5. Power division multiplexing

Non-orthogonal multiplexing access (NOMA) is key enabler of the next generation wireless communication. Although the concept of NOMA is very broad, the power domain NOMA is the simplest and most popular NOMA. In contrast to orthogonal multiplexing access (OMA) approaches, like TDM and FDM, which separate the signals in frequency or time domain in order to avoid interference, NOMA embraces interference in both time and frequency domains. NOMA establishes multiple concurrent transmissions over the shared medium by adjusting the power levels of different signals.

Figure 9.

An example of two-user network using power-domain NOMA in downlink transmission.

Overview of Multiplexing Techniques in Wireless Networks DOI: http://dx.doi.org/10.5772/intechopen.85755

and α is pathloss coefficient which depends on the surrounding area and object within there. For an open are and line of sight communication α≈2: So, if a user wants to adjust its power to maintain a certain signal strength at

destination, it takes the distance into the account. Hence, the emitted power of users far from the destination is pretty high. This is very probable in cellular

• Communication overhead and reduced overhead: to measure pathloss effect and adjust power, a sounding mechanism should be established to launch a two-way communication between source and destination. This sounding consumes available over-the-air time and reduces the overall throughput of the

Despite this challenge along with its other challenges like self-jamming and need

Non-orthogonal multiplexing access (NOMA) is key enabler of the next generation wireless communication. Although the concept of NOMA is very broad, the power domain NOMA is the simplest and most popular NOMA. In contrast to orthogonal multiplexing access (OMA) approaches, like TDM and FDM, which separate the signals in frequency or time domain in order to avoid interference, NOMA embraces interference in both time and frequency domains. NOMA establishes multiple concurrent transmissions over the shared medium by adjusting the

for precise synchronization, CDM have shown some prominent advantages, as follows, paving the way for implementing it in several real-world communication.

network where some users may be located at cell-edge.

• Efficient channelization and enhanced spectrum reuse

An example of two-user network using power-domain NOMA in downlink transmission.

network.

Multiplexing

• Soft hand-off

• Security

Figure 9.

38

• Immunity to interference

5. Power division multiplexing

power levels of different signals.

NOMA brings the massive connectivity, spectral efficiency, high throughput, and improved fairness all together and it is the key enabler of the fifth generation of wireless networks. By serving several users with available resources concurrently, it improves the connectivity and spectral efficiency. Also, it improves the network capacity, and prevent wasting the resources caused by assigning equal amount of resources to users with low data rate requirement or bad channel conditions. Another, brilliant feature of the NOMA is that it can be easily integrated into existing wireless communication technologies. For example, see its integration with LTE-A [12] and digital TV standard [13].

To illustrate how NOMA works, Figure 9 shows a simple example of NOMA usage in a two-user network. In this example user 1 goes in the deep fade while user two hears the signal coming from the access point (AP) very clearly. All nodes are equipped with a single omni-directional antenna. Assume the channel between the AP and the ith user is hi. Therefore, h<sup>1</sup> ≪ h2: The AP knows the global Channel State Information (CSI) perfectly. The AP intends to send message si to user i: To do so, it scales the si with power allocation factor α<sup>i</sup> such that more power is assigned to the message of weak user. The superimposed message is as follows.

$$
\mathfrak{s}\_m = \sqrt{a\_1}\mathfrak{s}\_1 + \sqrt{a\_2}\mathfrak{s}\_2 \tag{7}
$$

The received signal at the ith user is Yi.

