As the electromagnetic waves travel through open space they are attenuated. This attenuation is described as Free-space Loss. This loss depends on the distance travelled by signal and its frequency. Both parameters are in direct proportion. Longer distance means greater attenuation and higher frequency means greater attenuation. Free-space loss can be calculated thus:

FSL = 32.44 + 20log f + 20log D

Where:

To goal is to design a link so that the received signal is stronger than the receiver’s sensitivity at the required BER (typically 10-6). Since every radio signal in earth atmosphere is subject to fading, some difference between received signal level under normal circumstances and receiver sensitivity is needed to serve as a fade margin. The minimum value of fade margin can be calculated from the requirement for link availability (typically 99.999% of the time). The required margin depends on the length of the link as well as other factors such as rain attenuation, diffraction and multipath propagation.

If we ignore the additional loss along the path, the received signal strenght can be calculated using the formula for signal propagation in free space as follows:

P_R = P_T + G_T + G_R – FSL

Where

P_R must be:

P_R > P_S

Where:

The receiver’s sensitivity defines the minimum level of the received signal at which the receiver is able to process the received signal without losses or affecting the transmitted data (for BER better then 10^-6).

Determining sufficient fade margin is the most important step in microwave link design. If the margin is too small, the link will be unstable – as a result, sufficient availability of the link or quality of the provided services cannot be guaranteed. On the other hand, unnecessarily large margin makes the link more expensive (higher performance, larger and more expensive antennas) and increases the cost of creating the microwave link.

The following paragraphs describe the two most significant types of attenuation – rain and multipath attenuation, which are the most frequent along with free space loss. Mutual relation between rain and multipath attenuation rules out the possibility that the link could be affected by both types of attenuation at the same time – these types of attenuation do not add up. To determine the fade margin it is necessary to calculate both rain and multipath attenuation. The larger of the two types of attenuation determines the value of fade margin. In areas with high precipitation, rain attenuation can be expected to be more prominent. By contrast, links located in drier climates and little inclination, will suffer more from multipath attenuation.

FSL is not the only attenuation that influences the emitted signal. For frequency ranges upward of 10 GHz rain attenuation also plays a role. Precipitation is not identical in all areas which is why ITU released a recommendation Rec. ITU-R PN.837-1 for splitting into 15 regions according to precipitation intensity see Fig. 2.1, for more detail Appendix B, Rain Zone Map. In the areas with higher precipitation greater rain attenuation must be expected and a greater signal fade margin must be established, see the calculation of link availability.

The following properties are inherent to rain attenuation:

Fig. 2.1: Rain zone map, based on Rec.ITU-R PN.837-1

Raid attenuation can be calculated using ITU-R outage model, which consists of the following:

Obtain the rain rate R_0.01 exceeded for 0.01 per cent of the time (with an integration time of 1 min). R_0.01 values are defined for 15 rain zones and different time percentages and they are given in ITU-R Recommendation P.837.

Compute specific attenuation γ_R (dB/km) for the frequency, polarization, specific rain rate using ITU-R recommendation P.838. Rain attenuation for rain rate γ_R0.01 can be calculated as follows:

γ_R0.01 = k_h,v .R_0.01^α_h,v

where:

Fig. 2.2: Specific rain attenuation γ_R0.01 (dB/km) for H, V polarization and rain zones at 10 GHz

Fig. 2.2, “Specific rain attenuation γ_R0.01 (dB/km) for H, V polarization and rain zones at 10 GHz” shows that rain attenuation is greater for horizontal polarization. In regions with higher precipitation the difference in attenuation is more marked. This is why it is almost necessary to use vertical polarization and sufficient fade margin when designing links in high precipitation environment (regions K through Q).

Multipath fading is another dominant fading mechanism for 10 GHz frequency. A reflected wave causes a phenomenon known as multipath, meaning that the radio signal can travel multiple paths to reach the receiver. Typically, multipath occurs when a reflected wave reaches the receiver at the same time in opposite phase as the direct wave that travels in a straight line from the transmitter.

Multipath propagation gives rise to two kinds of signal degrading effects, i.e., flat fading and frequency selective fading. A flat fading is a reduction in input signal level where all frequencies in the channel of interest are equally affected and there is dependent on path length, frequency, and path inclination. In addition, it is strongly dependent on the geoclimatic factor K.

To calculate the probability of outage due to multipath propagation of microwave links in the 10 GHz band can be used ITU-R probability model which describes a single frequency (or narrowband) fading distribution suitable for large fade depths A in the average worst month in any part of the world (based on ITU-R p.530-12)5 and for detailed link design is given as follows [1]:

P₀ = Kd^3.2(1+|ε_P|)^-0.97×10^{0.032f-0.00085h_L–A/10}

where:

K = 10^{-4.2-0.0029dN1}

The term dN1 is provided on a 1.5° grid in latitude and longitude in ITU-R Recommendation P.453. The data are available in a tabular format and are available from the Radiocommunication Bureau (BR)

From the antenna heights h_e and h_r (meters about sea level), calculate the magnitude of the path inclination │ε_P│ (mrad) using the following expression:

where:

The position of obstacles between points of the bridge can significantly influence the quality of the microwave link. The radio signal doesn’t only radiate along the line of sight, but also in the area around it, i.e. in the so-called 1st Fresnel zone. Within this zone 90 % of the energy is transmitted between the transmitter and receiver antenna. This space has the shape of an ellipsoid. If it is disturbed the link has worse transmission properties and a higher quality antenna is required. For this reason the position of the antenna can be just as important as its height above ground. 60 % of the 1st Fresnel zone is considered as the most important.

Fig. 2.3: Fresnel zone

The general equation for calculating the first Fresnel zone radius at any point P in between the endpoints of the link is the following:

Where:

The cross sectional radius of each Fresnel zone is the highest in the center of link, shrinking to a point at the antenna on each end. For practical applications, it is often useful to know the maximum radius of the first Fresnel zone. From the above formula can be simplified calculation of the first Fresnel zone.

where: