-side interference cancellation
enables 1-layer RS to simultaneously enhance SE and reduce transceiver
complexity.

Figure 28: Weighted sum rate versus SNR comparison of different MA schemes for
an overloaded ten-user deployment with perfect CSIT, $M=2$ [53].

To further emphasize the capability of 1-layer RS to jointly boost the SE and
reduce the transceiver complexity, we consider an extremely overloaded
scenario with perfect CSIT in Fig. 28 where the BS has $M=2$ antennas and
serves ten single-antenna users. The user channels have i.i.d. complex
Gaussian entries following distribution $\mathcal{CN}(0,\sigma_{k}^{2})$. The
variances of the ten user channels are
$\sigma_{1}^{2}=1,\sigma_{2}^{2}=0.9,\ldots,\sigma_{10}^{2}=0.1$. To enable
service to multiple users in such an extremely overloaded scenario, we set the
QoS rate requirement of each user for SNR $=[0,5,\ldots,30]$ dB to be
$[0,0.001,0.004,0.01,0.03,0.06,0.1]$ bit/s/Hz, respectively. The precoders and
message splits are designed by solving $\mathcal{P}_{1}$ in Section IV.A. The
rate of each user is averaged over 10 randomly generated channels and the
weight of each user is assumed to be equal to 1. Fig. 28 shows an explicit WSR
gain of 1-layer RS over multi-antenna NOMA ($G=1$), SDMA, and multicast. RS
exploits the maximum DoF of 2 in the considered deployment (that is limited by
the two transmit antennas) by using the common stream to pack messages from
eight users while using the two private streams to serve the remaining two
users. In contrast, the DoF achieved by MU–LP is 1 because it cannot
coordinate the inter-user interference when there is a non-negligible QoS rate
requirement for each user, and its achieved DoF drops to 1. Multi-antenna NOMA
($G=1$) also achieves a DoF of 1. It makes inefficient use of the transmit
antennas and 9 layers of SIC (deployed but not always used) at each user.
Therefore, the WSR improvement of 1-layer RS comes with a much lower receiver
complexity compared with multi-antenna NOMA ($G=1$).

####  VI.C3 Operational region

As defined in [76], the operational region of an MA scheme is the region of
channel conditions that it prefers. We obey the following rules to select the
relevant MA scheme from RSMA, SDMA, NOMA, OMA:

  1. i)

if
$\textrm{WSR}_{\textrm{RSMA}}-\textrm{WSR}_{\textrm{OMA}}<\epsilon^{\prime}$,
RSMA boils down to OMA.

  2. ii)

if
$\textrm{WSR}_{\textrm{SDMA}}-\textrm{WSR}_{\textrm{OMA}}>\epsilon^{\prime}$
and
$\textrm{WSR}_{\textrm{RSMA}}-\textrm{WSR}_{\textrm{SDMA}}<\epsilon^{\prime}$,
RSMA boils down to SDMA.

  3. iii)

if
$\textrm{WSR}_{\textrm{NOMA}}-\textrm{WSR}_{\textrm{SDMA}}>\epsilon^{\prime}$
and
$\textrm{WSR}_{\textrm{RSMA}}-\textrm{WSR}_{\textrm{NOMA}}<\epsilon^{\prime}$,
RSMA boils down to NOMA.

  4. iv)

if
$\textrm{WSR}_{\textrm{RSMA}}-\textrm{WSR}_{\textrm{SDMA}}>\epsilon^{\prime}$
and
$\textrm{WSR}_{\textrm{RSMA}}-\textrm{WSR}_{\textrm{NOMA}}>\epsilon^{\prime}$,
RSMA is superior to all other MA schemes.

$\epsilon^{\prime}$ is the tolerance for selection. RSMA is selected as the
preferred scheme when it is not equivalent to any other MA scheme.

Following the evaluations in [76], we illustrate the preferred operational
regions for RSMA, SDMA, NOMA, and OMA for the two-user MISO BC with perfect
CSIT in Fig. 29. The transmitter is equipped with $M=2$ antennas and the
channel vectors are given by $\mathbf{h}_{1}=1/\sqrt{2}[1,1]^{H}$ and
$\mathbf{h}_{2}=\gamma/\sqrt{2}[1,e^{j\theta}]^{H}$. The precoders of all MA
schemes are designed using the WMMSE optimization framework developed in [58,
53] for solving $\mathcal{P}_{1}$ in Section IV.A for a certain weight pair
$u_{1},u_{2}$ with
$U_{n}(\mathbf{{P}},\overline{\mathbf{c}})=\sum_{k=1}^{K}u_{k}(\overline{R}_{k}+\overline{C}_{k})$
and $R_{k}^{th}=0$ bit/s/Hz. Readers are referred to [53] for more details on
the optimization of all MA schemes. The colors in Fig. 29 illustrate the
preferred MA schemes (RSMA, SDMA, NOMA, OMA) that maximize the WSR as a
function of
$\rho=1-\frac{|\mathbf{h}_{1}^{H}\mathbf{h}_{2}|^{2}}{\left\|\mathbf{h}_{1}\right\|^{2}\left\|\mathbf{h}_{1}\right\|^{2}}$
($1\leq\rho\leq 1$) and $\gamma_{\mathrm{dB}}=20\log_{10}(\gamma)$
($-20\textrm{dB}\leq\gamma_{\mathrm{dB}}\leq 0$). Therefore, user-1 and user-2
have a long-term SNR of 20dB and $0\textrm{dB}\leq
20\textrm{dB}+\gamma_{\mathrm{dB}}\leq 20\textrm{dB}$, respectively.

(a) $u_{1}=10^{0.5},u_{2}=1$

(b) $u_{1}=1,u_{2}=1$

(c) $u_{1}=1,u_{2}=10^{0.5}$

Figure 29: Regions of operation for different MA schemes, $K=2$, SNR = 20 dB.

From Fig. 29(a) and (b), we obtain that NOMA has no benefit at all when an
equal or higher weight is allocated to the user with the stronger channel
strength. Only when user fairness is considered, i.e., a higher weight is
allocated to the weaker user as in Fig. 29(c), RSMA boils down to NOMA,
especially for user deployments where the users are closely aligned with a
large channel strength disparity (i.e., small $\rho$ and large
$\gamma_{\mathrm{dB}}$). In all subfigures, we observe that RSMA boils down to
SDMA when $\rho$ is sufficiently large. SDMA is sufficient to manage inter-
user interference when the user channels are orthogonal. For different user
weights, there is always an explicit operational region for RSMA where it
provides a larger WSR than SDMA, NOMA, and OMA. In this critically loaded
scenario, RSMA offers high flexibility in all user deployments and is capable
of enhancing user fairness as well.

####  VI.C4 User fairness

(a) Max-min rate vs. SNR in dB.

(b) Power allocation to the common and private streams for 1-layer RS.

Figure 30: Max-min rate performance for the MISO BC with imperfect CSIT
$\alpha=0.5$, $M=K=6$. $P_{c}=\left\|\mathbf{p}_{c}\right\|^{2}$ is the power
allocated to the common stream. $P-P_{c}$ is the sum power allocated to all
private streams.

In practice, due to the disparate path losses experienced by users in
different locations, the issue of user fairness surfaces where users closer to
the transmitter are allocated with more (time/frequency/power) resources,
while users far from the transmitter are starving. To cope with this issue,
the max-min rate utility function is preferred for precoder design such that a
certain rate performance is guaranteed for all users. Next, we evaluate the
max-min rate performance among users when the precoders are designed via
solving $\mathcal{P}_{2}$ in Section IV.A with
$U_{n}(\mathbf{{P}},\overline{\mathbf{c}})={\min}_{k\in\mathcal{K}}(\overline{R}_{k}+\overline{C}_{k})$
and $R_{k}^{th}=0$ bit/s/Hz.

Fig. 30 illustrates the max-min rate performance and the corresponding power
allocation between the common and private streams for RSMA in the MISO BC with
imperfect CSIT when the transmitter is equipped with $M=6$ antennas and serves
$K=6$ single-antenna users. The imperfect CSIT model follows (29) with a CSIT
scaling factor of $\alpha=0.5$ and the results are averaged over 100 random
channel realizations. 1-layer RS shows superior max-min rate performance
compared to multi-antenna NOMA and SDMA in Fig. 30(a). As specified in Table
XI, the scheduler complexity and the receiver complexity of multi-antenna NOMA
are much higher than those for 1-layer RS and SDMA. At the transmitter, for
multi-antenna NOMA ($G=3$), the user grouping and decoding order have to be
jointly optimized with the precoders. When $K=6$, each user requires (but not
always uses all) 5 layers of SIC for multi-antenna NOMA ($G=1$). Such high
complexity, however, yields worse performance than 1-layer RS with a single
layer of SIC at each user or MU–LP without SIC. Therefore, multi-antenna NOMA
makes inefficient use of SIC as highlighted in [13].

To shed more light on the reasons behind the large max-min rate gain achieved
by 1-layer RS, the power allocation between the common and private streams is
illustrated in Fig. 30(b). The sum power allocated to all $K+1$ streams for
1-layer RS is
$P=\left\|\mathbf{p}_{c}\right\|^{2}+\sum_{k=1}^{K}\left\|\mathbf{p}_{k}\right\|^{2}$.
Let $P_{c}=\left\|\mathbf{p}_{c}\right\|^{2}$ be the power allocated to the
common stream $s_{c}$, then $P-P_{c}$ becomes the power allocated to all
private streams $s_{1},\ldots,s_{K}$. $\frac{P_{c}}{P}$ is therefore the
fraction of transmit power allocated to the common stream and
$\frac{P-P_{c}}{P}$ is the fraction of transmit power allocated to all private
streams. Fig. 30(b) shows that for all transmit SNR, 1-layer RS allocates a
large portion of power to the common stream and $P_{c}$ increases with the SNR
as the interference becomes stronger (compared to the noise) in the high SNR
regime. The common stream therefore plays an essential role in improving user
fairness in 1-layer RS. By adjusting the message split and the power
allocation to the common stream based on the level of interference that can be
canceled by the receiver, 1-layer RS realizes a powerful interference
management/cancellation strategy.

Figure 31: Throughput vs. SNR for different MA schemes for the MISO BC with
imperfect CSIT, $M=K=2$, $\alpha=0.6$ [79].

(a) $M=32,K=8,N_{r}=1,Q_{c}=Q_{p}=1$.

(b) $M=64,K=8,N_{r}=4,Q_{c}=Q_{p}=3$.

Figure 32: Throughput vs. user speed for different MA schemes for (massive)
MIMO BC with outdated CSIT employing OFDM and a 3GPP channel model, and $10$
ms CSI feedback delay [88]

.

####  VI.C5 LLS Performance

The PHY layer architecture illustrated in Section V.B has been used to
establish an LLS platform for RSMA, e.g., [79, 88, 90, 138]. In this section,
we study the throughput performance of RSMA obtained from LLS for a two-user
scenario, and compare the obtained throughput with the Shannon bounds.

The system throughput is defined as the total number of successfully recovered
information bits at all users per channel use. Denote $S^{(l)}$ and
$D_{s,k}^{(l)}$ respectively as the number of channel uses in the $l$-th
Monte-Carlo realization and the number of information bits successfully
recovered at user-$k$ for the intended common sub-message $\widehat{W}_{c,k}$
and private sub-message $\widehat{W}_{p,k}$. Then, the system throughput is
given as follows

$\textrm{Throughput
(bps/Hz)}=\frac{\sum_{l}\left(D_{s,1}^{(l)}+D_{s,2}^{(l)}\right)}{\sum_{l}S^{(l)}}.$
(44)

In total 100 Monte-Carlo realizations were used to obtain the throughput
performance results shown in Figs. 31 and 32(b), and $S^{(l)}=256,\forall
l\in\\{1,2,\ldots,100\\}$.

In Fig. 31, both the Shannon bounds and throughput levels achieved by RSMA,
SDMA, and NOMA for the MISO BC with imperfect CSIT are illustrated. The
transmitter has $M=2$ antennas and serves $K=2$ single-antenna users. The
imperfect CSIT model follows (29) with CSIT scaling factor $\alpha=0.6$.
Generally, the trend of the throughput performance obtained by the LLS is in
line with the corresponding Shannon bounds with a significant throughput gain
of RSMA compared to SDMA and NOMA. The throughput gain of RSMA over SDMA is
even larger than expected based on the Shannon bound. Furthermore, the
throughput of SDMA is observed to saturate in the high SNR regime. Due to
imperfect CSIT, SDMA frequently switches to single-user transmission (i.e.,
OMA) during the Monte-Carlo simulations of different channel realizations.
This results in a large transmission rate for a single user, which exceeds the
maximum SE achieved by the largest modulation order and code rate for a single
stream considered in the design. AMC therefore cannot assign an appropriate
modulation and coding scheme in such cases, resulting in a throughput loss.

Fig. 32(b) further extends the LLS to a (massive) MIMO BC with imperfect CSIT
where the transmitter has $M=64$ antennas and serves $K=8$ users, each with
$N_{r}=4$ receive antennas. As each user is equipped with multiple receive
antennas, the system can support more than one common and private streams for
each user. The number of common and private streams are chosen as
$Q_{c}=Q_{p}=2$, and in total $Q_{c}+KQ_{p}=18$ streams are transmitted from
the transmitter to the $K$ users.

In Fig. 32(b), the imperfect CSIT is caused by user mobility and delay in CSI
feedback from the users to the transmitter. The instantaneous channel vector
at time instant $t$ is

$\displaystyle\mathbf{H}_{k}[t]=\sqrt{\epsilon^{2}}\mathbf{h}_{k}[t-1]+\sqrt{1-\epsilon^{2}}\mathbf{E}_{k}[t],$
(45)

where $\epsilon=J_{0}(2\pi f_{D}T)$ is the time correlation coefficient
obeying the Jakes’ model, $J_{0}(.)$ is the modified Bessel function of the
first kind and order zero, $T$ is the channel instantiation interval, and
$f_{D}=vf_{c}/c$ is the maximum Doppler frequency for given user speed $v$,
speed of light $c$, and carrier frequency $f_{c}$. Both $\mathbf{H}_{k}[t]$
and $\mathbf{E}_{k}[t]$ have i.i.d. entries distributed according to
$\mathcal{CN}(0,1)$. In other words, the transmitter at time $t$ only has
knowledge of the channel vector observed at the previous time instant
$\mathbf{h}_{k}[t-1]$ due to the latency in CSI feedback. To simplify the RSMA
transmitter design, low-complexity zero-forcing (ZF) and block-diagonalization
(BD) methods are used to design the precoders of the private streams for MISO
and MIMO channels, respectively, while the leftmost eigenvector is used as the
precoder for the common streams. The system employs an Orthogonal Frequency
Division Multiplexing (OFDM) waveform in a frequency-selective channel
obtained according to the Clustered Delay Line (CDL) model of 3GPP. The
employed precoders are calculated for each subcarrier of the waveform for
optimal performance. The closed-form power allocation scheme proposed in [88]
for MISO channels is used to perform the power allocation between the common
and the private streams.

