# All publications of Prem Kamal . Hyderabad , India

**Optimal Resource Allocations for OFDM(A) by adopting Digital Modulation Techniques **

J.PremKamal Das T.Varshitha M.Ajay Kumar

Dept of ECE Dept of ECE Dept of ECE

MRIET MRIET Shri JJT University

[email protected] [email protected] [email protected]

*Abstract* - Orthogonal Frequency Division Multiple Access (OFDMA) has become the promising technique multiple access method. OFDMA technique is widely used for high speed data transmission in wireless broadband access. This research paper mainly concentrates on basics of OFDMA and the major objective is to explain the multi-carrier modulation scheme in OFDMA. In the present scenario, high data rate are provided by WLAN, WiMax and LTE/ LTE-Advanced (LTE-A). Providing a wireless system with more spectral efficiency under extending channel condition is a key challenge to come up with more bit rates with limited spectrum. OFDMA was adopted for the downlink of Long Time Evaluation (LTE) systems. Unlike, SC-FDMA was used for uplink of LTE. We discuss the history and implementation of OFDMA and problems linked with OFDMA.

*Keywords*—OFDMA, Wi-max, LTE, BER, SNR

**INTRODUCTION**

Orthogonal frequency division multiple access (OFDMA) has become appealing for a wide range of mercantile wireless systems because it delivers high data output in real-world environments, along with spectral efficiency, and link adaptability. OFDMA first came into wide use more than a dozen years ago in wireless local area network (LAN) applications and has recently spread rapidly to support wireless mobile voice and data in the form of the 3GPP long-term evolution (LTE) standard and the Worldwide Interoperability for Microwave Access (WiMAX) standard.

To understand OFDMA effectively, we will study about different related topics in this paper. The topics related to OFDMA are

1. Multipathing

2. Multiple Access

3. OFDMA Technique

4. SNR

5. BER

6. PAPR

** I. **multipath

Multipath routing is the routing technique of using multiple substitute paths through a network, which can provide a variety of benefits such as fault tolerance, increased bandwidth, or improved security. The multiple paths computed might be overlapped, edge-disjointed or node-disjointed with each other. Extensive research has been done on multipath routing techniques. In wireless and mobile communications, the multipath is the propagation technique that the results or outcomes in radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric ducting, ionospheric effective typical reflections and refraction, and reflections from water bodies and terrestrial objects such as mountains and buildings. Multipath propagation causes multipath interference, including constructive and destructive interference, and phase shifting of the signal; destructive interference causes fading. This may because a radio signal to become too weak in certain areas to be received adequately, so multipath propagation can be detrimental in radio communication systems. Where the magnitudes of the signals arriving by the various paths have a distribution known as the Rayleigh distribution, the fading is known as Rayleigh fading. Where one component (often, but not necessarily, a line of sight component) dominates, a Rician distribution provides a more accurate model, and this is known as Rician fading.

Multipath interference is a process in the physics of waves whereby a wave from a source travels to a detector via two or more paths and, under the right condition, the two (or more) components of the wave interfere. Multipath interference is a common cause of ghosting in analog television broadcasts and of fading of radio waves. The condition necessary is that the components of the wave remain coherent throughout the whole extent of their travel. The interference will arise owing to the two (or more) components of the wave having, in general, travelled a different length (as measured by optical path length – geometric length and refraction, and thus arriving at the detector out of phase with each other. The signal due to indirect paths interferes with the required signal in amplitude as well as phase which is called multipath fading.

The mathematical model of the multipath can be given below:

Suppose you want to transmit a signal, ideal Dirac pulse of electromagnetic power at time 0, i.e.

X(t) = δ(t)

At the receiver, due to the presence of the multiple electromagnetic paths, more than one pulse will be received, and each one of them will arrive at different times. In fact, since the electromagnetic signals travel at the speed of light, and since every path has a geometrical length possibly different from that of the other ones, there are different air travelling times (consider that, in free space, the light takes 3 μs to cross a 1 km span). Thus, the received signal will be expressed by

{\displaystyle x(t)=\delta (t)}y(t) = h(t) =

Where, N is received impulses

** II. MULTIPLE ACCESS TECHNIQUES**

In a communication system, it is unfeasible and unsustainable to provide a single line to every separate user on the network. To overcome this problem different types of methods are implemented to share a single limited band or channel into multiple users.

Multiple access techniques are based on multiplexing techniques. In communication, multiplexing techniques are used to allow many users to share together a finite amount of radio spectrum.

Basic communication multiple access techniques are listed below:

· FDMA

· TDMA

· CDMA

· WDMA

· SDMA

· OFDMA

**a) FDMA (Frequency division multiple access)**

FDMA is based on frequency division multiplexing. It is an operation of splitting a single channel or bandwidth into several bands of frequency. In this channel access scheme, every user gets separate sub-band of frequency like in FM radio. It enables many users to transmit at the same time but using different frequency channels. It is necessary to keep the channel wider, to accept the signal spectra of the conveyance to propagate.

Fig.1: Non-overlapping channels with Guard Bands

**b) TDMA (Time division multiple access)**

TDMA is based on time division multiplexing. In this channel access scheme, every user gets a separate time slot to transmit onto a standard frequency band. It allows users to send data or information using the same frequency band but different time slots.The primary purpose of introducing TDMA technology is to gain capacity over FDMA system by providing one band or frequency channels to multiple users. In TDMA we add time slots frequency band or channel so that many users can use single band or frequency.

Fig 2: Graphical Representation of TDMA

c*) CDMA (Code division multiple access)*

CDMA is a channel is a channel access method used by various radio communication technologies. Here, several transmitters can send information simultaneously over a single communication channel. CDMA is a spread spectrum multiple access technique. Each user in a CDMA system uses a different code to modulate their signal. Choosing the codes used to modulate the signal is very important in the performance of CDMA systems. The best performance occurs when there is good separation between the signal of a desired user and the signals of other users. The separation of the signals is made by correlating the received signal with the locally generated code of the desired user.

Fig 3: Illustration of CDMA

**d)WDMA (Wavelength division multiple access)**

WDMA is based on wavelength division multiplexing. At multiplexer side, multiple lights combine into a single light source and at the de-multiplexer, the light source converted again into various sources. Using FDMA, the bandwidth of an Optical Fibre can be subdivided. Different data source gets a different light frequency (referred to Wavelength, λ) to transmit. The FDMA technique in Optical Fibre is known as WDMA.

**e) SDMA (Space division multiple access)**

Space-division multiple access (SDMA) transmits different information in different physical areas. Examples include simple cellular radio systems and more advanced cellular systems which use directional antennas and power modulation to refine spatial transmission patterns.

*f) OFDMA *

*f) OFDMA*

Orthogonal Frequency Division Multiple Access is based on FDMA technique. Each subcarriers in the frequency band are overlapped with orthogonality principle. This is widely used to save the bandwidth and for high data transmission.

Fig 4: Orthogonality Mechanism

** III. OFDMA TECHNIQUE**

OFDMA was mainly introduced by Chang, at Bell labs in 1966. Later on the experiments, Weinstein & Ebert proposed use of FFT and Guard interval in the year of 1971. Cimini, the scientist was the main reason to discover OFDMA in cellular communication. According to IEEE standards OFDMA was used in IEEE 802.11a wireless LAN standards (Wi-Fi) in 1999. The OFDMA technique got used in IEEE 802.16 standards for wireless MAN (WiMAX) in 2004. By using OFDMA first LTE air interface implemented in 2007.

