Wider Transmission Bandwidth Frequency Computer Science Essay

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Demands for media-rich wireless data services have brought much attention to high speed broadband mobile wireless techniques in recent years. demand for higher data rate is leading to. utilization of a wider transmission bandwidth. With a wider transmission bandwidth, frequency >selectivity of the channel becomes more severe and thus the problem of inter-symbol interference (ISI) becomes more serious. In a conventional single carrier communication system, time domain equalization in the form of tap delay line filtering is performed to eliminate ISI. However, in case of a wide band channel, the length of the time domain filter to perform equalization becomes prohibitively large since it linearly increases with the channel response length.

One physical-layer technique that has gained much reputation due to its robustness against frequency selective fading channel is Multi-carrier Modulation. Orthogonal frequency division multiplexing (OFDM) is a multicarrier modulation technique which uses orthogonal subcarriers to convey information. In the frequency domain, since the bandwidth of a subcarrier is designed to be smaller than the coherence bandwidth, each sub-channel is seen as a flat fading channel which simplifies the channel equalization process. In the time domain, by splitting a high-rate data stream into a number of lower-rate data stream that are transmitted in parallel, OFDM resolves the problem of ISI in wide band communications [1]. Despite all the advantages of OFDM system, it faces two major drawbacks: (i) High Peak to Average Power Ratio (PAPR); signal with a high PAPR require highly linear power amplifiers to avoid excessive inter-modulation distortion. To achieve this linearity, the amplifiers have to operate with a large bacoff from their peak power. The result is low power efficiency (measured by the ratio of transmitted power to dc power dissipated), which places a significant burden on portable wireless terminals. (ii) High sensitivity to frequency offset; this problem derives from the inevitable offset in frequency references among the different terminals that transmit simultaneously. Frequency offset destroys the orthogonality of the transmissions, thus introducing multiple access interference [2]. Several methods have been proposed on how to reduce the high PAPR of an OFDM signal. However, most of these methods have limitations in terms of to what extent the power variations can be reduced. Furthermore, most of the methods also imply a significant computational complexity and/or a reduced link performance.

To overcome these disadvantages, there is an interest to consider also wider-band single-carrier transmission as an alternative to multi-carrier transmission, especially for the uplink, i.e. for mobile-terminal transmission. The wider-band single carrier transmission is a modified form of OFDMA, referred as single carrier frequency division multiple access. SC-FDMA utilizes single carrier modulation and frequency domain equalization is a technique that has similar performance and essentially the same overall complexity as those of OFDMA system. One prominent advantage over OFDMA is that the SC-FDMA signal has lower PAPR because of its inherent single carrier structure [3]. As in OFDMA, the transmitters in an SC-FDMA system use different orthogonal frequencies (subcarriers) to transmit information symbols. However, they transmit the subcarriers sequentially, rather than in parallel. Relative to OFDMA, this arrangement reduces considerably the envelope fluctuations in the transmitted waveform. SC-FDMA has drawn great attention as an attractive alternative to OFDMA, especially in the uplink communications where lower PAPR greatly benefits the mobile terminal in terms of transmit power efficiency. It is currently a strong candidate for uplink multiple access scheme in 3G Long Term Evolution of 3GPP [4].

This project report focuses on the PAPR for SC-FDMA signal and compared to that of traditional OFDMA system. Starting with a brief introduction of OFDM and discusses, along with detail discussion on SC-FDMA. This also contains a comparison of PAPR for different mapping techniques of SCFDMA along with OFDMA using complementary cumulative distribution function (CCDF).

Orthogonal Frequency Division Multiplexing

Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier transmission technique in which instead of a single carrier being modulated, a large number of evenly spaced subcarriers are modulated using with low rate data. Unlike the conventional single-carrier modulation schemes - such as AM/FM (Amplitude/Frequency Modulation for analogue) or ASK/FSK/PSK (Amplitude/Frequency/Phase Shift Keying in the case of digital communication systems) - that send only one signal at a time using one RF carrier. OFDM is a spread-spectrum technique that increases the efficiency of data communications by increasing data throughput because there are more carriers to modulate. In addition, as it sends multiple high-speed signals concurrently on specially computed, orthogonal, carrier frequencies. This results in a more efficient use of bandwidth and robust communications that withstands noise and other interferences.

FDM Frequency Division Multiplexing theory states that the total available bandwidth is divided into several sub-channels or sub-carriers, spaced with guard bands to reduce interference between adjacent channels, signals from multiple transmitters are transmitted simultaneously (at the same time slot) over multiple frequencies. Each frequency range (sub-carrier) is modulated separately by different data stream. (See Figure 2-1)

Similar to FDM, OFDM also exploit multiple subcarriers but these sub-carriers are narrowly spaced to each other without interfering, this is possible because the frequencies (subcarriers) are orthogonal, meaning the peak of one sub-carrier coincides with the null of an adjacent sub-carrier. Orthogonality, eliminates the need of guard bands between adjacent sub-carriers. Hence, OFDM system requires considerably less bandwidth than a traditional FDM system to carry the same amount of information which translates to higher spectral efficiency. In addition, it allows dynamic allocation of bits to sub-channels a.k.a. Adaptive Modulation. To maximize throughput of the system, OFDM can intelligently assign more bits to the sub-channels experiencing less channel noise. (See Figure 2-2)

Figure 2-3 illustrates OFDMA, which also make use of multiple narrowly spaced subcarriers, but these subcarriers are distributed into groups of subcarriers. Sub-channel is so called to each group. The subcarriers do not need to be adjacent to form a sub-channel. In the downlink, a sub-channel may be proposed for different receivers. In the uplink, a transmitter may be assigned one or more sub-channels.

The principles of orthogonal frequency division multiplexing (OFDM) modulation to combat ISI inter-Symbol Interference and ICI Inter-Channel Interference have been in existence for several decades. However, its practical implementation was historically limited to the speed and efficiency of the FFT Fast Fourier transform technique. But thanks to the availability of modern chips and advance in high-performance electronics leading to VLSI Very Scale Integration has enabled us to implement the OFDM system with quite less complexity.

Figure 2-1 Frequency Division Multiplexing (FDM)

Spacing is put between two adjacent sub-carriers.

Figure 2-2 Orthogonal Frequency Division Multiplexing (OFDM)

Sub-carriers are closely spaced until overlap.

Figure 2-3 Orthogonal Frequency Division Multiple Access (OFDMA)

Sub-carriers with the same color represent a sub-channel.

A Brief OFDM History

OFDM has been around since the mid 1960s and at that time, the idea of using parallel data transmission was there by means of frequency division multiplexing (FDM [5], [6]. The concept was to utilize parallel data sequences and FDM with overlapping sub-channels to get rid of using the high speed equalization and to tackle impetuous noise, and multipath distortion as well as to efficiently use the offered bandwidth. Weinstein and Ebert [7] applied the discrete Fourier transform (DFT) to parallel data transmission system as part of the modulation and demodulation process. In addition to eliminating the banks of subcarrier oscillators and coherent demodulators required by FDM, a completely digital implementation could be built around special-purpose hardware performing the fast Fourier transform (FFT). Recent advances in VLSI technology enable making of high-speed chips that can perform large size FFT at affordable price.

In 1980s, OFDM was studied for the use in High-speed Digital Modems, Digital Mobile Communications and High-Density recording. In this era, the system which used pilot tone for stabilizing carrier and clock frequency control was implemented. A variety of fast modems were also developed for the telephone networks. Since 1990s, OFDM has been turned out to be used practically for many High-speed communications applications such as Wideband Data Communications over Mobile Radio FM channels, Wireless LAN [8], High-rate Digital Subscriber Line (HDSL), Asymmetric Digital Subscriber Line (ADSL), Very High-Speed Digital Subscriber Line (VHDSL), Digital Audio Broadcast (DAB) [9], Digital Video Broadcast and HDTV terrestrial broadcasting. [10].

Understanding of OFDM

Orthogonality and OFDM

If the FDM system as stated in the previous section, had been able to use a set of subcarriers that were orthogonal to each other, a high level of spectral efficiency could have been attained.

The guardbands would no longer be needed that were necessary to allow individual demodulation of subcarriers in an FDM system. The usage of orthogonal subcarriers would allow the sub-carriers spectra to overlap, hence increasing the spectral efficiency. As long as orthogonality is sustained, it is still possible to recover the individual sub-carriers signals even though their spectrums are overlapped.

By definition, if the dot product of two deterministic random signals is equal to zero, these signals are said to be orthogonal to each other. Orthogonal really means at a right angle to. The signals are generated so they are orthogonal to one another, thereby producing little or no interference to one another despite the close spacing. In more practical terms, it means that orthogonality can be achieved by careful selection of carrier spacing, such as letting the carrier spacing be equal to the reciprocal of the symbol period of the data signals, the resulting sinc (sin x/x) frequency response curve of the signals is such that the first nulls occur at the subcarrier frequencies on the adjacent channels. Orthogonal sub-carriers all will have an integer number of cycles within the symbol period. With this agreement, the modulation on one channel will not produce inter-symbol interference (ISI) in the adjacent channels.

Mathematically, suppose we have a set of signals Ψ, where Ψp is the p-th element in the set. The signals are orthogonal if,


Where * indicates the complex conjugate and interval [x, y], is assumed as the symbol period. Mathematically, it can be proved quite simply that the series sin(nx) for n=1,2,… is orthogonal over the interval -p to p.

Mathematical description of OFDM

After the detail description of the system, it is equally important to mathematically define the modulation system. This will allows us to explain the generation of signal, the basic operation of the receiver and will give us means to understand the effects of imperfections introduced in the transmission medium. As stated above, Orthogonal Frequency Division multiplexing is the way of transmission of a large number of narrowband flat carriers, which are closely spaced in the frequency domain. In order to get rid of a large number of filters and modulators being deployed at the transmitter and corresponding filters and demodulators at the receiver, it is desirable to make use of modern DSP techniques, such as FFT Fast Fourier Transform Error: Reference source not found.

Mathematically, we can expressed each carrier as a complex wave


is the real part of the real signal, the amplitude and also phase of the carrier and can be varies on the basis of symbol to symbol. The parameter values will remain constant over the symbol periodt. OFDM comprises of many carriers. Hence, the complex signals can be represented by (Figure 2 Example of OFDM Spectrum, for a single sub-channel in a single bit/symbol duration)

Figure 2 Example of OFDM Spectrum, for a single sub-channel in a single bit/symbol duration


Figure 2 Example of OFDM Spectrum by 5 carriers, each sub-channels at the central frequency, no crosstalk between sub-channels



This is no doubt a continuous signal and if waveforms of each component of the signal are considered over the one symbol period, then and variables values can take on fixed, which will entirely depend on the frequency of specific carrier, and so it can be rewritten

If the signal is samples and the sampling rate use is 1/T, then the resultant signal can represented by


At this particular instant, the time over which this signal is being analyzed is constrained to N samples. Because of simplicity this sampling is done over one data symbol period. Therefore the relationship

By further simplification to Eq. 2.5, without a loss of generality by assuming , then the signal becomes


Comparing Eq. 2.6 with the generic form of the Inverse Discrete Fourier Transform expression,


In Eq. 2.6, the function is simply more or less the definition of the signal in the sampled frequency domain, and is showing the time domain representation.

Eqns. 2.6 and 2.7 are equivalent if:


Finally, we get the same condition which is required for orthogonality. Hence, it can be noted as a significance of maintaining orthogonality that OFDM signal can be expressed using Fourier Transform technique

OFDM compared to Single Carrier Modulation


Efficient use of the available bandwidth by allowing overlap of sub-channels.

OFDM spread out the frequency fading on many symbols by simply divides the available spectrum, this efficiently randomizes the burst error and hence therefore OFDM is more prone to frequency selective fading.

OFDM require simple equalization at the receiver comparatively to single carrier transmission, where a matrix inversion is required.

For given channel delay spread, the complexity of receiver with a time domain equalizer, is much lower than that of single carrier.

Throughput and capacity can be greatly increased by adopting different data rate per sub-carriers on the basis on signal to noise ratio of individuals.

Making use of FFT Fast Fourier Transform technique, the hardware/physical implementation of modulation and demodulation in OFDM is very efficient computationally.

By using the appropriate coding technique and interleaving the symbols lost due to the frequency selective nature of the channel can be recovered.

Eliminates ISI Inter-Symbol Interference and ICI Inter-Channel Interference through use of a CP Cyclic Prefix.

Maximum Likelihood Detector/Receiver design of each sub-channel is very simple.


A major weakness of OFDM is the high PAPR Peak-to-Average Power Ratio and requires PAPR reduction techniques or linear RF amplifiers, which are less power efficient.

OFDM is also more vulnerable to carrier frequency offset and requires an adaptive or coded scheme to overcome spectral nulls in channel.

System Block Diagram and Description

The description of the OFDM system how its work and block diagram (Figure 3) is given below. OFDM transmitter generates the carriers and the data signals simultaneously using purely digital circuits, residing in the dedicated DSP microchips. Digital signal generation used in OFDM is basically based on series of mathematical computations known as Inverse Discrete Fourier Transform (or simply IDFT), and the process results in the formation of a complex modulated waveform at the output. The transmitter first converts input incoming serial data from a serial stream to parallel sets using Shift Registers. Each dataset contains one symbol, Si, for each sub-carrier. For example, set of four data will be [S0 S1 S2 S3]. Prior to performing Inverse Fast Fourier Transform (IFFT), Corresponding to this example, dataset is organised on the horizontal fashion in the frequency domain as depicted in Figure 2. This agreement, which is symmetrical about the vertical axis is compulsory for using the IFFT to operate the data [12].

Figure 2: Frequency Domain Distribution of Symbols

IFFT converts back from frequency domain data to corresponding samples in time domain and from parallel to serial data for transmission A Guard Period (cyclic prefix) is inserted between consecutive symbols to avoid Inter-symbol Interference (ISI) caused by the Frequency Selective nature of the channel. The symbols are then converted from digital to analog and passed through a Low-Pass Filter (LPF) for RF up-conversion. The receiver simply executes the inverse process of the transmitter. Usually, in the receiver to correct channel distortion single single-tap equalizers are used [13].

Figure 3: System Block Diagram

OFDM Applications

The Multi-carrier Modulation scheme OFDM has been selected for several ongoing and upcoming communication systems all over the world. OFDM is used in major European wireless broadband standards such as Terrestrial Digital Video Broadcast (DVB-T) and Digital Audio Broadcast (DAB) systems [14], [15] for more than a decade and has been now considered as a fully grown and well-established technology for digital broadcasting systems. In US, OFDM has been espoused in Multipoint Multichannel Distribution system (MMDS) and also Japan has incorporated OFDM for number of digital applications. Thanks to its intrinsic worth various other broadband applications such as wireless asynchronous transfer mode and wireless networks [16], a variety of high speed wireless network standards such as IEEE 802.11a/g, IEEE 802.16 Broadband Wireless Access system and the latest European Telecommunication Standard Institute (ETSI's) HiperLAN/2 have incorporated OFDM as a modulation technique. OFDM-based system has already been used for various wired applications, such as ADSL, VHDSL and Cable Modems standards.

Figure 2 OFDM Technologies Mapped to the OSI Model

Rollout of OFDM has just beginning to go up, and the embracing of OFDM in the PHY layer for various new wireless standards is quite remarkable. AT&T's Limited-mobility residential wireless broadband service is built-around OFDM in the PHY layer, and is serving over 15 million homes. Also home networking space, working groups such as HomePlug and HomeRF have also embraced OFDM multi-carrier modulation.

The cellular world is not left behind either with the evolving LTE incorporated OFDM. In 4G technologies that are recently developed, the LTE downlink used OFDMA and the uplink used SC-FDMA technology, and all Ultra Mobile Broadband UMB related technical proposals adopted OFDM as the core technology. IEEE802.15.3a UWB standard for short-distance communication also mentioned OFDM in its proposal. Thus, it's quite obvious that almost all new emerging technologies in the wireless communication field have adopted OFDM as the core technology. In short, it could be said that OFDM now symbolizes the future of wireless communication technology.

Major advantages of using OFDM in the PHY layer include simple equalization for narrowband channels, immunity to noise and high system throughput for these applications.

3- SingLE CArrier Frequency division multiple access


Single Carrier Frequency Division Multiple Access (SCFDMA) is a modified adaptation of the Orthogonal Frequency Division Multiple Access (OFDMA), and is being considered as a capable technique for high data rate uplink communication in future cellular systems. Almost every orthogonal frequency division techniques make use of discrete set of orthogonal subcarriers which are distributed over the whole system bandwidth. They all mainly embrace discrete transforms to shift signals from the time domain to frequency domain and vice versa. In order to transmit multiple signals simultaneously the access techniques is used which allocate the signals to mutually exclusive different sets of subcarriers. Since broadband channels face frequency-selective fading, the FDMA techniques could embrace channel dependent scheduling to attain multi-user diversity and more importantly since fading characteristics of the equipment used as a terminals are statistically independent in different locations, the scheduling techniques can make the most of it by assigning each terminal to subcarriers with favourable characteristics of the transmission at the location of terminal.

The WiMAX, 802.16 standard exploit OFDMA for both uplink (mobile terminal to base station) and downlink (base station to mobile terminal). SCFDMA is recommended by Third Generation Partnership Project (3GPP) to be used for the uplink multiple access schemes in the Long Term Evolution (LTE) and OFDMA will continue to adopt for the downlink transmission in favour to make the mobile terminals power-efficient. It has been also anticipated that 3GPP2 is also working on a variation of SC-FDMA using code spreading for the uplink of the Ultra Mobile Broadband (UMB) technique [17]. One major disadvantage of OFDMA is the high PAPR, which increases the cost and degrade the power efficiency of a amplifier. SCFDMA has almost similar throughput performance and almost overall same complexity as OFDMA but the most important advantage of SCFDMA is the lower Peak-to-Average Power Ratio (PAPR) than that of OFDMA. With this lower PAPR, the transmitter's power amplifier at the mobile terminals can be made simpler by embracing SCFDMA and also can be more power efficient than the case of OFDMA. Although, due to its high signalling rate, the equalizer of SCFDMA will be far more complicated than an equalizer of traditional OFDMA, but with SCFDMA transmission limited to LTE uplink, these complex equalizers are only required at base stations and not at mobile stations which are quite acceptable [18].

In this chapter, we will introduce an overview of the SCFDMA, Subcarrier Mapping techniques

Such as, Localized FDMA (LFDMA), Distributed FDMA (DFDMA), and also Interleaved FDMA (LFDMA), which is a special case of distributed FDMA (DFDMA). This will also include Time Domain Representation of SCFDMA and comprehensive comparison of SCFDMA with OFDMA.


Conventional time domain equalizers are unfeasible for broadband multipath channels due to the complexity reason. For such channels, Frequency Domain Equalization (FDE) is recommended. Single carrier with frequency domain equalization (SC/FDE) is one more way to handle against frequency selective channels. SC/FDE has got similar performance and almost similar complexity as OFDM, even for quite long channel delays [19], [20]. Figure 3.1 shows the system block diagrams for SC/FDE and OFDM and highlighting their difference.

