Post on 14-Jun-2022
Modelling and Simulation of MIMO Channels
Matthias Patzold
Agder University College
Mobile Communications Group
Grooseveien 36, NO-4876 Grimstad, Norway
E-mail: matthias.paetzold@hia.no
Homepage: http://ikt.hia.no/mobilecommunications/
BEATS/CUBAN Workshop 20041/37
Contents
I. Introduction
II. Principles of Fading Channel Modelling
III. Modelling of MIMO Channels
IV. Simulation of MIMO Channels
V. Conclusion
BEATS/CUBAN Workshop 20042/37
I. Introduction
Mobile Communications Using Smart Antennas
T r a n s m i t t e r C h a n n e l)x,t,(h t ¢ R e c e i v e r
M o b i l e s t a t i o n B a s e s t a t i o n1
2
M R
0 1 1 0 1 0 0 1 1 0 1 0
S p a c e - t i m e s i g n a l p r o c e s s i n gD e m o d u l a t i o nD e c o d i n g
S p a c e - t i m e c o d i n gM o d u l a t i o n
1
2
M T
Realistic spatio-temporal channel models are required for the design, test, and optimization
of mobile communication systems employing smart antenna technologies.
BEATS/CUBAN Workshop 20043/37
Meaning of Channel Modelling and Simulation for Mobile Communications
Reference system:
+Channelmodel
Noise
Data source Data sink
Transmitter Receiverd(i) x(t) y(t) d(i)
⇒ Performance measure: Bit error probability Pb = f
(
Eb
N0
)
Simulation system:
+Channel
Noise
Data source Data sink
Transmitter Receiversimulator
d(i) x(t) y(t) d(i)
⇒ Performance measure: Bit error probability Pb = f
(
Eb
N0, ∆β
)
≈ Pb
↑Model error
• The model error ∆β describes the essential error which is introduced by the channel simulator.
Channel simulators are important for the test, the parameter optimization, and the perfor-
mance analysis of mobile communication systems.
BEATS/CUBAN Workshop 20044/37
The Two Main Categories of Fading Channel Simulators
Simulators based on reference models: Simulators based on measurements:
Simulation model
Reference model
Measurement
Real-world
Snapshot
measurementscampaigns
channel channelReal-world
Simulation model
Problem: Reference models are not
close to real-world channels.
Problem: Finding of typical scenarios.
⇒ The dilemma of mobile fading channel modelling.
BEATS/CUBAN Workshop 20045/37
Some Requirements for Fading Channel Simulators
• High precision w.r.t. a given reference model or w.r.t. measured channels
• High efficiency
• The underlying stochastic channel simulator must be ergodic to reduce the number of trials
• Easy to determine the model parameters
• Easy to understand and easy to implement
• Reproducibility for enabling fair performance comparisons
• Easy to extend (frequency selectivity, spatial selectivity, multi-cluster propagation scenarios, number
of antenna elements, etc.)
• Low complexity
BEATS/CUBAN Workshop 20046/37
II. Principles of Fading Channel Modelling
Two Fundamental Methods for Modelling of Coloured Gaussian Noise Processes
1. Filter method:
⇒ Stochastic process µ(t)
⇒ Reference model
2. Sum-of-sinusoids (SOS) method:
cos(2πf1t + θ1)
cos(2πf2t + θ2)
cos(2πfNt + θN)
c1
c2
cN
... ...
... ...∞ ∞
e -⊗ -
e -⊗ -
e -⊗ -
+- µ(t)
⇒ Stochastic process µ(t)
⇒ Reference model
BEATS/CUBAN Workshop 20047/37
For a finite number of harmonic functions N , we obtain:
Parameters: ensemble
θn = Random variable (RV)
fn = const.
cn = const.
cos(2πf1t + θ1)
cos(2πf2t + θ2)
cos(2πfNt + θN)
c1
c2
cN
... ...
e -⊗ -
e -⊗ -
e -⊗ -
+ - µ(t)
⇒ Stochastic process µ(t)
⇒ Stochastic simulation model
Parameters: single realization
θn = const.
fn = const.
