## An Overview of OFDM

OFDM has been the accepted standard for digital TV broadcasting for more than a decade. European DAB and DVB-T standards use OFDM. HIPERLAN 2 standard is also using OFDM techniques and so is the 5 GHz extension of IEEE 802.11 standard. ADSL and VDSL use OFDM. More recently, IEEE 802.16 has standardized OFDM for both Fixed and Mobile WiMAX. The cellular world is not left behind either with the evolving LTE embracing OFDM. What is it about OFDM that makes a compelling case for widespread adoption in new standards?

**Inter-symbol Interference (ISI)**

One fundamental problem for communication systems is ISI. It is a fact that every transmission channel is time-variant. Two adjacent symbols are likely to experience different channel characteristics including time delays. This is particularly true in wireless channels and mobile terminals communicating in multipath conditions. For low bit rates (narrowband signal), the symbol rate is sufficiently long so that delayed versions of the signal all arrive with the same symbol. They do not spill over to subsequent symbols and therefore there is no ISI. As data rates go up and/or the channel delay increases (wideband signal), ISI starts to occur. Traditionally, this has been overcome by equalization techniques, linear predictive filters and rake receivers. This involves estimating the channel conditions. This works well if the number of symbols to be considered is low. Assuming BPSK, a data rate of 10 Mbps on a channel with a maximum delay of 10 µs would need equalization over 100 symbols. This would be too complex for any receiver.

In HSDPA, data rate is as high as 14.4 Mbps. But this uses QAM16 and therefore the baud rate is not as high. Using a higher level modulation requires better channel conditions and a higher transmit power for correct decoding. HSDPA also uses multicode transmission which means that not all of the data is carried on a single code. The load is distributed on the physical resources thus reducing ISI further. Today the need is for even higher bit rates. A higher modulation scheme such as QAM64 may be employed but this would require higher transmission power. What could be a possible solution for solving the ISI problem at higher bit rates?

**Orthogonal Frequency Division Multiplexing (OFDM)**

Initial proposals for OFDM were made in the 60s and the 70s. It has taken more than a quarter of a century for this technology to move from the research domain to the industry. The concept of OFDM is quite simple but the practicality of implementing it has many complexities. A single stream of data is split into parallel streams each of which is coded and modulated on to a subcarrier, a term commonly used in OFDM systems. Thus the high bit rates seen before on a single carrier is reduced to lower bit rates on the subcarrier. It is easy to see that ISI will therefore be reduced dramatically.

This sounds too simple. When didn’t we think of this much earlier? Actually, FDM systems have been common for many decades. However, in FDM, the carriers are all independent of each other. There is a guard period in between them and no overlap whatsoever. This works well because in FDM system each carrier carries data meant for a different user or application. FM radio is an FDM system. FDM systems are not ideal for what we want for wideband systems. Using FDM would waste too much bandwidth. This is where OFDM makes sense.

In OFDM, subcarriers overlap. They are orthogonal because the peak of one subcarrier occurs when other subcarriers are at zero. This is achieved by realizing all the subcarriers together using Inverse Fast Fourier Transform (IFFT). The demodulator at the receiver parallel channels from an FFT block. Note that each subcarrier can still be modulated independently. This orthogonality is represented in Figure 1 [1].

**Figure 1: OFDM Subcarriers in Frequency Domain**

Ultimately ISI is conquered. Provided that orthogonality is maintained, OFDM systems perform better than single carrier systems particularly in frequency selective channels. Each subcarrier is multiplied by a complex transfer function of the channel and equalising this is quite simple.

**Basic Considerations**

An OFDM system can experience fades just as any other system. Thus coding is required for all subcarriers. We do get frequency diversity gain because not all subcarriers experience fading at the same time. Thus a combination of coding and interleaving gives us better performance in a fading channel.

Higher performance is achieved by adding more subcarriers but this is not always possible. Adding more subcarriers could lead to random FM noise resulting in a form of time-selective fading. Practical limitations of transceiver equipment and spectrum availability mean than alternatives have to be considered. One alternative is to add a **guard band** in the time domain to allow for multipath delay spread. Thus, symbols arriving late will not interfere with the subsequent symbols. This guard time is a pure system overhead. The guard time must be designed to be larger than the expected delay spread. Reducing ISI from multipath delay spread thus leads to deciding on the number of subcarriers and the length of the guard period. Frequency-selective fading of the channel is converted to frequency-flat fading on the subcarriers.

