kk

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The Power Delay Profile of the Mobile Channel for Above the Sea Propagation
Conference Paper · October 2006
DOI: 10.1109/VTCF.2006.20 · Source: IEEE Xplore
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2. 1
Abstract - this study focuses on sea propagation environments
and gives results on the characterization of the over the sea
wideband mobile radio channel. Conducted measurements led to
the development of pathloss, log-distance models. The behavior
of the Power Delay Profile is also investigated in details.
Generally mean excess delay and delay spread were estimated
below 0.5 μsec for line-of-sight propagation. However loss of line-
of-sight can cause rapid worsening of the propagation
parameters.
Index Terms - Wideband mobile channel, Sea communications,
Path loss, Power Delay Profile, Delay parameters
I. INTRODUCTION
HIS paper deals with measurements and statistical
representation of the wideband mobile radio channel
behavior for over the sea wireless paths at 1.9 GHz. The
measurement procedure, used on campaigns covering various
sea environments in the Aegean Sea, Greece, is described in
details. The purpose of the measurements was to model the
over the sea channel in order to develop a mobile wireless
ship to ship communication system. The label “over the sea
channel” is used in the current study to describe the wireless
channels at sea passages, where sea and land mixed together
form the propagation environment. The measurement
locations were carefully chosen to cover all the possible
scenarios (that is all kind of sea passages in Aegean). The
presented study gives typical results on large scale
characterization of the mobile path and focuses on the delay
profile, which can be regarded as the normalized plot of
received power versus delay, under the assumption that an
impulse is transmitted and eroded by the channel. During the
analysis, a clear discrimination of the results produced from
line-of-sight (LOS) and non–line-of-sight measurements
(NLOS) was made. This discrimination was necessary due to
the completely different shape of the path delay profile and
the expected difference on the statistical representation among
these two cases. Analysis of the measured data has shown that
in the case of omni directional transmission at the azimuth
plane, the delay profile can be seen as a series of spikes at
delays depended on the location of the scatterers (coastline,
islands etc). The power of each spike-path depends on the
nature of the scatterer (size, roughness etc) and it cannot be
easily modeled by simple mathematical expressions, e.g.
exponential power delay profile. As it is well known, the path
delay profile can be characterized by the following measures:
mean excess delay, rms delay spread and coherence
bandwidth. In this paper typical results for mean excess delay
and rms delay spread are presented. The statistical
characterization of each discrete path can thereafter be
modeled, based on the well known and commonly accepted
distributions (Rice, Rayleigh).
II. THEORY
Large scale characterization of the measured environments
can be done with the use of the log-distance path loss model.
According to [2] path losses are exponential function of
distance and path loss estimation can be done from the below
equation (in dB).
0
0
( ) ( ) 10 log (dB)
d
PL d PL d n
d
⎛ ⎞
⎟
⎜ ⎟
= + ⎜ ⎟
⎜ ⎟
⎜
⎝ ⎠
(1)
Parameter n, (also called attenuation factor) is the exponent
of the model, indicating the rate of attenuation growth as
distance increases. Attenuation factor n and the shadowing
factor σ, that expresses the variations and complexity of the
environment, are estimated from measurements in various
distances with the use of the non – linear mean square error
method. Factor n results from the fitting procedure and σ as
the root of the mean square error.
Small scale characterization of a radio channel includes time
dispersion (delay domain) analysis, time and space domain
analysis. In this study we focus on the delay domain.
The first step before moving to small scale analysis is to
separate measured data sequences in subsets of short period of
time, where we can assume the channel is WSSUS (Wide
Sense Stationary – Uncorrelated scattering). The procedure
that separates the data sequences into WSS sets is described at
the next section while uncorrelated scattering is assumed. A
critical measure for the dispersive nature of the WSSUS
channels is the Power Delay Profile (PDP), which is related to
the frequency autocorrelation function. The impulse response
of a WSSUS channel is usually modeled as a summation of
impulses, i.e., a set of discrete echoes, each one with its own
delay and complex amplitude, given by equation:
1: Mobile Radiocommunications Laboratory, School of Electrical and Computer Engineering, National Technical University of Athens,
Greece. Address: 9 Heroon Polytechniou Str, GR-15773, Zografou, Athens, Greece. e-mail: maliatsos@mobile.ntua.gr ,
loulis@mobile.ntua.gr, mchron@mobile.ntua.gr and fkonst@mobile.ntua.gr.
