Orthogonal frequency-division multiplexing (OFDM) has been adopted as the appropriate modulation and multiple-access technique to achieve outstanding system performance with wireless data. WiMAX and LTE are a couple of examples that witness the success of this special multicarrier transmission scheme, allowing them to cope well with mobile radio channel impairments.

Typically, these channels tend to be dispersive and time-variant. Being subdivided into narrow-band orthogonal sub-carriers makes OFDM highly spectrally efficient. Each sub-carrier can easily be recovered using a single-tap equalizer, promoting low complexity receiver implementation. Furthermore, OFDM scheme robustness against time-variant channels is achieved if channel coding is employed. This article discusses OFDM’s waveform parameters as a function of the mobile channel parameters as well as system performance such as throughput.

## OFDM Symbol Construction

Let’s first discuss a typical OFDM symbol construction. A stream with a high data symbol rate is converted into a low rate stream for modulation into M parallel sub-carriers. This M-fold symbol rate decrease makes the symbol duration longer than the channel delay spread, T_{d}. In practice, the M sub-carriers’ modulation is achieved using IFFT. Finally, prior to transmission, a cyclic prefix (CP) is inserted into the resulting time-domain signals, which are now parallel to serial converted. Shown in the figure below is a typical OFDM symbol of duration T_{u} + T_{CP}.

**Figure 1.** OFDM symbol and CP insertion

To avoid inter-symbol interference (ISI) the CP duration has to be longer than the propagation channel delay spread. On the other hand, longer CP will reduce system throughput.

It is also being argued that because of the orthogonality of the sub-carriers, receiver equalization can be accomplished with a single tap equalizer. However, this assumption relies on having the transmitter and receiver operate with exactly the same reference frequency, otherwise inter-carrier interference (ICI) is expected.

## Factors Contributing To Frequency Errors

Frequency errors, which are often referred to as carrier frequency offsets, originate from low-cost oscillators commonly found in mobile phones, which are in turn highly dependent on temperature, load and voltage variations.

Phase noise may also contribute to frequency errors. Even if the frequency error, *f*_{o}, is a fraction of the sub-carrier spacing, ∆*f*, orthogonality can be lost. Therefore OFDM systems can tolerate synchronization error of only a few percent of the sub-carrier spacing.

Doppler shifts,* f*_{d} , will also cause frequency error where the ICI power is a function of the Doppler spread. The sensitivity of the BER depends on the modulation order, so that QPSK modulation can tolerate up to 5% frequency error, whereas 64-QAM requires 1% frequency error as a fraction of the carrier spacing. On the other hand, OFDM reception is not degraded provided that the timing offset is less than T_{CP }– T_{d}. Therefore long delay spread channels pose stringent limitations on timing synchronization, especially if the CP length is insufficient.

The OFDM parameter dimensioning process analyzes the propagation channel characteristics, namely the delay spread, T_{d}, the maximum Doppler frequency, *f*_{d(max)}, and the system capacity/throughput.

As mentioned above, carrier spacing and CP length are tightly related to these channel characteristics. It is worth noting that a longer CP will result in either more energy used per transmitted bit or rate loss. To summarize the following three design criteria can be devised:

## Ideal Baseline Waveform OFDM Parameters

Nutaq’s OFDM reference design implements a QPSK modulation with 64-point FFT over a channel bandwidth of 20 MHz, resulting in subcarrier channel spacing of 312.5 kHz. 48 of the 64 subcarriers are used for data, and 4 as pilots, leaving 12 as guard-band subcarriers. Useful symbol time is 3.2 µsec over a total symbol duration of 4 µsec. These parameters are well adapted to lab environment, with short delay spread.

This combination of parameters makes for an ideal baseline waveform to experiment with, as it does not impose too many constraints on the RF section, while providing a theoretical non-coded throughput capacity of 72 Mbps (in SISO mode). These parameters are closely related to the ones of 802.11a/g, specifically made for indoor and short range communications.

References:

- Heiskala, Juha, and John Terry. 2001.
*OFDM Wireless LANs: A Theoretical and Practical Guide.*SAMS Publishing. - Sankar, Krishna. “Inter Carrier Interference (ICI) in OFDM due to frequency offset” (http://www.dsplog.com/2009/08/08/effect-of-ici-in-ofdm/)
- García, Martín, and Christian Oberli. 2009. “Intercarrier Interference in OFDM: A General Model for Transmissions in Mobile Environments with Imperfect Synchronization.”
*EURASIP Journal on**Wireless Communications and Networking*.**2009**:786040. doi:10.1155/2009/786040. http://jwcn.eurasipjournals.com/content/2009/1/786040 - Nutaq. 2012. “FPGA-based, SISO/MIMO OFDM PHY Transceiver”. https://nutaq.com/products/ofdm-reference-design