1. Introduction
As an efficient method of physical resource management, non-orthogonal multiple access (NOMA) is considered as a promising technology to achieve the targets of the fifth generation (5G) wireless communication systems (e.g., high capacity, massive connectivity, and low latency) [
1]. Among the available NOMA technologies, sparse code multiple access (SCMA) [
2] is a code domain multiplexing scheme, which can achieve an obvious increase in spectral efficiency compared to orthogonal multiple access (OMA). Different from low-density signature [
3], in SCMA, the incoming bits are mapped to sparse codewords selected from the predefined codebook [
4]. The SCMA encoder combines bits modulation and spreading together, and shaping gain is obtained from the multi-dimensional constellation [
5]. Multiple access is achieved by assigning different codebooks to different users, the codebook consists of some parameters of the bit modulation, such as spectrum resource, power, and multi-dimensional constellation points. Since the same time-frequency resource block can be shared by different codebooks, SCMA can obtain overloading gain. As a result of overload, the multi-user detection (MUD) technology is required. Benefiting from the sparsity feature of the codeword, message passing algorithm (MPA) can get a near optimal performance with low complexity [
6].
Similar to NOMA, wireless multicast is one of the technologies that is most likely to be applied to 5G and beyond [
7,
8], with the purpose of saving physical resources and satisfying future point to multipoint services. In the multicast system, the base station (BS) serves multiple users with a single physical resource because these receivers require the same content. To improve the performance of the multicast systems, two-stage cooperative transmission scheme has attracted wide attention [
9,
10,
11,
12,
13]. For example, in [
9], the outage probability and resource allocation for the cooperative multicast scheme are studied. Ref. [
10] proposed a probability-based power control method in cooperative multicast communications to minimize the user power consumption. Ref. [
11] investigated the energy efficient cooperative multicast, aiming to minimize the total transmission power.
There is an important observation that both NOMA and wireless multicast can alleviate the shortage of spectrum resource in 5G networks. Therefore, it is meaningful to study the performance of NOMA-based multicast systems. Most recently, Ref. [
14] designed a novel cooperation strategy for NOMA unicast-multicast, in which a multicast user is selected to forward a superposed message to unsuccessfully decoded unicast and/or multicast users. Ref. [
15] did research on the use of NOMA for mmWave cooperative multicast system. In [
16], the application of NOMA to multicast cognitive radio networks is investigated, and a dynamic cooperative transmission scheme is proposed. However, these studies are all focused on the power domain NOMA, and their results are not suitable for the SCMA system.
The research for the SCMA system is mainly focused on codebook design [
4,
17,
18], MUD technology [
19,
20,
21], and performance evaluation [
22,
23,
24,
25]. For example, Ref. [
4] applied lattice rotation to codebook design and proposed a systematic approach. In [
17], joint codebook design and assignment are considered to minimize the algorithm complexity of MPA. In order to take full advantage of the sparse characteristic of SCMA codebook, the codebook design and the advanced decoding strategy are studied in [
18]. Ref. [
19] investigated the improved MPA detector for SCMA, which could get a better error performance and a higher convergence speed. The performance evaluation of SCMA is studied in [
22], in which a linear sparse sequence modeling is used to derive the capacity of downlink multi-user SCMA system. Ref. [
23] applied SCMA into device-to-device (D2D) communication system and investigated the performance of SCMA in D2D and cellular hybrid network.
However, all the aforementioned research efforts on SCMA are limited in wireless unicast, where the message transmitted by the BS can only be received by one user. In these SCMA unicast strategies, if some users have the common interest (e.g., live sports streaming, video conferencing, etc.), the same data has to be sent separately, leading to low spectral efficiency and link utilization. Accordingly, when some users have the same interest, integrating cooperative multicast into SCMA can combine their advantages, and then improve the system capacity/reliability. Nevertheless, there is still a lack of the study on SCMA-based cooperative multicast systems.
For that reason, we propose a hybrid unicast-multicast downlink network, where SCMA is applied to unicast and multicast transmission. We divide users into two categories: the users who request the same content within the coverage of the BS, are called multicast users, and the BS transmits the message to these users using the same codebook simultaneously; the users who do not belong to a multicast group, are named unicast users, and the BS transmits the message to these users using different codebooks. The outage probability is used to measure the performance of the proposed network model, due to the diversity of channel gains for different receivers in the multicast group. To further improve the reliability of the unicast-multicast system, relay-assisted two-stage cooperative transmission scheme is introduced. The motivation for the proposed model is to take the advantage of SCMA and cooperative multicast to improve the spectral efficiency.
In this paper, a direct transmission scheme and two-stage cooperative transmission scheme in SCMA-based unicast-multicast hybrid network are developed. In the direct transmission scheme, the whole communication process is completed in one stage, where the relay is non-existent in the cell. In the two-stage cooperative transmission scheme, any number of relays are placed in the cell, and these relays are used to decode-and-forward (DF) the message to users. The BS broadcasts the requested message to users and relays in the first stage, and failed users receive the messages from multiple successful relays using a maximal ratio combiner (MRC) in the second stage. For the two-stage cooperative transmission scheme, the optimal relay design is considered to improve the performance of the system. Considering a delay constraint network, the BS transmits the message with a target rate for each unicast user/multicast group, the average outage probability is used to indicate the performance of the proposed network model. The main contributions of this work are summarized as follows:
We propose a network model of hybrid unicast-multicast based on SCMA, in which two transmission schemes (direct transmission and relay-assisted two-stage cooperative transmission) are discussed. The proposed strategy is able to achieve high spectral efficiency and link utilization.
