3. Frequency division multiplexing

Frequency division multiplexing (FDM) is a multiplexing technique which divides the available bandwidth into multiple sub-bands each of which is able to carry a signal. Therefore, FDM enables concurrent transmissions over a shared communication medium. As another common use, FDM enables the system to send a huge amount of data through several segments transmitted over independent frequency sub-bands.

sources use the same pulses for data transmission. Signals from the ith source lies within the ith frequency sub-band centered around f ci. Bandwidth of the base-band signals is <sup>B</sup> <sup>¼</sup> <sup>f</sup> <sup>B</sup> Hz which is less than sub-bands' width, i.e., SB <sup>¼</sup> <sup>f</sup> c ið Þ <sup>þ</sup><sup>1</sup> � fci. To prevent leaking signals into adjacent sub-bands, the sub-bands are separated by a guard band G ¼ f <sup>G</sup> Hz: Clearly, for appropriate signal transmission, the carrier

Conventional FDM allocates the available spectrum to the sources very generously, and the spectral efficiency is not among its concerns. With this motivation, OFDM has been introduced for efficient use of spectrum. OFDM is a multi-carrier modulation through which a data stream, like voice, video, or data, is distributed

OFDM-based system, the modulated samples over frequency domain, i.e., x k½ �, are distributed over different subcarriers via Inverse Fast Fourier Transform (IFFT)

> <sup>k</sup>¼�<sup>N</sup> 2 x k½ �e j2πkt

where x tð Þ denotes the time domain signal which is sum of multiple sinusoids and x k½ � is the kth modulated sample. Since the basis of the transformation is unit vectors with equally angular separated in polar plane, the spectrum of OFDM signal is composed of N shifted sinc functions. Figure 6 illustrates the spectral basis of an OFDM signal with four orthogonal subcarriers. The subcarrier spacing, i.e.,

on a null point of other subcarriers. Therefore, at the moment of sampling from the center of subcarriers, no interference is experienced from others. The time domain signal goes through another process called cyclic prefix (CP) insertion to be

immune against multipath fading. In this step, a certain amount of the time-domain signal's tail is copied and attached to the beginning of the time-domain signal. If the maximum delay in multipath environment does not exceed the time duration CP, the signal can be recovered perfectly. The CP-inserted OFDM signal is fed into a D/A converter. The baseband analog signal is then converted to a bandpass signal to

At the receiver side, the superimposition of the analog signals received from different paths within reception interval is sampled and converted to a baseband

, is chosen such that the center frequency of each subcarrier is located

<sup>N</sup> (1)

frequency spacing should be designed such that <sup>f</sup> ci <sup>þ</sup> <sup>f</sup> <sup>B</sup> <sup>&</sup>lt; <sup>f</sup> c ið Þ <sup>þ</sup><sup>1</sup> � <sup>f</sup> <sup>B</sup>:

among multiple subcarriers separated closely and precisely. In a simple

x tðÞ¼ ∑ N <sup>2</sup>�1

3.1 Orthogonal frequency division multiplexing (OFDM)

Spectrum of multiplexed signals via FDM for a system with N sources.

Overview of Multiplexing Techniques in Wireless Networks

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

as follows.

Figure 5.

<sup>Δ</sup><sup>f</sup> <sup>¼</sup> fiþ<sup>1</sup> � fi

33

be sent over the communication medium.

Figure 4 reveals basic principles of the conventional FDM. In the figure, signal of three independent sources are multiplexed to be sent over the medium. Each source has a flat signal with large width in time domain. Depending the value of the information bit, the signals can be x tðÞ¼�1: Hence, the spectrum of each signal is approximated by X f ð Þ≈ � δð Þf . The baseband signals are converted to wellseparated bandpass signals by multiplexer. The signals are conveyed by carriers with different frequencies such that each signal is located within a non-overlapping sub-band and does not leak onto other signals. The carrier frequencies spacing, and sub-band width are application-specific and depend on the available bandwidth. The multiplexed signal will be transmitted over the medium. At the receiver side, de-multiplexer employs proper filters to extract the desired bandpass signals. The intended bandpass signals will be converted to baseband signals for further processes at destinations.

