# OFDM Uncovered Part 1: The Architecture

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Over the past several years, orthogonal frequency division multiplexing (OFDM) has received considerable attention from the general wireless community and in particular from the wireless LAN (WLAN) standards groups. Groups such as IEEE802.11a and ETSI BRAN have selected OFDM as the best waveform for providing reliable high data rates for WLANs. This popularity is further highlighted by the recent selection of OFDM by the IEEE 802.11g committee as the modulation for extending the data rates of the very successful IEEE 802.11b or Wi-Fi WLAN standard.

What makes OFDM such a popular choice? The primary reason is that OFDM is intrinsically able to handle the most common distortions found in the wireless environment without requiring complex receiver algorithms. As it turns out, the wireless environment and, in particular, the WLAN environment presents a harsh channel for communications. Conventional modulation methods suffer from multipath in both the frequency domain and the time domain. In the frequency domain, multipath causes groups of frequencies to be attenuated and shifted in phase relative to each other which severely distorts the symbol. In the time domain, multipath basically smears adjacent symbols into each other. Many typical systems overcome these problems with expensive adaptive filters.

OFDM, on the other hand, uses groups of narrowband signals to pierce through this environment and employs a guard interval between symbols in order to counter the inherent time domain smearing. This allows OFDM systems to use lower complexity receivers and still maintain robust performance. In short, OFDM is a popular choice because it delivers robust performance in multipath without the need for complex receiver algorithms.

As with any waveform, OFDM has both advantages and disadvantages, but in many of the modern wireless applications, the disadvantages of OFDM can be overcome with careful design choices. Consequently, OFDM is frequently the best fit when optimizing cost and performance for wireless environments like WLAN's where multipath is the primary impairment to reliable communications.

In Part 1 of this series, we'll describe OFDM and detail the characteristics that make it well suited for WLAN and other wireless communication systems. In part 2, which will appear next week, we'll highlight some of the design issues required to implement OFDM like control of phase noise, peak-to-average ratio, and frequency offsets.

**The OFDM Bundle**

An OFDM signal is basically a bundle of narrowband carriers transmitted in parallel at different frequencies from the same source. In fact, this modulation scheme is often termed "multicarrier" as opposed to conventional "single carrier" schemes.

Each individual carrier, commonly called a subcarrier, transmits information by modulating the phase and possible the amplitude of the subcarrier over the symbol duration. That is, each subcarrier uses either phase-shift-keying (PSK) or quadrature-amplitude-modulation (QAM) to convey information just as conventional single carrier systems.

However, OFDM or multi-carrier systems use a large number of low symbol rate subcarriers. The spacing between these subcarriers is selected to be the inverse of the symbol duration so that each subcarrier is orthogonal or non-interfering. This is the smallest frequency spacing that can be used without creating interference.

At first glance it might appear that OFDM systems must modulate and demodulate each subcarrier individually. Fortunately, the well-known Fast Fourier transform (FFT) provides designers with a highly efficient method for modulating and demodulating these parallel subcarriers as a group rather than individually.

As shown in **Figure 1a**, an efficient OFDM implementation converts a serial symbol stream of PSK or QAM data into a size *M* parallel stream. These *M* streams are then modulated onto *M* subcarriers via the use of size *N (N ≤M)* inverse FFT. The *N* outputs of the inverse FFT are then serialized to form a data stream that can then be modulated by a single carrier. Note that the *N*-point inverse FFT could modulate up to *N* subcarriers. When *M* is less than *N*, the remaining *N -- M* subcarriers are not in the output stream. Essentially, these have been modulated with amplitude of zero. The IEEE802.11a standard for example specifies that 52 (*M* = 52) out of 64 (*N* = 64) possible subcarriers are modulated by the transmitter.

*Figure 1a: Block diagram of a simple OFDM transmitter.*

*Click here for larger version of Figure 1a*

Although it would seem that combining the inverse FFT outputs at the transmitter would create interference between subcarriers, the orthogonal spacing allows the receiver to perfectly separate out each subcarrier. **Figure 1b** illustrates the process at the receiver. The received data is split into *N* parallel streams that are processed with a size *N* FFT. The size *N* FFT efficiently implements a bank of filters each matched to the *N* possible subcarriers. The FFT output is then serialized into a single stream of data for decoding. Note that when *M* is less than *N*, in other words there are fewer than *N* subcarriers are used at the transmitter, the receiver only serialized the *M* subcarriers with data.

*Figure 1b: Block diagram of a simple OFDM receiver.*

*Click here for larger version of Figure 1b*

**Multipath Challenges**

In an OFDM-based WLAN architecture, as well as many other wireless systems, multipath distortion is a key challenge. This distortion occurs at a receiver when objects in the environment reflect a part of the transmitted signal energy. **Figure 2** illustrates one such multipath scenario from a WLAN environment.