2: INTRACOM S.A. Hellenic Telecommunications and Electronics Industry. Address: 19.5 km Markopoulou Ave, GR-19002, Peania
Athens, Greece. e-mail: pdal@intracom.gr , moik@intracom.gr
Measurements and Wideband Channel
Characterization for Over the Sea Propagation
Konstantinos N. Maliatsos1
, Student Member IEEE, Panagiotis Loulis1
, Michail Chronopoulos1
, Philip
Constantinou1
, Member, IEEE Panagiotis Dallas2
, Michail Ikonomou2
T

3. 2
( , ) ( ) ( )
h t t
κ κ
κ
τ α δ τ τ
= −
∑ (2)
Assuming impulse transmission the Power Delay Profile is
given by the equation:
2 2
( , ) ( , ) ( ) ( )
P t h t t
κ κ
κ
τ τ α δ τ τ
= = −
∑ (3)
The two statistical moments of P(t,τ) are regarded as
parameters that can be used to characterize and compare the
dispersive nature of channels. These parameters are the mean
excess delay and rms delay spread given by the equations:
( )
( )
0
0
,
Mean Excess Delay m=
,
P t d
P t d
τ τ τ
τ τ
∞
∞
∫
∫
(4)
( )
( )
2
0
0
( ) ,
Delay Spread S=
,
m P t d
P t d
τ τ τ
τ τ
∞
∞
−
∫
∫
(5)
assuming that the delay axis zero is centered to the first
arriving path.
III. DATA COLLECTIONS AND PROCESSING
A. Experiment Design
The measured quantity in these campaigns was the power
delay profile. Seven different locations in the Aegean were
chosen, representing four different types of propagation
environments. It was concluded from the results that these 4
propagation environments can give a full picture of all the
radio channel behaviors, as a ship sails the Aegean.
Furthermore, the complexity of the Greek coastline, allows the
use of the exported results to other sea environments, which
can be regarded as similar or particular cases of the measured
sea passages. In all scenarios, either the receiver either both
receiver and transmitter were moving. The antennas used in
all the campaigns were OMNI directional on the azimuth
plane with 17O
beamwidth in the vertical plane and 9 dBi
gain.
Five of these campaigns covered a variety of environments
including open sea, narrow and broad sea passages with or no
vegetation, steep rocks, even suburban surrounding (sea
passages: Makronissos Island - Laurio, Spetses Island – Porto
Cheli, Dokos Island – Hydra Island, Poros Island, Aigina
Island – Methana). The transmitter (Tx) and receiver (Rx)
antennas were mounted on two motor yachts, 8 meters height
above sea level. The measurements were conducted during the
summer time, with clear weather and average air speed (4 at
the Beaufort level). It should be noted that the sea wave
impact on the radio signal was not an objective of this work.
The distance between transmitter and receiver was varying
from 40 to 14000 meters. The absolute speed of the boats was
also varying from 0 to 22 knots, resulting a maximum relative
speed of 44 knots. The routes of the boats were planned in
such a way that all the possible relative ship to ship
movements were covered. Thus measurements were carried
out while the boats conducted parallel movement along the
passage, perpendicular movement across the passage (same
and opposite direction of motion), diagonal and random
movement in the location of interest. The position and speed
of Tx and Rx were recorded from a GPS. The 6th
set of
measurements was conducted in a harbor (Perama port, lightly
urban surrounding) in order to characterize the behavior of the
mobile over the sea channel when ships or boats are
approaching a port. During this measurement the transmitter
antenna was located at a fixed point 21.5 meters above sea
level while the receiver was mounted on a boat moving along
allowed routes into the harbor. The antenna height of the
receiver was 9 meters.
During the seventh measurement the transmitter was placed
in a fixed location on an onshore cliff at Salamina Island, 20
meters above sea level. The receiver was mounted on a van
moving on the onshore road at the opposite coast of Attica.
The sea passage was wide and the purpose of the
measurement was to characterize the radio channel in the case
where two ships are stranded near the shore and the coastline
consists of large and stiff hills. The distances between
transmitter and receiver were varying from 5 to 30 km and the
receiver speed ranged from 0 to 50 km/h.
