Multipath effects-unwanted echoes

In order to understand OFDM, it's best to first understand some of the side effects of transmitting radio signals over the air. In an ideal radio transmission, a transmitter would send out a signal that reaches the receiver in a single direct path, without any indirect paths reflecting off of walls and other objects. In this way, the received signal is an exact copy of the transmitted one. Unfortunately, this is often not the case. In actuality, the radio signal is modified as it passes through the channel (the physical space between the transmitter and the receiver). The transmitted signal can be assaulted with a combination of effects. It can be attenuated, reflected, refracted, and diffracted into many replicas of its original self. On top of all of this, the channel also introduces noise into the signal and can cause a shift in the carrier frequency (known as the Doppler effect) if the transmitter or receiver is moving. With all of these simultaneous effects, it's a wonder that radio transmission systems work as well as they do.

Severe modification of the signal can occur when the transmitted signal is reflected from objects such as walls, furniture, and other indoor objects. Under such circumstances, the transmitted signal may not have a single direct path to the receiver. Rather, there can be a number of different paths, or multipaths, each of which has a different distance to travel from the transmitter to the receiver and thus experiences a different delay. As a result, the signal can have multiple 'echoes' of itself and arrive at the receiver at different moments in time. Thus, from the receiver's point of view, it receives multiple copies of the same signal with many different signal strengths or powers.

The delay spread, tmax, is defined as the maximum time difference between the arrival of the first and last multipath signal seen by the receiver. The delay spread is a function of the transmission environment. Large delay spreads are usually found to be characteristic of large buildings because the distances between the transmitter and reflectors are greater in such large environments. In addition, delay spreads don't show any significant dependencies on the transmission frequency within a certain range. Measurements show similar behavior for frequencies ranging from 800 MHz to 6 GHz. Typical delay spread values for indoor transmission vary from 40 nanoseconds to 200 nanoseconds while outdoor values vary from 1 microsecond to 20 microseconds.

In order to understand the effects of multipath for high-speed data networking, assume that a radio is transmitting a discrete block of digital information-a symbol-every T time intervals. Under such conditions, a given, received symbol can be potentially corrupted by echoes from up to tmax/T previous symbols. This effect is defined as inter-symbol interference (ISI). ISI gets worse-the tmax/T ratio increases-as the transmitted bit rate is increased due to T decreasing. If this ratio becomes too large, correcting for multipath becomes a very complicated problem in the receiver.

The multi-carrier approach

One solution to decrease ISI is to somehow decrease the tmax/T ratio. Since delay spread is a function of the environment and can't be altered by the radio, the only recourse is to increase the transmission interval time T between the transmitted symbols. But this would slow down the transmission and run contrary to the mantra of high speed. OFDM finds a way to satisfy both requirements: instead of transmitting the information using one frequency, or carrier, at an interval of T, OFDM divides the transmission of all data among N different sub-carriers, each with a transmission interval time lengthened by N. Thus, despite the fact that the data rate for each individual sub-carrier has been reduced by a factor of N, the paralleling of N different transmissions means that the overall transmission rate of the system will remain the same.

In addition, the tmax/T ratio, with respect to each sub-carrier, has been decreased to tmax/(T * N). This means that each sub-carrier is now N times more multipath and ISI tolerant. In terms of the IEEE 802.11a and ETSI Hiperlan2 standards, N is equal to 52.

Besides increased immunity to ISI, the parallelism introduced by OFDM also has a benefit of making the transmitted symbol less susceptible to selective frequency fading. Imagine data being transmitted using only a single carrier. If the channel introduces interference at this frequency, the entire transmission can fail. This scenario will have a lesser effect on a multi-carrier system, as only a few of the sub-carriers would be affected. Error correcting codes can then be used to provide redundant information sufficient to restore the information lost in these few erroneous sub-carriers. OFDM systems that employ error-correcting codes to compensate for lost carriers are commonly referred to as COFDM (or Coded OFDM).

Despite the added robustness, OFDM's multi-carrier approach still might not be a cure-all for ISI. Figure 1a illustrates this for one directly received signal (no multipath) and another that has been shifted due to multipath delay, which is now smaller due to addition of the N sub-carriers. The overlapping of the current symbol with a delay previous symbol still produces ISI.

The remedy for this problem is to provide a guard time at the beginning of each transmitted symbol. This guard time acts as a buffer to allow time for multipath signals from the pervious symbol to die away before the information from the current symbol is gathered at the receiver (see Figure 1b). The length of the guard interval, therefore, should be at least equal to the delay spread. Typically, most systems set the guard interval to the maximum allowable delay spread plus some margin for error. For example, a maximum indoor delay spread of 200ns can be more than accommodated by a guard interval of 600ns to 800ns. Of course, the addition of this guard time isn't free since it reduces the net available time for symbol transmission.

The most effective guard period to use for OFDM is most commonly referred to as a cyclic prefix (CP). This is nothing more than a direct copy of the end of the symbol placed at the start of the symbol. The extra symbol length now serves as the guard period. A copy of the symbol is used in order to preserve the orthogonality of the waveform and prevent inter-carrier interference (ICI). Both of these topics will be discussed in the next section.

Where's the orthogonality?

To begin discussion of the orthogonality component of OFDM, it's best to understand the actual signals and waveforms that are generated and sent by the OFDM transmitter. For each sub-carrier, the data to be sent is encoded by a certain modulation scheme. In an OFDM system, the modulation scheme used is usually either phase shift keying (PSK), where the data is represented as different phase offsets of a signal, or quadrature amplitude modulation (QAM), where the data is represented by both different amplitudes and phases.

Once these sets of amplitudes and phase offsets for each sub-carrier are known, they are combined into one composite signal, in the time domain, using an Inverse Fast Fourier Transform (IFFT). The end result of this process is the conversion of individual data bits into a single, time domain signal containing a collection of sub-carriers. All of these sub-carriers together make up one OFDM symbol that is then sent out into the channel. (At the receiver side, the inverse function is performed; most notably, the separation of the sub-carrier signals into individual amplitudes and phase offsets is performed using an FFT.)

The orthogonality comes from the precise relationship between the sub-carriers that make up one OFDM symbol. Figure 2 shows an example of three sub-carriers within one OFDM symbol. In this figure, all sub-carriers have the same phase and amplitude in order to simplify the illustration. Note how:

- Each sub-carrier has exactly an integer number of cycles in a given T time interval. In other words, each sub-carrier frequency is an integer multiple of a base frequency (f1=f0, f2=2*f0, f3=3*f0, etc.).

- The number of cycles in a symbol period of two adjacent sub-carriers differs exactly by one. These properties account for the orthogonality between the sub-carriers and allow, simplistically, each sub-carrier to be received and to have its data bits demodulated independently and free from any interference from any other present sub-carrier.

The above two properties account for the orthogonality between the sub-carriers. Simplistically, they allow each sub-carrier to be received and to have its data bits demodulated independently and free from any interference from any other present sub-carrier. Another, more often quoted, way to view this orthogonality is seen in Figure 3. Here is an equivalent representation of Figure 2 in the frequency domain. Each sub-carrier's frequency spectrum is represented by a sinc function, one of whose properties is to peak at its center frequency and go to zero at all integer multiplies of this frequency. The OFDM receiver can effectively demodulate each sub-carrier because, at the peaks of each of these sinc functions, the contributions from other sub-carrier sinc functions are zero. Notice how all of the sub-carriers are packed very tightly against one another. The sub-carriers don't have an extra buffer between them. This allows a very efficient use of the frequency spectrum-a fact that should not go unnoticed by the designer.

At this point OFDM, orthogonality is introduced without the presence of any multipath effects. Will the presence of multipath derail OFDM's orthogonality qualities? The answer is no as long as guard time is implemented using CP (and the multipath delay is within the guard time). A delayed sub-carrier with CP still satisfies the orthogonality condition previously mentioned. However, the delayed sub-carrier without CP doesn't. This latter condition leads to the ICI phenomenon. This means that as each received sub-carrier is being demodulated, it will encounter some interference from another carrier because, within the FFT interval, there is no integer number of cycles between the two sub-carriers.

It's therefore evident that for orthogonality to be preserved, the OFDM sub-carriers must have guard times with CP and their precise inter-relationships carefully controlled or synchronized.

On your mark, get set, synchronize

In an OFDM system, the sub-carriers are perfectly orthogonal if they all have an integer number of cycles within the FFT interval. If there is a frequency offset, then the number of cycles in the FFT interval will no longer be an integer, and will thus result in ICI. Frequency offsets occur because the signal to be transmitted is usually not done at low baseband frequencies. Rather, it's modulated with a higher radio frequency (at 5 GHz in the IEEE 802.11a and ETSI Hiperlan2 standards). Manufacturing tolerances of the components that make up the transmitter and receiver are usually large enough that there can be a significant frequency error between the transmitter and receiver. In many cases this deviation is too large for reliable data transmission and must, therefore, be estimated and compensated.

For a 5-GHz OFDM system with sub-carrier spacing of 300 KHz and a negligible degradation of 0.1 dB, the maximum tolerable frequency offset is less than 1 percent of the sub-carrier spacing. This means that the oscillator frequency needs to be about 3 KHz or 0.6 ppm (parts per million) of the 5-GHz carrier. Most oscillators will not be able to meet this requirement. As such, a frequency synchronization technique needs to be applied before the FFT.

Similarly, timing synchronization is also needed. Before the OFDM receiver can demodulate the sub-carriers, it has to find out where the symbol boundaries are. This information is used to synchronize the receiver and transmitter time scales. This is essential for the proper removal of the CP and to ensure proper duration of the FFT interval.

Another related timing synchronization issue involves the need to perform sampling-clock synchronization.

At the transmitter, the signal produced by the IFFT will be converted into an analog signal with a certain time interval (sampling interval) between each value. After the signal is received, it's down converted. This signal is then sampled in order to obtain a discrete time signal for subsequent digital processing. These sampling times in the receiver must match very closely with those of the transmitter in order to avoid performance degradation.

The finish line

In order to perform frequency and timing synchronization, OFDM systems use special training symbols that are sent from the transmitter and compared to their known values at the receiver. Depending on the outputs of this comparison, desired timing and frequency offset information is obtained.

The international adoption of an OFDM modulation mechanism in new 5-GHz wireless standards allows fast and reliable data transmission capabilities. Paralleling this development are the continuous improvements in speed of standard, high volume CMOS technologies.

Designers are no longer handcuffed to exotic technologies such as gallium arsenide (GaAs) and silicon germanium (SiGe).

The availability of high-speed CMOS processes allows increased system integration and low manufacturing costs. Overall, the simultaneous pairing of a reliable transmission mechanism and low cost CMOS fabrication will fundamentally change the way people think about wireless networking technology. It will enable chipsets implementing these new standards to be ubiquitous in various Internet access devices and at "access points" in the home, enterprise, and public places. Finally, the promise of a high-speed, true Internet experience will become a reality.

James C. Chen, Ph.D. is the product manager for Atheros Communications (Sunnyvale, CA).

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