An Interim Channel Model for Beyond-3G Systems - Giovanni Del ...
An Interim Channel Model for Beyond-3G Systems - Giovanni Del ...
An Interim Channel Model for Beyond-3G Systems - Giovanni Del ...
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<strong>An</strong> <strong>Interim</strong> <strong>Channel</strong> <strong>Model</strong> <strong>for</strong> <strong>Beyond</strong>-<strong>3G</strong> <strong>Systems</strong><br />
Extending the <strong>3G</strong>PP Spatial <strong>Channel</strong> <strong>Model</strong> (SCM)<br />
Daniel S. Baum and Jan Hansen<br />
Communication Technology Laboratory<br />
ETH Zürich, Switzerland<br />
dsbaum@nari.ee.ethz.ch<br />
Jari Salo<br />
Radio laboratory/SMARAD<br />
Helsinki University of Technology, Espoo, Finland<br />
jari.salo@hut.fi<br />
<strong>Giovanni</strong> <strong>Del</strong> Galdo and Marko Milojevic<br />
Fachgebiet Nachrichtentechnik<br />
Technische Universität Ilmenau, Ilmenau, Germany<br />
{giovanni.delgaldo,marko.milojevic}@tu-ilmenau.de<br />
Pekka Kyösti<br />
Elektrobit<br />
Oulu, Finland<br />
pekka.kyosti@elektrobit.com<br />
Abstract— This paper reports on the interim beyond-<strong>3G</strong> channel<br />
model developed by and used within the European WINNER<br />
project. The model is a comprehensive spatial channel model <strong>for</strong><br />
2 and 5 GHz frequency bands and supports bandwidths up to 100<br />
MHz in three different outdoor environments. It further features<br />
a time-variable system-level parameters <strong>for</strong> challenging advanced<br />
communication algorithms, as well as a reduced variability<br />
tapped delay-line model <strong>for</strong> improved usability in calibration and<br />
comparison simulations.<br />
Keywords-beyond-<strong>3G</strong>, channel model, MIMO, SCM, <strong>3G</strong>PP<br />
I. INTRODUCTION<br />
In recent years Multiple-Input Multiple-Output (MIMO)<br />
wireless communication techniques have attracted strong<br />
attention in research and development due to their potential<br />
benefits in spectral efficiency, throughput and quality of<br />
service. Only recently, however, has this technology been<br />
considered to be included in wireless communication system<br />
standards, such as IEEE 802.11n <strong>for</strong> wireless LANs (WLAN),<br />
IEEE 802.16 <strong>for</strong> broadband fixed wireless access (FWA), and<br />
<strong>3G</strong>PP HSDPA <strong>for</strong> cellular mobile communications.<br />
<strong>An</strong>y wireless communication system needs to specify a<br />
propagation channel model that can act as a basis <strong>for</strong> per<strong>for</strong>mance<br />
evaluation and comparison. With advancing communication<br />
technologies, these models need to be refined as<br />
further characteristics of the channel can be exploited and thus<br />
need to be modeled. To enable MIMO, the standardization<br />
groups 802.11 and <strong>3G</strong>PP thus first defined spatial channel<br />
models suitable <strong>for</strong> their applications [1], [2].<br />
Upcoming communication systems will be based on new<br />
range of system parameters (e.g., extended bandwidth and new<br />
frequency bands), a broader range of and additional scenarios<br />
(e.g., mobile to mobile, mobile hotspot), and new<br />
communication techniques (e.g., tracking algorithms). This<br />
triggers new requirements on the underlying channel models.<br />
The European WINNER project [3], which is part of the<br />