The spectrum of a communication system with N sources benefiting from FDM is depicted in Figure 5. The multiplexer uses N equally spaced carrier frequencies. The carrier frequency for the ith user is fci. For further simplicity, consider that

Figure 4. Frequency division multiplexing.

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

Figure 5. Spectrum of multiplexed signals via FDM for a system with N sources.

sources use the same pulses for data transmission. Signals from the ith source lies within the ith frequency sub-band centered around f ci. Bandwidth of the base-band signals is <sup>B</sup> <sup>¼</sup> <sup>f</sup> <sup>B</sup> Hz which is less than sub-bands' width, i.e., SB <sup>¼</sup> <sup>f</sup> c ið Þ <sup>þ</sup><sup>1</sup> � fci. To prevent leaking signals into adjacent sub-bands, the sub-bands are separated by a guard band G ¼ f <sup>G</sup> Hz: Clearly, for appropriate signal transmission, the carrier frequency spacing should be designed such that <sup>f</sup> ci <sup>þ</sup> <sup>f</sup> <sup>B</sup> <sup>&</sup>lt; <sup>f</sup> c ið Þ <sup>þ</sup><sup>1</sup> � <sup>f</sup> <sup>B</sup>:

### 3.1 Orthogonal frequency division multiplexing (OFDM)

Conventional FDM allocates the available spectrum to the sources very generously, and the spectral efficiency is not among its concerns. With this motivation, OFDM has been introduced for efficient use of spectrum. OFDM is a multi-carrier modulation through which a data stream, like voice, video, or data, is distributed among multiple subcarriers separated closely and precisely. In a simple OFDM-based system, the modulated samples over frequency domain, i.e., x k½ �, are distributed over different subcarriers via Inverse Fast Fourier Transform (IFFT) as follows.

$$\mathfrak{x}(t) = \sum\_{k=-\frac{N}{2}}^{\frac{N}{2}-1} \mathfrak{x}[k] e^{\frac{j2\pi k}{N}} \tag{1}$$

where x tð Þ denotes the time domain signal which is sum of multiple sinusoids and x k½ � is the kth modulated sample. Since the basis of the transformation is unit vectors with equally angular separated in polar plane, the spectrum of OFDM signal is composed of N shifted sinc functions. Figure 6 illustrates the spectral basis of an OFDM signal with four orthogonal subcarriers. The subcarrier spacing, i.e., <sup>Δ</sup><sup>f</sup> <sup>¼</sup> fiþ<sup>1</sup> � fi , is chosen such that the center frequency of each subcarrier is located on a null point of other subcarriers. Therefore, at the moment of sampling from the center of subcarriers, no interference is experienced from others. The time domain signal goes through another process called cyclic prefix (CP) insertion to be immune against multipath fading. In this step, a certain amount of the time-domain signal's tail is copied and attached to the beginning of the time-domain signal. If the maximum delay in multipath environment does not exceed the time duration CP, the signal can be recovered perfectly. The CP-inserted OFDM signal is fed into a D/A converter. The baseband analog signal is then converted to a bandpass signal to be sent over the communication medium.

At the receiver side, the superimposition of the analog signals received from different paths within reception interval is sampled and converted to a baseband

using the preambles diminishes the need of synchronized clocks between

Frequency division multiplexing (FDM) is a multiplexing technique which divides the available bandwidth into multiple sub-bands each of which is able to carry a signal. Therefore, FDM enables concurrent transmissions over a shared communication medium. As another common use, FDM enables the system to send a huge amount of data through several segments transmitted over independent

Figure 4 reveals basic principles of the conventional FDM. In the figure, signal of three independent sources are multiplexed to be sent over the medium. Each source has a flat signal with large width in time domain. Depending the value of the information bit, the signals can be x tðÞ¼�1: Hence, the spectrum of each signal is approximated by X f ð Þ≈ � δð Þf . The baseband signals are converted to wellseparated bandpass signals by multiplexer. The signals are conveyed by carriers with different frequencies such that each signal is located within a non-overlapping sub-band and does not leak onto other signals. The carrier frequencies spacing, and sub-band width are application-specific and depend on the available bandwidth. The multiplexed signal will be transmitted over the medium. At the receiver side, de-multiplexer employs proper filters to extract the desired bandpass signals. The intended bandpass signals will be converted to baseband signals for further pro-

The spectrum of a communication system with N sources benefiting from FDM is depicted in Figure 5. The multiplexer uses N equally spaced carrier frequencies. The carrier frequency for the ith user is fci. For further simplicity, consider that

multiplexer and de-multiplexer.

Figure 3.

Multiplexing

frequency sub-bands.

cesses at destinations.

Figure 4.

32

Frequency division multiplexing.

3. Frequency division multiplexing

An example of asynchronous/statistical time division multiplexing.

since it possesses simple mathematical operations. It can be simply implanted with FFT and IFFT modules containing nothing more than adders, multipliers,

Example 1: Consider a transmission which requires 1 Mbps data rate and RMS delay spread is 10 μs and frequency selectivity condition is τrms>Tsym=10 where Tsym denotes symbol duration. The comparison of single-single carrier transmission and

• Single-carrier case: Tsym ¼ 1 μs and τrms>1 μs=10. Therefore, ISI is imminent.

• Multi-carrier case: in this case, data rate of a subcarrier is 7:8125 kbps. The Tsym for a subcarrier equals to 128 μs. Then, τrms < 128 μs=10, and the signal carried

In spite of aforementioned advantages, the OFDM technique suffers from two main disadvantages. High peak-to-average power ratio (PAPR) stems from the large range of amplitude of the OFDM signal and impedes proper performance of amplifiers at OFDM transceivers. Also, OFDM technique is very sensitive to carrier frequency offset (CFO). This effect emerges due to hardware impairment between transmitter and receiver local oscillators and cause inter-carrier interference (ICI).

Code division multiplexing (CDM), also called spread-spectrum technique, is a multiplexing technique which has been widely implemented in third generation of wireless network. It takes full advantage of the available spectrum. Through several concurrent transmissions over the spectrum, this technique has enhanced the capacity of network 18 times compared to first generation and 6 times compared to the second generation of wireless communication technologies. For transmitting multiple messages over the channel simultaneously, the multiplexer assigns a separate spreading code from a set of orthogonal pseudo-random sequences to each user. The orthogonality of these sequences will help users to recover their desired

Consider a system with 4 users as depicted in Figure 7. AP intends to send one bit to each user, say bi for user i. The sequence ci is used to encode/decode the bits

and registers.

OFDM technique with 128 subcarriers is as follows:

Overview of Multiplexing Techniques in Wireless Networks

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

4. Code division multiplexing

signals from the multiplexed signals.

An example of CDM for a network with four users.

Figure 7.

35

by each subcarrier experiences a flat fading channel.

Figure 6. Bandwidth requirement for an OFDM system using four orthogonally spaced subcarriers.

digital signal. The parallel to serial unit maps the sequence of received OFDM samples into N parallel samples. Then, the CP added by transmitter is removed. The remaining samples go through Fast Fourier Transform (FFT). The resulting series of modulated samples is fed into demodulator, and the desired data is recovered.

Due to promising performance of the OFMD technique and its very low computational complexity, this technique has been embedded in many wireless communication systems like IEEE WLAN standards [6–8], LTE/LTE-A [9–11]. The popularity of this technique stems from following advantages which make it highly amenable for real world application.


since it possesses simple mathematical operations. It can be simply implanted with FFT and IFFT modules containing nothing more than adders, multipliers, and registers.

Example 1: Consider a transmission which requires 1 Mbps data rate and RMS delay spread is 10 μs and frequency selectivity condition is τrms>Tsym=10 where Tsym denotes symbol duration. The comparison of single-single carrier transmission and OFDM technique with 128 subcarriers is as follows:


In spite of aforementioned advantages, the OFDM technique suffers from two main disadvantages. High peak-to-average power ratio (PAPR) stems from the large range of amplitude of the OFDM signal and impedes proper performance of amplifiers at OFDM transceivers. Also, OFDM technique is very sensitive to carrier frequency offset (CFO). This effect emerges due to hardware impairment between transmitter and receiver local oscillators and cause inter-carrier interference (ICI).

## 4. Code division multiplexing

digital signal. The parallel to serial unit maps the sequence of received OFDM samples into N parallel samples. Then, the CP added by transmitter is removed. The remaining samples go through Fast Fourier Transform (FFT). The resulting series of modulated samples is fed into demodulator, and the desired data is recovered. Due to promising performance of the OFMD technique and its very low computational complexity, this technique has been embedded in many wireless communication systems like IEEE WLAN standards [6–8], LTE/LTE-A [9–11]. The popularity of this technique stems from following advantages which make it highly

Bandwidth requirement for an OFDM system using four orthogonally spaced subcarriers.

• Resilience in frequency selective environments: OFDM decomposes whole available spectrum to several narrow channel in frequency domain. It is very likely that signals carried over a subcarrier experience a relatively flat channel although

• Resilience to inter-symbol interference (ISI): single-carrier communication is vulnerable to ISI specially when the data rate grows. OFDM tackle this problem with dispatching signals over multiple sub-channels. Indeed, OFDM technique changes a transmission with high rate into multiple low-rate transmissions. In this manner, it increases the symbol duration and push the duration beyond maximum delay of the channels. Lack of ISI also means simpler equalization mechanism and reduction in hardware cost of the OFDM receiver. At the end of this section, example 1 reveals how OFDM technique combats the frequency

• Resilience to narrow-band interference: narrow-band interference drastically diminishes the throughput of single-carrier systems either by blurring the reference signals for synchronization or corrupting the data. However, if the signal is transmitted using OFDM, only a portion of symbols is contaminated by interference. The erroneous parts caused by interference can be recovered with the aid of error correction codes and interleaving to isolate errors.

• Spectral efficiency: comparing Figures 5 and 6, it is clear that closely separated

• Low-computational complexity: although OFDM technique is more complex than conventional FDM, it intrinsically demands low-computational capability

frequency sub-channels yields higher spectral efficiency for OFDM.

amenable for real world application.

Figure 6.

Multiplexing

selectivity of the channel.

34

the channel may be frequency selective.

Code division multiplexing (CDM), also called spread-spectrum technique, is a multiplexing technique which has been widely implemented in third generation of wireless network. It takes full advantage of the available spectrum. Through several concurrent transmissions over the spectrum, this technique has enhanced the capacity of network 18 times compared to first generation and 6 times compared to the second generation of wireless communication technologies. For transmitting multiple messages over the channel simultaneously, the multiplexer assigns a separate spreading code from a set of orthogonal pseudo-random sequences to each user. The orthogonality of these sequences will help users to recover their desired signals from the multiplexed signals.

Consider a system with 4 users as depicted in Figure 7. AP intends to send one bit to each user, say bi for user i. The sequence ci is used to encode/decode the bits

Figure 7. An example of CDM for a network with four users.

to/from user i. These sequences are devised such that the inner product of two different sequences is zero, i.e., ci:cj¼0 i6¼j. The inner product of a sequence with itself is M which is the number of users. Also, the '0' is mapped to �1, and 1 is mapped to +1. The multiplexed sequence is sm¼∑<sup>4</sup> <sup>i</sup>¼<sup>1</sup>bici. Upon receiving the multiplexed sequence, user i recovers its desired information by multiplying its corresponding spreading sequence and received sequence and dividing the result by the length of sequences. The key component in CDM is the spreading code. Walsh code is among the most popular sequences used for CDM. Walsh codes with length of 2n, n ∈ ℕ, can be constructed with Hadamard matrices as follows.

$$H\_1 = [\mathbf{1}] \to H\_2 = \begin{bmatrix} \mathbf{1} & \mathbf{1} \\ \mathbf{1} & -\mathbf{1} \end{bmatrix} \to \dots \to H\_{2N} = \begin{bmatrix} H\_N & H\_N \\ H\_N & -H\_N \end{bmatrix} \tag{2}$$

where each row of H2<sup>N</sup> can be used as a sequence with length 2N: This procedure results four orthogonal sequences as follows.

