What Is Intersymbol Interference?

Intersymbol interference (ISI) is a form of signal distortion in digital communications in which the energy of one transmitted symbol spreads into adjacent symbol periods, causing those symbols to interfere with one another at the receiver. ISI degrades bit error rate performance and, when severe, causes receiver decision errors even in the absence of additive noise. The phenomenon arises whenever the channel's impulse response extends beyond a single symbol period, a condition encountered in wired links with limited bandwidth, wireless channels with multipath propagation, and optical fiber subject to chromatic dispersion.

ISI is a central concern in the design of every digital communication system that operates at rates approaching the channel's bandwidth. The analysis of ISI draws on linear systems theory, probability theory, and optimization, and its mitigation involves filter design, equalization, and channel coding. In additive white Gaussian noise (AWGN) and Gaussian channel models, ISI adds a deterministic interference term to the noise, complicating the derivation of optimal receiver structures and bit error probability bounds.

Causes and Channel Modeling

The mathematical cause of ISI is straightforward: if the channel impulse response h(t) is not a Dirac delta, the received waveform at any instant is a weighted sum of contributions from multiple transmitted symbols. Multipath propagation in wireless channels creates this condition because reflections from buildings, terrain, or atmospheric layers arrive at the receiver with different delays, each carrying a scaled copy of the transmitted signal. In bandwidth-limited wired channels, the frequency-selective attenuation of the channel rounds transmitted pulses, causing their tails to extend into neighboring symbol slots.

The Nyquist intersymbol interference criterion establishes the conditions under which a pulse shape allows zero ISI at the sampling instants: the combined response of transmitter filter, channel, and receive filter must satisfy the Nyquist criterion for zero ISI. Raised-cosine filters are the most widely used pulse-shaping solution in practice, as described in the Cambridge University Press treatment of digital communication systems theory. When the channel itself distorts the ideal pulse shape, equalization is required to restore the zero-ISI condition.

Equalization Techniques

Equalizers at the receiver compensate for ISI by applying an inverse filter to the received signal. A zero-forcing (ZF) equalizer inverts the channel response exactly, eliminating ISI but potentially amplifying noise in spectral regions where the channel has low gain. The minimum mean square error (MMSE) equalizer balances ISI suppression against noise enhancement, achieving a better trade-off for practical channels. Both are linear equalizers implemented as finite impulse response (FIR) filters whose coefficients are adapted using algorithms such as least mean squares (LMS) or recursive least squares (RLS).

For channels with severe ISI, nonlinear techniques offer better performance. Decision-feedback equalizers (DFE) use previous symbol decisions to cancel the causal component of ISI before deciding on the current symbol. Maximum-likelihood sequence estimation (MLSE) using the Viterbi algorithm finds the most probable transmitted sequence given the entire received signal, achieving near-optimal performance at the cost of exponentially growing complexity with the channel memory length. Research documented in IEEE Xplore on ISI equalization for 5G phased arrays demonstrates that these classical techniques require adaptation for massive MIMO systems where spatial ISI joins temporal ISI.

Channel Coding and Turbo Equalization

Channel coding provides an alternative or complement to equalization for managing ISI. Coded systems can tolerate more ISI than uncoded ones because the decoder can exploit redundancy to recover from errors. Turbo equalization iterates between an equalizer and a channel decoder, passing soft information in both directions to progressively refine estimates of the transmitted bits. The NIST Digital Library of Mathematical Functions provides the mathematical reference functions, including Q-functions and modified Bessel functions, that characterize error probability in systems with ISI and Gaussian noise.

Applications

Intersymbol interference has applications in a wide range of fields, including:

• High-speed wireline data transmission over telephone copper pairs (DSL) and coaxial cable
• Wireless cellular communications including LTE and 5G systems with OFDM modulation
• Optical fiber links at rates above 10 Gbit/s requiring dispersion equalization
• Storage channel read/write systems in hard drives and flash memory
• Satellite communications links subject to frequency-selective atmospheric fading