# Ofdm symbol

Orthogonal frequency-division multiplexing has become the standard modulation format for 5G New Radio. Refer to Refs. FDM is simply the idea that multiple communication channels can coexist by designating a slice of frequency spectrum for each channel. A common example of this is FM broadcast radio: the overall US frequency allocation is FDM frequency allocations must not overlap and often have guard bands between the channels to minimize adjacent channel interference. Figure 1. Frequency Division Multiplexing transmits signals on adjacent carrier frequencies.

Chang [see Ref 3], recognizing that bandlimited orthogonal signals can be combined with significant overlap while avoiding interchannel interference.

Using OFDM, we can create an array of subcarriers that all work together to transmit information over a range of frequencies. These subcarriers must be orthogonal functions. The precise mathematical definition for orthogonality between two functions is that the integral of their product over the designated time interval is zero. More loosely, we can consider orthogonal functions to be statistically unrelated. Figure 2 shows how N equally-spaced subcarriers can be combined to form an array of parallel signals.

Each of the subcarriers is modulated using QAM. These modulated subcarriers can be used to support independent baseband signals but more typically they are combined to provide the maximum data throughput for one stream of data. Figure 2. An OFDM modulator sums signals of different frequencies. We can represent these subcarriers mathematically, using the complex form consistent with the use of QAM.

The equations above are continuous functions and OFDM systems have been implemented in analog form. However, modern systems are almost all digital, taking advantage of the latest semiconductor process nodes and digital signal processing.

With N subcarriers spaced by. For simplicity, Figure 3 shows just four unmodulated subcarriers in the time domain. Figure 3. Figure 4 plots these same subcarriers in the frequency domain, shown with some modulation bandwidth to indicate the overlap between subcarriers. The subcarriers are orthogonal to each other and will exhibit minimal interference to the other subcarriers, resulting in efficient use of bandwidth.

Note that the amplitude of each subcarrier crosses zero at the center of other subcarriers, minimizing adjacent subcarrier impact. Figure 4. Frequency domain representation of a four-carrier OFDM signal. Figure 5 shows a basic block diagram of a complete end-to-end OFDM system consisting of a transmitter and receiver. The bit stream enters the system on the left of the diagram. Figure 5. A complete OFDM system includes a transmitter left and receiver right. Power amplifier in transmitter not shown.

This baseband signal is usually up-converted UP to a higher frequency and perhaps amplified before being transmitted via the over-the-air channel.

At the receiver, the process is reversed.If you understand the meaning of following keywords, you would have pretty good big picfure of OFDM. You will figure out what all these terms are about as you go through this page. This is the meaning of 'Frequency Division'. Since all the data on each of these subcarriers are transmitted simultaneously, we can say this is a kind of 'Multiplexing'.

Now you may have a question at this point. How small we can make it for each subcarrier subcarrier, divided frequency? For example, if you are given 1 Mhz bandwidth as a fullband, how many subcarriers we are supposed to split into?

If you split it into sub carriers with 10 Khz interval and carry one bit on each sub carrier, you can transmit bits at a time.

Which option you would take? Definately you would want to split it into sub carriers. But unfortunately it would not be possible to split it with too small intervals between sub carriers. If you split it into too many sub carriers with too small space between sub carriers, there would be much high possibility of interference between adjacent sub carriers. However, if you separate each subcarrier too much and have small number of sub carriers, you would have much less interference between sub carriers but in that case the data rate would be decreased.

### What is OFDM: Orthogonal Frequency Division Multiplexing

As a kind of optimal solution, OFDM split the band into multiple sub carriers in such a way as shown below. In the following illustration, at each sampling point in frequency domain there is only one carrier which has non-zero value and all other sub carriers has zero value at the sampling point.

If any two functions or vectors are orthogonal, it means that they are linear independent to each other. You can find the mathematical definition of Orthogonality from WiKi, but it would not be easy to figure out practical meaning of Orthogonality from it. OFDM is very good method of utilizing the given frequency wisely, but there is a drawback to this method. For this method to work efficiently the space between sub carriers should be maintained exactly at the specified position which satisfy the condition of orthogonality.

What if the space between sub carriers are not maintained accurately and they are drifting around. One example for this case is shown below. You would not see much differences when each sub carriers are plotted separately upper plotbut you would notice the differences when all of these sub carriers are summed together as shown on lower plot. Unfortunately, in reality there is no such an environment in which there is no frequency drift.

Most common sources to cause frequency drift of sub carriers would be 'Fading' and 'Doppler effect'. Try with different values for NoOfCarriers and fnoiseMax and see how the result get different. Cyclic Prefix. Now let's look at the signal in time domain.

Following is an illustraion showing two OFDM symbols in sequence. In ideal case, there is no problem with this signal, but what would happen if the first symbol get delayed a little bit.To overcome the effect of multi path fading problem available in UMTS, LTE uses Orthogonal Frequency Division Multiplexing OFDM for the downlink - that is, from the base station to the terminal to transmit the data over many narrow band careers of KHz each instead of spreading one signal over the complete 5MHz career bandwidth ie. OFDM uses a large number of narrow sub-carriers for multi-carrier transmission to carry data. Orthogonal frequency-division multiplexing OFDMis a frequency-division multiplexing FDM scheme used as a digital multi-carrier modulation method.

