What is cooperative non orthogonal multiple access (NOMA)?

What is cooperative communication?

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We know that NOMA involves successive interference cancellation (SIC), where one user decodes the message of the other user, from the superposition coded received signal, before decoding his own message. Specifically, the near user decodes the information of the far user while performing SIC. There is no escaping this step. The near user must decode the far user's data anyway.

Now that the near user has far user's data, he may as well relay that information to the far user to aid him. Since the far user has a poor channel with the transmitting base station (BS), the retransmission of his data by the near user will provide him diversity. That is, he will receive two different copies of the same message. One from the base station, and one from the near user who is acting like a relay. Thus, we can expect the outage probability of far user to decrease.

This concept is called cooperative communication/cooperative relaying. We can see that NOMA naturally allows cooperative communication because the near user has the far user's data because it must decode it anyway.

What are the advantages of cooperative communication?

• The advantage of cooperative communication is that we have established two links to transmit the same message. Even if one link is in outage, chances are the other link is good. The probability that both links simultaneously go into outage is very less compared to the probability that any one link fails.
• We get reduced outage probability and hence diversity gain without the need of additional antennas (i.e., MIMO).
• Another advantage is that relaying can virtually extend the coverage area of the base station.

System model

Now that we have seen what cooperative communication is, and how it is useful to our network, let us design a cooperative NOMA network. We are going to consider downlink transmission where there is a base station (BS) and two NOMA users. We have a near user who has a stronger channel with the BS and a far user with weak channel conditions.

The transmission occurs in two time slots. Let's call the first time slot as direct transmission slot and the second slot as relaying slot.

(i) Direct transmission slot

In the direct transmission slot, the BS uses NOMA to transmit data intended for the near user ($x_n$) and the far user ($x_f$). The near user does SIC to decode the far user's data first, and then proceeds to decode its own data. The far user just performs direct decoding.

At the end of the direct transmission slot, the achievable data rates at the near user and far user are,
\begin{align}
R_n &= \dfrac{1}{2}log_2(1 + \alpha_n\rho|h_n|^2)\\
R_{f,1} &= \dfrac{1}{2}log_2(1 + \dfrac{\alpha_f\rho|h_f|^2}{\alpha_n\rho|h_f|^2 + 1})
\end{align}

Notation

• $\alpha_n$ - power allocation coefficient for near user
• $\alpha_f$ - power allocation coefficient for far user
• $h_n$ - channel between BS and near user
• $h_f$ - channel between BS and far user
• $\rho$ - transmit SNR = $\dfrac{P}{\sigma^2}$, where $P$ is the transmit power and $\sigma^2$ is the noise variance
• As usual, $\alpha_f \gt \alpha_n$, and, $\alpha_n + \alpha_f = 1$

We have this factor of $\dfrac{1}{2}$ in front of the achievable rates because we have two time slots of equal duration and $R_n$, $R_f$ are the achievable rates during the first time slot alone.

(ii)Relaying slot

The next half of the time slot is called relaying slot. As we saw, the near user already has the far user's data because he decoded it in the previous time slot. In the relaying time slot, the near user just transmits this data to the far user. The achievable rate of the far user at the end of the relaying slot is, $$R_{f,2} = \dfrac{1}{2}log_2(1 + \rho|h_{nf}|^2)$$
Here, $h_{nf}$ is the channel between the near user and far user. We can already see that $R_{f,2} \gt R_{f,1}$ because of two reasons:

• There is no interference from other transmissions
• There is no fractional power allocation. The whole transmit power is given to the far user

Diversity combining

Now, at the end of the two time slots, the far user has two copies of the same information received through two different channels. The far user can now use a diversity combining technique. For example, he can use selection combining to choose the copy which was received with high SNR. After selection combining, the achievable rate of the far user would be, $$R_f = \dfrac{1}{2}log_2(1 + max(\dfrac{\alpha_f\rho|h_f|^2}{\alpha_n\rho|h_f|^2 + 1}, \rho|h_{nf}|^2))$$
If we DID NOT use cooperative relaying, the achievable rate of far user would be, $$R_{f,noncoop} = log_2(1 + \dfrac{\alpha_f\rho|h_f|^2}{\alpha_n\rho|h_f|^2 + 1})$$
The factor of $\dfrac{1}{2}$ is not here because the entire time slot will be used for transmission in non-cooperative communication.
If we DID NOT use NOMA, for example, if we use TDMA, we will allocate half of the time slot for transmission of far user data. Hence, the achievable rate of far user would be, $$R_{f,OMA} = \dfrac{1}{2}log_2(1 + \rho|h_{f}|^2)$$

MATLAB simulation

Now, let's simulate this network using MATLAB and plot the outage probabilities. Please refer this post for How to simulate outage probability for NOMA?
If we plot the outage probabilities, we get a graph like this. You can download the MATLAB code here.

From this graph, we order the performances of different schemes as: cooperative NOMA > non-cooperative NOMA > OMA. So, cooperative communication is clearly beneficial.

Reference

"Cooperative Non-Orthogonal Multiple Access in 5G Systems," Z. Ding, M. Peng, and H. V. Poor, IEEE communications letters, vol. 19, no. 8, 2015.