Since orthogonality is important for OFDM systems, synchronization in frequency and time must be extremely good. Once orthogonality is lost we experience **inter-carrier interference** (ICI). This is the interference from one subcarrier to another. There is another reason for ICI. Adding the guard time with no transmission causes problems for IFFT and FFT, which results in ICI. A delayed version of one subcarrier can interfere with another subcarrier in the next symbol period. This is avoided by extending the symbol into the guard period that precedes it. This is known as a **cyclic prefix**. It ensures that delayed symbols will have integer number of cycles within the FFT integration interval. This removes ICI so long as the delay spread is less than the guard period. We should note that FFT integration period excludes the guard period.

**Advanced Techniques**

Although subcarriers are orthogonal, a rectangular pulse shaping gives rise to a sinc shape in the frequency domain. Side lobes delay slowly producing out-of-band interference. If frequency synchronization error is significant, this can result in further degradation of performance due to these side lobes. The idea of **soft pulse shaping** has been studied such as using Gaussian functions. Although signal decays rapidly from the carrier frequency, the problem is that orthogonality is lost. ISI and ICI can occur over a few symbols. Therefore equalization must be performed. There are two advantages - equalization gives diversity gain and soft impulse shaping results in more robustness to synchronization errors. However, diverisy gain be obtained with proper coding and out-of-band interference can be limited by filtering. Thus, the technique of channel estimation and equalization seems unnecessary for OFDM systems [2].

**Frame and time synchronization** could be achieved using zero blocks (no transmission). Training blocks could be used. Periodic symbols of known patterns could be used. These serve to provide a rough estimate of frame timing. The guard period could be used to provide more exact synchronization. **Frequency synchronization** is important to minimize ICI. Pilot symbols are used to provide an estimate of offsets and correct for the same. Pilot symbols are used where fast synchronization is needed on short frames. For systems with continuous transmission, synchronization without pilot symbols may be acceptable if there is no hurry to get synchronized.

One of the problems of OFDM is a high **peak-to-average ratio**. This causes difficulties to power amplifiers. They generally have to be operated at a large backoff to avoid out-of-band interference. If this interference is to be lower than 40 dB below the power density in the OFDM band, an input backoff of more than 7.5 dB is required [2]. Crest factor is defined as the ratio of peak amplitude to RMS amplitude. **Crest factor reduction** (CFR) techniques exist so that designers are able to use a cheaper PA for the same performance. Some approaches to CFR are described briefly below:

- Only a subset of OFDM blocks that are below an amplitude threshold are selected for transmission. Symbols outside this set are converted to the suitable set by adding redundancy. These redundant bits could also be used for error correction. In practice, this is method is practical only for a few subcarriers.
- Each data sequence can be represented in more than one way. The transmitter choses one that minimises the amplitude. The receiver is indicated of the choice.
- Clipping is another technique. Used with oversampling, it causes out-of-band interference which is generally removed by FIR filters. These filters are needed anyway to remove the side lobes due to rectangular pulse shaping. The filter causes new peaks (passband ripples) but still peak-to-average power ratio is reduced.
- Correcting functions are applied to the OFDM signal where peaks are seen while keep out-of-band interference to a minimum. If many peaks are to be corrected, then entire signal has to be attenuated and therefore performance cannot be improved beyond a certain limit. A similar correction can be done by using a additive function (rather than multiplicative) with different results.

One of the problems of filtering an OFDM signal is the passband ripple. It is well-known in filter design theory that if we want to minimize this ripple, the number of taps on the filter should be increased. The trade-off is between performance and cost-complexity. A higher ripple leads to higher BER. Ripple has a worse effect in OFDM systems because some subcarriers get amplified and others get attenuated. One way to combat this is to equalize the SNR across all subcarriers using what is called **digital pre-distortion** (DPD). Applying DPD before filtering increases the signal power and hence out-of-band interference. The latter must be limited by using a higher attenuation outside the passband as compared to a system without predistortion. The sequence of operations at the transmitter would be as represented in Figure 2.

**Figure 2: Typical OFDM Transmitter Chain**

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