Framework 6 ef<strong>for</strong>t, is currently researching the outline of a<br />
system design of such a beyond-<strong>3G</strong> system. In WINNER, it is<br />
the goal of Work Package 5 to come up with channel models<br />
that suit the needs in the project.<br />
While the WINNER project only started recently, there is<br />
an immediate demand <strong>for</strong> models suitable <strong>for</strong> initial usage.<br />
This document presents the result of our studies in <strong>for</strong>m of a<br />
model that is used <strong>for</strong> initial evaluation of beyond-<strong>3G</strong><br />
technologies in outdoor scenarios within the WINNER project.<br />
Contributions. Our specific contributions are as follows:<br />
• We analyze shortcomings of current spatial channel<br />
model standards with respect to the identified<br />
requirements from other WINNER Work Packages.<br />
• We evaluated results found from literature search and<br />
derived from our own measurement data.<br />
• We propose a set of backward compatible extension to<br />
the <strong>3G</strong>PP Spatial <strong>Channel</strong> <strong>Model</strong> (SCM).<br />
This paper summarizes the results reported in [4].<br />
II.<br />
<strong>3G</strong>PP SCM<br />
We have identified two publications ([1], [2]) defining<br />
spatial / MIMO radio channel models that are commonly<br />
accepted and used. Other publications focus mainly on aspects<br />
and certain effects of the radio channel. As the 802.11n model<br />
is targeted towards indoor applications, we have chosen the<br />
<strong>3G</strong>PP SCM as a basis <strong>for</strong> outdoor channel model extensions.<br />
A. Properties<br />
The SCM is a so-called geometric or ray-based model. It<br />
defines three environments (Suburban Macro, Urban Macro,<br />
and Urban Micro) where the latter is differentiated in line-ofsight<br />
(LOS) and non-LOS (NLOS) propagation. There is a<br />
fixed number of 6 “paths” in every scenario, each representing<br />
a Dirac function in delay domain, but made up of 20 spatially<br />
separated “sub-paths” according to the sum-of-sinusoids<br />
method. Path powers, path delays, and angular properties <strong>for</strong><br />
both sides of the link are modeled as random variables defined<br />
through probability density functions (PDFs) and cross-
Scenario<br />
correlations. All parameters, except <strong>for</strong> fast-fading, are drawn<br />
independently in time, in what is termed “drops”.<br />
B. Shortcomings<br />
The SCM was defined <strong>for</strong> a 5 MHz bandwidth CDMA<br />
system in the 2 GHz band, whereas the currently defined<br />
WINNER system parameters are 100 MHz in both 2 and 5<br />
GHz frequency range. Other minor issues are the drop based<br />
concept, i.e., no short-term system-level time-variability in the<br />
model, the lack of Ricean K-factor models (LOS support) <strong>for</strong><br />
macro scenarios, and the lack of a rural scenario.<br />
III.<br />
TABLE 1. MIDPATH POWER-DELAY PARAMETERS<br />
Suburban Macro,<br />
Urban Macro<br />
Urban Micro<br />
No. mid-paths per path 3 4<br />
Mid-path power and<br />
delay relative to<br />
paths (ns)<br />
1 10/20 0 6/20 0<br />
2 6/20 7 6/20 5.8<br />
3 4/20 26.5 4/20 13.5<br />
4 - - 4/20 27.6<br />
INTERIM BEYOND-<strong>3G</strong> CHANNEL MODEL<br />
Our main goal <strong>for</strong> the extension was to keep it simple,<br />
straight<strong>for</strong>ward, and backward-compatible. This approach<br />
provides consistency and comparability. In the following we<br />
