OFDM Uncovered Part 2: Design Challenges
As designers begin turning to orthogonal frequency division multiplexing (OFDM) in system architectures, they will quickly realize that implementing this modulation scheme is not an easy task. Specifically, engineers are quickly learning that while ODFM provides some nice advantages to a wireless architecture, it also comes equipped with some design and implementation headaches.
This is the second part in our two-part series on OFDM design. In Part 1, we looked at the basic OFDM structure and multipath distortion. Now, we'll explore some of the design challenges engineers will face when implementing OFDM in a wireless system design.
Quick OFDM Overview
An OFDM signal is basically a bundle of narrowband carriers transmitted in parallel at different frequencies from the same source. Since a single stream of data is split up to individually modulate these multiple carriers, OFDM systems are sometimes referred to as multi-carrier systems in order to contrast them with the classic systems that modulate a single carrier.
The individual carriers in OFDM, commonly called subcarriers, are carefully spaced in frequency so that they are orthogonal and therefore do not interfere with each other. Since they do not interfere with each other even in the presence of multipath, the receiver needs only to implement a matched filter for each subcarrier in order to separate out the signals.
Implementing a matched filter for each subcarrier might sound complex at first glance particularly as the number of subcarriers gets large. However, the actual implementation of the matched filters can be greatly simplified by taking advantage of the well-known Fast Fourier transform (FFT).
To further enhance performance, OFDM symbols are protected from inter-symbol interference (ISI) by adding a redundant symbol extension called a guard interval. The guard interval is designed to buffer and absorb all the ISI from preceding symbols. Since the guard interval is redundant, it can be discarded at the receiver and the ISI will be eliminated. The combination of the narrowband orthogonal subcarriers with the ISI-absorbing guard interval make OFDM receivers robust to multipath distortion without the necessity of complex signal processing.
While the overall design of an OFDM system is simplified because of its robustness to multipath, there are several design issues that must be addressed in order to realize these advantages. At high data rates, these issues are minor compared to the multipath problem that single carrier systems face but they must be dealt with in order to realize the full power of OFDM as a modulation scheme. In this paper, we will focus on the impact that frequency offset, phase noise, and peak-to-average ratio (PAR) have on the performance and design of an OFDM-based wireless communications system.
One of the biggest challenges inherent in an OFDM design is removing frequency offset. Frequency offset can occur when the voltage-controlled oscillator (VCO) at the receiver is not oscillating at exactly the same carrier frequency as the VCO in the transmitter. For the receiver, this offset between the two VCOs is seen as frequency translation in the signal and can lead to an increase in the error rate. While this is generally true for all modulations, OFDM is particularly sensitive to frequency offsets.
What makes OFDM sensitive to frequency offset? Remember that OFDM receivers use the FFT to implement filters matched to each subcarrier. When there is no frequency offset, the matched filters line up perfectly with the received signal and there is no interference between the subcarriers at the matched filter output.
However, as illustrated by Figure 1, the presence of a frequency offset means that the received signal is shifted in frequency and as a result the matched filters are offset from the received signal. Consequently, energy from adjacent subcarriers will seep into each matched filter output. In other words, from the receiver's viewpoint, the subcarriers are no longer orthogonal. This leads to inter-carrier interference (ICI) as each of the subcarriers interferes with other subcarriers. If ICI is ignored in the system design, the error rate of OFDM can degrade rapidly.
Fortunately, there are many simple techniques for estimating and removing frequency offset. For example, packet-based systems like IEEE 802.11a usually contain a training sequence at the beginning of the packet that is specifically designed to aid the receiver in estimating the amount of offset between the transmitter and the receiver. Once the offset is known, it can be removed by adjusting the frequency of the VCO either in analog or digital hardware. Alternatively, OFDM systems can adaptively estimate the frequency offset on the basis of the received sequence.
Whichever technique is used, a reliable estimate of the frequency offset is very important for good OFDM system design.
Phase Noise Issues
In addition to the constant frequency offset discussed above, the frequency generated by a practical VCO tends to jitter, or vary, over time. To the receiver, this frequency variation looks like noise in the phase of the received signal and as a result this impairment is referred to as phase noise.
In many cases, the variation is slow relative to the signal and the receiver can track and remove the resulting phase noise by using a phase-lock loop (PLL). For OFDM systems, the design of the PLL can be simplified by inserting training data into the symbol stream.
The use of training symbols is common in single carrier systems as well, however with OFDM, there are some subtle differences. Unlike single carrier systems where training symbols are inserted periodically in time, every OFDM symbol contains a few subcarriers that are modulated with the known training data. These training subcarriers are usually referred to as pilot tones.