Fig. 32(b) reveals a significant throughput gain of RSMA over SDMA without and
with multi-antenna receivers. An immediate observation from Fig. 32(b)is the
that throughput performance of RSMA does not saturate with increasing SNR,
which is in contrast with the saturating throughput performance of SDMA. With
the same QoS constraint (i.e., 8 bps/Hz), RSMA supports a much higher user
speed (i.e., 40 km/h) than SDMA (i.e., 5 km/h). In Fig. 32(b), one can note
the non-monotonic behaviour of the RSMA throughput for SNR=$25$dB, which
occurs as the employed power allocation algorithm is suboptimal for MIMO
channels. The results clearly show that RSMA is indeed more robust to user
mobility than SDMA owing to its ability to partially decode interference and
partially treat interference as noise.

###  VI.D Advantages of RSMA

The above comparisons between RSMA and existing MA schemes including SDMA,
NOMA, OMA, and multicasting in terms of their respective framework,
complexity, and performance allow us to unveil the major advantages of RSMA,
which are summarized in the following:

  * •

Universality: RSMA is a universal MA scheme that subsumes SDMA, NOMA, OMA, and
multicasting as sub-schemes. In other words, RSMA is a superset of existing MA
schemes and therefore always achieves equal or better performance compared to
SDMA, NOMA, OMA, and multicasting. Henceforth, there does not seem to be a
need to investigate other MA schemes but rather use a single unified RSMA
framework.

  * •

Flexibility: RSMA is suited for different network loads
(underloaded/overloaded) and user deployments (diverse channel
directions/strengths). It is a powerful strategy that can manage multi-user
interference originating from different sources flexibly. Different from SDMA
that fully mitigates interference at the transmitter side or NOMA that fully
mitigates/cancels interference at the receiver side, RSMA creates common
streams to enable a smart combination of transmitter-side and receiver-side
interference mitigation. By adjusting the amount of resources allocated to the
common stream, the level of interference canceled at the transmitter and
receiver can be adjusted flexibly. In fact, RSMA employs a flexible
interference management strategy by partially decoding the interference and
partially treating the interference as noise, which generalizes the design
principle of fully treating interference as noise (as in SDMA), fully decoding
interference (as in NOMA), and single-user transmission to avoid interference
(as in OMA). By optimizing the power allocated to the common and private
streams, RSMA automatically simplifies to SDMA when the network is underloaded
and user channels are orthogonal with perfect CSIT and boils down to NOMA when
the network is extremely overloaded and user channels are aligned with certain
channel strength disparities. For other channel conditions, i.e., when the
user channels are neither orthogonal nor aligned, RS takes advantage of the
common streams to better manage the interference and outperforms all other MA
schemes.

  * •

Robustness: As the application of RSMA in multi-antenna networks is motivated
by its DoF optimality in the multi-antenna BC with imperfect CSIT, RSMA is
ideally suited to manage multi-user interference originating from imperfect
CSIT and is robust to CSIT inaccuracies resulting from different sources of
impairment, such as quantized feedback [92], pilot contamination [113],
channel estimation errors [58], and user mobility [88]. User mobility is one
of the major sources of interference in NR and is expected to become more
severe and to occur more frequently in 6G systems. Numerical results in [88,
144] have shown that RSMA has the capability to cope with the high mobility
envisioned in 6G. Contrary to SDMA, for which the sum-rate performance quickly
saturates for increasing SNR and drops quickly with the user speed, RSMA
ensures robust multi-user connectivity and achieves significant sum-rate and
throughput gains under user mobility. This is in contrast to the other MA
schemes (OMA, SDMA, NOMA), which are primarily designed for perfect CSIT and
are vulnerable to imperfect CSIT [77].

  * •

Higher spectrally efficiency: The SE of RSMA always exceeds or is equal to
that of the other MA schemes for both perfect and imperfect CSIT. When the
CSIT is perfect, the rate region of linearly precoded RSMA is larger than that
of MU–LP and NOMA, and is closer to the capacity region achieved by DPC. When
the CSIT is imperfect, linearly precoded RSMA can even achieve a larger rate
region than DPC. By marrying the benefits of RS and DPC, nonlinearly precoded
DPCRS further enlarges the rate region of the MISO BC with imperfect CSIT
beyond that of DPC and that of linearly precoded RS, as illustrated in Fig.
26. RSMA optimally exploits the available CSIT and the spatial dimension of
the multi-antenna BC. Furthermore, it achieves the optimum sum-DoF in both
perfect CSIT and imperfect CSIT (as illustrated Table XII and Fig. 23–25).

  * •

Higher energy efficiency: Since RSMA is a superset of OMA, SDMA, NOMA, and
multicasting, the performance gain of RSMA is not limited to SE, but also
extends to EE and their trade-off [81, 122, 133]. RSMA has been shown to
outperform existing MA schemes in terms of EE for various applications with a
wide range of network loads and user deployments [74, 84, 94, 96, 102, 107,
114, 126, 131].

  * •

Enhanced QoS and user fairness: RSMA not only better exploits the sum-DoF but
also the MMF-DoF in the multi-antenna BC with perfect and imperfect CSIT, as
illustrated in Table XII and Figs. 24, 25. In the finite SNR regime, RSMA also
exhibits a substantial max-min rate gain over the other MA schemes, as shown
in Fig. 30(a) and a number of recent works [56, 78, 87, 103, 108, 110, 111,
145, 125, 67, 137]. Moreover, the performance gain of RSMA becomes more
pronounced when the user rates are subject to QoS constraints or when a larger
weight is assigned to users with weaker channel strengths [53].

  * •

Lower complexity: RSMA entails a lower transceiver complexity than many
existing MA schemes. Although linearly-precoded RSMA achieves a larger rate
region than DPC, see Fig. 26, this gain comes with a simpler transmitter
design. Figs. 24, 25 and Figs. 27, 28 show that the sum/MMF-DoF gain and the
sum-rate gain of 1-layer RS over multi-antenna NOMA comes with lower
scheduling and receiver complexity. Different from multi-antenna NOMA, which
requires joint design of user grouping and ordering at the transmitter and
layer(s) of SIC at each user, 1-layer RS does not require user ordering and
grouping at the transmitter, and it only requires one SIC layer at each user.
Moreover, 1-layer RS is less sensitive to difference channel conditions, which
as a result, can further simplify the scheduler. Besides the merits of
reducing the scheduler and receiver complexity, RSMA is also capable of
reducing the CSI feedback overhead in the presence of quantized feedback [169,
95].

  * •

Coverage extension: It has been shown in [106, 108] that cooperative rate-
splitting (CRS), which incorporates cooperative user relaying with 1-layer RS,
and allows one user to decode and forward the common stream to the other
users, significantly improves the max-min rate when users with large channel
strength disparities are jointly served. Therefore, RSMA with coverage
extension techniques such as UAV/IRS/relay stations can further boost the rate
of the users at the cell edge and offers substantial coverage extension
benefits.

  * •

Low latency: URLLC is one major use case in NR and 6G. One approach to achieve
low-latency communication is reducing the transmitted packet size. RSMA has
been shown to improve throughput over SDMA and NOMA with finite length polar
codes in [79], and to attain the same transmission rate as SDMA and NOMA but
with shorter blocklength and therefore lower latency in [89, 144]. Hence, RSMA
is a promising enabling technology to reduce the latency in providing URLLC
services for 6G.

###  VI.E Disadvantages of RSMA

Despite of all the aforementioned advantages, RSMA inevitably also introduces
some disadvantages, which are summarized as follows.

  * •

Required SIC at receivers: As summarized in Table VIII, RSMA requires at least
one layer of SIC at each receiver. For some RSMA schemes, i.e., 1-layer RS,
2-layer HRS, 1-DPCRS, THPRS, the number of SIC layers at each user does not
depend on the number of user $K$. However, for generalized RS and M-DPCRS, the
number of SIC layers increases exponentially with the number of user $K$,
which imposes high receiver complexity.

  * •

Higher encoding complexity: For existing MA schemes including SDMA, NOMA, and
OMA, the number of data streams encoded at the transmitter is equal to the
number of users. In comparison, RSMA requires more data streams to be encoded
due to the message splitting (and recombining) at the transmitter as per Table
VIII. The encoding complexity of RSMA is therefore higher than that of other
MA schemes.

  * •

Higher signaling burden: As RSMA splits (and combines) user messages at the
transmitter, each receiver needs to know how to (split and) combine the
decoded messages in order to recover the intended message from the decoded
common and private messages. Therefore, a higher downlink signaling burden
might be imposed by RSMA-enabled transmission networks compared with other MA-
enabled networks so as to guarantee the transmitter and the receivers can
coordinate message splitting and combining.

  * •

Higher optimization burden: In terms of precoder optimization, RSMA requires
the precoders of the common and private streams to be jointly optimized with
the common rate allocation as per Section IV.A. Though the optimization space
is enlarged and more DoFs for precoder design are achieved, a higher
optimization burden is exerted by RSMA compared with the conventional SDMA
schemes. To reduce the computation time, efforts have been made to design low-
complexity precoders. However, as discussed in Section IV.B, the power
allocation between the common and private streams is crucial for the
performance of RSMA. The fraction of the transmit power allocated to the
private streams $\tau$ has to be optimized in order to guarantee the
performance gain of RSMA. However, a closed-form expression of $\tau$ is
challenging to obtain, which imposes a higher optimization burden to the
transmitter.

  * •

Higher complexity for Hybrid Automatic Repeat Request (HARQ): HARQ is an
important mechanism to improve the efficiency of packet-based transmission in
wireless networks. HARQ combines the MAC-layer ACK-NACK feedback mechanism
with channel coding to obtain an efficient re-transmission scheme for
recovering messages with missing packets. In modern communications systems,
HARQ is employed by encoding and re-transmitting the packets intended for
different users separately. In RSMA framework, this task is less
straightforward due to the message splitting and combining operations.
Therefore, there is a need for further study on how the user messages are
encoded and how the re-transmissions are performed for each user when RSMA is
combined with HARQ.

Although RSMA inevitably introduces the above problems, the appealing
advantages of RSMA far outweigh its disadvantages. As the study of RSMA is
still in its infancy, these problems are worth future exploration.

##  VII Emerging Applications, Challenges and Future Research Trends of RSMA

The appealing benefits of RSMA discovered for the multi-antenna BC have
spawned an explosion of RSMA studies on its applications to and interplay with
multifarious 5G/6G enabling communication techniques such as massive MIMO,
IRS, VLC, UAV, joint communication and sensing, and satellite communications
networks. Despite the substantial interest, the study of RSMA is still in its
infancy. For all applications listed in Section II, there are numerous open
problems in the categories of PHY layer design (such as coding and modulation,
precoder design, receiver design), cross-layer design (such as joint
scheduling and precoder design, sub-carrier allocation, large-scale networks,
stochastic geometry analysis), performance analysis (such as throughput, bit
error rate, outage probability), and so on. In this section, we summarize all
emerging applications of RSMA and the research challenges for each
application, followed by some potential research directions. Subsequently, we
discuss the standardization and implementation of RSMA.

###  VII.A RSMA for Enabling Technologies in 6G

####  VII.A1 MIMO BC

The studies of RSMA for the multi-antenna broadcast channel heretofore have
mainly considered a single antenna at each receiver (a.k.a. MISO BC). The
extension to multi-antenna receivers, however, is not well-understood in both
information theory and communication theory. When each user has multiple
receive antennas, it is capable of receiving vectors of common streams and
private streams, and the receive filter can be further designed for
interference management. Therefore, the number of common streams transmitted
in parallel, the DoF, and the transceiver design of RSMA all have to be
reconsidered for the MIMO BC.

In the information theoretical literature, an achievable DoF region of RSMA in
the two-user MIMO BC with asymmetric numbers of antennas and asymmetric levels
of partial CSIT has been established in [61], which is further shown to be the
optimal DoF region in [70]. The authors of [90] further establish the
achievable sum-DoF of RSMA in the $K$-user symmetric MIMO BC with $M$ transmit
antennas, $Q$ receive antennas at each user, and an arbitrary number of common
streams in the range of $[1,\min(M,Q)]$. In [65], RSMA was shown to achieve
the capacity region of the two-user MIMO BC with perfect CSIT within a
constant gap, but such constant-gap optimality does not extend to the three-
user case.

As for the communication-theoretic literature, [80] was the first work that
studied the precoder design for RS in the MIMO BC but with only a single
common stream. Each user therefore receives $Q$ replicated common streams and
a vector of private streams. Several practical stream combining techniques
along with regularized block diagonalization (RBD) linear precoders are
proposed in [80]. Even though the combining techniques for RS yield a sum-rate
gain over conventional multi-user MIMO (with linear precoding), the spatial
multiplexing gain of RS in the MIMO BC is not well exploited as multiple
receive antennas at each user enable a vector of common streams being
transmitted. Recent works [170] and [90] study the precoder optimization for
RSMA. The former is limited to the underloaded MIMO BC with perfect CSIT and a
fixed number of common streams, while the latter generalizes to both the
underloaded and overloaded MIMO BC with perfect and imperfect CSIT. The impact
of transmitting different numbers of common streams in the MIMO BC is also
investigated in [90]. Numerical results show a substantial ESR and sum-DoF
improvement for RSMA in all settings and that such gain increases with the
number of transmitted common streams when CSIT is imperfect. Besides the
theoretical results under the assumptions of Gaussian signaling and infinite
block lengths, the PHY layer architecture and the corresponding LLS of RSMA
for realistic finite constellation modulation, finite-length polar codes, and
AMC are studied in [90], [88]. The observed significant throughput gain of
RSMA over MU–MIMO and MIMO NOMA is consistent with its Shannon ESR gain.
Therefore, RSMA has a great potential for communication over the MIMO BC.

Challenges and future work: The capacity region of the $K$-user MIMO BC with
imperfect CSIT remains an open problem. As (linearly-precoded) RSMA is shown
to achieve the optimal DoF region in the 2-user MIMO BC with imperfect CSIT as
well as the optimal DoF region of the $K$-user MISO BC with imperfect CSIT,
there is a high chance that it will also achieve the entire DoF region and
even the capacity region of the $K$-user MIMO BC with imperfect CSIT. Such
problem, however, has not been studied yet. Even though the performance gain
of RSMA increases with the number of common streams, the receiver complexity
also increases. Therefore, in view of a practical implementation, the number
of common streams that RSMA requires to achieve a favorable tradeoff between
complexity and performance is worth further investigation.