The measurement for each location consisted of a sequence
of recorded snapshots of the power delay profile, which is the
received power versus delay in response to a narrow
transmitted pulse that can be considered as an impulse. Each
measurement lasted for more than 3 hours. Thus, the size of
the data set was quite large, in order to include measurements
for a vast range of distance, speed and type of environment.
Finally it must be emphasized that in the cases where the
LOS was lost during the measurements, the index and time of
the corresponding measurements were marked and extra
attention was given to them during post – processing.
B. Measurement Equipment
Measurements were conducted using a commercial channel
sounder. It is a transmit/receive set based on the principles of
the sliding correlation sounding technique, slightly altered [6,
7]. The carrier frequency of the transmitted signal was 1900
MHz. The transmitted signal was a pseudorandom noise (PN)
sequence. The sequence length which is related to the
maximum excess delay that can be recognized by the channel
sounder could take various values, given by the equipment
capabilities. After tests it was decided that the lowest value
(127 length), giving a 13 μsec excess delay, was sufficient for
the measured environments. The chip rate was 10 MHz and
the transmitted power 10 Watts. Two modes of operation were
supported, one for time dispersion analysis with 5 Hz
sampling rate and another for time variation analysis with 100
Hz sampling rate. Before the use of the equipment in external
measurements, a calibration procedure through back to back
Rx – Tx connection was necessary. Calibration files were
recorded and the received signals were de – convoluted during
post-processing, resulting the correct channel delay profile.
The specific channel sounder identifies and records to a file
the powers and the corresponding delays of the 13 strongest
echoes. This set of binate data form a recorded single
snapshot.
C. Processing of the recorded data
1. Noise

4. 3
The first step was the definition of a noise level. As
mentioned, the channel sounder records the 13 most powerful
paths. But if there are no significant echoes, or the received
signal is weak (near the receiver sensitivity), the receiver will
randomly record some noise peaks as signal echoes. These
peaks must be isolated and deleted from the delay profile. This
can be achieved by defining a reference threshold, as noise
floor, so that each recorded peak beneath this power level is
ignored. The noise level was determined by the following
procedure. In each location a dummy measurement was
performed. The transmitter was disabled and the receiver was
recording noise. The mean value of the recorded measurement
sets the noise threshold. For extra safety a 6 dB margin was
retained, reducing the probability of noise recording to very
small levels (1.5 %) [13]. Under these circumstances the noise
floor was set at a value near -97 dBm depending on the noise
measurement. Apart from this noise reduction measure, all the
echoes with power less than 30 dB from the main path, are
regarded insignificant and can be ignored.
2. Defining the delay bins
According to [10] when a signal is transmitted at a given
data rate rs, the echoes received that are separated with 1/rs
delay are uncorrelated and can be considered as different
signal echoes derived possibly by different scatterers. In our
case the chip rate is 10 MHz. Thus the delay axis can be
discriminated at 100 ns delay bins, with reference to the first
arriving path (τ1st =0). Now each of the recorded echoes can be
assigned to the proper delay bin. That is the nearest integer
multiple of 100ns to the recorded delay.
3. Grouping of measurements
The characterization of a specific measured environment
provides little service and information. Effort has been given
in order to group the measurements according to the type of
environment and finally extract common features that can be
used in any similar setting. In fact the grouping was confirmed
with a “forth – back” procedure. In the first step the
discrimination was done intuitive. The data of each
measurement were discriminated into a sequence of data
subsets according to any change of conditions that could have
happened, or according to variations of the environment
(based on notes during the measurements, maps and pictures).
Then every discrete subset of measurement was examined
separately and some preliminary results were extracted.
During this stage it was noticed that similar environments give
similar results. The final step was to group measurements of
similar environments into five sets and re–extract the results.
The new results for each set characterize the mobile channel
of the corresponding type of environment. As mentioned 4
types of environments were identified and 5 groups of
measurements were created (including NLOS measurements
as a separate group):
o Sea passages of average width, with hilly coastline and
light vegetation. It is a very typical case in the Aegean Sea
(Group 1)
o Ports, harbors and narrow sea passages with quite intense
mobility of the environment and urban / suburban onshore
surroundings (Group 2).
o Very wide sea passages and open sea environment
(Group 3).
o Sea passages where the coastline is characterized by stiff
and high cliffs and hills with no vegetation. Environment is
quite simple as there is no variety of reflectors and scatterers.
During these measurements the transmitter and/or receiver
were moving very close to the coast. The propagation
conditions could be quoted as “marginal LOS” (Group 4).
o Any case of propagation with NLOS conditions. In an
environment similar to the one studied, LOS could be lost
when an island intermediates between the transmitter and the
receiver, or when another ship cuts off the LOS.
Unfortunately during the measurements it was not possible to
meet many cases of lost LOS due to an intercepting ship and
also in these few cases LOS was lost for a very short time.
On the other hand when an island intermediates between Tx
and Rx, the conditions can be described as “heavy NLOS”
and can be studied as a unity (Group 5).
In conclusion the data set for each group finally consists of a
sequence of recorded path delay profiles (power vs delay) the
GPS position of the transmitter and the receiver for every
snapshot and the time instance when the snapshot was
recorded.
4. Speed Calculation
In order to proceed with the following steps, it is very
important that the speed of each boat and the relative speed
between transmitter and receiver are known. Based on the
recorded GPS coordinates, the instant absolute speed of each
boat was calculated as well as the relative speed between
transmitter and receiver.
5. Processing steps for large scale characterization
The procedure for calculation of the attenuation factor n and
the shadowing factor σ can be summarized as follows:
- Calculation of the received wideband power from the
recorded snapshots of the delay profile. Wideband power is
equal to the sum of the powers of each identified echo. Noise
removal has been described previously.
- Smoothing of the measured received power is performed in
order to cancel the effects of the small scale fading. This is
accomplished by replacing the measured power value at every
point with the local average of the measured power samples in
a given sample window. So a sliding window filtering is done.
A typical value for the window length in radio mobile
communications is 40 λ. In our case it was determined that the
length of the sliding window should be longer (50 to 80 λ,
depending on the environment), something that was expected,
since the environment of an over the sea channel cannot
change as rapidly as an urban mobile radio channel.
-Knowing the antenna gains, transmitted and received
power we can evaluate the path loss for each snapshot using
the simple equation:
(dB)
= − + + −
Tx Rx Tx Rx cables
PL P P G G L (6)
Using equation (1) and the non linear mean square error the
attenuation factor n is calculated. As a distance of reference
we used distances above 1000m (depending on the available
measurements) and PL (d0) was taken to be the average value
measured for this distance.
- The standard deviation of the samples from the estimated
curve gives us a measure of the goodness of fit, but also the
shadowing factor σ.

5. 4
- Goodness of fit is evaluated with various empirical
methods, e.g. check if the trend of the curve for grater
distances follows an expected raise, or check if the residuals
(scatter plots of the error) have or not a random behavior. The
randomness of residuals is a sign of good fit, since a trend in
their behavior indicate the existence of a better fit. In case of a
bad fit, a new distance of reference d0 or a different length of a
smoothing window is chosen and the procedure is repeated.
6. Processing steps for small scale characterization at the
delay domain
As it was mentioned before small scale characterization of a
mobile radio channel can be done only if we first define the
stationarity regions, that are the routes/sets of snapshots where
the channel can be regarded stationary in a wide sense (WSS).
Then for every WSS region, it is possible to determine the
correlation functions, the average power delay profile and
other important parameters. Besides the discrimination of the
measurements in sets that are studied as a unity, determination
of the WSS regions is important for canceling the effects of
large scale fading. As a conclusion, small scale fading is
studied in small parts of the recorded data, which present the
same statistic behavior and the same large scale effects.
The algorithm used for WSS determination based on [5] can
be summarized as follows:
Let S be available samples s=1…S of P(s,τ), which is the
recorded power delay profile.
Step 1: A window of samples with small length is chosen
intuitively (e.g. wl=10) and the value
1, [1, ]
( ) ( , )
l l
w s w
P P s ∈
τ = τ is calculated
Step 2: The window is being slided by 1 sample and the
value 2,
( ) l
w
P τ is calculated.
Step 3: The quantity described by the following equation is
evaluated:
max
min
max max
min min
1, 2,
2 2
1, 2,
( ) ( )
(1,2)
max ( ) , ( )
l l
l l
w w
w w
P P d
c
P d P d
τ
τ
τ τ
τ τ
τ ⋅ τ τ
=
⎧ ⎫
⎪ ⎪
⎪ ⎪
⎪ ⎪
τ τ τ τ
⎨ ⎬
⎪ ⎪
⎪ ⎪
⎪ ⎪
⎩ ⎭
∫
∫ ∫
(7)
Step 4: if c(1,2)>correlation factor (in our case it was chosen
0.75), then the window slides again by 1 sample and we
calculate c(1,3) etc.
Step 5: When the sample where c(1,j)<0.75 is identified the
procedure stops and samples from 1 to j-1 define a WSS
region.
Step 6: The procedure is repeated starting from sample j for
the determination of the next WSS region.
The next step is the normalization of the received power
delay profiles. First we calculate the mean received power at a
given WSS region. Then, we evaluate the power of each
snapshot as the sum of powers of the echoes, and then average
them over the WSS set. Finally, the power delay profiles of
the region are normalized by the average power.
In the following sections we present large scale and typical
small scale - delay domain results for groups 2, 4 and 5 of the
measurements. Through these results, the controversy between
NLOS and LOS propagation can be seen, as well as the
different LOS channel behavior at simple (group 4) and
complex (group 2) environments.
IV. RESULTS ON LARGE SCALE CHARACTERIZATION
In the following figures, the results of the large scale
processing and curve fitting procedure for groups of
measurements 2, 4 and 5 are presented. The measurements,
after applying the sliding window, are compared to the log –
distance curve that occurred by minimizing least square error.
Τhe 99% confidence bounds are also presented in the figures
as they were estimated from this set of measurements. Below
each figure, the name of the location, the computed
shadowing and attenuation factor as well as the group in
which the measurement (or the majority of the recognized
WSS regions) is classified are noted.
Figure 1
Location Poros - Group 2,
n=3.4, d0=405 m, PL(d0)=89.5 dB, σ=3.95 dB
Figure 2
Location Hydra - Group 4,
n=3.311, d0=2700 m, PL(d0)=102,9 dB, σ=1.84 dB
It should be noticed that unfortunately we could not use all
the NLOS measurements for large scale characterization,
because in many cases the received power did not cover the
requirements defined by receiver sensitivity. Generally loss of
LOS in this kind of environments can cause deep attenuation
of the received power. This is happening because long time
NLOS conditions for over the sea channels occur when the
land (island, peninsula etc) interrupts the direct path between

6. 5
transmitter and receiver. In the cases where the transmitter and
the receiver are close to the edge of the obstacle the received
signal still remains above the sensitivity of the equipment as
the as the diffracted signals at the edges are powerful enough
and path loss can be modeled by the below mentioned fit.
Figure 3
Non LOS measurements - Group 5,
n=3.606, d0=1025 m, PL(d0)=109,9 dB, σ=4.5 dB
It can be noticed that the NLOS model gives significantly
higher shadowing and attenuation factor comparing to the
LOS measurements. Moreover, Group 4 presents extremely
low shadowing factor (below 2 dB) due to the simplicity of
the environment. Group 2, where the environment was a
narrow sea passage with populated coasts (much more
complex than Group 4) resulted higher values.
The obtained results show that the large scale
characterization of the over the sea channels can be modeled
with the use of the log-distance model at distances above a
reference distance. This raises two questions. The first
question concerns the behavior of the channel at small
distances between transmitter and receiver. The second
question concerns the way that a suitable reference distance
can be determined. The answers can be found by analyzing
the measurements at smaller distances. In Figure 4, the
measurement results for Salamina – Perama sea passage for
distances from 300 to 2000 m are presented.