OFDM meets the LTE requirement for spectrum flexibility and enables cost-efficient solutions for very wide carriers with high peak rates. The basic LTE downlink physical resource can be seen as a time-frequency grid, as illustrated in Figure below:.

The OFDM symbols are grouped into resource blocks. The resource blocks have a total size of kHz in the frequency domain and 0. Each user is allocated a number of so-called resource blocks in the time. The more resource blocks a user gets, and the higher the modulation used in the resource elements, the higher the bit-rate.

Which resource blocks and how many the user gets at a given point in time depend on advanced scheduling mechanisms in the frequency and time dimensions. The scheduling mechanisms in LTE are similar to those used in HSPA, and enable optimal performance for different services in different radio environments.

The primary 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.

This mechanism also facilitates the design of single frequency networks SFNswhere several adjacent transmitters send the same signal simultaneously at the same frequency, as the signals from multiple distant transmitters may be combined constructively, rather than interfering as would typically occur in a traditional single-carrier system. High PAPR requires expensive and inefficient power amplifiers with high requirements on linearity, which increases the cost of the terminal and drains the battery faster.

SC-FDMA solves this problem by grouping together the resource blocks in such a way that reduces the need for linearity, and so power consumption, in the power amplifier. A low PAPR also improves coverage and the cell-edge performance. Previous Page. Next Page.

Previous Page Print Page. Dashboard Logout.In telecommunicationsorthogonal frequency-division multiplexing OFDM is a type of digital transmission and a method of encoding digital data on multiple carrier frequencies. Chang of Bell Labs in OFDM was improved by Weinstein and Ebert in with the introduction of a guard intervalproviding better orthogonality in transmission channels affected by multipath propagation.

This maintains total data rates similar to conventional single-carrier modulation schemes in the same bandwidth. 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.

## Introduction to OFDM – orthogonal Frequency division multiplexing

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 intersymbol interference ISI and use echoes and time-spreading in analog television visible as ghosting and blurring, respectively to achieve a diversity gaini.

This mechanism also facilitates the design of single frequency networks 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. This is done to overcome errors in mobile communication channels affected by multipath propagation and Doppler effects.

The following list is a summary of existing OFDM-based standards and products. For further details, see the Usage section at the end of the article. The advantages and disadvantages listed below are further discussed in the Characteristics and principles of operation section below. Conceptually, OFDM is a specialized frequency-division multiplexing FDM method, with the additional constraint that all subcarrier signals within a communication channel are orthogonal to one another.

In OFDM, the subcarrier frequencies are chosen so that the subcarriers are orthogonal to each other, meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard bands are not required. This greatly simplifies the design of both the transmitter and the receiver ; unlike conventional FDM, a separate filter for each sub-channel is not required. This stipulates that each carrier frequency undergoes k more complete cycles per symbol period than the previous carrier.

The orthogonality also allows high spectral efficiencywith a total symbol rate near the Nyquist rate for the equivalent baseband signal i.

Almost the whole available frequency band can be used. OFDM generally has a nearly 'white' spectrum, giving it benign electromagnetic interference properties with respect to other co-channel users.

OFDM requires very accurate frequency synchronization between the receiver and the transmitter; with frequency deviation the subcarriers will no longer be orthogonal, causing inter-carrier interference ICI i. Frequency offsets are typically caused by mismatched transmitter and receiver oscillators, or by Doppler shift due to movement.In modulations, information is mapped on to changes in frequency, phase or amplitude or a combination of them of a carrier signal.

OFDM is a combination of modulation and multiplexing. In this technique, the given resource bandwidth is shared among individual modulated data sources. OFDM is a multicarrier modulation technique, which employs several carriers, within the allocated bandwidth, to convey the information from source to destination. OFDM is very effective for communication over channels with frequency selective fading different frequency components of the signal experience different fading.

It is very difficult to handle frequency selective fading in the receiverin which case, the design of the receiver is hugely complex. Instead of trying to mitigate frequency selective fading as a whole which occurs when a huge bandwidth is allocated for the data transmission over a frequency selective fading channelOFDM mitigates the problem by converting the entire frequency selective fading channel into small flat fading channels as seen by the individual subcarriers.

Flat fading is easier to combat compared to frequency selective fading by employing simple error correction and equalization schemes.

In FDM, the given bandwidth is subdivided among a set of carriers. There is no relationship between the carrier frequencies in FDM. For example, consider that the given bandwidth has to be divided among 5 carriers say a,b,c,d,e. There is no relationship between the subcarriers ; a,b,c,d and e can anything within the given bandwidth. The first thing that should be considered in designing the OFDM transmitter is the number of subcarriers required to send the given data. As a generic case, lets assume that we have N subcarriers. Each subcarriers are centered at frequencies that are orthogonal to each other usually multiples of frequencies. The second design parameter could be the modulation format that we wish to use.