For example, the IEEE 802.11a standard uses 4 of the 52 subcarriers as pilot tones. In IEEE 802.11a, the pilot tones are modulated with a binary phase-shift keying (BPSK) sequence that is known by the receiver. Since the modulation sequence is known, these pilot tones can be used to track phase variations due to VCO variations, thus allowing IEEE 802.11a receivers to remove a majority of the phase noise seen at the receiver.
PAR for the Course
Another challenge OFDM designers face is accommodating the large dynamic range of the signal. This large dynamic range, or as it is often called a large peak-to-average ratio (PAR), means that the OFDM signal has a large variation between the average signal power and the maximum (or minimum) signal power.
A large dynamic range is inherent to multi-carrier modulations since each subcarrier is essentially independent. As a result, the subcarriers can add constructively and destructively and this creates the potential for a large variation in the signal power. In other words, it is possible for the data sequence to make all the subcarriers align constructively and sum to a very large signal. It is also possible for the data sequence to make all the subcarriers align destructively and sum to a very small signal. This wide variation creates a number of problems for both transmitter and receiver design because it requires both to accommodate a large range of signal power with a minimum of distortion.
The large dynamic range of OFDM systems presents a particular challenge for the power amplifier (PA) design. Practical PAs have both linear and non-linear regions where the non-linear regions occur for large output powers (i.e., near saturation). To minimize the amount of distortion and to reduce the amount of out-of-band energy generated by the transmitter, OFDM and other modulations need to operate as much as possible in the linear region. With its' inherently large dynamic range, this means that OFDM must keep its average power well below the non-linear region in order to accommodate the signal power peaks.
However, lowering the average power hurts the efficiency and range since it corresponds to lower output power for the majority of the signal in order to accommodate the infrequent peaks. As a result, OFDM designers must make a careful trade between distortion and output power. That is, they must choose an average input level that generates sufficient output power and yet does not introduce too much interference or violate any spectral constraints.
To examine this tradeoff further, consider the IEEE802.11a version of OFDM that used 52 subcarriers. In theory, all 52 subcarriers could add constructively and this would yield a peak power that is 10log(52) = 17.2 dB above the average power. However, this is an extremely rare event.
Instead, most simulations show that for real PAs, accommodating a peak that is 3 to 6 dB above average is sufficient. The exact value is highly dependent on the PA characteristics and the other distortions in the transmitter. In other words, the distortions caused by peaks above this range are infrequent enough to allow for low average error rates.
Is it possible to control the PAR of OFDM? Because the PAR of OFDM contributes to the complexity and cost, many researchers have focused on methods for controlling this problem and a number of elegant solutions have emerged.
One interesting class of approaches reduces PAR by constraining the modulation sequences for the subcarriers. In other words, the subcarriers are no longer independent but rather have a defined phase and amplitude relationship that is selected to keep the PAR small.
Along these lines, special block codes have been developed that generate low PARs. Using these special block codes as the subcarrier modulation rather than allowing the data to modulate the subcarriers directly can significantly reduce the peak-to-average ratio. In addition to reducing PAR, these block codes add an additional layer of error correcting capability to the system.
Another simple method for handling PAR is to limit the peak signals either by clipping or by replacing peaks with a smooth but lower amplitude pulse. Since this modifies the signal artificially, it does increase the distortion to some degree. However, it is done in a controlled fashion and generally limits the PA induced distortion. As a result, it can in many cases improve the overall output power.
For packet-based networks where the receiver can request a retransmission of any packet with uncorrectable errors, another simple but effective technique is to rely on a scramble sequence to control PAR on retransmission. In other words, the data is scrambled prior to modulating the subcarriers. This alone does not prevent large peaks and there will still be occasions when the transmitter introduces significant distortion due to a large peak power in the packet. When the distortion is severe, the receiver will not correctly decode the packet and will request a retransmission.
When the data is retransmitted however, the scramble sequence is changed. If the first scramble sequence caused a large PAR, the second sequence is extremely unlikely to do the same despite the fact that it contains the same data sequence.
Since IEEE 802.11a networks use packet retransmissions already, this technique is used to mitigate some of the problems with PAR. The downside to this technique is that it does impact the network throughput because some of the data sequences must be transmitted twice
This wraps up the second part in our two-part series. As can be seen in this article, the design challenges for OFDM include reducing the inherent frequency offset, controlling and tracking the phase noise, and designing the system to handle or control the peak-to-average ratio. While these are significant challenges, there are a number of fairly simple techniques for solving these problems.
Editor's Note: To view part 1 of this article, Click Here.
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 firstname.lastname@example.org.
Karen Halford is a stay-at-home mom that sometimes doubles as a consultant in the design and analysis 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 email@example.com.