In this work, an uplink wireless network scenario is considered. As shown in
Figure 1, it is assumed that a macro base station (BS) is located at the center of the cell, and some cooperation nodes (CNs) and wireless users are deployed in this cell. The users would play UE aggregation [
26,
27] with the CNs in which users upload messages by the assisting of CNs to the macro BS. A CN can be a relay node but, different from a traditional relay, a CN is also a special type of UE, for example, it could be a UAV or robot in a smart factory, or a normal UE with higher signal–processing capability, and a better channel condition. To better support the uplink service, users can reuse the same subchannel to communicate with the CN by NOMA technology, and the CN performs SIC decoding for the superimposed signals on the same subchannel. Let
denote the set of CN nodes, and users
are distributed within the cell. The total bandwidth of the system is
B, and the bandwidth can be divided into
K subchannels with a subchannel bandwidth
into a resource set. Considering the practical scenario where resources are limited,
is assumed. The maximum transmit power of users and CNs is
and
, respectively. Users with poor channel conditions could first broadcast their messages to CNs, and the CNs that receive the signal will forward these messages to the BS through the channel between the CNs and BS.
3.1. Two–Hop Cooperative Transmission with UE Aggregation
UE aggregation is a technology of cooperative transmission between users, and it is a two–hop transmission mechanism. In the first hop, users transmit the messages directly to the BS. For users being assisted, the performance of the direct link in terms of transmission rate and reliability is limited under high–channel fading.
The CN can detect and decode signals from users when the users send signals to the base station firstly. Let
be the signal from the
jth user to the BS on the
kth subchannel. The detectable signal at the
sth CN can be described as
where
denotes the channel coefficient of the link between the
jth UE and the
sth CN, which includes path loss, shadowing, and fast fading [
52]. The
th UE is the user reusing the subchannel
k.
represents the transmit power of the
jth user.
represents zero–mean additive white Gaussian noise (AWGN) and
represents a binary variable indicating whether a user reuses the subchannel
k; if
, this means the
jth user is reusing the
kth subchannel, otherwise
. The SINR of the
jth UE signal at the
sth CN can be expressed as
So, the data rate from the
jth users to the
sth CN is
. To decode the signal of the
jth user, the data rate should meet the constraint
, where
denotes the minimum decoding rate threshold.
After detecting and receiving signals from the
jth user, the CNs decode and forward these signals to the BS. This process can be considered as the second hop transmission. Assume the CN set
have successfully decoded the message of the
jth user, and the total number of these CNs is
. So, the SINR of the signal received by the BS can be given as
where
represents the interference on the
lth CN transmission within
caused by other users within the cell or users from neighboring cells occupying channel
k. All signals from the CNs are received at the base station and combined. Since the base station receives the same information, its reception rate is determined by the path with the highest rate. At the same time, assuming that the error probability of each path is
, the reliability of the data received at the base station can be denoted by
. For simplicity, we assume that central and edge users utilize different spectral resources, and we suppose that interference occurs only in the first hop of UE aggregation, namely the CN listening phase for UEs. Moreover, since in cooperative transmission, the rate from the user to the base station depends on the poorest link either from the user to the CN or from the CN to the base station, we assume that the phase where the CN listens to the UE is the weaker link.
3.2. Design of NOMA-Based Joint Transmission Pair
To support the access of a large number of devices, we consider that users communicate with CNs and BS by the NOMA scheme. Unlike traditional orthogonal multiple access (OMA) schemes, where a subchannel can only be used by one user at a time, in the NOMA scheme, a subchannel can be shared by multiple users. Therefore, systems that consider NOMA are expected to achieve higher spectral efficiency, which can reduce the waste of spectral resources associated with OMA schemes. Considering the above aspects, we assume each user can be allocated at most one subchannel, and all the users share the kth subchannel in a NOMA group to upload data. To eliminate co-channel interference, the receiver can perform SIC technique decoding to separate the superimposed signals coming from the same channel. The optimal decoding order is the descending order in terms of channel power gain.