####  VII.A2 MIMO IC

The entire capacity region and the corresponding capacity-achieving strategy
for the MIMO IC remain unknown for both perfect and imperfect CSIT. The HK
scheme proposed for the SISO IC has been proved to achieve the capacity region
of the two-cell MIMO IC within a constant gap [171]. The authors of [60]
further show that RSMA achieves the best known DoF region for the $K$-cell
MISO IC with imperfect CSIT and the result has also been extended to the (two-
cell) MIMO IC with an arbitrary number of antennas at each node in [61]. In
[122], coordinated beamforming for RSMA for the multi-cell MISO IC with
perfect CSIT is studied and is shown to achieve a better SE–EE tradeoff than
SDMA and NOMA. A comprehensive performance analysis for the $K$-cell RSMA-
aided MIMO IC is provided in [172], where the benefits of integrating RSMA
with interference alignment (IA) are investigated in terms of the average sum
rate, outage probability, and symbol error rate.

Challenges and future work: Motivated by the DoF, SE, and EE performance
enhancement introduced by RSMA in the MIMO IC, it is of high interest to
further explore its potential for achieving the entire DoF and capacity region
of the MIMO IC for both perfect and imperfect CSIT. In terms of practical
designs, the PHY layer design and LLS of the RSMA-aided MIMO IC have not been
studied, yet. Existing works on the MIMO IC mainly resort to IA to confine
undesired interference at each receiver into a lower-dimensional subspace.
Such method however is very sensitive to CSIT inaccuracies. The integration of
RSMA and IA has great potential to marry the advantages of both techniques so
as to further enhance the SE of transmission. The resulting open problems such
as transceiver design and cross-layer resource allocation for different
objectives are worth studying.

####  VII.A3 Massive MIMO

Massive MIMO is a MU-MIMO technique where the transmitter is equipped with a
large number of antennas and serves multiple users in the same resource block.
It has been considered as the most promising air interface technique for
achieving high SE and EE for 5G NR. To realize its substantial potential
gains, massive MIMO heavily relies on accurate CSIT, which however is
particularly challenging to attain when the number of transmit antennas is
large. The unaffordable feedback overhead in FDD massive MIMO, and the
imperfect channel estimation during the training phase and pilot contamination
in TDD massive MIMO, make imperfect CSIT a major bottleneck for realizing the
benefits of massive MIMO.

As has been highlighted in Section VI.D, RSMA is more robust to CSIT
inaccuracies (resulting from different kinds of impairment sources) than
existing MA schemes, which therefore makes the integration of RSMA and massive
MIMO a promising approach to tackle the aforementioned bottleneck of massive
MIMO. The authors of [92] pioneered the integration of RSMA and (FDD) massive
MIMO. To reduce the CSI feedback, a commonly used approach in FDD massive MIMO
is two-tier precoding, where the outer precoder controls the inter-group
interference based on long-term CSIT and the inner precoder controls intra-
group interference based on a short-term effective channel [173, 174, 175].
Motivated by the two-tier precoding, 2-layer HRS, as illustrated in Fig. 11,
was proposed in [92]. By utilizing two layers of common streams to
respectively manage the inter-group and inner-group interference, 2-layer HRS
reaps the rate saturation at high SNR and achieves a significant sum-rate gain
over existing two-tier precoding strategies. For TDD massive MIMO, RSMA has
been studied in a more realistic scenario where the channel estimation at the
transmitter is hampered by hardware impairments in [93]. The authors of [113]
further investigate the potential of RSMA to mitigate pilot contamination.
1-layer RS has been shown to achieve a substantial gain over conventional
massive MIMO based on MU–LP when CSIT is compromised by two different
impairment sources (hardware impairments and pilot contamination). The impact
of user mobility on (TDD/FDD) massive MIMO was studied in [88]. As illustrated
in Fig. 32(b), RSMA yields a significant throughput gain over conventional
massive MIMO based on MU–LP and it is able to maintain multi-user connectivity
in mobile deployments. Besides CSIT imperfection, RSMA has also shown its
capability of mitigating self-interference at relay stations equipped with
massive antennas in multi-pair massive MIMO relay systems [97].

Challenges and future work: Encouraged by the appealing performance gain of
RSMA in massive MIMO, the study of RSMA in cell-free massive MIMO is another
promising research direction. Cell-free massive MIMO extends single-cell
massive MIMO to multi-cell scenarios without cell boundaries, and therefore,
enjoys the benefits of both network MIMO and massive MIMO [176]. Cell-free
massive MIMO usually assumes no instantaneous CSI sharing among users, and
relies on the use of non-orthogonal uplink pilot sequences for channel
estimation, which therefore results in pilot contamination. This could be
successfully resolved by RSMA as in conventional massive MIMO [113]. Another
issue that hinders the wide use of massive MIMO is its high power consumption
dominated by the power used by the digital-to-analog converters (DACs) and
analog-to-digital converters (ADCs) in each RF chain. To alleviate the power
consumption burden, low-resolution ADCs/DACs could be used, which however,
distort the transmit/received signals. Whether RSMA is more robust against the
impact of low-resolution ADCs/DACs, and whether RSMA can help reduce the
resolution of ADCs/DACs while maintaining comparable performance as
conventional approaches are topics worth investigating.

####  VII.A4 Millimeter-wave

The explosive growth of mobile data traffic and the scarcity of the spectrum
resources available for cellular networks have motivated the investigation of
millimeter-wave (mmWave) communication which exploits the frequency band from
30 GHz to 300 GHz for wireless communication. However, mmWave communication
suffers from many challenges, among which high propagation loss is the most
significant one. To compensate such loss, one effective approach is to deploy
massive antennas at the transmitter for providing high array gain. The small
carrier wavelength of mmWave systems enables deploying massive antennas in a
small physical space, but makes fully digital arrays impractical. Hybrid
analog/digital processing, consisting of a high-dimensional analog beamformer
cascaded with a reduced-dimensional digital precoder, has been shown to be a
more practical solution [177]. Its performance, however, is limited by
imperfect CSIT and strong multi-user interference. The conventional feedback
procedure for mmWave massive MIMO relies on a two-stage approach to
sequentially feedback the indices of the codewords for the analog precoders
and the quantized effective channel, which entails high complexity and
overhead [178].

Inspired by the advantages of RSMA in the multi-antenna BC, the interplay of
RSMA and mmWave was first studied in [95]. By leveraging statistical CSIT to
design digital precoders, RSMA further reduces the training and feedback
complexities via a simple one-stage feedback while achieving a sum-rate
comparable to that of conventional mmWave massive MIMO based on MU–LP and two-
stage feedback. The authors [179] further study the joint analog and digital
precoder optimization for the RSMA-aided mmWave model proposed in [95]. The
extension to a UAV network was studied in [102] where the RSMA-aided mmWave
UAV network was shown to provide higher EE than NOMA for the practical 3GPP
Standardized 5G channel model.

Challenges and future work: To further reduce the feedback overhead and to
exploit the sparse nature of mmWave channels in the angle domain, compressive
sensing or deep learning-based approaches could be applied in RSMA-aided
mmWave massive MIMO networks to compress the pilot measurements into lower-
dimensional matrices. As quantization distortion is more tolerable with RSMA,
the joint use of CSI compression techniques and RSMA in mmWave massive MIMO
would be beneficial to ease the feedback overhead.

####  VII.A5 Multigroup multicasting

PHY layer multicasting characterizes the point-to-multipoint transmission when
a transmitter simultaneously sends one multicast content to a group of
recipients. It has been introduced as Multimedia Broadcast/Multicast Service
(MBMS) in 3GPP Release 9 for 4G and evolved MBMS (eMBMS) in 3GPP Release 11
for LTE-A [180]. Due to the diverse requirements of different user groups,
multigroup multicasting has emerged as an extension of conventional
multicasting where multiple multicast contents are simultaneously disseminated
to different groups of users (a.k.a. multicast group). Though such approach is
promising to enhance SE, inter-group interference is introduced.

Motivated by the superior interference management capability of RSMA, research
efforts have been dedicated to its application in multigroup multicasting
networks [59, 96, 110, 67, 111, 132, 145, 138, 141]. Reference [59] is the
first work that studied the integration of RSMA and multigroup multicasting.
For the MISO BC with perfect CSIT, RSMA was shown to achieve notable MMF-DoF
gains at high SNR and a max-min rate enhancement at low SNR by enabling
partial decoding of the inter-group interference and partially treating the
inter-group interference as noise. The authors of [67] further extended the
DoF and rate analysis of RSMA to the imperfect CSIT setting for a more
practical multibeam satellite communication application, and showed large DoF
and rate gains for RSMA when the CSIT quality is poor. RSMA was also shown to
achieve higher EE in multi-cell multigroup systems [96] and enhanced user
fairness in multi-carrier multigroup multicast systems [110]. PHY layer design
for multigroup multicasting was studied in [138] and LLS results were
presented for multigroup multicast cellular and satellite communications, and
in [132] for multicarrier multigroup multicast.

Challenges and future work: Each multicast stream in multigroup multicasting
has to be decoded by all users in the corresponding user group, which
therefore limits its achievable rate to the worst-case rate amongst the users.
The large fluctuation of terrestrial channels often results in deep channel
fades at the users, which therefore degrades the achievable rate of some
multicast streams. Contrary to terrestrial communications, satellite
communications provide a larger coverage, and are well-suited for providing
multicasting services for users distributed in a wider range. Integrated
terrestrial-satellite networks, aiming at providing ubiquitous services for
ground users via cooperative transmission between BSs and satellites, have
therefore been introduced as a new paradigm for the next generation of
communication networks [181]. Inspired by the DoF, SE, and EE gains of RSMA-
aided multigroup multicasting in both terrestrial and satellite networks, the
application of RSMA in integrated terrestrial-satellite networks is
interesting and promising to simultaneously reap its benefits in both
component networks.

####  VII.A6 Non-orthogonal unicast and multicast

Non-orthogonal unicast and multicast transmission (NOUM) enables concurrent
delivery of both unicast and multicast services to users in the same time-
frequency resource block. It was approved by 3GPP as a study item in 5G NR
Release 14 [182], applied in the digital TV standard ATSC 3.0 under the name
layer division multiplexing [183], and further included in the 3GPP Release 16
as LTE-based 5G Broadcast [184]. In multi-antenna NOUM, a conventional
approach is to adopt MU–LP at the transmitter to superpose the multicast
stream on top of the unicast streams and to use SIC at each user to decode and
remove the multicast stream before decoding the intended private stream. Such
MU–LP-aided approach does not fully exploit the advantages of SIC as SIC is
only used to manage interference between unicast and multicast streams and the
interference between unicast streams is fully treated as noise.

Motivated by the performance gains of RSMA for unicast-only and multicast-only
transmissions, RSMA has been applied to NOUM. The authors of [107] propose a
novel RSMA-aided NOUM where the unicast messages are split into common and
private parts at the transmitter, and the common parts are encoded with the
multicast message into a super-common stream for all users. Each user can
still use one layer of SIC to sequentially decode the super-common and the
intended private stream, but the function of SIC is better exploited in RSMA-
aided NOUM as SIC is used not only for managing the interference between the
multicast and unicast streams, but also for managing the interference between
the unicast streams. The proposed RSMA-aided NOUM was shown to yield SE and EE
gains over conventional NOUM without increasing the receiver complexity, which
therefore makes RSMA well-suited for NOUM. The authors of [109] further
propose a dirty paper coded RS-aided NOUM and showed its capability to enlarge
the rate region achieved by conventional DPC-aided NOUM and linearly precoded
RS-assisted NOUM when CSIT is imperfect.

Challenges and future work: The existing works [107, 109] are limited to the
case when the multicast message is intended for all users, i.e., a single
multicast group. When multiple multicast groups are considered, each user
receives three-dimensional interference, namely, interference among the
multicast streams, interference between the multicast and unicast streams, and
interference among the unicast streams. How to design the transceiver for RSMA
for such non-orthogonal unicast and multigroup multicasting networks in order
to deal with the three-dimensional interference remains unknown.

####  VII.A7 Multi-cell MIMO including coordinated multi-point (CoMP), cloud-
radio access network (C-RAN), and fog-radio access network (F-RAN)

The advancement of RSMA in the single-cell MIMO BC has motivated its study for
multi-cell networks for both coordinated transmission and cooperative
transmission, as illustrated in Section III.D. In coordinated multi-cell
networks with only CSI shared among all BSs, RSMA has been shown to achieve
enhanced SE and EE performance when the inter-cell interference is fully
treated as noise and RSMA is applied to only manage the intra-cell
interference [96, 122], or when the inter-cell interference is partially
decoded and partially treated as noise via RSMA [42, 43, 60, 36, 160].
Apparently, schemes that manage inter-cell interference via RSMA outperform
their counterparts that fully treat inter-cell interference as noise. However,
the former approach imposes higher decoding burdens at the receiver side.

Recent research has investigated cooperative multi-cell networks [99, 101,
100, 103, 114, 115, 116, 128, 127] where all BSs share the CSI and data of all
users through fronthaul (a.k.a. backhaul in some papers) links as this allows
the users in different cells to share the same common stream(s), which
therefore simplifies the receiver design. Reference [99] was the first work
that investigated RSMA in cooperative multi-cell networks under the assumption
of unlimited fronthaul capacity, where RSMA was shown to achieve higher SE
than MU–LP and multi-antenna NOMA for various inter-user and inter-cell
channel strength disparities. Considering practical cooperative multi-cell
networks with non-ideal limited fronthaul capacity, C-RAN has attracted
intense research interests [185]. The application of RSMA in C-RAN has been
widely studied for both perfect CSIT [101, 100, 103, 114, 115, 116] and
imperfect CSIT [128], where RSMA was shown to alleviate the fronthaul capacity
limitation for a given QoS rate requirement. To further ease the pressure of
information exchange and signal processing at the central processor, F-RAN has
been proposed as a new paradigm for 5G and beyond to exploit intelligence at
the network edge. Specifically, F-RAN enables edge-caching to prefetch content
with high reuse probability from the centralized processor at the remote radio
heads or end-users. RSMA in cache-aided C-RAN and F-RAN has been studied in
[141, 129, 133], where RSMA based on RS–CMD was shown to achieve significant
performance gains over MU–LP and NOMA requiring a much smaller caching size
and fronthaul capacity. Therefore, RSMA has great potential to enhance user
performance and simplify the transceiver design in cache-aided C-RAN.

Challenges and future work: Existing works on RSMA-aided F-RAN assume that the
cache placement is determined in advance (without using RSMA), and RSMA is
only used in the delivery phase. All messages, no matter whether they are
cached or not, are split and transmitted as in conventional C-RAN and caching
only influences the fronthaul capacity constraint. Though cache placement
normally uses a much larger timescale than content delivery, it is still
possible to jointly optimize content placement and delivery based on a mixed
timescale to better enhance the system performance for a limited cache size in
RSMA-aided F-RAN.

####  VII.A8 Simultaneous wireless information and power transfer (SWIPT)

SWIPT unifies wireless information transfer (WIT) and wireless power transfer
(WPT) by enabling the transmitter to deliver information and energy to the
corresponding information receivers (IRs) and energy receivers (ERs) at the
same time. One major issue in conventional multi-antenna SWIPT networks based
on MU–LP is that a dedicated energy-carrying signal is needed for each ER to
guarantee its harvested power [186] if ERs and IRs are separated.

Inspired by the appealing WIT performance of RSMA, RSMA for multi-antenna
SWIPT was proposed in [104] where a multi-antenna transmitter is serving
multiple separated IRs and ERs. Numerical results show that for a given lower
bound on the power harvested at the ERs, the rate region of the IRs for
1-layer RS outperforms that of MU–LP. Moreover, the rate region performance
for dedicated energy-carrying signals is almost the same as the one without
dedicated energy-carrying signals. The common stream of 1-layer RS is capable
of improving the interference management among IRs, and at the same time can
guarantee the energy harvested at the ERs. When the IRs and ERs are co-
located, i.e., each receiver requires both information and energy, RSMA can
save more transmit power than SDMA as illustrated in [105, 124].

Challenges and future work: One major challenge of SWIPT is the limited
transmission range to the ERs, which is a common limitation of WPT. A
potential approach to resolve this issue is to exploit other coverage
extension techniques such as user relaying, intelligent reconfigurable surface
(IRS), etc. The performance of RSMA in these SWIPT scenarios remains unknown.
In addition, ensuring information security is more challenging in SWIPT as ERs
are normally located closer to the transmitter compared with IRs. ERs are
therefore capable of eavesdropping the information transmitted to the IRs with
relatively higher received signal strengths. As RSMA encodes the information
of each IR into common and private streams, only when both the intended common
and private streams are successfully decoded at the ERs, the information of
that IR can be wiretapped. Therefore, RSMA has great potential to address the
security issue of SWIPT, which merits further investigation in future works.

####  VII.A9 Cooperative user relaying

Cooperative user relaying is a promising technique to enhance system capacity,
transmission reliability, and coverage without requiring extra antennas at the
transceivers. Motivated by the broadcast nature of wireless transmissions,
cooperative user relaying allows users to overhear the information of other
users emitted by the transmitter and then forward what is received to the
intended users. By creating spatially independent transmission paths from the
transmitter and relaying user, cooperative user relaying improves the spatial
diversity and enhances the received signal strength. Therefore, it has been
included in several wireless standards such as IEEE 802.11, IEEE 802.15.4a,
and IEEE 802.16 standards [187, 188, 189]. One of the most attractive
strategies for cooperative user relaying is cooperative NOMA. As NOMA requires
multiple users to decode the messages of other users, it can be easily
integrated with cooperative user relaying. However, as discussed in Section
I.A3, NOMA suffers from limitations imposed by the full decoding of the
interference and this drawback also limits cooperative NOMA.

Inspired by the advantages of 1-layer RS in the multi-antenna BC and the need
of all users to decode the common stream, the authors of [106] first studied
cooperative user relaying and RSMA in a two-user MISO BC and proposed a novel
RSMA strategy, namely, cooperative rate-splitting (CRS). The authors of [108]
further extended the proposed transmission framework to the $K$-user case.
Specifically, the transmission requires two phases. In the first phase, the
RSMA-enabled transmitter serves all users as in the conventional BC. In the
second phase, the selected relaying user(s) opportunistically forward the
decoded common stream to the remaining users so as to further enhance the rate
of the common stream. CRS is indeed a general strategy that includes 1-layer
RS as a special case when the second phase of CRS is turned off. The numerical
results in [106, 108] have shown substantial rate region and max-min fairness
gains of CRS over cooperative NOMA, 1-layer RS, and MU–LP, even when the SNR
is low. Furthermore, CRS is capable of enhancing PHY layer security, as shown
in [123].

Challenges and future work: Existing works on CRS all assume perfect CSIT. As
imperfect CSIT is the major bottleneck in current wireless networks, more
research attention should be dedicated to CRS with imperfect CSIT resulting
from different sources of impairment. Besides the heuristic relaying user
selection algorithm proposed in [108], more sophisticated selection algorithms
including a joint optimization of precoding and relaying user selection are
worth investigating.

####  VII.A10 Wireless caching

Wireless caching is an auspicious technology to ease backhaul traffic loads
and address the issues of spectrum scarcity and latency in future wireless
networks. There are two phases involved in cache-aided transmission, namely,
the placement and the delivery phases. Popular contents are prefetched to
local nodes such as small-cell BSs and end users during the placement phase
while the transmitter delivers the requested data, including the cached and
uncached contents, to the users during the delivery phase. Caching has been
shown to be beneficial in wireless networks to manage interference by allowing
multiple transmitters to cache and transmit the same content collaboratively
[190].

Motivated by the excellent interference management capability of RSMA, its
application in cache-aided networks has received significant attention [57,
191, 192, 141]. By splitting each user message into a cached part and an
uncached part during the placement phase, and using 1-layer RS to transmit the
uncached parts during the delivery phase, RSMA-aided caching has been shown to
boost the DoF and the coded-caching gain, and it further reduces the CSIT
requirement at the transmitter [57].

Challenges and future work: Existing works on RSMA-aided caching mainly tackle
information-theoretic problems. The optimization of caching methods (including
placement and delivery policies) to enhance SE/EE or to reduce the
transmission delay are worth studying. Moreover, RSMA-aided caching in F-RAN
with fronthaul constraints still needs more efforts as mentioned in Section
VII.A7.

####  VII.A11 Unmanned aerial vehicles-aided communications

UAV (a.k.a. drones) are gaining prominence in 5G NR and 6G for their merits of
coverage extension, convenient deployment, and low cost and highly
controllable 3D mobility.

Applications of RSMA in UAV-aided communications have emerged recently [101,
102, 118, 119, 131]. In [101], the UAVs are used to replace broken BSs in
order to maintain service to mobile users. By applying RSMA at the UAVs and
BSs, the sum-rate performance shows significant improvement over conventional
SDMA. The authors of [102] consider RSMA in UAV-aided mmWave transmission,
where the UAVs are receivers and served by a terrestrial BS, and RSMA is shown
to achieve superior EE compared to NOMA. The transition of MA from OMA and
NOMA to RSMA for aerial networks has been documented in [118]. The issue of
UAV placement is addressed in [119], and RSMA is shown to achieve WSR gains
over SDMA and NOMA. In [193], RSMA is further shown to improve the sum-rate in
satellite and aerial integrated networks.

