Need for equalization and basic technique

Need for equalization

In mobile channels the transmitted signal arrives over many paths with different delays. When the delay spread is comparable to or larger than the symbol period (or the signal bandwidth exceeds the coherence bandwidth), each symbol overlaps the following symbols. This is inter-symbol interference (ISI). ISI causes:

• High, irreducible bit error rate that cannot be cured by raising power.
• A limit on the maximum data rate of the link.

Equalization is needed to compensate for this ISI (and for band-limited, frequency-selective channels) so that high data rates can be sent reliably.

Basic equalization technique

The equalizer is a filter at the receiver whose response is the inverse of the channel. If f(t) is the combined impulse response of transmitter, channel and receiver RF/IF, and h_eq(t) is the equalizer's, the target is

f(t) * h_eq(t) = δ(t), i.e. F(f) · H_eq(f) = 1

so the overall response is flat and ISI-free.

 x(t)->[Modulator]->[Channel f(t)]->(+)->[Rx RF/IF]
                                     ^        |
                                   n(t)       v y(t)
            +-----------------+       +-------------+
 d~(k) <----| Decision device |<------| Equalizer   |
    |       +-----------------+ d^(k) | h_eq(t)     |
    |                                 +-------------+
    +--> e(k) = d(k) - d^(k) --> adjust taps --^

Steps

1. Training: a known training sequence is sent first. The equalizer compares its output with the known symbols and adjusts its taps (e.g. by LMS) to minimise the error.
2. Tracking: user data follows; the equalizer uses its own decisions to keep adjusting as the channel changes.
3. The training is repeated periodically, e.g. each TDMA time slot.

Structure: the most basic form is a linear transversal (FIR) equalizer: a tapped delay line with delays T and tap weights wₖ:

d̂(k) = Σₙ wₙ · y(k − n)

Non-linear types (decision feedback equalizer, MLSE) are used when the channel has deep spectral nulls.