Summary

Chapter 6 Summary: Small-Scale Fading and Statistical Channel Models

Key Points

• 1.

  Multipath propagation causes small-scale fading: the signal fluctuates by 30–40 dB over distances of $\lambda/2$ due to constructive and destructive interference of multiple reflected, diffracted, and scattered copies.

• 2.

  The channel is an LTV filter with time-variant impulse response $h(\tau; t)$. The received signal is $r(t) = \int h(\tau; t)\,s(t-\tau)\,d\tau + n(t)$.

• 3.

  Rayleigh fading ($K=0$, no LOS) gives an exponentially distributed instantaneous power. Ricean fading ($K>0$, LOS present) is less severe. The K-factor is the LOS-to-scattered power ratio.

• 4.

  Doppler shift $f_D = v/\lambda$ governs how fast the channel changes. The Clarke/Jakes model gives the U-shaped Doppler spectrum. Coherence time $T_c \approx 0.423/f_D$.

• 5.

  Coherence bandwidth $B_c \approx 1/(5\sigma_\tau)$ determines flat vs frequency-selective fading. OFDM converts a frequency-selective channel into many flat-fading subchannels.

• 6.

  Bello's four system functions — $h(\tau;t)$, $H(f;t)$, $S(\tau;\nu)$, $B(f;\nu)$ — are related by 2D Fourier transforms. Under WSSUS, the scattering function $C_S(\tau;\nu)$ fully characterises the channel.

• 7.

  The TDL model $r[n] = \sum_l h_l[n]\,s[n-l] + w[n]$ is the standard discrete-time representation. 3GPP defines TDL-A through TDL-E with pre-specified tap powers and K-factors.

• 8.

  Standardised channel models (3GPP TR 38.901, WINNER, QuaDRiGa) use the GSCM approach: cluster-based geometry with stochastic parameters, covering 0.5–100 GHz for 5G NR.