Models for Communication Technologies
3.1 Microwave Radio Links
Chapter 3
Models for Communication
• GT x represents the transmitter gain in dBi;
• GRxrepresents the receiver gain in dBi;
• Asysrepresents the losses related to equipment like cables, modulators among other components in dB. It is typically smaller than 3 dB, which is the value considered along the project for this variable;
• A0represents the free space attenuation in dB.
The power at the transmitter, PT x, and the transmitter and receiver gains,GT x andGRx respec- tively, are parameters provided by the manufacturers for each different type of equipment. Free space attenuation,A0, is dependent on the connection distancedand on the frequencyf considered, as can be seen on Equation 3.2 [15]:
A
0= 92.4 + 20 log
10(d
[km]) + 20 log
10(f
[GHz]). (3.2)
Besides free space attenuation, there are additional attenuations due to the Earth’s atmosphere that one must consider when designing an MRL.
Attenuation by Atmospheric Gases
Uncondensed water vapour and oxygen can be strongly absorptive of radio signals, especially at millime- tre -wave frequencies and higher (tens to hundred of GHz). This depends on the bands of frequencies where these gases naturally absorb photon energy. These wave signals can be significantly attenu- ated, to the point where link margins must be widened substantially, or propagation limited to very short ranges. Figure 3.1 shows the attenuation of oxygen and water, as a function of frequency.
The absorption attenuation caused by these atmospheric gases can be described by:
A
abs[dB]= (γ
o0+ γ
w0) × d, (3.3)
whereγo0andγw0represent, respectively, the attenuation caused by oxygen and water by unit of length, as seen on Figure 3.1.
Figure 3.1: Atmospheric absorption attenuation by Oxygen molecules (dashed line) and Water molecules (solid line) [16].
Rain Attenuation
Because rain is highly variable, considering time and location, it is not possible to predict its occurrence with certainty. Therefore, in order to design a communication system taking rain into consideration, it is important to determine the percentage of time that a given amount of rain attenuation will be exceeded at a certain location. This way a margin in the link budget is taken into account, which will guarantee this link will surpass rain attenuation in the percentage of time considered.
When striking a raindrop, a plane wave’s energy can be either absorbed (water is a lossy dielectric) or scattered. These two phenomena lead to what is called extinction of the wave by the raindrop. For computing the rain attenuation constant,αr, the following expression can be used:
α
r[dB/km]= k × R
α, (3.4)
in whichRis the rain rate in mm/hour andkandαare constants dependant on the frequency used and on the temperature considered. The total rain attenuation is computed by Equation 3.5:
A
r[dB]= α
r× d
ef, (3.5)
wheredef is the effective distance through a rainy path that can be obtained from Equation 3.6:
d
ef= d 1 +
dd0
. (3.6)
The variabled0assumes:
d
0=
35e
−0.015Ri(0.01), R
i(0.01)[mm/h]≤ 100 100, R
i(0.01)[mm/h]> 100
(3.7)
The value forRi(0.01)can be obtained from local weather data or, more simply, by using the standard values suggested by Recommendation P.837-1 from International Telecommunications Union Recom- mendations (ITU-R) [17]. The constantRi(0.01)is the value of rain intensity, in mm/h, that is not exceeded in 0.01 percent of the time in a certain place. This way, it is guaranteed that the planned link surpasses the rain attenuation during 99.99% of time. By using this value for the computation, the rain attenuation, Ar, will be obtained for the same 0.01 percent of time. In case the rain attenuation is required for a different time percentage,p, in order to plan for a more or less robust link, the following expression can be used:
A
pr= A
0.01r× 0.12p
−(0.546+0.043 log10p). (3.8)
Obstacle Attenuation
Another factor affecting MRLs is line-of-sight. Radio waves may encounter an obstacle (like trees, build- ings or hills for example), which can deflect the signal and reach the receiving end, which can be “out
of phase” and which can reduce the power of the arriving signal, also called “Phase Cancelling”. Us- ing lower frequency equipments will provide with a larger beam diffraction which will result in a lower attenuation.
The attenuation caused by an obstacle can be computed using Equation 3.9:
A
obs[dB]= 6.9 + 20 log
10( p
(ν − 0.1)
2+ 1 + ν − 0.1), (3.9)
whereν is proportional to the amount of the Fresnel ellipsoid obstructed by the obstacle. Equation 3.10 shows that this value can be obtained using:
ν = h √ 2
r
1e. (3.10)
The radius of the first Fresnel ellipsoid,r1e, can be obtained using Equation 3.11 [18]:
r
1e[m]= 17.32
s d
[km]4f
[GHz]. (3.11)
Still regarding Equation 3.10, h represents the height difference between the obstacle and the direct line between the transmitter and receiver. As can be seen from Figure 3.2, thishcan be positive, if the obstacle is above the line-of-sight, negative, if the obstacle is bellow the line-of-sight, or null if the obstacle is exactly in line with both the transmitter and emitter.
Forν≤ −0.85, which meansh≤ −0.6r1e, the attenuation caused by the obstacle is approximately zero. This means that an obstacle can obstruct up to 40% of the first Fresnel ellipsoid without disturbing the link [19].
Fade Margin
After taking the additional attenuations into consideration, they should be incorporated in Equation 3.1 in order to obtain the final expression for the power of the signal detected at the receiver:
Figure 3.2: Cases of Fresnell zone blockage [20].
P
Rx= P
T x+ G
T x+ G
Rx− A
sys− A
0− A
abs− A
r− A
obs. (3.12)
The receiver sensitivity,SRx, is defined as the weakest signal power that a radio equipment needs to receive in order to detect a signal, and it is a specific parameter of each equipment model. If the estimated received power is sufficiently large, then the link budget is said to be sufficient for sending data under perfect conditions. The amount by which the received power exceeds receiver sensitivity is called the Fade Margin [21],Mf ade, which is defined as:
M
f ade= P
Rx− S
Rx. (3.13)
The bigger the Fade Margin, the more robust the link will be, as it will be prepared for eventual extra attenuations. In this project the minimum Fade Margin accepted will be of 3 dB [8].
Signal-to-Noise Ratio and BER Ratio
In order to estimate the Signal-to-Noise Ratio under ideal propagation conditions, it is necessary to compute the Noise at the receiver,N:
N = N
f+ N
0(3.14)
where:
• Nf is the receiver noise factor, which is provided by the manufacturer of each specific equipment, in dBW.
• N0is the thermal noise, in dBW.
In order to calculateN0, Equation 3.15 is used:
N
0= −204 + 10 log
10(B
W). (3.15)
The noise bandwidth,BW, given by:
B
W= M
log
2(m) , (3.16)
whereM is the link throughput andmrepresents the modulation order being used. The signal band- width,brf is given by
b
rf= (1 + β) × B
W, (3.17)
in whichβis the roll-off factor (usually a value between 0.2 and 0.5). A higher-order modulation means
it is possible to transmit more bits per symbol. However it also means the signal is more susceptible to a higher bit error rate (BER), so, higher-order Quadrature Amplitude Modulation (QAM) can deliver more data less reliably than lower-order QAM. The BER is defined as the ratio of errored bits to the total number of received bits and for this project the minimum BER accepted will beBER= 10−6. Figure 3.3 shows the minimum Signal-to-noise Ratio under ideal propagation conditions (SN RIP C) that should be considered for different BER values and QAM modulations.
Figure 3.3: MinimumSN RIP C for specific BER and QAM modulation considered [22].
It is then possible to obtainSN RIP C using Equation 3.18 and check if the BER condition is being satisfied for the considered modulation.
SN R
IP C= P
RxIP C− N
f− N
0(3.18)
Other Error Performance Parameters
Since error performance is a critical component of transmission quality in digital networks, the ITU-R has published a number of Recommendations laying down error performance parameters and objectives.
The most important parameters are [23]:
• SESR (Severely Errored Second Ratio) which is the number of Severely Errored Seconds (SES) to total seconds in available time during a fixed measurement interval. SES is a one-second period which contains 30% errored blocks, or at least one defect.
• BBER (Background Block Error Ratio) which is the ration of Background Block Errors (BBEs) to total blocks in available time during a fixed measurement interval. A BBE is an errored block not occurring as part of an SES.
• ESR (Errored Second Ratio) which is the ratio of Errored Seconds (ESs) to total seconds in avail- able time during a fixed measurement interval. An ES is a one-second period with one or more errored blocks or at least one defect.
ITU-R G.826 Recommendation presents values for these parameters that should be satisfied, for different bitrates, where the value of B has provisionally been agreed to be in the range of 0.075 to 0.085 [24]:
Table 3.1: End-to-end error performance objectives [24].
In the scope of this dissertation, only bitrates larger than 160 Mbps will be considered. According to Table 3.1, ESR estimation is not applicable for these bitrate values, so only SESR and BBER will be taken into account. To compute the margins associated with SESR and BBER it is necessary to calculate the margins associated with fading. These margins are the uniform margin, mu, selective margin,ms, and real margin,mr, which relate (in linear units) through Equation 3.19.
1 m
r= 1
m
u+ 1
m
s, (3.19)
where the selective margin,mscan be easily obtained through Equation 3.20 using the appropriates value from Table 3.2:
m
s= 8000
s (3.20)
Table 3.2: Typical values ofsused in Equation 3.20 for different QAM Modulations [15].
Modulation s 16QAM 25 to 30 64QAM 35 to 40 256QAM 45 to 50 1024QAM 55 to 65
The next step is to calculate the real margin, mr for both BBER and SESR. Regarding SESR, it can be obtainedmsesrr using Equation 3.21, the appropriateSESRvalue from Table 3.1 andK, which is given by Equation 3.22:
m
sesrr= K
nsesr (3.21)
K
n= 1.4 × 10
−8× f
[GHz]× d
3.5[km](3.22)
When it comes to computingmbberr , it is necessary to determine what will be denoted assesrbber, using Equation 3.23:
sesr
bber=
BBER − N
b× rber α
32.8 × α
2× (sl
bber− 1) α
1, (3.23)
whereslbbercan be obtained from: