With the exponential increase in number of users, the conventional multiple access techniques showed limitations and congestion increased. Hence a different access technique known as Orthogonal Frequency Division Multiple Access (OFDMA) was put into practice. OFDMA is a combination of modulation scheme that OFDM and a multiple access scheme that combines TDMA and FDMA.

1) Principle of OFDM

The data which is to be transmitted are divided into symbols called OFDM symbols. The total bandwidth of the carrier $(W)$ is divided into N narrow frequency bands, each of bandwidth $\Delta f $ such as $W= N \Delta f$. The narrow frequency band is called as subcarrier. They are orthogonal to each other. The orthogonality means the null of one subcarrier coincides with the maximum of adjacent subcarrier. The orthogonal sub-carriers are illustrated in Figure 13.

Each subcarrier is represented by a different colour. As seen, because of orthogonality the peak of one subcarrier occurs at the null of other subcarrier. Hence there is no interference even after modulation which eliminates the need of guard bands.

i) Orthogonality principle

Mathematically, the Orthogonality principle can be expressed as follows:

Three signal vectors A, B and C are orthogonal if they satisfy the following condition

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

In terms of real function space, if $f_{1}(t) $ and $f_{2}(t)$ are two real time domain signals such that,

$f_{1}(t) = A\ sinw(t)$ and $f_{2}(t) = B\ cos(wt)$ then $f_{1}(t)$ and $f_2(t)$ are orthogonal to each other if following condition is satisfied i.e.,

$\int_\tau^{\tau + T} \ f_1(t) \ f_2(t) dt =0$

Similarly if $f_{m}(t) = M \ sin(mwt)$ and $f_{n}(t) = N \cos (nwt)$

$\int_\tau^{\tau + T} \ f_{m}(t) \ f_{n}(t) dt =0$

These orthogonal signals can be represented as,

ii) Illustration of OFDM signal generation:

• Consider, there are four subcarriers available and following information bits are to be transmitted,

$\quad \quad 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, …$

• Convert the incoming serials bits into 4 parallel bit streams, $C_{1}$, $C_{2}$, $C_{3}$ and $C_{4}$ as follows,

• Each parallel bit stream (column bits) is modulated with corresponding sub-carrier using BPSK.

The final OFDM signal is the sum of all modulated parallel bit stream signals ($C_{1}$, $C_{2}$, $C_{3}$ and $C_{4}$) and can be expressed as,

$$V{(t)} = \sum_{n =1}^{4}C_{n}\ sin(2 \pi nt).$$

The resultant OFDM signal looks as follows,

If there are N subcarriers, then OFDM signal can be expressed as,

$$V{(t)} = \sum_{n =1}^{N} C_{1} \ sin(2 \pi nt).$$

Note: A set of orthogonal subcarriers (used for OFDM) allocated to a user is called as subchannel. In the previous example, a subchannel consists of $N = 4$ subcarriers.

2) Principle of OFDMA

It is an implementation of FDMA - TDMA technique on OFDM.

i) The available frequency resources are divided into narrow orthogonal sub-channels and time slots.

ii) A narrow subchannel in one time slot is called as a OFDMA traffic channel or Resource element (RE).

iii) Each user gets a group of REs to transmit depending upon the QoS requirement.

iv) Thus multiple users can transmit using the same bandwidth and during the same time slot without any interference.

3) Advantages of OFDMA

- Multi-user Diversity: Broadband signals experience frequency selective fading. OFDMA allows different users to transmit over different portions of the broadband spectrum as illustrated in Figure 18. Different users experience different channel qualities, a deep faded channel for one user may still be favorable to others as illustrated in Figure 18.

- Receiver Simplicity: Only FFT processor is required at the receiver.

- Capacity Improvement: It eliminates the intra-cell interference avoiding CDMA type of multi-user detection hence more capacity depending upon the number of resource elements.

- Improved Bit Error Rate performance: It is due to fact that different users have different fading statistics. Hence deep fading for one user may be favorable to other user due to use of different subcarriers. The advantage of multiuser diversity helps in getting accurate detection in Fading environment too.

4) Disadvantages of OFDMA

- Peak to average power ratio (PAPR): The PAPR is the ratio of the maximum power of a sample in a given OFDM transmit symbol to 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. In a multicarrier system when the different sub-carriers are out of phase with each other, at that instant their values are different. 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 value 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 approximately 12dB. PAPR is expressed as,

$$PAPR = \frac{|x(t)|^2}{P_{avg}}.$$

Where, $x(t)$ is the instantaneous amplitude of that sample and $P_{avg}$ is the average power of the signal.

- Synchronization

In OFDMA, tight Synchronization between users are required for FFT in receiver and Pilot signals are used for synchronizations.

- Co-channel interference

Dealing with co channel interference is more complex in OFDM system than CDMA system. Dynamic channel allocation with advanced coordination among adjacent base stations is required.

OFDMA Transmitter

Figure 20 illustrates the OFDM transmitter. Consider there are U users in the system.

Each user's data bit stream is converted into parallel bit streams using Serial to Parallel converters. These bit streams are fed for Inverse fast fourier transform. In transmitters using OFDM as a multicarrier modulation technology, the OFDM symbol is constructed in the frequency domain by mapping the input bits on the I- and Q- components of the QAM symbols and then ordering them in a sequence with specific length according to the number of subcarriers in the OFDM symbol. That is by the mapping and ordering process, one constructs the frequency components of the OFDM symbol. To transmit them, the signal must be represented in time domain. This is accomplished by the inverse fast Fourier transform IFFT.

So, in summary the signal is easily synthesized in discrete frequency domain in the transmitter and to transmit it must be converted to discrete time domain by IFFT. OFDM scheme proposes to reduce of ISI effect provided that can preserve orthogonality.

Orthogonality OFDM subcarrier can be achieved with addition of guard time (guard interval). The OFDM guard time can be done by insert zero padding (ZP) or cyclic prefix (CP). CP is to extend the OFDM symbol by copying the last samples of the OFDM symbol into its front. CP is introduced before the OFDM symbol. Let $T_G$ denote the length of CP and T_{sub} denotes the duration of OFDM symbol without guard time. So, the extended OFDM symbols now have the duration of $T_{sym} =T_{sub} + T_G$. Guard time is selected longer than multipath delay so as not to cause inteference with the next OFDM symbol. The other advantage of CP is combating Inter Carrier Inteference (ICI) which is crosstalk between the subcarriers.

OFDMA Receiver

Received signal will be received many times due to multipath propagation specially in urban environment or mobile device are moving at high speed. Line of sight and multipath signals have difference arrival times. It is called delay spread which can cause Inter Symbol Inteference (ISI). OFDM system needs synchronization in the receiver side to find the beginning of each symbol correctly. Synchronization parameters include finding the right time delay, frequency deviation and phase shift of each symbol in the subcarrier. These parameters can be determined with addition redundancy in some of the subcarriers which are transmitted. The redundancy is called pilot symbol or preamble. The parameters are known by looking pilot signal from data received and will be calculated for synchronization and channel estimation process. The density of pilots detemine quality of synchronization but decrease of data rate transmission.

The received signal is first converted to digital using ADC, It is then fed for FFT processing to get the data symbol back and then it is demodulated.