$$c\_1 = [1, \mathbf{1}, \mathbf{1}, \mathbf{1}], c\_2 = [1, -\mathbf{1}, \mathbf{1}, -\mathbf{1}], c\_3 = [\mathbf{1}, \mathbf{1}, -\mathbf{1}, -\mathbf{1}], c\_4 = [\mathbf{1}, -\mathbf{1}, -\mathbf{1}, \mathbf{1}] \tag{3}$$

Consider the following set of bits as an example, b1¼b2¼b3¼1, and b4¼�1. Therefore, the multiplexed signal is:

$$s\_{\mathfrak{m}} = \sum\_{i=1}^{4} b\_i c\_i = [+2, +2, +2, -2]. \tag{4}$$

As described, choosing a well-defined code plays a critical role in spreading process. The question may arise here is why the process of multiplying the code sequences to bits is called spreading process. To find the answer of this question, Figure 8 illustrates an insightful example where the base-band information is converted to the transmitted signal via spreading code. Every bit in the information flow is represented by a pulse with Tb width in time domain. Hence, the effective bandwidth of the original data is proportional to 1=Tb. Then, the information flow goes through spreading process where the pulses of data flow will be multiplied (in some systems it is XOR) by the spreading code sequence. Since the pulse duration for the spreading code is Tc which is smaller than the Tb, the generated signal by spreading signal is affected by Tc and it becomes a series of pulses with Tc width in time domain. The bandwidth of the transmitted signal is proportional to 1=Tc called chip rate. Therefore, the bandwidth of the transmitted signal is larger than original baseband signal. The ratio of spread spectrum and original base-band information is

Spreading Factor <sup>¼</sup> chip rate

by using the same spreading code with pre-known chip rate. The de-spreading process, i.e., multiplying the multiplexed signal with a spreading code needs a delicate requirement. At a node in the network, all the received signals multiplied by different spreading codes should be received with equal strength, otherwise the de-spreading process causes interference due to non-zero mutual correlation of spreading codes. This impedes recovering desired signal at that node. This problem is called near-far problem. The near far problem originally refers to a situation where reception of some strong signals makes it impossible to recover weak signals. Here, the unbalanced signal strength causes this intricate challenge. To cope with this problem, a power control mechanism is mandatory to ensure that all the signals from different sources will be received with equal strength. This matter brings two

Clearly, the spreading for the example illustrated in Figure 8 is four since the

Until this point, it seems very easy to decode the signal at the intended receiver

• High power consumption for far users: the power of a signal emitted on the air is attenuated by factor of d<sup>α</sup> where d is the amount of distance the signal passes

Spreading process on (�1,1,�1,1) via spreading code of (�1,1,1,1) with spreading factor of 4.

bit rate <sup>¼</sup> Tb

Tc

(6)

called spreading factor and can be expressed as follows.

Overview of Multiplexing Techniques in Wireless Networks

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

chip rate is fourfold of bit rate.

main challenges:

Figure 8.

37

The first user recovers its desired data ^ <sup>b</sup>1¼sm:c<sup>T</sup> <sup>1</sup> =4: And other users do the same procedure with their own sequences.

$$\hat{b}\_1 = \frac{1}{4}[\mathbf{1}, \mathbf{1}, \mathbf{1}, \mathbf{1}] \times [\mathbf{2}, \mathbf{2}, \mathbf{2} - \mathbf{2}]^T = \frac{4}{4} = +\mathbf{1}.\tag{5}$$

Similarly, ^ <sup>b</sup>2¼1, ^ <sup>b</sup>3¼1, and ^ b4¼�1: As seen in the example the Walsh code is used as spreading code. However, a variety of codes can be utilized for this purpose, which can be classified into two major categories.


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

to/from user i. These sequences are devised such that the inner product of two different sequences is zero, i.e., ci:cj¼0 i6¼j. The inner product of a sequence with itself is M which is the number of users. Also, the '0' is mapped to �1, and 1 is

multiplexed sequence, user i recovers its desired information by multiplying its corresponding spreading sequence and received sequence and dividing the result by the length of sequences. The key component in CDM is the spreading code. Walsh code is among the most popular sequences used for CDM. Walsh codes with length

where each row of H2<sup>N</sup> can be used as a sequence with length 2N: This procedure

c<sup>1</sup> ¼ ½ � 1; 1; 1; 1 , c<sup>2</sup> ¼ ½ � 1; �1; 1; �1 , c<sup>3</sup> ¼ ½ � 1; 1; �1; �1 , c<sup>4</sup> ¼ ½ � 1; �1; �1; 1 (3)

<sup>b</sup>1¼sm:c<sup>T</sup>

Consider the following set of bits as an example, b1¼b2¼b3¼1, and b4¼�1.

<sup>4</sup> ½ �� <sup>1</sup>; <sup>1</sup>; <sup>1</sup>; <sup>1</sup> ½ � <sup>2</sup>; <sup>2</sup>; <sup>2</sup> � <sup>2</sup> <sup>T</sup> <sup>¼</sup> <sup>4</sup>

used as spreading code. However, a variety of codes can be utilized for this purpose,

• PN codes: pseudo-random noise code is a sequence of pulses which shows the appropriate features to be used in CDM. Although PN sequences look like noise, they can be exactly generated at both multiplexer and demultiplexer locally using a finite number of shift registers with a pre-defined initial state. The finite length of linear shift registers makes these codes deterministic. A local sequence has a high correlation with itself, but almost zero correlation with other sequences or a time-shifted version of itself. The term "pseudo" refers to the fact that a sequence starts to repeat a certain pattern after its period. In cryptography applications, to ensure security, using PN codes with very large period is a necessity. However, this is not a strict requirement for

• Non-random orthogonal codes: this kind of codes is designed in a specific and predefined manner and has a special set for desired length while satisfying primary features required by CDM. An instance of these codes is Walsh code shown in the previous example. Walsh code is used in the IS95/CDMA 2000

of 2n, n ∈ ℕ, can be constructed with Hadamard matrices as follows.

1 �1  <sup>i</sup>¼<sup>1</sup>bici. Upon receiving the

HN �HN 

(2)

! … ! <sup>H</sup>2<sup>N</sup> <sup>¼</sup> HN HN

bici ¼ þ½ � 2; þ2; þ2; �2 : (4)

b4¼�1: As seen in the example the Walsh code is

<sup>1</sup> =4: And other users do the same

<sup>4</sup> ¼ þ1: (5)

mapped to +1. The multiplexed sequence is sm¼∑<sup>4</sup>

<sup>H</sup><sup>1</sup> <sup>¼</sup> ½ �!<sup>1</sup> <sup>H</sup><sup>2</sup> <sup>¼</sup> 1 1

sm ¼ ∑ 4 i¼1

results four orthogonal sequences as follows.

The first user recovers its desired data ^

^ <sup>b</sup><sup>1</sup> <sup>¼</sup> <sup>1</sup>

<sup>b</sup>3¼1, and ^

which can be classified into two major categories.

Therefore, the multiplexed signal is:

procedure with their own sequences.

<sup>b</sup>2¼1, ^

Similarly, ^

Multiplexing

CDM.

system.

36

As described, choosing a well-defined code plays a critical role in spreading process. The question may arise here is why the process of multiplying the code sequences to bits is called spreading process. To find the answer of this question, Figure 8 illustrates an insightful example where the base-band information is converted to the transmitted signal via spreading code. Every bit in the information flow is represented by a pulse with Tb width in time domain. Hence, the effective bandwidth of the original data is proportional to 1=Tb. Then, the information flow goes through spreading process where the pulses of data flow will be multiplied (in some systems it is XOR) by the spreading code sequence. Since the pulse duration for the spreading code is Tc which is smaller than the Tb, the generated signal by spreading signal is affected by Tc and it becomes a series of pulses with Tc width in time domain. The bandwidth of the transmitted signal is proportional to 1=Tc called chip rate. Therefore, the bandwidth of the transmitted signal is larger than original baseband signal. The ratio of spread spectrum and original base-band information is called spreading factor and can be expressed as follows.

$$\text{Spreading Factor} = \frac{\text{chip rate}}{\text{bit rate}} = \frac{T\_b}{T\_c} \tag{6}$$

Clearly, the spreading for the example illustrated in Figure 8 is four since the chip rate is fourfold of bit rate.