cn = const.
cos(2πf1t + θ1)
cos(2πf2t + θ2)
cos(2πfNt + θN)
c1
c2
cN
... ...
e -⊗ -
e -⊗ -
e -⊗ -
+ - µ(t)
⇒ Deterministic process µ(t)
⇒ Deterministic simulation model
BEATS/CUBAN Workshop 20048/37
Relationships Between Stochastic Processes, Random Variables,
Sample Functions, and Real-Valued Numbers
Gaussian process: µ(t) = limN→∞
N∑
n=1cn cos(2πfnt + θn) (cn = const., fn = const., θn = RV)
Stochastic process: µ(t) =N∑
n=1cn cos(2πfnt + θn) (cn = const., fn = const., θn = RV)
simulation model
Deterministic
Stochastic simulation model
modelReference
Gaussian process
Stochastic process
Randomvariable
Sample function
Real number
t = t0
θn = const. t = t0
µ(t0) = µ(t0, θn)
µ(t0) = µ(t0)
µ(t) = µ(t, θn)
N < ∞N → ∞
µ(t) = µ(t, θn)
µ(t) = µ(t, θn)
θn = const.
θn = RV
BEATS/CUBAN Workshop 20049/37
Principle of Deterministic Channel Modelling
Step 1: Starting point is a reference model derived from one, two or several Gaussian
processes.
Step 2: Derive a stochastic simulation model from the reference model by replacing each
Gaussian process by a sum-of-sinusoids with fixed gains, fixed frequencies, and
random phases.
Step 3: Determine the deterministic simulation model by fixing all model parameters of the
stochastic simulation model, including the phases.
Step 4: Compute the model parameters of the simulation model by using a proper param-
eter computation method.
Step 5: Simulate one (or some few) sample functions (deterministic processes).
BEATS/CUBAN Workshop 200410/37
Example: Derivation of a channel simulator for Rice processes
Step 1: Reference model Steps 2 & 3: Simulation model
ρµ (t)
(t)µ2
1(t)µ
πf t+θm (t)= ρ ρ)ρ2 sin(2
cos(2 πf t+θm (t)=1 ρ ρ)ρ
H (f)
H (f)(t)2v
(t)1v
ξ(t)
ρµ
ρµ (t)
(t)WGN
WGN
2
1
⇐⇒
⇒ Stochastic Rice process ξ(t) ⇒ Deterministic Rice process ξ(t)
Step 4: Compute the model parameters by fitting the statistics of the deterministic simulation
model to those of the stochastic reference model.
Step 5: Simulate the deterministic Rice process ξ(t).
BEATS/CUBAN Workshop 200411/37
Methods for the Calculation of the Model Parameters
Deterministic process: µi(t) =
Ni∑
n=1
ci,n cos(2πfi,nt + θi,n)
↗ ↑ ↖Model parameters: gains frequencies phases
Historical overview
Methods Disadvantages
Rice method (Rice, 1944) Small period
Jakes method (Jakes, 1974) Special case only
Monte Carlo method (Schulze, 1988) Non-ergodic
Method of equal distances (Patzold, 1994) Small period
Method of equal areas (Patzold, 1994) Slow convergency
Harmonic decomposition technique (Crespo, 1995) Small period
Mean-square-error method (Patzold, 1996) Small period
Method of exact Doppler spread (Patzold, 1996) Special case only
Lp-norm method (Patzold, 1996) –
Method porposed by Zheng and Xiao (2002) Non-ergodic
BEATS/CUBAN Workshop 200412/37
Classes of SOS Channel Simulators and Their Statistical Properties
Deterministic process: µi(t) =Ni∑
n=1ci,n cos(2πfi,nt + θi,n)
Class Gains Frequencies Phases First-order Wide-sense Mean- Autocor.-
ci,n fi,n θi,n stationary stationary ergodic ergodic
I const. const. const. – – – –
II const. const. RV yes yes yes yes
III const. RV const. no/yes a no/yes a no/ yes a no
IV const. RV RV yes yes yes no
V RV const. const. no no no/yes a no
VI RV const. RV yes yes yes no
VII RV RV const. no/yes a no/yes a no/yes a no
VIII RV RV RV yes yes yes no
a If certain boundary conditions are fulfilled.
