NetSim Technology Library- Propagation models

Ver 11.1 1
Propagation Models
Contents
1 Propagation models in NetSim ..............................................................................................2
1.1 Propagation Loss .......................................................................................................................2
2 Path loss...............................................................................................................................3
2.1 Path loss models........................................................................................................................3
2.1.1 Friis Free space propagation model.........................................................................3
2.1.2 Log distance .............................................................................................................4
2.1.3 Hata Urban...............................................................................................................4
2.1.4 Hata Suburban .........................................................................................................5
2.1.5 COST231 Hata Urban and COST231 Hata Suburban................................................5
2.1.6 Indoor office and Indoor factory..............................................................................6
2.1.7 Indoor home: ...........................................................................................................6
3 Shadowing models................................................................................................................7
3.1 Log normal shadowing ..............................................................................................................7
4 Fading models ......................................................................................................................7
4.1 Nakagami Fading.......................................................................................................................8
4.2 Rayleigh Fading .........................................................................................................................8
5 SINR Calculation ...................................................................................................................9
6 Bit Error Rate (BER) Calculation........................................................................................... 10

Ver 11.1 2
1 Propagation models in NetSim
Propagation models are used to model signal attenuation for all wireless links. These include
WLAN – 802.11, Legacy Networks, ZigBee / IOT / WSN – 802.15.4, LTE, Cognitive radio –
802.22 and VANET.
1.1 Propagation Loss
Three different and mutually independent propagation phenomena influence the power of
the received signal: path loss, shadowing and multipath fading.
The different models available in NetSim are
1. Path loss Models
 Friis Free Space Propagation (Default option in GUI)
 Log Distance
 HATA Suburban
 HATA Urban
 COST 231 HATA Suburban
 COST 231 HATA Urban
 Indoor Office
 Indoor Factory
 Indoor Home
 No Path Loss
2. Shadowing Models
 None
 Constant
 Lognormal
3. Fading Models
 None
 Rayleigh
 Nakagami

Ver 11.1 3
2 Path loss
Path loss is the reduction in power density of an electromagnetic wave as it propagates
through space. Path loss may be due to many effects, such as free reflection, aperture-
medium coupling loss, and absorption. The general formula by which path loss is calculated
is
RXpower = TXpower + GainTX + GainRX – PL1meter – 10 log Dn
Where n is the path loss exponent, whose value is normally in the range of 2 to 5. In NetSim,
the default value for path loss exponent is 2 and D is the distance between transmitter and
the receiver, usually measured in meters.
And PL1meter is the path loss at reference distance (here taken as 1m). This value varies
depending on the radio and is a user input available in the PHY layer of the radios. For
802.11b this value is 40dB
And the Gain represents the transmit and receive antenna gains
Example:
Calculating the received power at 2 due to node 1 transmission. The transmitter power of
node1 is 100mW (20dBm), frequency is 2412MHz
Rx_Power (dbm) = 20dBm + 0 + 0 – 40dB – 40dB = -60dBm
The default value for reference distance d0 and path loss at reference distance PL_d0 are
1. 802.11 a / b / g / n / ac / p
a. 2.4 GHz : Default d0 = 1m and PL_D0 = 40dB
b. 5 GHz: Default d0 = 1 m and PL_D0 = 47 dB
2. 802.15.4 - Default d0 = 8m and PL_D0 = 58.5 dB
3. In LTE the calculation is done for each carrier for uplink and download. Default d0 =
1m and PL_D0 = 32 dB
2.1 Path loss models
2.1.1 Friis Free space propagation model
The free space propagation model is used to predict received signal strength when the
transmitter and receiver have a clear, unobstructed line-of-sight path between them. Satellite