discuss the underlying concepts and the reasoning behind the<br />
proposed extensions.<br />
A. Bandwidth<br />
To extend the model in a way such that its characteristics<br />
remain unchanged if compared at the original 5 MHz<br />
resolution bandwidth, we add intra-path delay-spread (DS),<br />
which is zero in the SCM. A possible power-delay profile<br />
(PDP) is a one-sided exponential function. This approach of<br />
intra-cluster delay-spread was originally proposed by Saleh and<br />
Valenzuela <strong>for</strong> indoor propagation modeling [7]. It has also<br />
been adopted as the intra-cluster delay-spread model <strong>for</strong><br />
outdoor scenarios in the COST259 [8] model. Following the<br />
SCM philosophy, which is based on COST259, we use this as<br />
our guideline.<br />
The path DS was chosen under the following considerations<br />
• Similar to the definition of a constant path AS <strong>for</strong> a<br />
specific scenario in SCM, we set the path DS to be<br />
constant. The path AS and DS then define the<br />
minimum observable total (over all paths) AS and DS.<br />
• Both from measurements and intuition it follows that<br />
this minimum total spread lies somewhere between<br />
zero and a fraction of the mean total spread.<br />
• The error in power between an exponential PDP and<br />
the SCM definition (no DS) is illustrated in Figure 1.<br />
For a path DS of 10 ns, this error is slightly below -20<br />
dB and can be considered reasonably small. We set it<br />
equivalent to this value <strong>for</strong> all paths.<br />
We split the 20 sub-paths into subsets, denoted “midpaths”,<br />
which we then move to different delays relative to the<br />
original path. Even though a mid-path consists of multiple subpaths,<br />
it remains a single tap (delay-resolvable component).<br />
This approach limits the diversity increase to reasonable<br />
values, and avoids that single sub-paths become delayresolvable.<br />
Furthermore, lumping together a number of subpaths<br />
keeps the fading distribution of that tap close to Rayleigh<br />
and thus aids a potential implementation with the classic<br />
Gaussian-distributed number generator. We found that 4 is the<br />
absolute minimum number of sinusoids to yield a reasonable<br />
Rayleigh distribution.<br />
The number of mid-paths, and the power and delay<br />
parameters chosen <strong>for</strong> each mid-path are tabulated in Table 1.<br />
The mid-path powers, i.e. number of sub-paths, were chosen by<br />
considering the decreasing power with delay while staying<br />
above the minimum number of sub-paths. The delays <strong>for</strong> the<br />
mid-paths were then derived by employing the method from<br />
[5] and using the constraint that the DS is equal to the<br />
predetermined value of 10 ns and given the predetermined set<br />
of powers <strong>for</strong> the mid-paths.<br />
Each sub-path has an angle relative to the path mean angle<br />
assigned to it. By perturbing the set of sub-paths assigned to a<br />
mid-path, the AS of that mid-path can be varied. It has been<br />
reported, e.g. [6], that the intra-cluster AS conditioned on the<br />
intra-cluster delay is approximately independent of the delay.<br />
Hence, the mid-path ASs (AS m ) were optimized such that the<br />
deviation from the path AS (AS p ), i.e. the AS of all mid-paths<br />
combined, is minimized. The result is tabulated in Table 3.<br />
Finally, to aid in channel model implementation, we<br />