Figure 4: Small distance pathloss measurements and the plane earth model
As shown in the above figure, some sudden deep fades are
observed at distances less than 2500 meters. These fades
remind the variations of the predicted path losses when using
the plane earth model. This model assumes perfect reflection
from the ground and takes into account that the reflecting
wave can partially cancel the power of the direct wave. The
model is described by the following equation:
( ) R
T
T
R
T
R G
G
P
d
h
h
d
P
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
=
λ
π
π
λ 2
sin
4
4
2
2
2
(8)
In the figure above, are also plotted the results given by the
plane earth model for the system that was used at the specific
measurement. Antenna heights were 21.5 and 9 m. It can be
concluded that although plane earth model does not give fit to
the measured data, there is definitely a connection between the
fades observed to measurements with the ones given by the
model. This can be explained on the one hand by the fact that
sea is a strong reflector, but not a perfect one and on the other
hand clearly sea is not the only reflector/ scatterer in these
environments.
As Tx – Rx distance increases above 2500 m, the log -
distance model becomes valid. Thus the reference distance of
the model should be longer than 2500 m when antenna heights
are 21.5 and 9 m. Consequently when antenna heights
decrease/increase, the reference distance should
decrease/increase too. This means that for the conducted
measurements where antenna heights were 8 m, reference
distance should be more than 1000 m. This distance is
equivalently longer than the distance where the last deep fade
from the plane earth model occurs. Then log-distance model
results can be used from this distance and on. Also, a rough
approximation of the distances where deep fades occur can be
done from the plane earth model. Finally it has to be noticed
that although transmitter and receiver were moving over small
distances at the narrow sea passage of Poros (figure 1), no
clear deep fades were noticed. This can be explained by the
fact that when moving at this particular passage, the main
reflecting surface in many occasions was land, decks or even
small boats and not just sea.
V. DELAY DOMAIN RESULTS
A. Power Delay Profiles
The next step of the study was the characterization of the
channel at the time delay domain. As explained before, the
measurement data are sorted out to data sets where WSS
assumption is valid. Thus for every WSS region, the
measurement set comprises a number of instantaneous power
delay profiles ( , )
P t τ . Assuming ergodicity, we calculate the
average power delay profile for each WSS region:
{ }
( ) ( , )
av
P E P t
τ τ
= (9)
Averages, rather than just measurement snapshots, are
required for many reasons. First of all noise and measurement
error reduction is being performed and furthermore we can

7. 6
focus exclusively to the delay domain, ignoring the time
variance and stochastic behavior of each signal echo.
Moreover, averaging can lead to the cancellation of some
echoes that appear instantly due to random or accidental
events and do not characterize the channel.
In Figures 5, 6 and 7 are depicted some typical results that
occurred during measurements for measurement groups 2, 4
and 5.
Figure 5: Power Delay Profile examples for Group 2
It can be easily understood that there is no simple
mathematical expression able to model the shape of the power
delay profile for these environments. In order to give a
description of the channel power delay spectrum, some
remarks can be easily made. For LOS measurements direct
path is dominant. During the first 1 μsec of excess delay (or
more depending on the distance from the coast), power of the
received signal echoes rapidly decreases. Then a number of
echoes follows as a series of low power spikes.
Figure 6: Power Delay Profile examples for Group 4
Figure 7: Power Delay Profile examples for Group 5
In the case of a complex environment (group 2) the echoes
are plenty and cover the entire delay axis until 8 μsec. On the
other hand in the case of a simple environment (group 4),
there is a small number of spikes in specific delays. This
shape of the channel’s response can be empirically explained
by the nature of the measured environment. This over the sea
channel environment consists of big, discrete scatterers
(fragments of land that form the sea passage).distributed in a
non uniform manner. This simply means that reflecting
objects that can produce any value of delay do not always
exist. As an example the map of a measured environment from
group 4 is presented. We will first simplify the problem by
making the following assumptions: powerful echoes can be
produced by a simple reflection or scattering mechanism;
echoes from multiple reflections are considered not detectable;
the coast is the only reflection or scattering surface (which
was true in this particular case because the coast was consisted
of big and steep cliffs and no other boats or ships were
present). Finally we only take into consideration possible
reflections where incidence angle is greater than 900
. Based
on these assumptions, we can estimate the delay values where
signal echoes are expected to arrive.