Based on the presented network model, we derive the expressions of outage probability for these two schemes. From the results of calculation and simulation, we can observe that SCMA outperforms OMA in terms of average outage probability. We can also observe that the outage performance of cooperative transmission is better than direct transmission.
For the two-stage cooperative transmission scheme, relay design is considered to improve the system performance. We first obtain an asymptotic approximation of average outage probability in the high signal-to-noise ratio (SNR) regime. Then, based on this tight asymptote, we are able to determine the optimal relay locations and power allocation for the cooperative scheme. Simulation results show that the proposed system design scheme can effectively reduce the average outage probability.
The rest of this paper is organized as follows:
Section 2 presents the system model of direct transmission and cooperative transmission. In
Section 3, the outage probabilities of two transmission schemes are analyzed, and their expressions are derived, respectively. Approximation of outage probability is studied in
Section 4, and the optimal relay location and power allocation are obtained. In
Section 5, the simulation results of two transmission schemes are demonstrated and discussed. The conclusions of this work are provided in
Section 6.
4. Optimal Design of Cooperative Transmission
In this section, the optimal power allocation and relay position
of cooperative transmission scheme are analyzed. Letting
be the power allocation factor and
be the relay location factor, Equation (
27) is a function of the average outage probability with variables
and
. However, it is difficult to derive the optimal
and
due to the complicated expression of Equation (
27). Instead, the approximate value of
in a high SNR scenario is considered. To facilitate the following analysis, we take
,
, and
as an example, which is easy to extend to other situations. When
is large, Equation (
21) can be approximated as
In Equation (
28), we use the Taylor series approximation
for
x close to 0, which is tight in a high SNR scenario. In addition, the high-order term
in Equation (
28) is omitted. Equations (
22), (
24), and (
25) can also be approximated as
and
respectively. Based on Equations (
28)–(
31), a high SNR approximation of
can be expressed as Equation (
32):
In Equation (
32), the lowest order is
, after omitting the terms of
and using the approximation
, we get the approximation of
:
4.1. Optimal Power Allocation
Based on the approximation of average outage probability, we calculate the optimal power allocation in this section. In Equation (
33),
depends on the total number of relays
and their locations
but not the transmission power. Thus, the problem of power allocation can be expressed as
subject to
Since
is the power of all successful relays on each codeword, we need to get the average number of successful relays, which can be obtained by
In addition, with large
,
and we can have
. Replace
N in Equation (
35) with
, the average value of
can be expressed as
From Equations (
38) and (
39), we can get the maximum value of
when
. Thus, the optimal power allocation factor is
, and the average power of each codeword on each relay is
.
4.2. Optimal Relay Location
Based on the analysis of the optimized power allocation, we investigate the optimal relay location
in this section. Substituting
and
into Equation (
33), with some algebraic manipulations, the approximate value of average outage probability can be rewritten as
Therefore, the problem of minimizing
can be approximated to minimize
. The expression of
can be rewritten as Equation (
41), which is a function of
and
. For Equation (
41), we obtain the optimal
for each
by Monte Carlo and numerical methods.
Table 1 lists the optimal
with a different number of relays (
from 2 to 6):
To summarize, the relay design scheme in the high SNR region has been given, and the pseudocode is given by Algorithm 2. In the proposed scheme of relay design, the computational complexity is mainly dominated by the numerical solution of Equation (
41), the complexity of which is
(
is the calculation accuracy in this work). In the low SNR region, the computational complexity of the relay design is higher compared to the high SNR region because it is difficult to deal with Equation (
27). For the numerical solutions of minimize
in the low SNR region, its computational complexity is
.
Algorithm 2 Optimal design of cooperative transmission. |
Input: transmit power P, transmit rate , number of relays . Output: power allocation factor , relay location factor . - 1:
According to Equation ( 33), we can observe that and are two parts that do not affect each other. Then, we can obtain the optimal values of and separately. - 2:
The calculation of the optimal value of : - 3:
According to Equation ( 34), is optimal when reaches the maximum value. - 4:
After obtaining (the average number of successful relays), get the expression of the average value of . - 5:
Establish the equation . - 6:
Solving the derivative of the above equation, we have . - 7:
The optimal power allocation factor is . - 8:
The calculation of the optimal value of : - 9:
Initialization , , . - 10:
fordo - 11:
for do - 12:
Calculate according to Equation ( 41). - 13:
end for - 14:
Search for the value of when is the minimum, and this is optimal. - 15:
end for - 16:
The calculation is completed.