Assuming the sth CN forwards the signals of the users, the ith paired NOMA group users are denoted as . Additionally, unlike a traditional C–NOMA relay, we perform SIC decoding at the CN. The paired NOMA users can transmit messages to the CN or the BS on the same subchannel. Paired NOMA users can be categorized into strong and weak users based on channel gains. For the same CN node s, the channel gain typically satisfies , where denotes the channel gain parameter between the first user of the ith NOMA group and the sth CN. This also means that at the receiving end, the decoding order of SIC is executed such that the message of the user with the highest channel gain is decoded first.
Power–domain NOMA relies on differentiating users’ signals based on their power levels. Let
denote the power allocation of the users in group
. Specifically,
represents the power allocation factor for the
th user in the
NOMA group. The transmit power of the
qth user can be expressed as
, and
satisfies
. Therefore, solving for the optimal
determines the optimal power allocation for the NOMA group. To ensure the successful execution of SIC, the transmission power of users must be carefully allocated. Additionally, when the
ith NOMA group is assisted by the
sth CN, the following equation must be satisfied at the receiver.
where
denotes the minimum received power gap required to enable SIC. In the same NOMA group, the SIC decoding order for the signals of each user is in descending order of their respective channel gains. If
, then
. The SINR of the signal of the
th user from the
ith NOMA group at the
sth CN can be given as
Obviously, in a NOMA group, the signal of the th user will only be interfered with by users with higher indices after performing SIC. Thus the received data rate of the th user in the NOMA group i is .
It can be observed that in each NOMA group, the user decoded last can enjoy interference–free transmission. Moreover, we find that for the
ith NOMA group
, the feasible CNs are not unique, which means that different interference–free users in
can be observed at different CNs. This implies that when NOMA users reuse the same subchannel, an interference–free signal can be obtained at different suboptimal CNs, which mitigates the impact of interference on the rate. For simplicity, we assume that SIC is perfect when the aforementioned conditions Equation (
4) are met.
Therefore, we allow more CNs to detect the data transmitted by the NOMA group. Let
be the set of CNs the
ith NOMA group could choose; to ensure the rationality of this choice, the rate of the CNs should follow
This ensures that users in the NOMA group have the opportunity to be successfully decoded by the CNs in the selected set of CNs.
For each user, having their broadcast signals monitored by more CNs is beneficial, as when NOMA groups can transmit via multiple CNs, the achievable rates of these NOMA users are determined solely by the best CN of a particular user, which means that for the NOMA user q, the optimal CN within satisfies that , which can achieve the maximum rate for q at this CN. Relative to the best CN for user , can be considered as a near user in the NOMA group, and within the NOMA group, the user is the far user of this CN. Similarly, for the best CN of user , is the near user, and is the far user. Therefore, we refer to this combination of a NOMA group and its multiple optimal CNs as a joint transmission pair (JTP). A JTP consists of a NOMA group and a set of CNs and can be represented as .
For example, as shown in
Figure 1, JTP1 is a joint transmission pair, wherein two CNs assist in the transmission of two users, namely CN1 and CN2, and user 1 and user 2. For user 1, CN1 is the best CN, where user 1 is the near user of CN1, and user 2 is the far user of CN1. Thus, at the receiving end CN1, SIC is executed by first decoding the signal from the near user, user 1, and then subtracting this decoded signal from the original signal to obtain the signal for the far user of user 2. For simplicity, we operate under the assumption of perfect SIC, the SINR at CN1 from user 1 and user 2 can be represented, respectively, as
It can be observed that, as the far user, user 2 is able to send a signal to CN1 without interference. At this point, by connecting to CN1, the data rates of user 1 and user 2 are and . Similarly, when there exists another optimal CN in the NOMA group, specifically the best CN for user 2, which is CN2, user 1 then becomes the far user. As a result, user 1 is able to send data to CN2 on subchannel k without interference. The data rates of user 1 and user 2 received at CN2 are, respectively, and .
In an uplink scenario with CN collaboration, the data rate of a NOMA user is determined by the maximum rate it can achieve. In the example above, the data rate of user 1 is
and similarly for user 2. In a NOMA system with multiple CNs, all users within the NOMA group have the opportunity to transmit without interference. Therefore, the maximum achievable uplink rate for the
qth NOMA user can be represented as
In a system with multiple CNs, the order of NOMA users in each NOMA group determines the level of interference each user experiences. Particularly in the scenario with two users and two CNs, it is possible to find two users who can access the CN on the same sub-channel without interfering with each other. After receiving the messages, these CNs then forward them to the base station.