Diversity Reception
Required fade margin and diversity gain of selection, equal-gain and maximal-ratio combining with N receivers, from the irradiance correlation at their separation in weak turbulence.
Rytov variance σ_R²
0.199
Scintillation index σ_I² (point)
0.192
Irradiance correlation b_I(5.00 cm)
-0.0241
Fresnel zone 1.57 cm
Log-irradiance correlation ρ_ln
-0.0264
negative ρ treated as 0 (conservative)
Fade margin, single receiver
9.04 dB
for P_out = 1.00e-6
Fade margin, Equal-gain, N = 2
4.88 dB
Diversity gain
4.16 dB
single margin − combiner margin
Required margin by combiner (N = 2)
| Combiner | Margin (dB) | Gain (dB) |
|---|---|---|
| Selection | 6.01 | 3.03 |
| Equal-gain | 4.88 | 4.16 |
| Maximal-ratio | 4.82 | 4.22 |
Diversity gain vs separation
Irradiance correlation vs separation
Model
M = −10·log10(t), P(combined irradiance < t⟨I⟩) = P_out
Point receivers with log-normal irradiance, σ_I² from the all-regime plane-wave expression and the spatial correlation b_I(d) of the Kolmogorov spectrum; ρ_ln is the correlation of ln I. Equicorrelation assumes every pair of receivers is separated by d, which is conservative for a line or grid array. Each receiver has the single receiver's aperture, so EGC and MRC include the √N array gain. All three combiners are computed exactly (to < 0.001 dB): given the common part of the fading the receivers are independent, and the sum of N independent log-normals is built by numerical convolution.
Valid for weak fluctuations (σ_R² < 1). Margins are relative to one receiver's mean irradiance.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Weak fluctuations: log-normal receivers correlated by the plane-wave irradiance covariance at one separation d. SC, EGC and MRC outages are exact for that model (numerical convolution, < 0.001 dB).
- Lee E. J., Chan V. W. S. (2004). Part 1: Optical communication over the clear turbulent atmospheric channel using diversity. IEEE J. Sel. Areas Commun. 22(9), 1896–1906. doi:10.1109/jsac.2004.835751
- Navidpour S. M., Uysal M., Kavehrad M. (2007). BER performance of free-space optical transmission with spatial diversity. IEEE Trans. Wireless Commun. 6(8), 2813–2819. doi:10.1109/twc.2007.06109
- Andrews L. C., Phillips R. L. (2005). Laser Beam Propagation through Random Media, 2nd ed. SPIE. Weak-fluctuation plane-wave irradiance covariance function.