Ver 11.1 4
communication systems and microwave line-of-sight radio links typically undergo free space
propagation. As with most large scale radio wave propagation models, the free space model
predicts that received power decays as a function of T-R separation distance raised to some
power. The free space power received by a receiver antenna which is separated from a
radiating transmitter antenna by distance d, is given by the Friis free space equation
𝑃𝑟 = [𝑃𝑡] + [𝐺𝑡] + [𝐺𝑟] + 20𝑙𝑜𝑔10 [𝜆/ (4 ∗ 3.14 ∗ 𝑑𝑜)] + (10 ∗ 2 ∗ 𝑙𝑜𝑔10 (𝑑𝑜/𝑑))
where Pt is the transmitted power
Pr is the received power
Gt is the transmitter antenna gain
Gr is the receiver antenna gain
d is the T-R separation distance in meters
L is the system loss factor
λ is the wavelength in meters
2.1.2 Log distance
The average received power logarithmically decreases with distance, whether in outdoor or
indoor radio channels. The average large-scale path loss for an arbitrary T-R separation is
expressed as a function of distance by using path loss exponent n.
𝑃𝑟 = [𝑃𝑡] + [𝐺𝑡] + [𝐺𝑟] + 20𝑙𝑜𝑔10 [𝜆 / (4 ∗ 3.14 ∗ 𝑑𝑜)] + (10 ∗ 𝑛 ∗ 𝑙𝑜𝑔10 (𝑑𝑜/𝑑))
Where n = 2 - path loss exponent which indicates the rate at which the path loss increases
with distance,
d0 is the close in-reference distance which is determined from measurements close
to the transmitter
d is the T-R separation distance
2.1.3 Hata Urban
The hata model is an empirical formulation of the graphical path loss data provided by
Okumura. Hata presented the urban area propagation loss as a standard formula and
supplied correction equations for applications to other situations. The standard formula for
median path loss in urban areas is given by
𝑃𝑟 = [𝑃𝑡] − 𝐿50 (𝑑𝐵)

Ver 11.1 5
𝐿50(𝑑𝐵) = 69.55 + 26.16log(𝑓𝑐) – 13.82log(ℎ𝑡𝑒) – 𝑎(ℎ𝑟𝑒) + (44.9 – 6.55 log(ℎ𝑡𝑒))log(𝑑)
− − − − − − − − − − − −𝑒𝑞(1)
Where
L50 (dB) = 50th
percentile (median) value of path loss
fc = Frequency in MHz
hte = Transmitter antenna height ( Range 30m to 200m, default 30m)
hre = Receiver antenna height ( Range 1m to 10m, default 1m)
d = Separation distance in km. So if input is in meter, this should be divided by 1000
to convert to km
a (hre) = correction factor for effective mobile antenna height which is a function of
the size of coverage area.
𝑎 (ℎ𝑟𝑒) = 8.29 (𝑙𝑜𝑔 1.54 ℎ 𝑟𝑒 )2 – 1.1 𝑑𝑏 for fc < 300 MHz
𝑎 (ℎ𝑟𝑒) = 3.2 (𝑙𝑜𝑔 11.74 ℎ 𝑟𝑒 )2 – 4.97 𝑑𝑏 for fc >= 300 MHz
2.1.4 Hata Suburban
To obtain path loss in suburban area, the standard Hata formula in equation 1 is modified as
𝑃𝑟 = [𝑃𝑡] − 𝐿50 (𝑑𝐵)
𝐿50 (𝑑𝐵) = 𝐿50(𝑢𝑟𝑏𝑎𝑛)(𝑑𝐵) – 2[𝑙𝑜𝑔𝑓𝑐/28]^2– 5.4 − − − − − − − −𝑒𝑞(2)
2.1.5 COST231 Hata Urban and COST231 Hata Suburban
The European Co-operative for Scientific and Technical Research (EURO-COST formed
COST231 working committee to develop an extended version of the Hata model COST231
proposed the following formula to extend Hata’s model. The proposed model for path loss is
𝑃𝑟 = [𝑃𝑡] − 𝐿50 (𝑑𝐵)
𝐿50(𝑑𝐵) = 46.3 + 33.9log(𝑓𝑐) – 13.82log(ℎ𝑡𝑒) – 𝑎(ℎ𝑟𝑒) + (44.9 – 6.55 log(ℎ𝑡𝑒))log(𝑑) + 𝐶𝑀
Where CM =
3 dB for urban
0 dB for suburban

Ver 11.1 6
2.1.6 Indoor office and Indoor factory
Office buildings have large open areas which are constructed by using moveable office
partitions so that the space may be reconfigured easily and use metal reinforced concrete
between floors. Partitions that are formed as part of building structure are called hard
partitions and partitions that may be moved and which do not span to the ceiling are called
soft partitions. Partitions vary widely in their physical and electrical characteristics
𝑃𝑟 = [𝑃𝑡] + [𝐺𝑡] + [𝐺𝑟] + 20𝑙𝑜𝑔10 [𝜆/ (4 ∗ 3.14 ∗ 𝑑𝑜)] + (10 ∗ 𝑛 ∗ 𝑙𝑜𝑔10 (𝑑𝑜/𝑑))
Where n =
2.1.7 Indoor home:
Houses typically use a wood frame partition with plaster board to form internal walls and
have wood or nonreinforced concrete between floors
𝑃𝑟 = [𝑃𝑡] + [𝐺𝑡] + [𝐺𝑟] + 20𝑙𝑜𝑔10 [𝜆/ (4 ∗ 3.14 ∗ 𝑑𝑜)] + (10 ∗ 𝑛 ∗ 𝑙𝑜𝑔10 (𝑑𝑜/𝑑))
Where n = 3
The default values of path loss exponent for all path loss models in NetSim are as shown
below:
Path loss model
Path loss exponent
(default)
Friis free space 2
Log distance 2
COST231 Urban -
COST231 Hata
Suburban
-
Hata Urban -
Hata Suburban -
Indoor Office 2.6
Indoor Factory 2.1
Indoor Home 3
2.6 for Indoor_office
2.1 for Indoor_factory

Ver 11.1 7
3 Shadowing models
3.1 Log normal shadowing
The mode in the Friis free space propagation equation does not consider the fact that the
surrounding environmental clutter may be vastly different at two different locations having
the same T-R separation. This leads to measured signals which are vastly different than the
average value predicted by the above equation. Measurements have shown that at any
value of d, the path loss PL (d) at a particular location is random and distributed log-normally
about the mean distance-dependent value i.e.
𝑃𝐿(𝑑)[𝑑𝐵] = 𝑃𝐿(𝑑) + 𝑋𝜎 = 𝑃𝐿(𝑑0) + 10𝑛𝑙𝑜𝑔(𝑑/𝑑0) + 𝑋𝜎
Where Xσ is a zero-mean Gaussian distributed random variable (in dB) with standard
deviation σ (in dB)
The log normal distribution describes random shadowing effects which occur over a large
number of measurement locations which have the same T-R separation, but have different
levels on the clutter propagation path. This phenomenon is referred to as log-normal
shadowing
The default values of standard deviation (dB) for all shadowing models in NetSim are as
shown below:
Shadowing Model Standard Deviation
Log Normal 5
Constant 5
4 Fading models
Fading is caused by interference between two or more versions of transmitted signal which
arrive at the receiver at slightly different times. These waves, called multipath waves,
combine at the receiver antenna to give a resultant signal which can vary widely in amplitude
and phase, depending on the distribution of the intensity and relative propagation time of the
waves and the bandwidth of the transmitted signal.

Ver 11.1 8
In built-up urban areas, fading occurs because the height of the mobile antennas are well
below the height of surrounding structures, so there is no single line-of-sight path to the base
station. The code for calculating fading power is present in
fn_NetSim_IEEE802_11_Phy_In() function in IEEE_802_11.c file inside IEEE802_11
project.
The default values of Fading parameters in NetSim are as shown below:
Fading Model Parameter Value
Rayleigh Fading Figure 5
Nakagami
Fading Figure 5
Shape parameter 1
Omega 2
4.1 Nakagami Fading
The Nakagami distribution is related to the gamma distribution. In particular, given a random
variable
𝑌 ~ 𝛾(𝐾, Ө)
it is possible to obtain a random variable
𝑋 ~ 𝑁𝑎𝑘𝑎𝑔𝑎𝑚𝑖 (𝑚, 𝛺)
by setting k = m, Ө= Ω/m and taking the square root of Y
𝑋 = 𝑆𝑞𝑟𝑡 (𝑌)
4.2 Rayleigh Fading
In mobile radio channels, the Rayleigh distribution is commonly used to describe the
statistical time varying nature of the received envelope of a flat fading signal, or the envelope
of an individual multipath component. It is well known that the envelope of the sum of two
quadrature Gaussian noise signals obeys a Rayleigh distribution. The Rayleigh distribution
has a probability density function (pdf) is given by
𝑃(𝑟) =
𝑟
𝜎2
𝑒𝑥𝑝(−
𝑟2
2𝜎2
) 0 <= 𝑟 <= ∞
𝑃(𝑟) = 0 𝑟 < 0
Where σ = rms value of the received voltage signal before envelope detection

Ver 11.1 9
σ^2 = time-average power of the received signal before envelope detection
The probability that the envelope of the received signal does not exceed a specified value R
is given y corresponding cumulative distribution function (CDF) is given by
𝑃(𝑅) = Pr(𝑟 ≤ 𝑅) = ∫ 𝑝(𝑟)𝑑𝑟
𝑅
0
= 1 − 𝑒𝑥𝑝(−
𝑅2
2𝜎2
)
The mean value rmean of the Rayleigh distribution is given by
𝑟𝑚𝑒𝑎𝑛 = 𝐸[𝑅] = ∫ 𝑟𝑝(𝑟)𝑑𝑟 = 𝜎√
𝜋
2
∞
0
= 1.2533𝜎
And the variance of the Rayleigh distribution is given by σr
2
which represents the ac power in
the signal envelope
𝜎𝑟2
= 𝐸[𝑟2]– 𝐸2
[𝑟] = ∫ 𝑟2
𝑝(𝑟)𝑑𝑟 −
𝜎2
𝜋
2
∞
0
= 𝜎2
(2 −
𝜋
2
)
5 SINR Calculation
Analogous to the SNR used often in wired communications systems, the SINR is defined as
the power of a certain signal of interest divided by the sum of the interference power (from all
the other interfering signals) and the power of some background noise.
The interference power is the difference between the total power received by the receiver
and the power received from one particular transmitter.
The background thermal noise in dBm at room temperature is given by:
P (in dBm) = −174 + 10 × 𝑙𝑜𝑔10(𝛥𝑓)
Where Δf is the Bandwidth in Hertz. For 802.15.4, Δf = 2 MHz. For 802.11a, b, g, Δf = 20
MHz, and for 802.11n, Δf = 20 MHz or 40 MHz.
P (in mW) = 10(
𝑃 (𝑖𝑛𝑑𝐵𝑚)
10
)
Therefore, SINR in dBm is calculated as:
SINR (in dBm) = 𝑙𝑜𝑔10 (
𝑅𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑝𝑜𝑤𝑒𝑟 (𝑖𝑛 𝑚𝑊)
𝐼𝑛𝑡𝑒𝑟𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑁𝑜𝑖𝑠𝑒 (𝑖𝑛 𝑚𝑊) + 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑁𝑜𝑖𝑠𝑒 (𝑖𝑛 𝑚𝑊)
)

Ver 11.1 10
6 Bit Error Rate (BER) Calculation
The bit error rate (BER) is the number of bit errors divided by the total number of transferred
bits during a studied time interval. The BER calculation is calculated using as SNR – BER
tables for different modulation schemes. These codes for these tables are not available for
user modification. In the case of LTE an SNR-BER table is looked up for each MCS.
Note: Floating numbers may lose precision when converting from dbm to mw or vice (Ref:
https://msdn.microsoft.com/en-us/library/c151dt3s.aspx). Hence
 If the received power (in mw) is less than 0.0001 then it’s assumed to be zero.
 If the received power (in mw) is 0 then dbm value for same is -10000.0 not -inf
 While adding two powers, decimal points after fifth digit is ignored. Ex
2.0000005+3.0000012 = 5.0

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