### 3.4.2.2 Power allocation for first two users in each frequency layer

For this step we assume that the last user (strong user) in each frequency layer has been removed by interference cancellation. These two users in each frequency layers are to be decoded using Log-MPA. As mentioned in equation 3.61 and 3.62 that power allocation to each of these users is according to their channel gains. From factor graph matrix 3.57 it can be seen that it is user 1,2,3 and 4 that are the remaining users after interference cancellation of strongest user in each frequency layer. We intend to calculate the value of $\mathcal{E}\mathbf{b}/\mathcal{N}\mathbf{0}$ for which the final target BER$=10^{-5}$ or intermediate target BER$=10^{-1}$ can be achieved.

It can be seen from figure 3.19 that feasible values of $\vartheta$ and $\mathcal{E}\mathbf{b}/\mathcal{N}\mathbf{0}$ for intermediate

<figure><img src="image_65.png" /><figcaption>Figure 3.19: Values of $\vartheta$ for different values of $\mathcal{E}\mathbf{b}/\mathcal{N}\mathbf{0}$ for BER$=10^{-1}$</figcaption></figure>

target BER$=10^{-1}$ are for values of $\mathcal{E}\mathbf{b}/\mathcal{N}\mathbf{0}$ greater than 12dB. In order to illustrate mathematically, for instance, we defined to achieve this target at $\mathcal{E}\mathbf{b}/\mathcal{N}\mathbf{0}=16\text{dB}$

**Target BER$=10^{-5}$ at $\mathcal{E}\mathbf{b}/\mathcal{N}\mathbf{0}=16\text{dB}**

The aim is to minimize the value $\vartheta$ so that remaining fraction of power can be allocated to strong user. Value of $\vartheta$ to achieve intermediate BER$=10^{-1}$ can be computed by plotting BER for different values of $\vartheta$. Figure 3.20 shows BER results for $J' = 4$ users for different values of $\vartheta$. For each value of $\vartheta$; the values of $\alpha_1$ and $\alpha_2$ in each frequency layers are calculated according to 3.61 and 3.62. As power allocation is done according to channel gains so all the remaining four users have almost same BER values at different $\mathcal{E}\mathbf{b}/\mathcal{N}\mathbf{0}$.

When the value of $\vartheta$ is set to the maximum i.e. equal to one, it is observed in figure 3.20a that BER for $J' = 4$ users, the intermediate target BER$=10^{-1}$ can be achieved at $\mathcal{E}\mathbf{b}/\mathcal{N}\mathbf{0}=11\text{dB}$. Similarly, when the value of $\vartheta$ is decreased to 0.8 the same target is achieved at higher values of $\mathcal{E}\mathbf{b}/\mathcal{N}\mathbf{0}$ in figure 3.20b. The aim is to achieve this value of BER at $\mathcal{E}\mathbf{b}/\mathcal{N}\mathbf{0}=16\text{dB}$. It is observed in figure 3.20d that for value of
<figure><img src="image_66.png" /><figcaption>Figure 3.20: Power allocation for first two user in each frequency layer with different values of $\vartheta$ at output of SCMA decoder</figcaption></figure>

$\vartheta$ less than 0.4, we can achieve the intermediate target BER at Eb/N0=16dB. Average BER values for all remaining four users is plotted in figure 3.21. It can be confirmed from this figure that intermediate target BER can be achieved for $\vartheta$ less than 0.4 at Eb/N0=16dB.

In order to find relatively accurate value of $\vartheta$ for BER=10⁻¹ at output of SCMA decoder at Eb/N0=16dB, equation 3.58 can be written as

$$10^{-1} \le \frac{1}{M^{J'} \times J' \log_2(M)} \sum_{\mathbf{x}_a} \sum_{\mathbf{x}_b \neq \mathbf{x}_a} P_s\{\mathbf{x}_a \to \mathbf{x}_b\} \quad (3.64)$$

where

$$P_s\{\mathbf{x}_a \to \mathbf{x}_b\}_{\text{Rayleigh}} \approx \frac{1}{12} \prod_{k=1}^{K} \frac{1}{1 + \frac{\Lambda_k}{4N_0}} + \frac{1}{6} \prod_{k=1}^{K} \frac{1}{1 + \frac{\Lambda_k}{3N_0}} \quad (3.65)$$

$\vartheta$ is divided among each of two users according to their channel gains so $\Lambda_k = \sum_{j' \in \zeta_k} ||\sqrt{\vartheta}\delta_{j',k}||^2$ in equation 3.65 with $\zeta_k$ is the set of users connected to k-th frequency layer and $j' \in J'$. Similarly Eb/N0=16dB gives the value of N0 for above equation as well. The only unknown value in equation 3.64 and 3.65 is $\vartheta$. Solving
<figure><img src="image_67.png" /><figcaption>Figure 3.21: Average BER for $J = 1 \rightarrow 4$ user at output of SCMA decoder

these equations gives the its value as $\vartheta \ge 0.36$</figcaption></figure>

<figure><img src="image_68.png" /><figcaption>Figure 3.22: $\vartheta$ values for first 2 users in each frequency layer at Eb/N0=16dB</figcaption></figure>
<figure><img src="image_69.png" /><figcaption>Figure 3.23: BER for $J' = 4$ users at output of LDPC decoder with $\vartheta = 0.36$</figcaption></figure>

When equations 3.64 and 3.65 are plotted graphically in figure 3.22 for different values of $\vartheta$, it can be seen the BER$=10^{-1}$ is achieved at $\vartheta \ge 0.36$. After $\vartheta$ has been computed, power coefficient $\alpha_1$ and $\alpha_2$ are computed according to equations 3.61 and 3.62. Results for BER at output of LDPC decoder for user 1 to user 4 with $\vartheta_{min} = 0.36$ can be seen in figure 3.23. It can be seen that with the calculated value of $\vartheta$ the final target BER at Eb/N0=16dB is achieved for $J' = 4$ of SCMA.

### 3.4.2.3 Power allocation for last user (strong user) in each frequency layer

After minimum value of $\vartheta$ has been calculated, the value $\alpha_3$ is calculated as

$$ \alpha_3 = 1 - \vartheta_{min} = 0.64 \qquad (3.66) $$

with value of $\alpha_3$ in equation 3.66, since it is greater than 0.62, the threshold value 2.23 is satisfied. With power allocation coefficient for strong user, it is hard decoded, considering remaining users as Gaussian noise. Equation 3.55 is used to compute BER for user 5 and user 6 in their respective frequency layers. Actual BER and analytical BER, using expression in 3.55 for these strong user; when they are hard decoded while considering other users as Gaussian noise is given by figure 3.24. It can be seen in this figure that intermediate target BER is well achieved before Eb/N0=16dB.
<figure><img src="image_70.png" /><figcaption>Figure 3.24: Hard decoding for user 5 and user 6 with $\alpha_3 = 0.64$</figcaption></figure>

Finally, we check for all six user under the calculated power allocation coefficient and results are shown in figure 3.25. Slight degradation can be seen for the BER results

<figure><img src="image_71.png" /><figcaption>Figure 3.25: Joint HIC-Log MPA decoding for $J = 6$ users with LDPC decoder with optimized power allocation</figcaption></figure>
for user 1 and user 2 which to due the fact the error propagation has occurred during
interference cancellation.Although user 5 and user 6 seem to have to almost zero
BER at Eb/N0=16dB but these BER results are depicted after error correction from
LDPC decoder whereas interference cancellation is done prior to LDPC decoding of
these users to avoid higher latency in the system.

**3.5 Conclusion**

In this chapter at the beginning, we have discussed error probabilities for a single user using multi-dimensional constellations for AWGN and Rayleigh Fading Channel. This idea has been extended to multiple users using multi-dimensional constellations for same channels as in case of a single user. Error probabilities for SCMA system have been derived based on these ideas, but these error probabilities formulations do not take into account the ordered statistics.

We have formulated the BER expression for the strong user while considering Gaussian Approximation. Interference noise from the weak users and ordered statistics have been taken into consideration to derive an expression for single user (strong user) in an SCMA system. For the remaining users, we have defined error probability expressions to find minimum total power required by these weak users. Simulation results are in coherence with mathematical formulations. While comparing results of this optimized power allocation in figure 3.25 with same HIC-Log MPA decoding in figure 2.12 where both the systems have same computational complexity, it can been seen that BER results for user 1 and user 2 have improved with optimized power allocation. A certain QoS has been guaranteed for all the users in SCMA system with optimized power allocation.
# PART III

## GENERAL CONCLUSION AND FUTURE PROSPECTS
General conclusion

It is quite evident that forthcoming generations of mobile communication will be asked for massive connectivity with higher data rates and low latency for connected devices. Multiple Access techniques are the important aspect of physical layer, and it has to be researched upon as well in order to meet these objectives for future mobile communication. Over the course of this work, multiple access technique which is able to allocate users in a non-orthogonal way have been studied. NOMA has emerged as a potential candidate for 5G mobile communication. This thesis has been focused on SCMA that is code domain NOMA. SCMA has been presented in order to understand its implementation to cope with frequency bandwidth limitation and improve spectral efficiency. For the encoding part of SCMA, a lot of research is being done for the design of unique sparse codebooks for SCMA users. While for decoding part of SCMA is also, under a lot of investigation in order to improve implementation complexity, to achieve better BER results etc.

As proof of concept, we have implemented a feedback in an LDPC encoded SCMA system to improve the BER results, and also worked on reducing the complexity of SCMA systems. We have also proposed a low complexity power allocation scheme for uplink SCMA. Target BER can be achieved by implementing an efficient decoder like LDPC. In this thesis, LDPC complexity is estimated to face with noise and SCMA interference and an abacus has been assessed to correlate target BER with SCMA output BER. The main results of the thesis are summarized below:

* First chapter provides a brief introduction on NOMA scheme, particularly focusing on SCMA. Some basic domains of NOMA have been discussed. Moreover, basic principles of NOMA have also been mentioned. Whereas codebooks design is concerned, we give an overview of an idea about the generation of codebooks. We also discuss in detail the message passing algorithm in SCMA decoding. Some of design objectives for NOMA and optimization of resource allocation in NOMA have been explained. Finally issues and challenges in optimization of resource allocation have also been discussed in detail.

* In the second chapter, we briefly discuss the classical SCMA which is using Log-MPA decoder for its decoding part and we also discuss encoded SCMA using LDPC decoding where users are decoded by Log-MPA followed LDPC decoder. A feedback from LDPC decoder has been proposed to improve the BER results. In this chapter we have also proposed HIC-Log MPA decoder to decrease the complexity of LDPC encoded uplink SCMA. HIC is hybrid interference cancellation technique which chooses between hard or soft decoding based on the value of a threshold. The threshold value is defined to choose between the two. Complexity simulations in this chapter show that HIC-Log MPA has improved results in terms of complexity as compared to MPA decoding. Moreover, interference cancellation is done at each instant which improves the latency of the system.

* In the third chapter, analytically defining the BER for SCMA users has been studied first. The idea of single and multiple users using multidimensional constellation has been extended to SCMA users. Optimization of power allocation
for target BER has been proposed for HIC-Log MPA discussed in chapter 2.
BER expressions are derived for SCMA user in presence of interference noise
from other users and order statistics are considered while deriving these expres-
sions. Simulation results depict that HIC-Log MPA with same low complexity
as compared to MPA is able to achieve target BER with proposed optimized
power allocation.

Future prospects

Based on the study and results obtained in this dissertation, following are some
problems that can be considered in future works.

* Third chapter of this thesis is just a proof of concepts. The work undertaken deserves to be consolidated through a parametric study taking into account different code rates and number of iterations for LDPC, different QoS for each user, different modulation order can be considered as well and the abacus can be enriched to have in depth detail of BER expression at different decoding blocks of LDPC encoded HIC-Log MPA.

* The work in this thesis has relied on assumption of perfect channel estimation. Perfect estimation of CSI in real time scenarios is difficult to realize as it requires more and more pilot signals to be sent in order to have more accurate channel estimation which results in reduction of spectral efficiency. So the impact of imperfect CSI needs to be addressed. System overhead is significant while requiring CSI at the transmitter end. Investigating imperfect CSI for optimization of power allocation for each user would be interesting for future perspectives.

* Imperfect SIC for power allocation has been studied in [126]. Error propagation during interference cancellation would be more realistic approach during successive interference cancellation.

* Joint user clustering and power allocation optimization may be worth investigating for an uplink HIC-Log MPA SCMA system.

* Machine learning and deep learning are promising methods to optimize resource allocation. Few research has been carried out for deep learning in resource allocation in NOMA. [127] uses deep enforcement learning to solve sub carrier allocation problem with constraint of QoS and cellular power constraint. It will worth studying deep enforcement learning solve problems of optimization in resource allocations.

* This study is based on single cell scenario. In realistic scenarios such as multi-cell scenario there presence of inter-cell interference. It would be interesting to investigate optimization of resource allocation for proposed model in multi-cell scenario to handle inter-cell interference.
Scientific publications

International refereed Journals

* Ghani, B., Launay, F., Pousset, Y. et al. Low-complexity hybrid interference cancellation for sparse code multiple access. J Wireless Com Network 2022, 95 (2022). https://doi.org/10.1186/s13638-022-02162-y

International Conferences

* Ghani, B., Launay, F., Cances, J.P., Perrine, C., Pousset, Y. (2020). Iterative Decoding for SCMA Systems Using Log-MPA with Feedback LDPC Decoding. UNet 2019. Lecture Notes in Computer Science, vol 12293. Springer, Cham. https://doi.org/10.1007/978-3-030-58008-7_2
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