Originally posted Mar 10, 2014
Equalizer math can make a channel “flat” but that may not be what you really want
My previous post on adaptive equalization and OFDM summarized the basics of equalization and the use of a dedicated training sequence in OFDM preambles to configure a receiver’s equalizer. Theoretically, this approach allows the receiver to completely correct for channel frequency response errors in the channel and in the transmit/receive equipment, providing a frequency response that is flat in amplitude and group delay.
Great! Perfectly corrected signals for demodulation! Alas, you know that’s too good to be true, and if the universe worked that way you wouldn’t have much job security. When dealing with a real-world channel and the training sequence recovered at the downstream end, there are good reasons to avoid correcting it to be completely flat.
For example, let’s start with an 802.11a OFDM signal I captured at my desk a while back using a bent paper clip as an antenna, stuck into a BNC adapter.* Using the gating settings I described last time reveals the training sequence as recovered by the receiver.
This gated spectrum measurement of the channel estimation sequence (top) shows the amplitude frequency response of the RF channel at 5.8 GHz in an office environment. The vertical scale is 5 dB/div and the frequency response varies by 12 to 15 dB.
The subcarrier peaks trace out the frequency response of the channel at 5.8 GHz and can be used for corrections in terms of magnitude/phase or I/Q. However, there are limitations in the use of this training sequence, mostly related to noise.
First, note that the channel frequency response varies by about 12 to 15 dB. If the largest subcarriers are used as a reference it means that the smallest ones will be boosted by 12 to 15 dB, and so will the noise associated with those subcarriers. Because these small subcarriers are relatively close to the noise level, the equalizer will give noise power a significant boost. If the effect of multipath were to create a null at some subcarrier frequencies—which it sometimes does—the equalizer would boost the noise at these frequencies even more, effectively replacing modulated subcarriers with noise.
Noise also creates uncertainty in the construction of the equalizer filter. Each received subcarrier from a training sequence represents a very limited amount of energy, acquired over a very short time, and it can be a challenge to construct a good equalizer filter from such limited information. Errors from bad equalization can cause demodulation errors.
There are several ways to mitigate these problems, including intelligent and dynamic limits on the gain of equalizer filters. Filters may be trained progressively over multiple bursts, implementing a kind of averaging function, with a time constant related to how rapidly the channel is expected to change. Clever design of filter construction algorithms may also be effective at sorting subcarrier energy from noise.
Because energy and information are related in this situation, more information may be gathered by training the equalizer on the data signal itself, in addition to the training sequence. This combination of decision feedback and a training sequence will require more processing power, but that is usually not a problem in today’s receivers.
Equalizers, no matter how advanced and well-trained, can’t fix every subcarrier. When modulation fails on one or more subcarriers, coding can come to the rescue by reconstructing missing data from other subcarriers. Systems can even change coding schemes on the fly, to respond to dynamic channel conditions.
Equalization operations can also be useful in troubleshooting. In tools such as the 89600 VSA software, the training method is often selectable for OFDM signals. The equalizer filter can be created from either the training sequence alone or a combination of the training sequence and received data, and the filter can be viewed directly. Switching between these techniques while watching EVM and the equalizer filter can give you insights about channel impairments and system performance.
* Don’t scoff. A paper clip cut to the right length is a pretty good antenna at 5.8 GHz, and using an inexpensive BNC adapter kept me from damaging my analyzer’s expensive input connector.