*Figure 2: Multipath reflections, such as those shown here, create ISI problems in OFDM receiver designs.*

*Click here for larger version of Figure 1b*

Multipath reflected signals arrive at the receiver with different amplitudes, different phases, and different time delays. Depending on the relative phase change between reflected paths, individual frequency components will add constructively and destructively. Consequently, a filter representing the multipath channel shapes the frequency domain of the received signal. In other words, the receiver may see some frequencies in the transmitted signal that are attenuated and others that have a relative gain.

In the time domain, the receiver sees multiple copies of the signal with different time delays. The time difference between two paths often means that different symbols will overlap or smear into each other and create inter-symbol interference (ISI). Thus, designers building WLAN architectures must deal with distortion in the demodulator.

Recall that OFDM relies on multiple narrowband subcarriers. In multipath environments, the subcarriers located at frequencies attenuated by multipath will be received with lower signal strength. The lower signal strength leads to an increased error rate for the bits transmitted on these weakened subcarriers.

Fortunately for most multipath environments, this only affects a small number of subcarriers and therefore only increases the error rate on a portion of the transmitted data stream. Furthermore, the robustness of OFDM in multipath can be dramatically improved with interleaving and error correction coding. Let's look at error correction and interleaving in more detail.

**Error Correction and Interleaving**

Error correcting coding builds redundancy into the transmitted data stream. This redundancy allows bits that are in error or even missing to be corrected.

The simplest example would be to simply repeat the information bits. This is known as a repetition code and, while the repetition code is simple in structure, more sophisticated forms of redundancy are typically used since they can achieve a higher level of error correction. For OFDM, error correction coding means that a portion of each information bit is carried on a number of subcarriers; thus, if any of these subcarriers has been weakened, the information bit can still arrive intact.

Interleaving is the other mechanism used in OFDM system to combat the increased error rate on the weakened subcarriers. Interleaving is a deterministic process that changes the order of transmitted bits. For OFDM systems, this means that bits that were adjacent in time are transmitted on subcarriers that are spaced out in frequency. Thus errors generated on weakened subcarriers are spread out in time, i.e. a few long bursts of errors are converted into many short bursts. Error correcting codes then correct the resulting short bursts of errors.

**Handling ISI**

The time-domain counter part of the multipath is the ISI or smearing of one symbol into the next. OFDM gracefully handles this type of multipath distortion by adding a "guard interval" to each symbol. This guard interval is typically a cyclic or periodic extension of the basic OFDM symbol. In other words, it looks like the rest of the symbol, but conveys no 'new' information.

Since no new information is conveyed, the receiver can ignore the guard interval and still be able to separate and decode the subcarriers. When the guard interval is designed to be longer than any smearing due to the multipath channel, the receiver is able to eliminate ISI distortion by discarding the unneeded guard interval. Hence, ISI is removed with virtually no added receiver complexity.

It is important to note that discarding the guard interval does have an impact on the noise performance since it reduces the amount of energy available at the receiver for channel symbol decoding. In addition, it reduces the data rate since no new information is contained in the added guard interval. Thus a good system design will make the guard interval as short as possible while maintaining sufficient multipath protection.

Why don't single carrier systems also use a guard interval? Single carrier systems could remove ISI by adding a guard interval between each symbol. However, this has a much more severe impact on the data rate for single carrier systems than it does for OFDM. Since OFDM uses a bundle of narrowband subcarriers, it obtains high data rates with a relatively long symbol period because the frequency width of the subcarrier is inversely proportional to the symbol duration. Consequently, adding a short guard interval has little impact on the data rate.

Single carrier systems with bandwidths equivalent to OFDM must use much shorter duration symbols. Hence adding a guard interval equal to the channel smearing has a much greater impact on data rate.

**Wrap up on Part 1**

In conclusion, OFDM is extremely well suited for wireless communication in environments where multipath is a major source of distortion such as that found in typical WLAN deployments. The combination of multiple narrow subcarriers with interleaving and error correction coding allows OFDM to perform well in multipath while the guard interval gives the receiver an extremely simple method for eliminating ISI. These built in waveform features allow for the design of reliable, high-rate digital wireless communications systems without the complexity that would be required by conventional single carrier systems.

That wraps up Part 1 of this series. In part 2, which will appear on CommsDesign.com next week, we'll look at some of the design challenges for implementing OFDM in a wireless system architecture.

**About the Authors**

**Steve Halford** is currently a systems engineer for Intersil's Prism Wireless Products group. Steve received B.S. and M.S. degrees in electrical engineering from the Georgia Institute of Technology and a Ph.D. degree in electrical engineering from the University of Virginia. He can be reached at shalford@intersil.com.

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Karen Halford is a stay-at-home mom that sometimes doubles as a consultant in the design and analysis of communications systems. Karen received B.S. and M.S. degrees from the Georgia Institute of Technology and a Ph.D. degree from the University of Virginia in the field of electrical engineering. Karen can be reached at khalford.ee88@gtalumni.org.*