Power Delay Profile (PDP)

The relative time offset at which a multipath component arrives at the receiver, measured in nanoseconds. The delay spread between the first and last significant tap defines the maximum excess delay of the channel.

• Typical indoor values: 50–200 ns
• Typical outdoor urban values: 1–5 µs
• Hilly terrain values: Up to 20 µs

Tap delays are quantized to the sampling period of the emulation system. Closely spaced taps represent unresolvable multipath that causes flat fading, while widely spaced taps cause frequency-selective fading.

The average power level of each multipath component, typically expressed in dB relative to the strongest tap. The power distribution across taps defines the power delay spectrum and determines the severity of inter-symbol interference.

• Exponential decay: Common in indoor channels where each successive echo is weaker
• Uniform profile: Used for worst-case testing with equal-power taps
• Two-ray model: A dominant direct path and a single strong reflection

Tap powers are normalized so the sum of linear gains equals 1, preserving the total channel energy.

The total count of resolvable multipath components in the PDP model. This parameter directly determines the computational complexity of the TDL convolution and the frequency selectivity of the emulated channel.

• ITU Indoor A: 2–3 taps for simple office environments
• ITU Vehicular A: 6 taps for urban mobile scenarios
• 3GPP Extended Pedestrian A: 7 taps with dense scattering
• Custom high-fidelity models: 12–24 taps for wideband military or radar channels

More taps create deeper frequency-domain nulls, challenging equalizer and fingerprinting model robustness.

Each tap in a PDP can be assigned an independent Doppler power spectral density to model the motion of scatterers contributing to that specific multipath component. This transforms a static PDP into a time-varying channel impulse response.

• Jakes spectrum (Classic): Isotropic scattering with a U-shaped spectrum, defined by maximum Doppler shift f_d = v/λ
• Rician spectrum: Jakes spectrum plus a dominant frequency-shifted LOS component
• Flat spectrum: Uniform Doppler spread for emulating dense, chaotic scattering
• Pure Doppler shift: A single frequency offset for a moving reflector

Doppler modeling is critical for testing fingerprinting models against time-selective fading and coherence time constraints.

The ratio of the power in the dominant line-of-sight (LOS) component to the total power in all scattered multipath components, expressed linearly or in dB. A K-factor parameterizes the PDP for Rician fading channels.

• K = 0 (or -∞ dB): No LOS component; channel degenerates to Rayleigh fading
• K = 10 (10 dB): Strong LOS with moderate scattering, typical of open outdoor environments
• K = 100 (20 dB): Very dominant LOS, approaching an AWGN channel with minor fading

In a TDL implementation, the first tap is assigned the LOS power while remaining taps model the scattered Rayleigh-distributed components.

The second central moment of the power delay profile, calculated as the square root of the weighted variance of tap delays. RMS delay spread is the single most important metric for predicting inter-symbol interference (ISI) severity without simulating the full channel.

• Coherence bandwidth ≈ 1 / (5 × RMS delay spread)
• Flat fading occurs when: Signal bandwidth << Coherence bandwidth
• Frequency-selective fading occurs when: Signal bandwidth > Coherence bandwidth

A channel with 100 ns RMS delay spread has a coherence bandwidth of approximately 2 MHz. Signals wider than this will experience significant ISI, requiring equalization.

A discrete-time filter structure that directly implements a Power Delay Profile. Each tap represents a resolvable multipath component with a specific delay, amplitude, and Doppler spectrum. The TDL convolves the input signal with the channel impulse response, making it the standard computational model for channel emulators and link-level simulators. TDL models are defined by standards bodies like 3GPP for consistent testing.

The process of convolving a synthetic signal with a time-varying channel impulse response to replicate real-world propagation. This goes beyond static PDP application by incorporating time selectivity through Doppler spectra. Emulation can be purely software-based or use Hardware-in-the-Loop (HIL) setups with vector signal generators to subject physical receivers to controlled, repeatable fading conditions.

The time-domain representation of a multipath channel's effect, serving as the filter kernel for synthetic impairment. The CIR is the continuous-time equivalent of a PDP's discrete tap definition. Key characteristics include:

• Delay spread: The temporal extent of multipath energy
• Coherence bandwidth: The frequency range over which the channel response is correlated
• Tap phases: Often modeled as uniformly distributed for Rayleigh fading

A statistical model for dense multipath environments with no dominant line-of-sight (LOS) path. The received signal envelope follows a Rayleigh distribution, and the phase is uniformly distributed. This model applies when the PDP contains numerous taps of comparable power, typical of urban and indoor non-LOS scenarios. The Jakes model is commonly used to generate the associated Doppler spectrum.

A statistical model where a dominant LOS component coexists with scattered multipath energy. Defined by the K-factor—the ratio of LOS power to scattered power. A K-factor of 0 reduces to Rayleigh fading; a very high K-factor approaches an AWGN channel. This model is essential for emulating satellite links, rural macro-cells, and indoor environments with direct visibility.

The simulated change in carrier frequency caused by relative motion between transmitter and receiver. A PDP alone is static; Doppler adds time selectivity. The Doppler spectrum defines the power distribution of frequency shifts. Common models include:

• Jakes spectrum: Classic U-shaped spectrum for isotropic scattering
• Flat spectrum: Uniform distribution for simplified testing
• Custom spectra: Derived from ray-tracing for specific environments