Challenges and future work: One major challenge in UAV-aided communication is
the UAV deployment and trajectory design based on the estimated channels
between the UAVs and the ground nodes. Perfect tracking of the channels is
impossible due to the 3D channel structure and the high mobility of UAVs,
which therefore results in severe co-channel interference. RSMA has great
potential to address this issue thanks to its robustness towards CSIT
inaccuracy. However, the trajectory design problem for RSMA and UAV-aided
communication systems and the influence of UAV mobility on the system
performance have not been investigated, yet. Moreover, whether using RSMA can
help overcome the lifetime limitation of UAVs merits investigation.

####  VII.A12 Physical layer security

Privacy/security is one of the most challenging and critical issues in
wireless communications due to the broadcast nature of wireless channels. One
promising method to enhance security is to protect the data transmission in
the PHY layer by preventing the eavesdroppers from decoding data while
ensuring successful decoding at the legitimate users.

To bring RSMA on the map of the next generation communication networks, it is
necessary to investigate the secrecy performance of RSMA. Reference [125] was
the first work to study the secrecy performance of RSMA in a two-user MISO BC
where the multi-antenna transmitter simultaneously served two legitimate users
and there was one eavesdropper. By maximizing the minimum secrecy rate of the
two legitimate users, 1-layer RS was shown to achieve an explicit max-min
secrecy rate gain over MU–LP and NOMA. The common stream in 1-layer RS was not
only used as a useful means to enhance the transmission rate of the legitimate
users, but also as artificial noise to confound the eavesdropper. The authors
of [123] further investigate the secrecy rate of CRS when cooperative user
relaying is enabled at the two legitimate users such that one user decodes and
forwards the common stream to the other user. Again, CRS yields a secrecy sum-
rate gain over cooperative NOMA and MU–LP. Jamming is another important
approach in PHY layer security, which aims at generating noise signals to
confuse potential eavesdroppers. The authors of [135] further investigate RSMA
for joint communication and jamming where the transmitter simultaneously
serves multiple information users (IUs) with imperfect CSIT and performs
jamming on pilot subcarriers of adversarial users (AUs) based on statistical
CSIT. For the same amount of jamming power at the AU pilot subcarriers, RSMA
achieves a significantly higher sum-rate for the IUs than SDMA.

Challenges and future work: Ensuring the secrecy in RSMA is challenging when
the eavesdroppers are internal legitimate users, i.e., one legitimate user
decodes the intended streams, and then eavesdrops the private streams of the
other legitimate users. After decoding the intended common and private
streams, the interference impairing the private stream of the other legitimate
users also becomes smaller. Such problem, however, has not been studied, yet.
Moreover, in TDD massive MIMO, the uplink channel estimation could be affected
by pilot-contamination attackers who are actively sending the same pilot
sequence as the legitimate users in order to deteriorate the estimated CSIT of
the legitimate users. Inspired by the enhanced robustness of RSMA against
pilot contamination [113], it is interesting to investigate the secrecy rate
performance of RSMA in TDD massive MIMO to understand whether it is suitable
for combating pilot contamination attacks.

####  VII.A13 Satellite Communications

To further enhance the coverage and transmission reliability especially in
areas where terrestrial infrastructures are difficult to deploy, the
development of satellite networks as complements to terrestrial cellular
networks has been investigated. Satellite networks have evolved from single-
beam to multibeam architectures, where the satellite is typically equipped
with multiple feeds and serves multiple users groups within multiple co-
channel beams. Such multibeam satellite communication follows the cellular
multigroup multicasting paradigm, which introduces inter-beam interference.

The benefits of RSMA discovered for multigroup multicasting transmission in
cellular networks have inspired the study of RSMA for multibeam satellite
communications [98, 67, 149, 138, 137, 193, 131, 194]. The authors of [98]
initiated the study of RSMA in a two-beam satellite communication network
where the inter-beam interference was managed by RSMA while the inter-user
interference within each beam was coordinated via TDMA. The rate region of the
proposed RSMA-aided satellite communication framework was shown to be larger
than that of other strategies which do not use RS or beam cooperation. The
authors of [149, 67] further demonstrate MMF-DoF and max-min rate gains of
RSMA over MU–LP in a generalized framework considering multiple beams in the
same time-frequency resource blocks and multiple users in each beam with
imperfect CSIT. RSMA is further applied to satellite systems with multiple
gateways and feeder link interference in [137] and is shown to be powerful in
handling inter-gateway interference. PHY-layer designs and LLS for satellite
communications are provided in [138] with significant throughput gains
achieved by RSMA over MU–LP. To further guarantee seamless and ubiquitous
service, integrated terrestrial-satellite networks have been proposed and are
a promising approach. RSMA has been studied in [193, 131, 195] for integrated
terrestrial-satellite networks, where RSMA is shown to achieve significant
sum-rate, secrecy rate, and EE gains over conventional MU–LP.

Challenges and future work: Existing works on RSMA in integrated terrestrial-
satellite networks are limited to single beam without inter-beam interference
and the inter-user interference is completely managed by the BS on the ground.
Furthermore, the cooperation between BSs and satellites has not been fully
exploited yet. How satellites can efficiently act as a complement and
cooperatively serve users with poor terrestrial channels is still unknown.

####  VII.A14 Integrated Radar/Sensing and Communication

The growing issue of radio spectrum congestion has catalyzed the
electromagnetic RF convergence paradigm by enabling cooperative spectrum
sharing among multiple RF systems. Integrated sensing and communication (ISAC)
is one such approach that allows both functionalities to share the same
transmit signals and even the same hardware platforms. However, such new
paradigm incurs interference between communication and sensing, which has
become one of the major challenges in ISAC [196].

Inspired by the formidable interference management capability of RSMA, an
RSMA-aided dual-functional radar-communication (DFRC) transmission framework
was first proposed in [197, 117] considering one multi-antenna transmitter
simultaneously detecting radar targets and serving multiple communication
users based on 1-layer RS. By designing the precoders to simultaneously
maximize the WSR of the communication users and minimize the MSE for radar
beampattern approximation, RSMA improves the tradeoff between WSR and MSE
compared to conventional SDMA-based DFRC. RSMA not only better manages the
interference among communication users, but also successfully handles the
interference between communication and radar. The authors of [140] further
show the tradeoff gain of RSMA-aided DFRC for imperfect CSIT. The authors of
[139] further consider low resolution digital-to-analog converter (DAC) units
for RSMA-aided DFRC. RSMA is shown to achieve significant sum-rate gains over
SDMA for all considered numbers of quantization bits.

Challenges and future work: The spectrum sharing between communication and
radar raises security concerns, especially for military applications. Whether
RSMA-aided DFRC can enhance PHY layer security has not been investigated yet.
The tradeoff between radar detection and secrecy rate is indeed worth
studying.

####  VII.A15 Cognitive radio

Cognitive radio (CR) is a promising technique to overcome the scarcity of
radio resources and enhance SE by allowing secondary users (SUs) to
opportunistically use the frequency band shared by the licensed primary users
(PUs) as long as the interference from SUs to PUs is controlled within a
certain level. One major challenge in CR is the interference management
between SUs and PUs as PUs are normally unaware of the existence of the SUs
and the burden of interference management is moved to the transmitter and SUs.

The powerful interference management capability of RSMA makes it a perfect fit
for MIMO CR networks. The authors of [124] first investigated RSMA-aided MIMO
CR networks. By minimizing the transmit power subject to a minimum data rate
constraint at the SU and a maximum interference power level constraint at the
PUs, RSMA was shown to reduce the power consumption at the transmitter
compared with SDMA. The authors of [136] further identify the performance