Coherence BandwidthEdit
Coherence bandwidth is a fundamental concept in the study of wireless channels and digital communication systems. It characterizes the range of frequencies over which a channel’s response can be considered essentially constant. In practical terms, if a signal occupies a bandwidth smaller than the coherence bandwidth of the channel, the channel behaves like a flat fading channel, and a single set of equalization and coding strategies can often work across the whole band. Conversely, when the signal bandwidth exceeds the coherence bandwidth, the channel exhibits frequency-selective fading, and designs must account for variation across frequency. Coherence bandwidth is shaped by the physical propagation environment, including multipath, delay spread, and user mobility, and it is commonly discussed alongside related concepts such as the RMS delay spread RMS delay spread and the Doppler spread Doppler spread.
Because coherence bandwidth is a statistical property rather than a single fixed number, engineers often treat it as a characteristic that depends on measurement and design criteria. It serves as a guide for decisions about modulation, equalization, and multi-carrier techniques like OFDM in wireless systems. The idea rests on the intuition that a channel with many distinct propagated paths tends to distort different frequency components by different amounts, reducing the coherence of the channel across frequency. The broader the spread of arrival times among those paths (the larger the RMS delay spread), the smaller the coherence bandwidth tends to be, all else equal. See also the role of multipath in shaping frequency selectivity and channel smoothness.
Definition and intuition
The coherence bandwidth represents the bandwidth over which the channel’s frequency response H(f) remains highly correlated. A common, though approximate, rule of thumb relates coherence bandwidth to the RMS delay spread τ_rms of the channel by B_c ≈ 1/(2π τ_rms). In some contexts, alternative formulations use thresholds like 3 dB or 10 dB to define the practical bandwidth over which the channel remains “flat enough.” The exact value depends on how aggressively a system designer defines “approximately flat.” For a widely used link model, the channel’s impulse response h(t, τ) and its statistical properties under models such as WSSUS frames the interpretation of B_c in terms of how quickly frequency components decorrelate.
Coherence bandwidth is closely tied to the delay spread RMS delay spread and to Doppler effects that govern time variation, which together determine whether a channel is more likely to be flat-fading or frequency-selective. When the environment produces a small delay spread, B_c is relatively large, making a broader portion of the spectrum effectively constant. When the delay spread is large, B_c drops, increasing the likelihood of frequency-selective fading and the need for equalization or subcarrier modulation. See also the relationship to Doppler spread Doppler spread and channel time variation.
Measurement and modeling
In practice, coherence bandwidth is not measured as a single quantity, but inferred from channel sounding experiments that estimate the channel impulse response h(t, τ) and its time-varying statistics. By computing the average frequency response and its correlation across frequency, engineers determine the bandwidth over which the correlation remains above a chosen threshold. This process may involve evaluating the channel’s autocorrelation function in frequency or analyzing the averaged magnitude of H(f) across frequency. See Channel sounding for methods used to acquire these measurements.
A common modeling approach expresses coherence bandwidth through the delay profile, often under the WSSUS assumption framework, where the channel is described by a distribution of multipath components with various delays and Doppler shifts. The RMS delay spread RMS delay spread then provides a link to B_c, though real channels may deviate from idealized models depending on the environment and mobility.
Practical values of coherence bandwidth vary by setting and scenario. Indoor channels with dense multipath and short path lengths tend to yield larger τ_rms and smaller B_c, while outdoor or line-of-sight scenarios can produce smaller delay spreads and larger coherence bandwidths. The exact numbers depend on measurement bandwidth, threshold criteria, and the statistical model used.
Implications for system design
If the signal bandwidth is smaller than B_c, the channel can be treated as flat fading, and design emphasis may focus on antenna configuration, power efficiency, and robust coding against amplitude and phase variations. In such cases, a single-carrier approach can be effective, and equalization requirements are typically modest.
If the signal bandwidth exceeds B_c, the channel exhibits frequency-selective fading, which causes different subbands to fade differently. This drives the use of multi-carrier techniques such as OFDM or sophisticated equalizers in single-carrier systems. Frequency-domain processing can mitigate intersymbol interference and exploit diversity across subcarriers. See discussions on how coherence bandwidth informs decisions about modulation, coding, and equalization strategies.
The concept also informs spectrum policy and technology choices in modern wireless standards. Although policy questions are broader, understanding coherence bandwidth helps engineers assess how spectrum should be allocated, how much guard band is necessary, and where to place subcarriers or pilots to achieve reliable communication under varying propagation conditions. Related topics include Multipath, Delay spread, and Channel modeling.
Environment and real-world variability
Real channels are time-varying, so the coherence bandwidth can change with mobility and environmental dynamics. Urban environments with moving objects, vehicles, and rich scattering can produce rapid changes in the channel, altering B_c over short time scales. Indoor environments with dense furniture and devices can create highly variable delay profiles, affecting coherence bandwidth measurements across a building or floor.
Analysts often present a range of plausible B_c values for a given scenario rather than a single figure, emphasizing the probabilistic nature of wireless channels. The goal is to design systems that maintain performance across typical variations in coherence bandwidth and delay spread, rather than optimizing for a single, static number.