$$Y\_i = \mathfrak{s}\_m h\_i + \mathfrak{n}\_i = \sqrt{\alpha\_1} \mathfrak{s}\_1 h\_i + \sqrt{\alpha\_2} \mathfrak{s}\_2 h\_i + \mathfrak{n}\_i \tag{8}$$

where ni is additive white Gaussian noise. At the first user, i.e., weak user, the desired signal has a high power compared to the interference which is ffiffiffiffiffi α2 p s2h<sup>1</sup> to be decoded. This user decodes its desired signal by treating interference as noise. However, at the second user, i.e., strong user, the desired signal is drawn into strong interference. This user will pursue a decoding procedure called successive interference cancellation (SIC). Since the strong user knows the codebook used at the AP, it is able to decode interference, ^s1. Then, it subtracts the decoded interference from received signal. In the next step, the strong user endeavors to recover its desired signal from Yð Þ<sup>2</sup> 2 :

$$Y\_2^{(2)} = \left(\sqrt{a\_1}\mathfrak{s}\_1\mathfrak{h}\_2 - \sqrt{a\_1}\mathfrak{i}\_1\hat{\mathfrak{h}}\_2\right) + \sqrt{a\_2}\mathfrak{s}\_2\mathfrak{h}\_2 + \mathfrak{n}\_2 = \mathfrak{e}\_1 + \sqrt{a\_2}\mathfrak{s}\_2\mathfrak{h}\_2 + \mathfrak{n}\_2\tag{9}$$

If the channel is estimated perfectly and the interference is decoded flawless, error e<sup>1</sup> ¼ 0, and the desired signal, s<sup>2</sup> can be recovered successfully. Assuming perfect CSI estimation, the sum-rate of the network is as follows.

$$R\_{sum} = R\_1 + R\_2 = \log\_2\left(1 + \frac{a\_1|h\_1|^2}{a\_2|h\_1|^2 + 1/\rho}\right) + \log\_2\left(1 + a\_2\rho|h\_2|^2\right) \tag{10}$$

where ρ ¼ Pt=N<sup>0</sup> and Pt is available power budget. This approach can be easily extended to N�user case. Assuming that channels'strength are sorted in ascending order, hi j j<sup>2</sup> <sup>&</sup>lt; hj � � � � <sup>2</sup> for any <sup>i</sup> <sup>&</sup>lt; <sup>j</sup> and i, j<sup>∈</sup> f g <sup>1</sup>; <sup>2</sup>…; <sup>N</sup> , the decoding order is 1ð Þ ; <sup>2</sup>; …; <sup>N</sup> : It means the SIC at user l begins with decoding interference s1, and then decodes the second powerful interference, i.e., s2, and follows the interference subtraction until removing si�1. After subtracting all interferences which are stronger than desired signal, the user is capable of recovering its intended signal si. The Rsum can be expressed as follows.

$$R\_{sum} = \sum\_{i=1}^{N} \log\_2 \left( 1 + \frac{a\_i |h\_i|^2}{\frac{1}{\rho} + \sum\_{j=i+1}^{N} a\_j |h\_i|^2} \right) \tag{11}$$

To put it briefly, the performance of NOMA depends on its three key components: (i) grouping mechanism; (ii) power allocation scheme; and (iii) SIC at all user except the weakest one. While the grouping mechanism aims at finding best pairs among all users to be fed into power allocator, the power allocation scheme should assign a portion of available power to intended messages of user included in the pairs such that the minimum required data rate of all users is met and the decoding order at the user side is preserved. At the AP, depending on the application, there are two main strategies for power allocation. The first one is maximiza-

• Privacy of weak users: the first and foremost problem of the NOMA is privacy of weak user since their message will be decoded by all users possessing higher decoding order. Indeed, at the end of a cycle of NOMA, the ith user knows the

 

completion, the strongest user identifies all the messages sent by the AP for

• Long processing delay for strong users: in SIC approach, a user first removes all the interference messages stronger than desired signal. This inflicts a huge amount of computational complexity and long processing delay to strong users which

• Error propagation: the performance of SIC is highly intertwined with accurate interference reconstruction on subtraction. This fact mandates reliable channel estimation and accurate interference decoding. Failure in these steps for one of strong interferences will introduce an error which impacts the SIC operation for decoding and removing the weaker interferences at the same user. Accumulation of errors within the whole process makes it very difficult to recover the desired signal polluted by errors and residual interferences.

