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The orthogonal frequency divisions multiplexing technique, was introduced since the mid of 1960s . Since then the OFDM has been implemented in number of non-cellular wireless systems such as Digital Video Broadcast (DVB) and recently some of the 802.11 family of wireless local loop standards (Wi-Fi) beside the use in wire line technologies such as Asymmetric Digital Subscriber Line (ADSL) [4, 5]. The high power consumption requirement for FFT operation (the core of the OFDM transceiver as we will see in the following sections) represents the main obstacle for using the OFDM in cellular systems. Fortunately the advances in the signal processing technologies and the handheld device industry pave the way for using efficient signal processing module so the power consumption is no longer a reason to avoid OFDM, nowadays both the IEEE's IEEE802.16e/802.16m (mobile WiMax) and the 3GPP's LTE standards adopt the Orthogonal Frequency Division Multiplexing (OFDM) as core modulation scheme . The two standards (i.e. WiMAX <E) use the Orthogonal Frequency Division Multiple Access (OFDMA) as the multiple access techniques in the downlink direction, but they use different implementation approaches in term of the frame structure, resource grouping and allocation . However in the uplink direction the two systems go different ways, while mobile WiMAX uses OFDMA (Orthogonal Frequency Division Multiple Access), the 3GPP (3rd Generation Partnership Project) standardization group has decided to use SC-FDMA (Single Carrier Frequency Division Multiple Access) instead . SC-FDMA utilized a modified version from the OFDM transmission scheme in order to overcome the high peak to average power ratio (PAPR) problem inherited from using multiple subcarriers in OFDM, this technique also known as DFT-spread orthogonal frequency division multiple accesses . The Low PAPR property makes SCFDMA more attractive for uplink transmission especially in the case of low-cost devices with limited transmit power.
The aim of this chapter is to provide an insight to the proposed multiple access techniques in the forthcoming 4G systems, more specifically OFDMA and SC-FDMA, by introducing the basic principles of OFDM/SC-FDM modulation techniques and their multiuser transmission counterparts OFDMA/SC-FDMA. Other issues such as the subcarriers allocation schemes and the peak to average power ratio will be covered as well, the chapter will be concluded by summarized the most important concepts beside some pros and cons of OFDMA/SCFDMA technologies.
Single User transmission (OFDM and SC/FDE basic concepts):
In the orthogonal frequency division multiplexing (OFDM) modulation technique, the available spectrum band is divided into orthogonal narrowband channels referred to as subcarriers. Instead of transmitting one high data rate information stream in one carrier (which required smaller symbol duration); the information is divided into many lower rate streams transmitted among number of subcarriers (which relatively, required wider symbol duration).The choice of subcarriers is performed in a way to guarantee that they are orthogonal to each others; by this way each subcarrier can easily be separated from other subcarriers at the receiver end. This approach leads to a better spectral efficiency than that achieved in FDMA systems, in which no spectral overlap of carriers/subcarriers is allowed as depict in figure 1. As mentioned the main concept behind OFDM is to utilize many subcarriers with small bandwidth smaller than the coherence bandwidth of the channel, by this way any sub-channel will appears as flat fading channel in corresponds to each specific subcarrier.
Figure 1. OFDM subcarriers overlapping 
The traditional implementation of OFDM transceiver system relay on using bank of frequency oscillators at the transmitter and receiver side but thanks for the discrete signal processing technologies, a more practical implementation based on the use of the discrete Fourier transform (DFT) and its inverse (IDFT) can be achieved as illustrated in figure 2. The DFT/IDFT operation is realized usually by using the fast Fourier transform (FFT) and the inverse FFT (IFFT) pair algorithms to achieve more efficient processing speed .
OFDM transmitter side : The Inverse Discrete Fourier Transform (IDFT) or more practically the IFFT module can be consider as the heart of the OFDM transmitter, this module converts the baseband modulated symbols X(k) by the available subcarriers into one time domain symbol Z(n), which can be described by the following equation:
This step is followed by adding guard period between OFDM symbols to compensate of symbol dispersion caused by the channel delay spread (Tm), in other words to reduce the inter-symbols interference effect. This guard addition operation is described in figure 3 by the block box "Add cyclic prefix (CP)", in which number of last samples in the OFDM symbol/signal are copied and appended to the beginning of the sequence Z (n) as indicated below:
Figure 2: Cyclic prefix addition 
The reason behind adding the CP to the begging of the Z (n) sequence is due to the fact that circular convolution property needs to be created between the transmitted signal and the channel impulse response. This need is due to fact that when the data signal propagates through the channel, it linearly convolves with the channel impulse response in order to recover the original signal the equalizer at the receiver side should invert the channel impulse response effect, by performing the same type of convolution as the channel, either linear convolution or circular convolution. The DFT-based FDE equalization operation performed at the receiver side is circular convolution, so in order to match the two operations a CP (cyclic prefix) is added in the transmitter to make the channel filtering look like a circular convolution . After the CP addition, a pulse shaping (filtering) is applied in order to reduce side lobes in the frequency domain and limit the out-of-band interference.
Figure 2 Basic OFDM transceiver 
Receiver side: as depicted in figure 2, first the added CP (cyclic prefix) samples are removed after that the OFDM symbol is converted back to frequency domain using DFT operation. The DFT performs circular convolution in time domain which is equivalent to multiplication in frequency domain as described below:
Channel equalization, the next stage, is performed in the frequency domain to inverse the added channel effect to the transmitted signal. The channel effect can be seen as linear time invariant system operation, which performs linear filtering in the transmitted signal, in other word it is a convolution operation in the time domain and a point-wise multiplication operation in the frequency domain between the transmitted signal frequency components and the channel frequency components. As mentioned before the DFT Fourier transform operation at the receiver side converts the received time domain signal to its frequency domain components, which easily can be equalized by dividing it point-by-point by estimated channel frequency response components . Number of equalization techniques can be implemented such as minimum mean square error (MMSE) equalizer and the least-squares (LS) equalizer. The final stage is to detect the transmitted binary information using suitable detection techniques such as hard decision detection or soft decision detection techniques.
One of the main drawbacks of OFDM transmission technique is the sensitivity towards the frequency selectivity characteristics of the multipath channel, an alternative technique can be adopted to overcome this effect by using a modulation format in time domain instead of in frequency domain and apply the frequency domain equalization (FDE) at the receiver side [6,8]. This technique known as single carrier modulation with frequency domain equalization (SC-FDE), in which a performance similar to OFDM with essentially the same overall complexity can be achieved. The basic SC-FDE transceiver looks similar to its OFDM counterparts, however as depict in figure 4, a noticeable difference in the position of the IDFT module can be seen. In SC-FDE both the IDFT and DFT operations are performed at the receiver while in OFDM the IDFT operation is performed in the transmitter side. Both the two techniques perform a frequency domain equalization on the after the DFT operation. The difference is that modulation and demodulation in OFDM is performed in the frequency domain, while in SC-FDE these operations are performed in the time domain .
Figure 4: OFDM and SC-FDE transceiver comparison 
Multi Users transmission (OFDMA and SC-FDMA basic concepts):
In the previous section the single user transmission based on the OFDM/SC-FDE modulation schemes has been introduced, however when we deal multi-users transmission scenario it worth to emphasis that both of the OFDM/ SC-FDE aren't multiple access technique so suitable multiple access strategy that organizes the transmission and provides orthogonal, i.e. non-interfering communication between the active users is needed. The traditional multiple access strategies are based on dividing the available resources among the multiple users through the use of frequency, time, or code division multiplexing techniques. In time division multiple accesses (TDMA), each user is given a unique time slot, either on demand or in a fixed rotation. In frequency division multiple access (FDMA), each user receives a unique carrier frequency and bandwidth. While in code division multiple access each user will has unique code for his transmission, allowing each user to share the entire bandwidth and time slots with many other users . The forthcoming mobile communication systems (LTE/LTE-advanced and mobile) adopt different multiple access techniques namely the orthogonal frequency division multiple access (OFDMA) and Single Carrier Multiple Access (SC-FDMA), which are the context of our discussion in the next sections.