quantize the delay values to multiples of 1 ns.<br />
B. Frequency Range<br />
1) Path-Loss <strong>Model</strong><br />
The SCM path-loss model is based on the COST-Hata-<br />
<strong>Model</strong> [10] <strong>for</strong> Suburban and Urban Macro scenarios. The<br />
COST-Walfish-Ikegami-<strong>Model</strong> (COST-WI) [10] is defined <strong>for</strong><br />
error power below original signal in dB<br />
0<br />
-5<br />
-10<br />
-15<br />
-20<br />
-25<br />
-30<br />
-35<br />
-40<br />
-45<br />
3 mid-paths<br />
4 mid-paths<br />
10 0 10 1<br />
delay-spread in ns<br />
Figure 1. Relative power of channel impulse response difference when path-<br />
DS is added, compared at 5 MHz bandwidth
TABLE 3. SUB-PATHS TO MID-PATHS ASSIGNMENT AND RESULTING<br />
NORMALIZED MID-PATH ANGLE-SPREADS<br />
Midpath<br />
3 mid-path configuration 4 mid-path configuration<br />
Pwr Sub-paths AS m /<br />
AS p<br />
Pwr Subpaths<br />
AS m /<br />
AS p<br />
1 10/20 1, 2, 3, 4, 5,<br />
6, 7, 8, 19, 20<br />
2 6/20 9, 10, 11, 12,<br />
17, 18<br />
Urban Micro. Some further references on path loss were found<br />
([11]-[18]), however only few of them allow direct comparison<br />
between equivalent measurements at 2 and 5 GHz. These few<br />
however indicate that the most significant difference can be<br />
attributed to different gains in free-space path-loss, which is 8<br />
dB higher at 5 GHz compared to 2 GHz. Thus, <strong>for</strong><br />
comparability reasons, we propose a 5 GHz path-loss model<br />
that has an offset of 8 dB to the current 2 GHz model.<br />
There are some issues here though. The COST-231-Hata-<br />
<strong>Model</strong> was derived <strong>for</strong> the purpose of GSM coverage<br />
prediction and has a distance range of 1-20 km. The 5 GHz<br />
band on the other hand is likely going to be used <strong>for</strong> shortrange<br />
high-throughput services. In this case, a path-loss based<br />
on the COST-WI model with a distance range of 0.02-5 km is<br />
much more suitable. Note that this model has also been<br />
accepted by the ITU-R and was selected as Urban / Alternative<br />
Flat Suburban path-loss model in the IEEE 802.16 standard <strong>for</strong><br />
fixed wireless access [19]. Furthermore, the model<br />
distinguishes between LOS and NLOS situations.<br />
We propose to use the COST-WI model <strong>for</strong> all scenarios<br />
with the following parameters: base station (BS) antenna<br />
height: 32 m – Macro, 10 m – Micro; building height: 12 m –<br />
Urban, 9 m – Suburban; building to building distance: 50 m,<br />
street width: 25 m, mobile station (MS) antenna height: 1.5 m,<br />
orientation: 30° <strong>for</strong> all paths, and selection of medium sized<br />
city / suburban centres – Macro, metropolitan - Micro. The<br />
Scenario<br />
TABLE 2. PATH-LOSS MODEL<br />
Suburban<br />
Macro<br />
31.5 +<br />
35.0 log 10(d)<br />
Urban<br />
Macro<br />
34.5 +<br />
35.0 log 10(d)<br />
SCM pathloss<br />
NLOS<br />
(dB),<br />
d is in m LOS - -<br />
Urban<br />
Micro<br />
34.53 +<br />
38.0 log 10(d)<br />
30.18 +<br />
26.0 log 10(d)<br />
SCM shad. NLOS 8 8 10<br />
std. dev. (dB) LOS - - 8<br />
Alternative.<br />
short-range<br />
path-loss<br />
Alt. shad. std.<br />
Dev. (dB)<br />
5 GHz PL<br />
ext.<br />
NLOS<br />
LOS<br />
7.17 +<br />
38.0 log 10(d)<br />
30.18 +<br />
26.0 log 10(d)<br />
0.9865 6/20 1, 2, 3,<br />
4, 19, 20<br />
1.0056 6/20 5, 6, 7,<br />
8, 17, 18<br />
3 4/20 13, 14, 15, 16 1.0247 4/20 9, 10,<br />
15, 16<br />
4 - - - 4/20 11, 12,<br />