In Figure 8 are highlighted all the possible non–direct paths
that a wave can cross from the receiver to the transmitter,
given the above assumptions, grouped in 4 path sets. The
direct path was 8196 m, so from the path difference the excess
delay can be evaluated. Hence:
PATH 1 2 3 4
Excess Delay
(μsec)
0.1 –
0.82
2.2 –
2.8
3.5 –
5.5
6.1 – 6.7
Table 1: Predicted excess delays for non – direct paths

8. 7
Figure 8: Map of the measured environment
In Figure 9, the measured power delay profile for the
corresponding measurement after the first processing steps is
depicted:
Figure 9: Measured Power Delay Profile for the Group 4 example
As noticed in this case, the echo delays from the measured
power delay profile agree with the predicted delays. Moreover
this power delay profile fits the descriptions that concluded
before. First, there are the power decreasing echoes below 1
μsec and then the low power spikes at discriminate delays.
The discontinuous shape of the delay profile, as shown from
the previous analysis, is caused by the inexistence of scatterers
in the sea that can give powerful multipath at delays from 1 to
2, 2.8 to 3.5 and 5.5 to 6.1 μsec. On the other hand, because of
the distances, detectable paths occur at smooth and plane
reflecting surfaces. For example if there is dense vegetation,
paths are expected weak, e.g. the scattering surface for paths
of set 3 of the above analysis contains trees and bushes and
the arriving echoes are weaker than those that crossed longer
distance. It must be noticed that the described analysis does
not give result as the propagation environment becomes more
complex and unpredicted.
Finally, as far as the NLOS Power Delay Profile is
concerned we can notice that there is no dominant path in
general. The only remark that can be made is that echoes at
lower excess delays are stronger.
B. Delay Parameters – Mean Excess Delay, RMS Delay
Spread
The next step, after grouping measurements and extracting
the average normalized power delay profile for each region of
stationarity, is the calculation of the delay parameters, that are
mean excess delay and rms delay spread. First, the noise has
to be removed, as described before, because these parameters
(especially rms delay spread) are very sensitive to noise.
Given that the delay axis has been split to discrete delay bins
and that zero of the delay axis was set to the first arriving
path, the equations that will calculate the delay parameters are:
max
,
0
max
,
0
( , )
( )
( , )
av norm i i
i
τ
av norm i
i
P s τ τ
m s
P s τ
=
=
⋅
=
∑
∑
for mean excess delay (10)
max
2
,
2
0
max
,
0
( , )
( ) ( )
( , )
av norm i i
i
τ τ
av norm i
i
P s τ τ
σ s m s
P s τ
=
=
⋅
= −
∑
∑
(11)
for rms delay spread. Variable s is a consecutive number that
is used for indexing WSS regions for each group of
measurements.
Since we have calculated the delay parameters of all WSS
regions for a measurement group, we can plot the empirical
cumulative density function (CDF) that gives the proportion
of delay values (mean excess or rms) less than or equal to a
given delay. In Figures 10 and 11 the empirical CDFs for the
LOS groups 2 and 4 are presented.
Figure 10: LOS mean excess delay empirical CDFs

9. 8
Figure 11: LOS rms delay spread empirical CDFs
In Figures 12 and 13 are depicted the empirical CDF of the
NLOS case in comparison with the CDF of all the LOS cases.
Figure 12: NLOS vs LOS mean excess delay empirical CDFs
Figure 13: NLOS vs LOS rms delay spread empirical CDFs
The conclusions drawn from these figures are: a) mean
excess delay remains below 0.5 μsec at a percentage above 90
% for LOS propagation conditions, b) Mean excess delay for
group 2 is usually larger due to the complex environment that
produces more multipath, c) rms delay spread ranges at the
same levels for all LOS groups, which can be explained by the
fact that there is a tradeoff and when the width of a sea
passage increases, echo delays increase, but the multipath
number and power reduces, d) in all the cases propagation in
NLOS conditions is much worse causing a great raise at the
parameters value, justifying our characterization as heavy
NLOS conditions.
VI. CONCLUSIONS
Measured data have shown that: 1) Large scale
characterization of the channel depends strongly on the
environment and the antenna heights, and the results can be
correlated to some theoretical models, e.g. path losses at small
transmitter–receiver distances present similarities to plain
earth model results; 2) Power delay profile has a spiky shape;
3) The delay parameters for LOS propagation mostly remain
at low levels. Moreover in some occasions fading can be
regarded as flat; 4) NLOS propagation conditions cause
remarkable increase of the delay parameter values
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