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Adaptive Equalization and OFDM Demodulation

Blog Post created by benz on Sep 15, 2016

Originally posted Mar 20, 2014

Soothing the sins of the RF channel – and some hardware sins, too

Adaptive equalization has been an important part of wireless for decades and it’s an essential element of modern standards including the various flavors of 802.11 WLAN, LTE and WiMAX. Although the operation of some equalization techniques can be somewhat obscure, they’re usually easy to see in OFDM schemes and simple measurements can be important tools for troubleshooting.

The main idea is to construct a digital filter in a receiver to compensate for frequency-response errors in the channel. The filter can compensate for errors in the transmitter and receiver itself, though the channel errors usually dominate. Here, “adaptive” refers to filters that adjust to the channel frequency response as it changes over time.

Since the modulation is complex (I/Q), these filters perform complex compensation. And because they are digital, the filters are often specified or measured in terms of impulse response rather than frequency response—but the two representations are equivalent.

Some equalizers use decision feedback, adjusting themselves with algorithms based on the demodulated data. However, most equalizers use some form of training sequence, which is a portion of the transmitted signal known to the receiver. In OFDM signals, training sequences are often part of a preamble, at the beginning of a frame, and also contain synchronizing and control information. WLAN signals are an excellent example, as shown in the figure below. This is the same preamble with Sneaky little RF power errors, as discussed in a previous post.

A gated spectrum measurement (top trace) of the first portion of an 802.11n WLAN frame shows the short training sequence, which is primarily used for synchronization and frequency correction. Only every fourth subcarrier—of the system’s normal 52 subcarriers—is transmitted and this subset of subcarriers should all be the same amplitude. The lower trace shows the RF envelope with gate markers.

A gated spectrum measurement (top trace) of the first portion of an 802.11n WLAN frame shows the short training sequence, which is primarily used for synchronization and frequency correction. Only every fourth subcarrier—of the system’s normal 52 subcarriers—is transmitted and this subset of subcarriers should all be the same amplitude. The lower trace shows the RF envelope with gate markers.

The 89600 VSA software is a great tool for understanding signals like this. Its gated spectrum measurements can be configured graphically or by entering the desired gate timing and length. Above, the gate begins at the start of the frame and is 8 µs or two symbols long, matching the signal’s short training sequence. As you can see, the sequence is composed of every fourth subcarrier and the subcarrier amplitudes provide a basic idea of the frequency response.

The OFDM symbols are continuous over the length of a symbol or self-windowing. That allows a uniform or rectangular FFT window to be selected for the gated measurement, providing optimum (narrow) frequency resolution.

Resolution isn’t a problem for the measurement above, but the next element of the preamble—the channel-estimation sequence—is another matter. That sequence is the primary training element for the adaptive equalizer and it contains all of the closely spaced OFDM subcarriers as a way for the receiver to measure the channel in fine-grained detail. Moving the gate window 8 µs to the right yields the measurement below.

A gated spectrum measurement of the channel estimation sequence (top) shows how the OFDM equalizer is trained. The individual subcarriers are transmitted at a lower power than the short training sequence but there are more of them, yielding consistent total power as shown in the RF envelope measurement (bottom).

A gated spectrum measurement of the channel estimation sequence (top) shows how the OFDM equalizer is trained. The individual subcarriers are transmitted at a lower power than the short training sequence but there are more of them, yielding consistent total power as shown in the RF envelope measurement (bottom).

The optimized frequency resolution of the uniform window allows all 52 subcarriers to be resolved and measured, in much the same way a receiver would train its own equalizer.

Note that the total RF power level is constant over the preamble, though there are changes in power statistics due to changing preamble content.

These measurements were made in a vector spectrum mode, and similar ones are available in the 89600 VSA when using demodulation. They’re a useful troubleshooting tool and also powerful for optimizing signal quality because they show how linear errors are corrected. They also allow linear errors to be separated from nonlinear errors, providing insight into which ones are most worth correcting and which ones will be fixed automatically. All sins are not the same!

If you’d like to see what frequency-response errors look like in a real-world environment at short range, see my “hand waving” post and the video link there.

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