13, 14<br />
11.14 +<br />
38.0 log 10(d)<br />
30.18 +<br />
26.0 log 10(d)<br />
31.81 +<br />
40.5 log 10(d)<br />
30.18 +<br />
26.0 log 10(d)<br />
(N)LOS 8 8 8<br />
1.2471<br />
0.9145<br />
0.8891<br />
0.7887<br />
(N)LOS + 8 dB + 8 dB + 8 dB<br />
results are summarized in Table 2.<br />
2) <strong>Del</strong>ay-Spread, <strong>An</strong>gle-Spread and Ricean K-factor<br />
A preliminary measurement analysis indicates that <strong>for</strong><br />
Urban Micro the 5 GHz PDP and PAS do not significantly<br />
deviate from the 2 GHz one and we thus leave it unchanged.<br />
However, there is evidence that in urban macro and suburban<br />
macro there is noticeable difference in the decay rates of the 2<br />
GHz and 5 GHz PDP. There<strong>for</strong>e, <strong>for</strong> these environments, we<br />
propose rms delay spread values based on 5 GHz measurement<br />
analysis.<br />
Similarly, we propose using the 2 GHz K-factor <strong>for</strong> 5 GHz<br />
range. More energy escapes in reflections at 5 GHz but also the<br />
direct path is more attenuated, so the effects cancel out in a first<br />
order approximation. We apply the same argument in the case<br />
of shadowing and make no differentiation <strong>for</strong> frequency range.<br />
C. Other Extensions<br />
1) LOS <strong>for</strong> All Scenarios<br />
In the SCM, the LOS model consisting of path-loss and<br />
Ricean K-factor definition is a switch selectable option <strong>for</strong> the<br />
Urban Micro scenario only. We extend the K-factor option to<br />
cover also Urban and Suburban Macro scenarios as follows.<br />
Urban and Suburban Macro are assigned the same<br />
parameters. The probability of having LOS is calculated as [20]<br />
⎛ h ⎞⎛ ⎞<br />
= ⎜ −<br />
B d<br />
P ⎟<br />
⎜ −<br />
⎟<br />
LOS<br />
1 1 , d<br />
co<br />
< 300 , h<br />
BS<br />
> hB<br />
⎝ hBS<br />
⎠⎝<br />
d<br />
co ⎠<br />
and is zero otherwise. Here, h BS is the BS height, h B the average<br />
height of the rooftops, and d co is the cut-off distance. Values <strong>for</strong><br />
these parameters are proposed in [8].<br />
We use the empirical K-factor model presented in [21] <strong>for</strong><br />
typical (American) suburban environments and BS heights of<br />
approximately 20 m. In [22], an excellent agreement with this<br />
model was reported based on independent measurements under<br />
similar conditions. We propose the following parameters: MS<br />
antenna height 1.5 m, MS beamwidth: 360°, and selection of<br />
season: summer. The resulting model is<br />
K = 15.4<br />
− 5.0 ⋅ log10 ( d ) (dB)<br />
where d is the BS-MS distance in m.<br />
2) Time-Evolution<br />
The literature on dynamic channel models, that is, channel<br />
models with time-varying parameters, is relatively scarce.<br />
Initial references dynamic channel models appear to be [24],<br />
[25], [26]. Dynamic channel models <strong>for</strong> indoor environments<br />
are developed in [27], [28], [29], of which the first reference<br />
focuses on dynamic delay domain characterization and the<br />
latter two also incorporate spatial dynamics of the indoor<br />
channel. The standard [30] defines a simple model <strong>for</strong> varying<br />
tap delays and tap birth-death. However, this model is intended<br />
<strong>for</strong> receiver testing and does not represent a realistic channel.<br />
<strong>An</strong>alytical tools <strong>for</strong> characterization of non-stationary radio<br />
channel have been presented in [31].