Figure 3.1: SC/FDE and OFDM

When we compare both the systems, it is very well clear the similarities between these two systems. In short, these both systems use same component blocks and the only major difference is of the location of the IDFT block. Hence, it can anticipate that these two systems have similar link level performance and spectral efficiency.

However, having a similar link structure comparatively to OFDM but SC/FDE provides a variety of advantages over OFDM such as Low PAPR due to its single carrier structure at the transmitter, Low sensitivity to carrier frequency offset, also robustness to spectral nulls than the case of OFDM and more importantly lower complexity which benefit the mobile terminals in cellular uplink communication [21].

Single Carrier FDMA (SCFDMA) is just an extension of SC/FDE which is used to accommodate multi user access.


A block diagram of a SCFDMA system is shown in Figure 3.2. SCFDMA can also be regarded as Discrete Fourier Transform (DFT)-spread OFDMA, in which time domain data symbols are converted to frequency domain by using DFT before they go through to OFDMA modulation [22]. The user orthogonality stems from the fact that each and every user occupies different subcarriers in the frequency domain, similar to the case of traditional OFDMA. Since the overall transmit signal is inherently a single carrier, Peak-to-Power Ratio (PAPR) is intrinsically lower relatively to the OFDMA which generates a multi-carrier signal [23].

On the very first, the SCFDMA transmitter converts a binary input to a sequence of modulated subcarriers and at the transmitter input, a baseband modulator is used to convert the binary input to a multilevel series of the complex numbers in several possible modulation format, which includes binary phase shift keying (BPSK), quaternary PSK (QPSK), and 16 level quadrature amplitude modulation (16-QAM). The SCFDMA transmitter will next groups the modulated symbols into blocks, each block contains N symbols. A Block is the time taken by transmitter to transmit all of subcarrier once. The next very important step in SCFDMA subcarriers modulation is to execute an N-point DFT, in order to generate a frequency domain representation of an input symbols. After N-point DFT, it maps each of the N-DFT result to one of the (M>N) orthogonal subcarriers that can be transmitted. As for the OFDMA case, a typical value which is used for M is 256 subcarriers and N=M/Q is an integer multiple of M.Q. If N symbols per block are transmitted by all the terminals then without any co-channel interference, this system can easily handle Q simultaneous transmission. Q is the bandwidth expansion factor of the symbol sequence. As in the OFDMA system, an M-Point inverse DFT (IDFT) converts the amplitudes of the subcarriers to a complex time domain signal and then all the modulated symbols are transmitted sequentially.

Prior to transmission, the transmitter performs two other signal processing operations. Firstly, it inserts some sets of symbols which are referred to as cyclic prefix (CP) which basic purpose is to provide a guard time to avoid Inter-Block Interference (IBI) results due to the multipath propagation.

Secondly, it also performs linear filtering operation termed as pulse shaping filter which basic purpose is to reduce out-of-band signal energy.

Figure 3.2: A Block diagram of an SC-FDMA System

However, generally cyclic prefix is a replica of the end part of the particular block, which is added at the beginning of every block for the number of reasons as shown in the Figure 3.3. At very first, cyclic prefix (CP) is used to provide as a guard band between the two consecutive blocks to avoid interfere from each other as a result of the time dispersion caused by the multipath propagation and the condition on which it highly dependent is, if the length of the CP which we added is more than the maximum delay of the multipath propagation, or approximately equal to the channel impulse response, in that case there is no Inter-block-interference. Secondly, as CP is obtained by copying the end part to the beginning of the symbol block, it changed the linear convolution to the circular convolution. This way the receiver can independently process every frame, in order to approximate the transmitted information. Hence, by this way transmitted information propagating through the channel can be regarded as a circular convolution of the transmitted information block and channel impulse response, which we already know is the point-wise multiplication of the DFT frequency samples in the corresponding frequency domain. In order to remove the channel disturbance usually termed as distortion, the received signal DFT can be easily utilize and get them divided by the DFT of the channel response or by just implementing the refined frequency domain equalization techniques [24].

Figure 3.3: The cyclic prefix insertion

The most generally used pulse-shaping-filter is raised cosine filter. It can be represented in time domain and frequency domain as follows

Where Symbol period is denoted by T and roll-off factor by α.

Figure 3.4 (a), (b) illustrates the graphical representations of raised-cosine filter both in frequency and time domain. Roll-off factor (α) is an important identity, which can vary its value from 0 to 1 and useful to manage the out-of-band radiation amount. When α=0, filter behaves like an ideal bandpass filter that generates no out-of-band radiation and as its value increases towards 1, it increases out-of-band radiation values as well. The pulse contains higher side lobes when α is very close to 0 in the time domain and this results in the higher peak-to-average power ratio (PAPR) of the transmitted signal after filtering of pulse shaping. This entails a trade-off between out-of-band radiation and PAPR performance since PAPR decreases with increasing roll-off factor.



Figure 3.4: Amplitude of the raised-cosine (a) Frequency, (b) Time

Figure 3.5 illustrating the SC-FDMA transmit symbols generation. There are in total M subcarriers and around N (<M) carriers are fully occupied by the input user data. The input symbol has got symbol duration period of T seconds and this duration compressed to Ť = (N/M).T after SC-FDMA modulation.

Figure 3.5: Generation of SC-FDMA transmit symbols. There are M total number of

subcarriers, among which N (<M) subcarriers are occupied by the input data.

The receiver will use DFT for the received signal to transforms back into frequency domain, then it will de-maps the carriers, and finally will carry out frequency domain equalization. Any of time domain equalization techniques can be used such as decision feedback equalization (DFE), Minimum mean square equalization (MMSE) and also turbo equalizations [25-30] in order to combat against ISI due to single carrier structure. The equalized symbols are then converted to time domain by using IDFT, and finally the detection and decoding process will take place in time domain.

3.4 Subcarrier Mapping

The process of the data symbols mapping after DFT process termed as Subcarrier Mapping. The subcarrier mappings allocate complex values of the DFT output as amplitude on several selected subcarriers. There are in general two methods which are mainly used for subcarrier mapping classified into; localized subcarrier mapping and distributed subcarrier mapping as shown in Figure 3.6.

Figure 3.6: Subcarrier mapping modes

In distributed mapping, DFT complex output for the input data are assigned over the whole bandwidth with a zeros padding into the unused subcarriers, while in the case of localized mapping method, consecutive subcarriers are allocated for the DFT complex outputs of the user input data. We refer the distributed mapping method for SC-FDMA as Distributed Frequency Division Multiple Access (DFDMA) and localized mapping method as Localized Frequency Division Multiple Access (LFDMA). For this particular condition M = Q. N in the case of distributed mapping with equidistance among the allocated subcarriers called as Interleaved Frequency Division Multiple Access (IFDMA) [31], [32], [33], which is a very special case of distributed mapping for SCFDMA and it is very effective in a sense that the transmitter can able to modulate the user signal firmly in the time domain and not including the DFT and IDFT process.

As an example Figure 3.7 illustrating transmits symbols of SC-FDMA in frequency domain representation for N =4, M=12 and Q=3. Figure 3.8 is also depicting a multi-user view for SCFDMA.

Figure 3.6: An example of SC-FDMA transmit symbols in the

frequency domain for N = 4, Q=3 and M=12.

Figure 3.7: Subcarrier allocation methods for multiple users (Q=3

users, M=12 subcarriers, and N=4 subcarriers allocated per user)

From the point of view of resource allocation, there is further classification for subcarrier mapping mode as channel-dependent scheduling (CDS) and static scheduling methods. CDS basically allocate subcarriers depending on the channel frequency response for every user. If we compare both scheduling methods then distributed mapping method is one which offers frequency diversity since the transmitted signals are spread over whole bandwidth. CDS incrementally provides perk in the performance of distributed mapping method when used. By contrast, once used CDS with localized mapping is of great advantage because it offers considerable multi-user diversity.