OFDMA scheme is used as Multi Carrier Modulation Method. Each subcarrier (signal) is modulated with a conventional modulation scheme at a low symbol rate. This maintains total data rates similar to conventional single-carrier modulation schemes in the same bandwidth. QAM and PSK are the modulation techniques used in OFDMA modulator. Demodulation is based on Fast-Fourier Transform. The main advantage of OFDM over single-carrier schemes is its ability to cope with severe channel conditions (for example attenuation of high frequencies in a long copper wire, narrowband interference and frequency-selective fading due to multipath) without complex equalization filters. Channel equalization is simplified because OFDM may be viewed as using many slowly modulated narrowband signals rather than one rapidly modulated wideband signal. The low symbol rate makes the use of a guard interval between symbols affordable, making it possible to eliminate inter-symbol Interference (ISI) and use echoes and time-spreading (in analog television visible as ghosting and blurring, respectively) to achieve a diversity gain, i.e. a signal-to-noise ratio improvement. This mechanism also facilitates the design of single frequency network (SFNs) where several adjacent transmitters send the same signal simultaneously at the same frequency, as the signals from multiple distant transmitters may be re-combined constructively, sparing interference of a traditional single-carrier system.

OFDMA works on the Orthogonality Principle.

**a) Orthogonality Principle**

The orthogonality principle states that, the dot product of two similar quantities tends to zero. This orthogonality principle can be applied on the vectors and real time functions. The below figure shows the orthogonality principle on the three vectors A,B and C

Fig.5 Representation of Orthogonality

The above figure consists of three vectors A,B and C. according to the orthogonality principle we derive the equation as

A.B = B.C = C.A = 0

The orthogonality principle is also applicable to real function which is the main working principle for OFDMA. Consider f1(t) and f2(t) are the two functions then we have,

**b) Working of OFDMA with Orthogonal Principle**

The OFDMA technique is mainly worked on the orthogonal principle. When the sub carriers are placed in the overlapped manner, there the interference of the symbols or signals may occur. But using the orthogonal principle, at every peak point of the sub carrier the remaining signals can’t be interfere with its peak value signal. This occurs because of the orthogonality principle, when a signal reaches to its peak value, product of the remaining signals are tends to zero.

Fig.6 Working of OFDMA

The above figure shows the working of OFDMA with orthogonality principle. This technique is widely popular for saving the bandwidth and high speed data transmission. In FDMA, guard bands are used to avoid interference of the symbols but in OFDMA cyclic prefix is used as guard band to protect the data from inter-symbol-interference (ISI).

*c) Cyclic Prefix *

Cyclic prefix is also a fundamental concept of OFDMA which protects the data from ISI. The name itself denotes that prefix is added to the input data to avoid ISI. When a prefix is added, the linear convolution becomes circular convolution. Hence this phenomenon is known as Cyclic Prefix. In simple, assume that we are transmitting 8bits of data. There must exists little amount of noise, a new bit is generated which consumes the all the noise which are presented in the previous bits and it carry forward. By this phenomenon the inputs bits will be free from noise when it get demodulated.

### a) Block Diagram of OFDM

Fig 7: Block diagram of OFDM

Initially, the serial bits are converted into parallel bits by using various algorithms. The converted bits are performed Inverse Fast Fourier Transform. This transform is based on the number of inputs which are given. For the output of the IFFT bits cyclic prefix is added i.e., last bit is repeated again at the starting of the bit stream. This is the operation of OFDMA transmitter.

When it comes to the receiver end, it recognizes the bit which are added as cyclic prefix, the will removed from the bits and it performs the Fast Fourier Transform. The output of FFT are in parallel and they are converted into the serial order and produces the output.

OFDM allows simultaneous low-data-rate transmission from several users. Pulsed carrier can be avoided in this technique. Lower maximal transmission power for low-data-rate users, shorter delay and constant delay are possible with this efficient technique. Contention-based multiple access (collision avoidance) is simplified at OFDMA.OFDM is used in a number of other of systems from WLAN and WiMAX to broadcast technologies including DVB and DAB. OFDM has many advantages including its robustness in the face of multipath fading and interference. Although it may appear to be a particularly complicated form of modulation, it is in fact well suited to digital signal processing techniques.

**IV. SIGNAL TO NOISE RATIO**

SNR stands for Signal to Noise Ratio, it is defined as the ratio of power of the signal to the power of the noise

Whereas,

Ps = power of the signal and

Pn = power of the noise

It is the standard measure of analog noise, SNR is used to analyze the quality of the demodulated signals in Orthogonal Frequency Division Multiple Access system. The approach is based on the statistic properties The approach is based on the statistic properties of random process after Fourier Transform.

Both signal and noise power must be measured at the same and equivalent points in a system, and within the same system bandwidth. Depending on whether the signal is a constant (s) or a random variable (S), the signal to noise ratio for random noise N with expected value of zero becomes:

Where E refers to the expected value.

If the signal and the noise are measured under the same impedance the Signal-to-noise ratio can be obtained by calculating the square of its amplitude ratio, i.e..,

SNR =

Whereas,

As = Amplitude of the signal and

An = Amplitude of the noise

Because many signals have a very wide dynamic range signals are often expressed using the logarithm decibel scale. Based upon the definition of decibel, signal and noise may be expressed in decibels (dB) as,

PsdB = 10log10 (Ps) and

PndB= 10log10 (Pn)

In the similar manner, SNR can also be measured in decibels

SNRdB = 10log10 (SNR)

By using the definition of SNR

SNRdB = 10log10

Using the quotient rules for algorithm we write as,

10log10 (Ps/Pn) = 10log10[Ps-Pn]

Substituting the definitions of SNR, signal, and noise in decibels into the above equation results in an important formula for calculating the signal to noise ratio in decibels, when the signal and noise are also in decibels{\displaystyle \mathrm {SNR_{dB}} ={P_{\mathrm {signal,dB} }-P_{\mathrm {noise,dB} }}.}

SNRdB = Psdb - PndB

In the above formula, P is measured in units of power, such as watts (W) or mill watts (mW), and the signal-to-noise ratio is a pure number.

**V. BIT ERROR RATIO**

BER is stands for Bit Error Rate, it is defined as the number of bit error per unit time. Bit error ratio is a unitless performance measure but it is expressed in terms of percentage. The bit error probability per is the expectation value of bit error rate.

In this analysis, only uniform quantization is considered, since in the case of non-uniform quantization, the quantization errors may not be approximated as Gaussian random variables, and the analysis may become very difficult if not impossible. Our analysis is based on the Gaussian approximation of the nonlinear noise, and the suitability of this approximation is confirmed by computer simulation.

Fig 8: Graphical Representation of BER

The transmission BER is the number of detected bits that are incorrect before error correction, divided by the total number of transferred bits (including redundant error codes). The information BER, approximately equal to the decoding error probability, is the number of decoded bits that remain incorrect after the error correction, divided by the total number of decoded bits (the useful information). Normally the transmission BER is larger than the information BER. The information BER is affected by the strength of the forward error correction code.

The BER may be evaluated using stochastic computer simulations. If a simple transmission channel mode and data model is assumed, the BER may also be calculated analytically. An example of such a data source model is the Bernoulli source.

Examples of simple channel models used in information channel are:

· Binary symmetric channel (used in analysis of decoding error probability in case of non-bursty bit error on the transmission channel)

· Additive white Gaussian noise (AWGN) channel without fading.

A worst-case scenario is a completely random channel, where noise totally dominates over the useful signal. This results in a transmission BER of 50% (provided that a Bernoulli binary data source and a binary symmetrical channel are assumed, see below).

Bit-error rate curves for BPSK, QPSK, 8-PSK and 16-PSK, AWGN channel.

BER comparison between BPSK and differentially encoded BPSK with gray-coding operating in white noise. In a noisy channel, the BER is often expressed as a function of the normalized carrier to noise ratio measure denoted Eb/No, (energy per bit to noise power spectral density ratio), or Es/No (energy per modulation symbol to noise spectral density).

For example, in the case of QPSK modulation and AWGN channel, the BER as function of the Eb/N0 is given by

BER=1/2(erfc[Eb/No] )

People usually plot the BER curves to describe the performance of a digital communication system. In optical communication, BER(dB) vs. Received Power(dBm) is usually used; while in wireless communication, BER(dB) vs. SNR(dB) is used.

Measuring the bit error ratio helps people choose the appropriate forward error correction codes. Since most such codes correct only bit-flips, but not bit-insertions or bit-deletions, the hamming distance metric is the appropriate way to measure the number of bit errors. Many FEC coders also continuously measure the current BER.

A more general way of measuring the number of bit errors is the levenshtein distance. The Levenshtein distance measurement is more appropriate for measuring raw channel performance before frame synchronization, and when using error correction codes designed to correct bit-insertions and bit-deletions, such as Marker Codes and Watermark Codes.

**VI .PEAK AVERAGE POWER RATIO**

The PAPR is the relation between the maximum power of a sample in a given OFDM transmit symbol divided by the average power of that OFDM symbol. In simple terms, PAPR is the ratio of peak power to the average power of a signal. It is expressed in the units of dB. PAPR occurs when in a multicarrier system the different sub-carriers are out of phase with each other. At each instant they are different with respect to each other at different phase values. When all the points achieve the maximum value simultaneously; this will cause the output envelope to suddenly shoot up which causes a ‘peak’ in the output envelope.

Due to presence of large number of independently modulated subcarriers in an OFDM system, the peak value of the system can be very high as compared to the average of the whole system. This ratio of the peak to average power value is termed as Peak-to-Average Power Ratio. In LTE system, OFDM signal PAPR is approx. 12dB.

In general, the PAPR (χ) of the time-domain sequence s = {s [n]} is defined as the ratio between the maximum instantaneous power and its average power, that is

χ = PAPR{s} =

Where E {·} denotes expected value.

In the literature, the most common way to evaluate the PAPR is to determine the probability that this PAPR exceeds a certain threshold χ0. This is represented by the Complementary Cumulative Distribution Function (CCDF), which is a random variable, as: CCDF(χ) = Prob(χ > χ0) = 1 − 1(1 − e χ0 )

The transmit signals in an orthogonal frequency-division multiplexing (OFDM) system can have high peak values in the time domain since many subcarrier components are added via an inverse fast Fourier transformation (IFFT) operation. As a result, OFDM systems are known to have a high peak-to-average power ratio (PAPR) when compared to single-carrier systems. In fact, the high PAPR is one of the most detrimental aspects in an OFDM system as it decreases the signal-to-quantization noise ratio (SQNR) of the analog-digital convertor (ADC) and digital-analog convertor (DAC) while degrading the efficiency of the power amplifier in the transmitter. As a side note, the PAPR problem is more of a concern in the uplink since the efficiency of the power amplifier is critical due to the limited battery power in a mobile terminal.

An OFDM symbol would have a PAPR around 17 dB (since *K*=52), which is fairly high. However, this number is the worst-case scenario and the probability of getting this high number is very unlikely as the modulated data on each subcarrier is theoretically random and uncorrelated.

For this reason, the PAPR of an OFDM system is usually interpreted as a random variable with a distinct probability density function (PDF). So, when we are talking about PAPR reduction, we are usually talking about increasing the probability of getting low PAPR values overall. Here is an example of the PDF for an OFDM signal with 8 subcarriers, using a QPSK modulation

Fig 9: QPSK output with N=8

Fig 10: QPSK output with N=16

To reduce the peak average power ratio there are several technique methods listed below

1. Signal distortion reduces PAPR by making the OFDM signal distorted non-linearly. Clipping and filtering, peak windowing has nonlinear process leading to in-band and out-band interference (OBI), non-linear companding technique reduces OBI. These methods degrade the BER performance.

2. In probabilistic techniques, the scrambling of each OFDM signal is scrambled with different phase sequence and chooses the sequence that provides optimum PAPR. Selective Mapping (SLM) and partial transmit sequence (PTS) technique scramble the OFDM signal by multiplying each OFDM signal sequence with phase sequence or dividing the sequence into disjoint sub blocks which are computed with complex phase factors. In SLM the hardware complexity increases and in PTS computational complexity increases. For both the techniques there is a usage of side information (SI) bits which can be minimized.

3. Coding techniques decreases PAPR by introducing different error detection and correction codes such as linear block codes and turbo codes to the data.

4. Pre-distortion methods increase the diversity and decreases the PAPR by using spreading methods.

The techniques which are used to reduce the peak average power ratio are classified into two methods

**(i) Signal Distortion Techniques**

Ø Clipping and Filtering

Ø Envelope Scaling

Ø Peak Reduction Carrier

Ø Peak Windowing

**(ii) Signal Scrambling Techniques**

** **

Ø Partial transmit sequence

Ø Selected Mapping

Ø Interleaving Technique

Ø Tone Reservation

Ø Block – coding Technique

Ø Tone Injection

Ø Block coding technique with error correction

** **

**VII. DIGITAL MODULATION TECHNIQUES USED IN OFDMA**

Digital Modulation provides more information capacity, high data security, quicker system availability with great quality communication. Hence, digital modulation techniques have a greater demand, for their capacity to convey larger amounts of data than analog modulation techniques. There are many types of digital modulation techniques and also their combinations, depending upon the need. Of them all, we will discuss the prominent ones.

QAM is based on the application of ASK and PSK to two sinusoidal waves of the same frequency but with a phase difference of 90°. Sinusoidal waves 90° apart are said to be in a quadrature phase relationship. It is customary to refer to one of these waves as the I wave, or in-phase wave or component, and the other as the Q wave, or quadrature wave or component.

Fig 11: Input Signal for QAM

The above figure is the input signal i.e., sine signal. Now we can observe the quadrature amplitude modulation output i.e., cosine signal, as shown in fig.

Fig12: Output of QAM

a) 16-QAM

This is a modulation technique in which the carrier can exist in one of sixteen different states. As such, each state can represent four bits – 0000 through to 1111, per symbol change. Constellation diagram of 16 bit QAM is given below. The diagram shows a pair of axes. The X axis is labelled I and has points minus 3, minus 1, 1 and 3 marked on the axis. The Y axis is labelled Q and likewise has points minus 3, minus 1, 1 and 3 marked on the axis.

Fig 13: Constellation Diagram of 16 bit QAM

There are 16 dots positioned between the axes in a square formation, four rows of four. There is a dot at the intersection of each of the points marked on the axes. Thus the dots are spaced at regular intervals, the same distance apart.

The bit sequence of the 16 bit QAM shown below

Fig 14: Bit Sequence of 16 bit QAM

**VIII. SIMULATION RESULTS**

Fig 15: Relation between SNR and BER

The above graph represents a relation between the signal to noise ratio and bit error ratio among three modulation techniques which are of QPSK, 16-QAM, 64-QAM. In QPSK as signal to noise ratio increases the bit error ratio gets decreased. 16-QAM will have less bit error ratio than compared to the QPSK. Similarly, 64-QAM will have lower bit error ratio than compared both 16-QAM and QPSK. Hence, the efficiency of 64-QAM will be very high than compared to QPSK and 16-QAM techniques.

Fig 16. Comparison of Scattering and Reflection

The above graph indicates the relation between fading and interference level among propagation mechanisms of reflection and scattering. It is clearly found that the scattering mechanism will have more interference than compared to the reflection mechanism. Hence, as reflection mechanism is having lower interference level its efficiency is high.

**IX. CONCLUSION**

In this research work, the efficiency of different modulation methods are clearly explained which is suitable for OFDMA technique, Moreover various propagation mechanisms are illustrated that cause severe signal fading which are resulting for probability of errors and also fundamental approaches that are adopted in past mobile generations are briefed by which OFDMA has better efficiency by comparing with TDMA, CDMA.

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