The concept of drops in SCM can be seen as relatively<br />
short channel observation periods that are significantly<br />
separated from each other in time or space such that systemlevel<br />
parameters become constant and independent during<br />
these periods. Our approach is to virtually extend the lengths of<br />
these periods by adding short-term time-variability of some<br />
system-level parameters within the drops. All parameters<br />
remain independent between drops. The three effects we model<br />
are discussed in the following.<br />
a) Drifting of Tap <strong>Del</strong>ays<br />
Based on the geometric modeling and the propagation<br />
parameters, the delay drift ( ∆ τ) of a tap delay (τ) can be<br />
calculated directly from the velocity of MS (v), direction of MS<br />
movement (θ v ), the AoA (θ AoA ), and sample density per<br />
wavelength (D S ), where the angles are defined with respect to<br />
the normal of antenna broadside.<br />
The time between two consecutive samples (not drops) and<br />
the distance moved by the MS during this time is<br />
∆<br />
λ<br />
t =<br />
2vD S<br />
and λ<br />
l = , respectively.<br />
2<br />
D S<br />
The change in tap-delay between two consecutive samples<br />
can be derived as<br />
∆<br />
τ<br />
l<br />
= cos(θ) , where θ = θ v<br />
−θ<br />
AoA<br />
c<br />
and c is the speed of light.<br />
b) Drifting of <strong>An</strong>gles of Arrival<br />
In the case of AoA, the drift can be geometrically<br />
calculated as well, but one of the parameters is the distance<br />
between MS and last-bounce scatter, and this is unknown.<br />
SCM is not a single-bounce geometrical model and thus there<br />
is only a weak statistical dependence between AoAs and AoDs.<br />
Hence the unknown distance cannot simply be inferred from<br />
the geometry, and instead we propose a stochastic model where<br />
the distance is a random variable. As an initial model <strong>for</strong> the<br />
PDF, we selected a log-normal distribution with a constant,<br />
small offset and parameters according to Table 4.<br />
In general, the angle θ is a function of time. For BS-MS<br />
distances above 10 m, a linearization of this function yields a<br />
very good approximation <strong>for</strong> observation periods over<br />
hundreds of meters. If θ is linear in time, the rate of change ∆ θ<br />
is constant and can be derived as<br />
∆<br />
θ = ∆<br />
θ 0<br />
<strong>for</strong> d<br />
n<br />
< d<br />
n<br />
∆<br />
where<br />
d<br />
⎛ d ⎞<br />
n<br />
sin( θ<br />
n<br />
)<br />
θ =<br />
⎜<br />
⎟<br />
0<br />
arcsin<br />
⎝ d<br />
n+<br />
1 ⎠<br />
=<br />
d<br />
+ s<br />
θ = 180−<br />
θ otherwise,<br />
,<br />
+1 ∆<br />
∆ 0<br />
− 2d<br />
l cos( θ<br />
2 2<br />
n+<br />
1 n<br />
n n<br />
and n is the sample-time index.<br />
c) Drifting of Shadow Fading<br />
)<br />
TABLE 4. DISTRIBUTION PARAMETERS FOR d 0<br />
= d min<br />
+ X AND<br />
CORRELATION DISTANCES FOR SHADOW FADING<br />
Scenario<br />
Suburban Macro 10<br />
Urban Macro 10<br />
d min<br />
Parameters of log(X)<br />
(m) mean var.<br />
The time-evolution of shadow fading is determined by its<br />
spatial autocorrelation function. References show that an<br />
exponential function fits well and the drifting can thus be<br />
modeled by a first order autoregressive process.<br />
Derived from publications on measurement data around 2<br />
GHz ([32]-[38]), we propose using correlation distances (50%<br />
correlation point) listed in Table 4.<br />
3) Tapped <strong>Del</strong>ay-Line <strong>Model</strong><br />