Since we assumed that there are N subcarriers allowed for the OFDM transmission, we name the subcarriers from 0 to N Now, the Serial to Parallel converter takes the serial stream of input bits and outputs N parallel streams indexed from 0 to N Lets call this output S 0 ,S 1.

The conversion of parallel data D into the digitally modulated data S is usually achieved by a constellation mapper, which is essentially a look up table LUT. Once the data bits are converted to required modulation format, they need to be superimposed on the required orthogonal subcarriers for transmission.

This is achieved by a series of N parallel sinusoidal oscillators tuned to N orthogonal frequencies f 0 ,f 1 ,…f NHave you ever wondered just "how" OFDM subcarriers are able to be spaced so tightly together without any guard band in-between? Most Wi-Fi textbooks will simply state that the spacing of the subcarriers allows the harmonics to overlap, thus canceling out any interference. OFDM subcarrier spacing creates "nulls" canceling out inter-carrier interference ICI without the need for guard bands or expensive bandpass filters.

OFDM is a form of frequency division multiplexing FDDwhich typically requires guard bands between carriers and specialized hardware with bandpass filters to remove interference.

Each 20 MHz channel, whether it's This spacing is chosen because we use point FFT sampling.

QAM and OFDM Basics

If using a short guard interval of 0. So, as stated earlier, "subcarrier spacing is equal to the reciprocal of symbol time. And this in turn drives the duration of the useful symbol time and is the reason why we use 3. Another advantage of OFDM is that by using a reduced symbol rate ofsymbols per second the negative effects of multipath distortion are reduced. However, multipath also has a negative effect on OFDM, especially when clients are mobile.

The orthogonality of the subcarriers can be lost when movement and multipath are present because signal delays the delay spread impact the reciprocal relationship of the subcarriers and the useful symbol time IFFT. The fix for this is to include a cyclic prefix with each symbol, which is part of the guard interval, that allows channel estimation and equalization.

Thus, contrary to popular belief, the guard interval is actually not empty airtime but actively used for cyclic prefixing to allow proper OFDM operation in a multipath environment. We take a serial data stream and perform parallel data transmission across the frequency domain. Search on any of this any you're likely to end up finding research papers with difficult math equations. OFDM divides a given channel into many narrower subcarriers. This comes about by having the subcarrier spacing equal to the reciprocal of symbol time.

All subcarriers have a complete number of sine wave cycles that upon demodulation will sum to zero.Accordingly, OFDM, Orthogonal Frequency Division Multiplexing is used for many of the latest wide bandwidth and high data rate wireless systems including Wi-Fi, cellular telecommunications and many more. The fact that OFDM uses a large number of carriers, each carrying low bit rate data, means that it is very resilient to selective fading, interference, and multipath effects, as well providing a high degree of spectral efficiency.

Early systems using OFDM found the processing required for the signal format was relatively high, but with advances in technology, OFDM presents few problems in terms of the processing required. The use of OFDM and multicarrier modulation in general has come to the fore in recent years as it provides an ideal platform for wireless data communications transmissions.

However the concept of OFDM technology was first investigated in the s and s during research into methods for reducing interference between closely spaced channels. IN addition to this other requirements needed to achieve error free data transmission in the presence of interference and selective propagation conditions. Initially the use of OFDM required large levels of processing and accordingly it was not viable for general use.

Some of the first systems to adopt OFDM were digital broadcasting - here OFDM was able to provide a highly reliable form of data transport over a variety of signal path conditions.

Once example was DAB digital radio that was introduced in Europe and other countries. OFDM was also used for digital television. Later processing power increased as a result of rising integration levels enabling OFDM to be considered for the 4G mobile communications systems which started to be deployed from around OFDM is a form of multicarrier modulation. An OFDM signal consists of a number of closely spaced modulated carriers. When modulation of any form - voice, data, etc. It is necessary for a receiver to be able to receive the whole signal to be able to successfully demodulate the data.

As a result when signals are transmitted close to one another they must be spaced so that the receiver can separate them using a filter and there must be a guard band between them. This is not the case with OFDM. Although the sidebands from each carrier overlap, they can still be received without the interference that might be expected because they are orthogonal to each another. This is achieved by having the carrier spacing equal to the reciprocal of the symbol period.

To see how OFDM works, it is necessary to look at the receiver. This acts as a bank of demodulators, translating each carrier down to DC. The resulting signal is integrated over the symbol period to regenerate the data from that carrier.

The same demodulator also demodulates the other carriers. As the carrier spacing equal to the reciprocal of the symbol period means that they will have a whole number of cycles in the symbol period and their contribution will sum to zero - in other words there is no interference contribution. One requirement of the OFDM transmitting and receiving systems is that they must be linear. Any non-linearity will cause interference between the carriers as a result of inter-modulation distortion. This will introduce unwanted signals that would cause interference and impair the orthogonality of the transmission.

In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the peaks whilst the average power is much lower and this leads to inefficiency.

### The basics of 5G’s modulation, OFDM

In some systems the peaks are limited. Although this introduces distortion that results in a higher level of data errors, the system can rely on the error correction to remove them.

The traditional format for sending data over a radio channel is to send it serially, one bit after another. This relies on a single channel and any interference on that single frequency can disrupt the whole transmission.