|
5. Numerical Results and Discussion
In this section, the Monte Carlo simulation and Numerical results based on Matlab are presented to evaluate the performance of the SCMA-based hybrid unicast-multicast network. We assume that the number of OFDMA tones is
, the number of non-zero elements in each codebook is
, the number of codebooks is
[
19,
20,
21], the target rate is
bit/s/Hz, the radius of the cell is
m, and the path-loss exponent is
. The OMA is used to compare the performance with SCMA on the basis of same parameters as above. Different from SCMA, the resource unit of OMA is OFDMA tone. For fair comparison, we consider equivalent physical resources in both networks. Thus, the total number of unicast users/multicast groups can be accessed in OMA network is
K, and the transmit power of each user is
P. Firstly, the simulation results of the outage probability for different schemes are presented. Then, the accurate and approximate results of average outage probability in the high SNR regime are verified. Finally, the simulation results with optimal relay location and power allocation are demonstrated.
represents the transmit SNR of each codeword in the direct transmission scheme. Accordingly, the transmit SNRs of each codeword in stage one, stage two with
and
are
,
and
, respectively.
We use
(number of relays),
(power power allocation factor) and
(relay location factor) as an example.
Figure 3 shows the average outage probability versus
. In
Figure 3, the performance of direct transmission and cooperative transmission with different numbers of relays in both SCMA and OMA networks are simulated. We can see that SCMA outperforms OMA in terms of outage probability for both direct and cooperative transmission schemes, which is because users in the SCMA network obtain spreading gain compared to OMA network. The cooperative transmission scheme has lower outage probability compared to direct transmission scheme in the high SNR regime, and the increasing number of relays can reduce the user’s outage probability. For example, maximum gain (about 3 dB) is obtained when
is increases from 2 to 6. This phenomenon can be explained the fact that the cooperative transmission provides array gain compared to the direct transmission.
Currently, there are fewer works focusing on the development of SCMA-based system. In [
31], layered multicast is introduced to maximize the multicast system capacity. Although Scheme [
31] is different from the target of this work, it would be interesting to compare the outage probability between cooperative multicast and layered multicast.
Figure 4 demonstrates the average outage probability of direct multicast, cooperative multicast with
, and layered multicast in the SCMA network. In
Figure 4, all
C codebooks are assigned to one multicast group, and other parameters are the same as in
Figure 3. It can be seen that the layered multicast has a better outage performance than other schemes in low SNR regime. This is because the users has higher outage probability when the SNR is lower. Moreover, to guarantee the minimum service quality of all users, the layered multicast allocates more resources to the basic layer. As the transmit SNR increases, cooperative multicast obtains an array gain. Therefore, cooperative multicast outperforms layered multicast [
31] in terms of outage probability in the high SNR regime.
In
Figure 5, the simulation and exact (Equation (
20)) results of the direct transmission scheme are presented. Meanwhile, the simulation, exact (Equation (
27)), and approximate (Equation (
33)) results of the two-stage cooperative transmission scheme are also presented. The simulation parameters are the same as in
Figure 3. We can clearly see that the exact outage probability curves are in good agreement with the Monte Carlo simulation results. The asymptotic curves almost overlap with the exact performance curves when
is large, which verifies our derivation of the average outage probability in the high SNR regime.
Figure 6 and
Figure 7 show that the effect of power allocation factor
on the average outage probability, where
dB are used as examples. In
Figure 6, the number of relays is
, and
. In
Figure 7, the number of relays is
, and
. From these two figures, we can observe that the power allocation factor has a significant impact on the average outage probability. Thus, it is necessary to find out the optimal power allocation factor. Additionally, the average outage probability decreases first and then increases with the increasing of power allocation factor
, and it reaches the minimum value when
. This is consistent with the conclusion in
Section 4.1, i.e., the first stage occupies half of the total energy consumed.
Figure 8 gives the trend of outage probability with the locations of relays, in which optimal power allocation factor
is used. From this figure, we can observe that the
in
Table 1 achieve the lowest outage probability when
is greater than 60 dB, which verifies our results from
Section 4.2. It is worth noting that the results of
Table 1 are obtained in high SNR region and the optimal power allocation and relay positions in the low SNR region (e.g., when
dB) may be different from our analysis in
Section 4.
Using optimal power allocation factor
and optimal relay locations specified in
Table 1,
Figure 9 shows the average outage probability versus
. We can see that optimal relay design effectively reduce the average outage probability. For example, the maximum gain (about 1 dB) is obtained when
. The cooperative transmission scheme achieves a maximum gain of 8 dB compared to the direct transmission scheme.
Figure 10 and
Figure 11 show that the effect of
on the achievable rate and the transmission delay, respectively, where the optimal power allocation factor and optimal relay locations are used. The achievable rate is the maximum allowable transmission rate of each codebook under the constraint of the outage probability (
in
Figure 10 and
Figure 11). The delay is the time required to transmit a packet at the achievable rate. To be more intuitive, we assume that the size of the packet is 1, and then the delays in
Figure 11 are the time required to transmit a unit packet. From the two figures mentioned, we can see that the proposed cooperative transmission has a higher achievable rate and lower delay than the direct transmission scheme.