In the SCM specification most parameters are defined by<br />
their PDFs. While this provides richness in variability, it can<br />
turn out to be a headache <strong>for</strong> accurate simulations where the<br />
simulation time grows exponentially with the number of<br />
random parameters. As a practical add-on we have thus defined<br />
a set of fixed values <strong>for</strong> the power, delays, and angles of cluster<br />
and intra-cluster taps. This is similar to the SCM link-level<br />
model. However, while this model targets <strong>3G</strong>PP comparability,<br />
our solution is close to the system-level model and furthermore<br />
optimized <strong>for</strong> small frequency autocorrelation.<br />
The fixed delays of the 6 paths defined in SCM were fitted<br />
to the PDP of the SCM system-level model using the method<br />
from [5]. These delays were then perturbed until a satisfactory<br />
frequency decorrelation was achieved.<br />
IV.<br />
τ<br />
2 + 2<br />
τ<br />
τ<br />
2 + 2<br />
τ<br />
−τ<br />
−τ<br />
IMPLEMENTATION<br />
The original SCM has been implemented in MATLAB 1 and<br />
is available [23] under a public license. Please check the<br />
referenced website <strong>for</strong> updated in<strong>for</strong>mation about any<br />
extensions of the implementation.<br />
REFERENCES<br />
[1] V. Erceg, L. Schumacher, P. Kyritsi, A. Molisch, D. S. Baum, A. Y.<br />
Gorokhov et al., “TGn <strong>Channel</strong> <strong>Model</strong>s”, IEEE 802.11-03/940r2, Jan.<br />
2004.<br />
[2] <strong>3G</strong>PP TR 25.996, “3rd Generation Partnership Project; technical<br />
specification group radio access network; spatial channel model <strong>for</strong><br />
MIMO simulations (release 6)”, V6.1.0.<br />
[3] 6 th Framework Programme, In<strong>for</strong>mation Society Technologies, Wireless<br />
World Initiative New Radio (WINNER), IST-2003-507591, [online]<br />
https://www.ist-winner.org/<br />
[4] D. S. Baum, G. <strong>Del</strong> Galdo, J. Salo, P. Kyösti, T. Rautiainen, M.<br />
Milojevic, and J.Hansen, “SCM Extensions,” WINNER WP5.5, Jan.<br />
2005.<br />
1 MATLAB is a registered trademark of The MathWorks, Inc.<br />
1<br />
50%<br />
correlation<br />
point (m)<br />
n 1<br />
1 200<br />
P<br />
−τ<br />
−τ<br />
n 1<br />
1 50<br />
Urban Micro 10 2 1 5<br />
P<br />
1
TABLE 5. TAPPED DELAY-LINE PARAMETERS<br />
Scenario Suburban Macro Urban Macro Urban Micro<br />
Power-delay parameters:<br />
relative path power (dB) /<br />
delay (µs)<br />
1 0 0 0 0 0 0<br />
2 -2.6682 0.1408 -2.2204 0.3600 -1.2661 0.2840<br />
3 -6.2147 0.0626 -1.7184 0.2527 -2.7201 0.2047<br />
4 -10.4132 0.4015 -5.1896 1.0387 -4.2973 0.6623<br />
5 -16.4735 1.3820 -9.0516 2.7300 -6.0140 0.8066<br />
6 -22.1898 2.8280 -12.5013 4.5977 -8.4306 0.9227<br />
Resulting total DS (µs) 0.231 0.841 0.294<br />
Path AS at BS, MS (deg) 2, 35 2, 35 5, 35<br />
<strong>An</strong>gular parameters:<br />
AoA (deg) /<br />
AoD (deg)<br />
1 156.1507 -101.3376 65.7489 81.9720 76.4750 -127.2788 0.6966 6.6100<br />
2 -137.2020 -100.8629 45.6454 80.5354 -11.8704 -129.9678 -13.2268 14.1360<br />
3 39.3383 -110.9587 143.1863 79.6210 -14.5707 -136.8071 146.0669 50.8297<br />
4 115.1626 -112.9888 32.5131 98.6319 17.7089 -96.2155 -30.5485 38.3972<br />
5 91.1897 -115.5088 -91.0551 102.1308 167.6567 -159.5999 -11.4412 6.6690<br />
6 4.6769 -118.0681 -19.1657 107.0643 139.0774 173.1860 -1.0587 40.2849<br />
Resulting total AS at BS,MS (deg) 4.70, 64.78 7.87, 62.35 15.76, 62.19 18.21, 67.80<br />
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