Also known as: intersymbol interference, ISI
Intersymbol interference (ISI) is the corruption of a digital symbol by energy that has smeared in from adjacent symbols, so that the value sampled at one symbol instant no longer depends only on the symbol sent then.1 It arises whenever the channel or filtering spreads each pulse in time — from bandlimiting, from imperfect pulse shaping, or from multipath echoes — and it is a leading cause of bit errors in a receiver that is otherwise seeing plenty of signal.
How it works
Every symbol is sent as a pulse, and a real pulse is never a perfect spike — it has tails that extend before and after its peak. If those tails are still non-zero at the instant a neighboring symbol is sampled, the neighbor’s decision is biased by this symbol, and vice versa: the samples become a weighted sum of many transmitted symbols rather than one. Harry Nyquist showed the condition that avoids this: a pulse whose overall (transmit-times-receive) response passes through zero at every other symbol instant contributes nothing at neighboring sampling times, even though it is non-zero in between. The raised-cosine family satisfies this, which is why digital systems split it as a root-raised-cosine filter across transmitter and receiver so the combined response is Nyquist and ISI-free at the sampler.
ISI shows up unmistakably on an eye diagram: a clean Nyquist channel leaves a wide-open eye, while ISI blurs the traces and narrows — or entirely closes — the opening, shrinking the margin against noise. Two things reintroduce ISI even with good pulse shaping: sampling at the wrong instant (a timing error moves you off the zero-crossings), and a dispersive channel such as multipath, whose echoes are literally delayed copies of past symbols.
It is worth separating the two sources because the cures differ. ISI from filtering and pulse shaping is fully under the system designer’s control and is eliminated by choosing a Nyquist pulse and sampling correctly — no channel knowledge needed. ISI from the propagation channel is not known in advance and varies as the radio or reflectors move, so it cannot be designed away; it must be measured and undone at the receiver by an adaptive equalizer that learns the channel’s impulse response and subtracts the interfering tails. A useful mental model is that a Nyquist-shaped symbol stream arriving through a multipath channel is the clean stream convolved with the channel, and equalization is the deconvolution that restores it.
Variants
Not all ISI is unwanted. Partial-response signalling (such as duobinary and the Gaussian-filtered GMSK used in GSM) deliberately introduces a controlled, known amount of ISI to shrink bandwidth or smooth the phase trajectory, then removes its effect with a matched detector that expects it. In that light the Nyquist criterion is not “no pulse overlap” but “no uncontrolled pulse overlap at the decision instants” — overlap is fine as long as the receiver knows exactly what it is.
Relevance to SDR
Controlling ISI is a central job of any digital demodulator, GopherTrunk’s included. Its receivers apply a root-raised-cosine matched filter so the composite pulse is Nyquist and ISI is nulled at the correct sampling instant, and a timing-recovery loop keeps the sampler on those instants; drift off them and ISI reappears as a closing eye and rising error rate. For the C4FM and π/4-DQPSK carriers in P25 and DMR the symbol rate and RRC roll-off are specified precisely so transmitter and receiver agree on an ISI-free composite. When the channel itself is dispersive — multipath in a mobile or simulcast environment — pulse shaping alone is not enough and the residual ISI must be removed by an equalizer that estimates and subtracts the interfering symbol tails.
In practice
The amount of tail energy, and thus sensitivity to timing error, is governed by the pulse’s roll-off factor: a sharper (low-alpha) filter saves bandwidth but has longer, larger tails that make the system less forgiving of timing jitter, a direct bandwidth-versus-robustness trade.
Sources
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Intersymbol interference — Wikipedia, for the definition and causes; Nyquist ISI criterion for the zero-crossing condition. ↩