complicated scenarios, like MISO and MIMO. For example, in MISO case, the channel between a user, say user i, and one of AP's antennas may be so weak while the channel of the same user and other antennas at the AP is very strong. In these cases, to sort the users'strength, the different measures are taken into account, like distance from AP, norm of the channel vector, etc. These metrics stem from theoretical aspects of wireless channels and may show

• Sub-optimal performance: at the AP side, power allocation problem becomes a non-trivial task for large pairs and nodes with multiple antenna (see, e.g., [14]). Due to several requirements imposed by either user or nature of SIC, the problem is a non-convex problem with several variable. In almost all cases, there is no closed-form solution for optimal power allocation. To reach a solution, the problem will be relaxed into a simpler problem, or a heuristic algorithm reaches to a near optimal solution. So, the power allocation problem

• Non-trivial grouping: although the grouping mechanism seems very straightforward for single-antenna AP and single-antenna users (SISO network), the channel strength concept becomes ambiguous for more

unacceptable outcome when implemented in practice.

< ∣hi∣. For example, after SIC

tion of throughput using all available power budget. The second strategy is minimization of the power consumption while requirements of all users are met. After a proper power allocation, all users except the weakest one should be able to recover all strong interference based on decoding order through and accurate and reliable SIC. Although NOMA shows a promising performance theoretically, it faces several challenges in practice. These challenges are described in what follows.

messages of all weaker user, i.e., sj if hj

Overview of Multiplexing Techniques in Wireless Networks

DOI: http://dx.doi.org/10.5772/intechopen.85755

must iterate this process several times.

other users

41

For better illustration of NOMA gain over conventional OMA schemes, like TDM and FDM, let us look at the following example.

Example 2: Consider two asymptotic cases with high power budget in two-user scenario: (i) the users' channel are equally strong (h<sup>1</sup> ¼ h<sup>2</sup> ¼ hÞ ; (ii) one channel is very strong while the other one is very weak ð Þ h<sup>1</sup> ≪ h<sup>2</sup> . The power is proportionally allocated to messages. The gain of power domain NOMA over OMA in each case is as follows.

Case 1: Let us say the power budget is PT and ρ ¼ PT=N<sup>0</sup> where N<sup>0</sup> stands for variance of additive white Gaussian noise. In this case, the sum-capacity of network using OMA is COMA.

$$\mathbf{C\_{OMA}} = \mathbf{0.5} \log \mathbf{2} \left( \mathbf{1} + \rho |h|^2 \right) + \mathbf{0.5} \log \mathbf{2} \left( \mathbf{1} + \rho |h|^2 \right) \approx \log \mathbf{2} \left( \rho |h|^2 \right) \tag{12}$$

where 0.5 coefficients lie in the fact that OMA shares the resources between users equally. In the NOMA approach, the whole spectrum is shared among both users. Due to power allocation strategy and equally strong channels α<sup>1</sup> ¼ α<sup>2</sup> ¼ 1=2: The sum-capacity of the network using the NOMA is CNOMA.

$$\begin{split} \mathbf{C}\_{\text{NOMA}} &= \log\_2 \left( \mathbf{1} + \rho |h|^2 a\_2 \right) + \log\_2 \left( \mathbf{1} + |h|^2 a\_1 / \left( |h|^2 a\_2 + \frac{\mathbf{1}}{\rho} \right) \right) \\ &\approx \log\_2 \left( \mathbf{1} + \rho |h|^2 / 2 \right) + \log\_2 (2) \approx \log\_2 \left( \rho |h|^2 \right) \end{split} \tag{13}$$

Therefore, OMA reaches to the performance of NOMA. Case 2: In this case, h<sup>1</sup> ≪ h<sup>2</sup> and ρj j h<sup>1</sup> <sup>2</sup> ! 0 and <sup>α</sup><sup>1</sup> ! 1.

$$C\_{OMA} = 0.5 \log\_2 \left( 1 + \rho |h\_1|^2 \right) + 0.5 \log\_2 \left( 1 + \rho |h\_2|^2 \right) \approx 0.5 \log\_2 \left( 1 + \rho |h\_2|^2 \right) \tag{14}$$

$$\begin{split} \mathbf{C}\_{\text{NOMA}} &= \log\_2 \left( \mathbf{1} + \rho |h\_2|^2 a\_2 \right) + \log\_2 \left( \mathbf{1} + |h\_1|^2 a\_1 / \left( |h\_2|^2 a\_2 + \frac{\mathbf{1}}{\rho} \right) \right) \\ &\approx \log\_2 \left( \mathbf{1} + \rho |h\_2|^2 a\_2 \right) + \log\_2 \left( \mathbf{1} + \frac{a\_1}{a\_2} \right) = \log\_2 \left( \rho |h\_2|^2 \right) \end{split} \tag{15}$$

Obviously, in the latter case, CNOMA ¼ 2 � COMA. Based on these bounds, the performance of the NOMA for two users can be expressed as follows:

$$\mathcal{C}\_{\text{OMA}} \le \mathcal{C}\_{\text{NOMA}} \le 2 \times \mathcal{C}\_{\text{OMA}} \tag{16}$$

The previous example shows that the performance of NOMA is highly dependent on the channel difference among serving users. Therefore, when an AP serves many active users, it is very critical to employ a grouping mechanism to pair a strong and weak user among all possible choices such that the overall throughput of the network is maximized. Each pair will be served separately in different time slot. When the AP has just one antenna, best strategy is measuring the magnitude of the channels of different users, sorting the users based on their channel strength, and then choosing a N-user group in which the channel strength difference among two adjacent users in decoding order is larger than a certain threshold.

### Overview of Multiplexing Techniques in Wireless Networks DOI: http://dx.doi.org/10.5772/intechopen.85755

Rsum ¼ ∑ N i¼1

TDM and FDM, let us look at the following example.

COMA <sup>¼</sup> <sup>0</sup>:5 log <sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>ρ</sup>j j <sup>h</sup> <sup>2</sup> � �

CNOMA <sup>¼</sup> log <sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>ρ</sup>j j <sup>h</sup> <sup>2</sup>

<sup>≈</sup>log <sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>ρ</sup>j j <sup>h</sup> <sup>2</sup>

<sup>2</sup> � �

≈ log <sup>2</sup> 1 þ ρj j h<sup>2</sup>

Case 2: In this case, h<sup>1</sup> ≪ h<sup>2</sup> and ρj j h<sup>1</sup>

COMA ¼ 0:5 log <sup>2</sup> 1 þ ρj j h<sup>1</sup>

40

CNOMA ¼ log <sup>2</sup> 1 þ ρj j h<sup>2</sup>

as follows.

Multiplexing

using OMA is COMA.

log <sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>α</sup><sup>i</sup> hi j j<sup>2</sup> 1 <sup>ρ</sup> þ ∑ N j¼iþ1

0

BBB@

For better illustration of NOMA gain over conventional OMA schemes, like

Example 2: Consider two asymptotic cases with high power budget in two-user scenario: (i) the users' channel are equally strong (h<sup>1</sup> ¼ h<sup>2</sup> ¼ hÞ ; (ii) one channel is very strong while the other one is very weak ð Þ h<sup>1</sup> ≪ h<sup>2</sup> . The power is proportionally allocated to messages. The gain of power domain NOMA over OMA in each case is

Case 1: Let us say the power budget is PT and ρ ¼ PT=N<sup>0</sup> where N<sup>0</sup> stands for variance of additive white Gaussian noise. In this case, the sum-capacity of network

where 0.5 coefficients lie in the fact that OMA shares the resources between users equally. In the NOMA approach, the whole spectrum is shared among both users. Due to power allocation strategy and equally strong channels α<sup>1</sup> ¼ α<sup>2</sup> ¼ 1=2:

<sup>þ</sup> log <sup>2</sup> <sup>1</sup> <sup>þ</sup> j j <sup>h</sup> <sup>2</sup>

þ 0:5 log <sup>2</sup> 1 þ ρj j h<sup>2</sup>

þ log <sup>2</sup> 1 þ j j h<sup>1</sup>

<sup>þ</sup> log <sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>α</sup><sup>1</sup>

Obviously, in the latter case, CNOMA ¼ 2 � COMA. Based on these bounds, the

The previous example shows that the performance of NOMA is highly dependent on the channel difference among serving users. Therefore, when an AP serves many active users, it is very critical to employ a grouping mechanism to pair a strong and weak user among all possible choices such that the overall throughput of the network is maximized. Each pair will be served separately in different time slot. When the AP has just one antenna, best strategy is measuring the magnitude of the channels of different users, sorting the users based on their channel strength, and then choosing a N-user group in which the channel strength difference among two

<sup>þ</sup> log <sup>2</sup>ð Þ<sup>2</sup> <sup>≈</sup> log <sup>2</sup> <sup>ρ</sup>j j <sup>h</sup> <sup>2</sup> � �

<sup>2</sup> ! 0 and <sup>α</sup><sup>1</sup> ! 1.

2

α2 � �

α1= j j h<sup>2</sup>

COMA ≤CNOMA ≤ 2 � COMA (16)

� � � �

<sup>2</sup> � �

<sup>α</sup>1<sup>=</sup> j j <sup>h</sup> <sup>2</sup>

� � � �

The sum-capacity of the network using the NOMA is CNOMA.

α2 � �

=2 � �

Therefore, OMA reaches to the performance of NOMA.

2 α2

> 2 α2

performance of the NOMA for two users can be expressed as follows:

adjacent users in decoding order is larger than a certain threshold.

� �

� �

<sup>þ</sup> <sup>0</sup>:5 log <sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>ρ</sup>j j <sup>h</sup> <sup>2</sup> � �

<sup>α</sup><sup>j</sup> hi j j<sup>2</sup>

1

CCCA

<sup>≈</sup>log <sup>2</sup> <sup>ρ</sup>j j <sup>h</sup> <sup>2</sup> � �

α<sup>2</sup> þ 1 ρ

≈0:5 log2 1 þ ρj j h<sup>2</sup>

<sup>2</sup>: � �

2 α<sup>2</sup> þ 1 ρ

¼ log <sup>2</sup> ρj j h<sup>2</sup>

<sup>2</sup> � �

(11)

(12)

(13)

(14)

(15)

To put it briefly, the performance of NOMA depends on its three key components: (i) grouping mechanism; (ii) power allocation scheme; and (iii) SIC at all user except the weakest one. While the grouping mechanism aims at finding best pairs among all users to be fed into power allocator, the power allocation scheme should assign a portion of available power to intended messages of user included in the pairs such that the minimum required data rate of all users is met and the decoding order at the user side is preserved. At the AP, depending on the application, there are two main strategies for power allocation. The first one is maximization of throughput using all available power budget. The second strategy is minimization of the power consumption while requirements of all users are met. After a proper power allocation, all users except the weakest one should be able to recover all strong interference based on decoding order through and accurate and reliable SIC. Although NOMA shows a promising performance theoretically, it faces several challenges in practice. These challenges are described in what follows.


entails high computational cost and may yields a non-optimal solution which diminish the gain of the NOMA over OMA.

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Although, the term NOMA has referred to power domain multiplexing through this section, the concept of NOMA is much broader and includes other kind of schemes which are totally different from presented one. Actually, in this section, the power domain NOMA is presented. To read more about other variation of NOMA, see [15, 16].