Until this point, it seems very easy to decode the signal at the intended receiver by using the same spreading code with pre-known chip rate. The de-spreading process, i.e., multiplying the multiplexed signal with a spreading code needs a delicate requirement. At a node in the network, all the received signals multiplied by different spreading codes should be received with equal strength, otherwise the de-spreading process causes interference due to non-zero mutual correlation of spreading codes. This impedes recovering desired signal at that node. This problem is called near-far problem. The near far problem originally refers to a situation where reception of some strong signals makes it impossible to recover weak signals. Here, the unbalanced signal strength causes this intricate challenge. To cope with this problem, a power control mechanism is mandatory to ensure that all the signals from different sources will be received with equal strength. This matter brings two main challenges:

• High power consumption for far users: the power of a signal emitted on the air is attenuated by factor of d<sup>α</sup> where d is the amount of distance the signal passes

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

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

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

> α1 <sup>p</sup> <sup>s</sup>1hi <sup>þ</sup> ffiffiffiffiffi

where ni is additive white Gaussian noise. At the first user, i.e., weak user, the

α2

α2

<sup>p</sup> <sup>s</sup>2h<sup>2</sup> <sup>þ</sup> <sup>n</sup><sup>2</sup> <sup>¼</sup> <sup>e</sup><sup>1</sup> <sup>þ</sup> ffiffiffiffiffi

<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> :

<sup>p</sup> <sup>s</sup><sup>2</sup> (7)

<sup>p</sup> <sup>s</sup>2hi <sup>þ</sup> ni (8)

α2

þ log <sup>2</sup> 1 þ α2ρj j h<sup>2</sup>

<sup>p</sup> <sup>s</sup>2h<sup>2</sup> <sup>þ</sup> <sup>n</sup><sup>2</sup> (9)

<sup>2</sup> � � (10)

α2 p s2h<sup>1</sup> to be

message of weak user. The superimposed message is as follows.

Yi <sup>¼</sup> smhi <sup>þ</sup> ni <sup>¼</sup> ffiffiffiffiffi

α1 <sup>p</sup> ^ŝ<sup>1</sup> ^ h2 � � <sup>þ</sup> ffiffiffiffiffi

Rsum <sup>¼</sup> <sup>R</sup><sup>1</sup> <sup>þ</sup> <sup>R</sup><sup>2</sup> <sup>¼</sup> log <sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>α</sup>1j j <sup>h</sup><sup>1</sup>

perfect CSI estimation, the sum-rate of the network is as follows.

α2j j h<sup>1</sup>

!

sm <sup>¼</sup> ffiffiffiffiffi α1 <sup>p</sup> <sup>s</sup><sup>1</sup> <sup>þ</sup> ffiffiffiffiffi

desired signal has a high power compared to the interference which is ffiffiffiffiffi

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

α2

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

2

<sup>2</sup> <sup>þ</sup> <sup>1</sup>=<sup>ρ</sup>

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

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

LTE-A [12] and digital TV standard [13].

Overview of Multiplexing Techniques in Wireless Networks

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

The received signal at the ith user is Yi.

signal from Yð Þ<sup>2</sup>

Yð Þ<sup>2</sup>

order, hi j j<sup>2</sup> <sup>&</sup>lt; hj

39

� � � �

expressed as follows.

2 :

<sup>2</sup> <sup>¼</sup> ffiffiffiffiffi α1 <sup>p</sup> <sup>s</sup>1h<sup>2</sup> � ffiffiffiffiffi

• 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 network.

Despite this challenge along with its other challenges like self-jamming and need for precise synchronization, CDM have shown some prominent advantages, as follows, paving the way for implementing it in several real-world communication.

