JPL's Wireless Communication Reference Website

Chapter: Analog and Digital Transmission. Section: Multi-Carrier Modulation

COFDM performance expectations

contributed by Dusan Matic

The following expectations are based on the research for the digital terrestrial television broadcasting [Zou and Wu].

It should be noted that for the additive white Gaussian channel, COFDM and single carrier modulation have comparable performance. However, the broadcasting channel for HDTV consists of various other impairments: random noise, impulse noise, multipath distortion, fading and interference. Also, at the high end of the UHF band the wavelengths are short (around 0.5 m). Thus, characteristics of these holes and peaks in this band are better modeled by a statistical distribution known as a Rayleigh distribution.

Multipath/fading

It is believed that with properly designed guard interval, interleaving and channel coding, COFDM is capable of handling very strong echoes. The BER improvement, which resulted from the multiple echoes, was indicated by the computer simulations and laboratory demonstrations. With the assumption of withstanding strong multipath propagation, COFDM might allow the use of omni-directional antenna in urban areas and mobile reception where C/N is sufficiently high.

In addition to channel fading, time-variant signals caused by transmitter tower swaying, airplane fluttering and even tree swaying generate dynamic ghosts and consequently produce errors in digital transmission. With its parallel transmission structure as well as the use of trellis coding, COFDM systems might present advantages in fading and time-invariant environments.

Phase noise and jitter

A COFDM system is much more affected by carrier frequency errors. A small frequency offset at the receiver compromises the orthogonality between the subchannels, giving a degradation in a system performance that increases rapidly with frequency offset and with the number of subcarriers. Phase noise and jitter can be influenced by the transmitter up-converter and tuner. A possible solution is the use of pilots which can be used to track phase noise in the demodulation. However, this is done under the penalty of reducing the payload data throughput.

Carrier recovery / Equalization

In the severe channel conditions, such as low C/N, strong interference and fading, COFDM signal must be designed to provide robust carrier recovery. Carrier frequency detection could be one of the biggest limitations in COFDM design. The use of pilots and reference symbols are efficient methods for carrier recovery and subchannel equalization. A pilot can be a sine wave or a known binary sequence. A reference symbol can be a chirp or a pseudo-random sequence.

The two-dimensional (time/frequency) signal feature in COFDM makes pilot and reference symbol insertion very flexible. Pilots can be inserted in frequency-domain (fixed carriers) and reference symbols in the time domain (fixed data packets). Because they are transmitted at the predetermined positions in the signal frame structure, it can be captured in the receiver whenever the frame synchronisation is recovered. In a frequency-selective channel, high correlation between the complex fading envelopes of the pilots and data must be ensured. The appropriate complex correction can be obtained by interpolating among the pilots. Cimini [Cimini] reported that interpolation in real and imaginary parts of the complex fading envelopes outperformed the interpolation in amplitude and phase.

For a single carrier system, equalization is done in the time domain. For a QAM system with a N-tap equalizer, there are about N complex multiplication, or 4N real multiplication-accumulation per input symbol. For a VSB system, its symbol rate needs to be twice that of a QAM system for the same data throughput. Assuming the same echo range as for the QAM system, a 2N-tap equalizer is required, which is a computational complexity of about 2N multiplication-accumulations per input symbol.

For a COFDM system, assuming multipath delay is less than the guard interval, a frequency domain one-tap equalizer could be used for each subchannel to correct the amplitude and phase distortions. This corresponds to 4 real multiplication-accumulations per data symbol. Additionally, the FFT operations requires a computational complexity that is proportional to C*log2M, where M is the size of the FFT and C is the constant between 1.5 to 4 depending on the FFT implementation.

The number of pilots and reference symbols used in a COFDM system determines the trade-off between payload capacity and transmission robustness.

Simulation results indicated that an OFDM system with equalization performed better than that of a single carrier system with a linear equalizer.

Impulse interference

COFDM is more immune to impulse noise than single carrier system, because a COFDM signal is integrated over a long symbol period and the impact of impulse noise is much less than that for single carrier systems. As a matter of fact, the immunity of impulse noise was one of the original motivations for MCM. In a report submitted to the CCITT [Telebit], which presented comparative performance results for asymmetrical duplex V.32 (extended) and multicarrier modems, was shown that the threshold level for the impulse noise, at which errors occur, can be as much as 11 dB higher for MCM than for a single carrier system. Meanwhile, studies indicated that the best approach of impulse noise reduction for OFDM involves a combination of soft and hard error protection.

Peak-to-average ratio

The peak-to-average ratio for a single carrier system depends on the signal constellation and the roll-off factor a of the pulse shaping filter (Gibbs’ phenomenon). For the Grand Alliance 8-VSB system (single-carrier rival for the HDTV broadcast), a =11.5 %. The corresponding peak-to-average power ratio is about 7 dB for 99.99 % of the time.

Theoretically, the difference of the peak-to-average power ratio between a multicarrier system and a single carrier system is a function of the number of carriers as:

where N is the number of carriers. When N=1000, the difference could be 30 dB. However, this theoretical value can rarely occur. Since the input data is well scrambled, the chances of reaching its maximum value are very low, especially when the signal constellation size is large.

Since COFDM signal can be treated as a series of independent and identically distributed carriers, the central limiting theorem implies that the COFDM signal distribution should tend to be Gaussian when the number of carriers, N, is large. Generally, when N>20, which is the case for most of the OFDM systems, the distribution is very close to Gaussian. Its probability of above three times (9.6 dB peak-to-average ratio) of its variance, or average power, is about 0.1 %. For four times of variance, or 12 dB peak-to-average power ratio, it is less than 0.01 %.

It should be pointed out that, for each COFDM subchannel, there is usually no pulse shaping implemented. The peak-to-average power ratio for each subchannel depends only on the signal constellation.

In common practice, signals could be clipped because of limited quantization levels, rounding and truncation during the FFT computation as well as other distribution parameters after D/A conversion. It is safe to say that the Gaussian model can be used as the upper bound for the COFDM signals.

Nonlinear distortion

Since a broadcast transmitter is a nonlinear device, clipping will always happen for COFDM signal. However, clipping of a COFDM signal is similar to the impulse interference on which COFDM systems have strong immunity. Tests show that when clipping occurs at 0.1% of the time, the BER degradation is only 0.1-0.2 dB. Even at 1% of clipping, the degradation is 0.5-0.6 dB. However, the BER performance of COFDM system under nonlinear distortion might not be the decisive factor. When clipping occurs, energy would spill into the adjacent channels. More studies are required in this area. It has been reported that, for an OFDM system, a 9 dB output back-off causes negligible BER degradation and adjacent channel interference. Another study indicated that, for modern solid-state transmitters, a prudent back-off level would be around 6 dB.



JPL's Wireless Communication Reference Website © Dusan Matic, 1999