Orthogonal Frequency Division Multiple Access (OFDMA):
OFDMA is an OFDM-based multiple access scheme that adopted in the downlink direction in both LTE and WiMax standards. As illustrated in figure 5, the OFDMA can be seen as a hybrid technique from the FDMA and TDMA techniques. In this hybrid technique each user is provided with a unique fraction of the system bandwidth by assigning a subset of tones (subcarriers) of OFDM at specific time slot which guarantee that each subcarrier will not be occupied by more than one terminal/user at any time [1, 6]. Many of the OFDMA advantages are inherited from the single user OFDM such as achieving better spectral efficiency compared to FDMA technique as depicted in figure 1. This enhancement in spectral efficiency is due the use of overlapped subcarriers in frequencies domain to transmit the user data [7, 9]. The OFDMA also has the ability to perform the resource scheduling based on the channel time and frequency responses which allow the assigning of different subcarriers group to each user based on his channel condition this also known as multiuser diversity 
Figure 5: OFDMA basic operation 
Single Carrier Frequency Division Multiple Access (SC-FDMA): SC-FDMA can be regarded as DFT-spread orthogonal frequency division multiple access (OFDMA), where time domain data symbols are transformed to frequency domain by DFT before going through OFDMA modulation as illustrated in figure 6 .The orthogonality of the users stems from the fact that each user occupies different subcarriers in the frequency domain, similar to the case of OFDMA. The only different between the OFDMA and the SCFDMA is introducing an additional DFT module at the transmitter and IDFT and the receiver side. The equalization is performed in frequency domain in both cases. The OFDMA perform e the modulation and demodulation operation in the frqency domain as well while the SC-FDMA performs these operations in the time domain.
SC-FDMA effectively spreads each modulated symbol across the entire channel bandwidth so it's less sensitive to frequency-selective fading than OFDMA, in which the modulated symbols is transmitted in narrow bands (subcarriers bandwidth). But the use of narrow bands add advantages to OFDMA over SC-FDMA by allowing possible adaptation of the symbol modulation and power per individual subcarriers, that why OFDMA is able to achieve better capacity limit for a given channel than SC-FDMA [6,8].The most important advantage and difference between the OFDMA and the SC-FDMA is the low peak to average power ratio of the SC-FDMA. The SC-FDMA emulates the single carrier transmission while the OFDMA transmits a multicarrier signal, more details about low PAPR characteristics of SC-FDMA will be introduce in upcoming section .
Figure 6: OFDMA and SC-FDMA transceiver comparison 
In the case of the multiuser transmission, the sub-carriers assignment among different users can be performed using two main techniques as follow :
1- Consecutive (or localized) frequency mapping
2- Distributed frequency mapping
Localized subcarriers mapping scheme: as shown in figure 6, the localized frequencies mapping means that number sub-carriers are allocate in one contiguous block to each specific user. The major drawback of this method is that it is sensitive to frequency selective fading .
Distributed/interleaved frequency mapping scheme: in this schemes the allocate subcarriers to each specific user are distributed across the whole OFDM bandwidth as shown in figure 6 using. In some literature, the term interleaved used to describe distributing the subcarriers among the whole bandwidth which distributed mapping refer to partial distribution (not the whole bandwidth is cover). This scheme exploits the channel's frequency diversity but in other hand it needs robust frequency synchronization . The good frequency diversity property of the distributed scheme will lead to better BER performances but in other the complexity of channel estimation and equalization process is increased. In contrast localized mapping scheme does not have good frequency diversity as the distributed mapping scheme but the channel estimation and equalization processes are less complex. One way to exploit the benefits of the two schemes is to introduce a mid way scheme which called Block-wise consecutive frequency mapping, in which multiple blocks with equidistant frequency spacing are allocated to users, where each block consists of few number of consecutive subcarriers.
Figure 7: Basic subcarriers mapping schemes 
Beside the above mentioned categorization of the subcarriers mapping schemes, another description can carry out from the resource allocation point of view namely static and channel dependent scheduling (CDS). In CDS scheme the assign subcarrier to each user terminal depends on its channel frequency response (channel condition).