BEATS/CUBAN Workshop 200413/37
Application of the Scheme to Parameter Computation Methods
Stochastic process: µi(t) =Ni∑
n=1ci,n cos(2πfi,nt + θi,n)
↗ ↑ ↖Model parameters: gains frequencies phases (RVs)
Parameter computation methods Class FOS WSSMean-ergodic
Autocor.-ergodic
Rice method II yes yes yes yes
Monte Carlo method IV yes yes yes no
Jakes method II yes yes yes yes
Harmonic decomposition technique II yes yes yes yes
Method of equal distances II yes yes yes yes
Method of equal areas II yes yes yes yes
Mean-square-error method II yes yes yes yes
Method of exact Doppler spread II yes yes yes yes
Lp-norm method II yes yes yes yes
Method proposed by Zheng and Xiao IV yes yes yes no
BEATS/CUBAN Workshop 200414/37
Applications of the Principle of Deterministic Channel Modelling
• Frequency-nonselective channels (Rayleigh, Rice, ext. Suzuki, Nakagami, etc.),
• Frequency-selective channels (COST 207, CODIT),
• Space-time wideband channels (COST 259),
• Multiple cross-correlated Rayleigh fading channels,
• Multiple uncorrelated Rayleigh fading channels,
• Perfect modelling and simulation of measured 2-D and 3-D channels,
• Frequency-hopping fading channels,
• Design of ultra fast channel simulators (tables system),
• Design of burst error models,
• Development of MIMO channels.
BEATS/CUBAN Workshop 200415/37
III. Modelling of MIMO Channels
Block Diagram of a MIMO Mobile Communication System
Transmitter Receiver
x1
x2
xMT
r1
r2
rMR
h11
h12
h21h
MR 1
h22
hM
R2
h 1MT
hMRMT
h 2MT
•
•
•
•
•
•
•
•
•
•
•
•
5
5
5
5
5
5
-
-
-
HHHHHHHHHHHHj
SS
SS
SS
SS
SS
SS
SS
SSw
©©©©©©©©©©©©*
HHHHHHHHHHHHj¶¶
¶¶
¶¶
¶¶
¶¶
¶¶
¶¶
¶¶7
´´
´´
´´
´´
´´
´3
• Channel coefficients: The channel coefficient hij(t) describes the transmission behavior of the
channel from the jth transmit antenna to the ith receive antenna.
• Channel matrix: H(t) = [hij(t)] ∈ CMR×MT
• Channel capacity: C(t) = log2 det
(
IMT+
SBS, total
MTNnoiseH(t)HH(t)
)
[bits/s/Hz]
(MR ≥ MT )
BEATS/CUBAN Workshop 200416/37
Generalized Principle of Deterministic Channel Modelling
Step 1: Starting point is a geometrical model with an infinite number of scatterers, e.g.,
(a) one-ring model (b) two-ring model (c) elliptical model
BS MS BS MS BS MS
Step 2: Derive a stochastic reference model from the geometrical model.
Step 3: Derive an ergodic stochastic simulation model from the reference model by using
only a finite number of N scatterers.
Step 4: Determine the deterministic simulation model by fixing all model parameters of the
stochastic simulation model.
Step 5: Compute the parameters of the simulation model by using a proper parameter
computation method, e.g., the Lp-norm method (LPNM).
Step 6: Generate one (or some few) sample functions by using the deterministic simulation
model with fixed parameters.
BEATS/CUBAN Workshop 200417/37
Illustration of the Generalized Principle of Deterministic Channel Modelling
3 4 6
5
21
Infinite complexity
(N → ∞)
⇒ ⇒sample functions sample functions
Non-realizable Realizable⇒sample functions
Non-realizable
Reference model
E{·} E{·} < · >
Statistical properties
Deterministic SoSsimulation model
computationParameter
Simulation ofsample functions
Fixedparameters
Stochastic SoSsimulation model
Finite complexity
One (or some few)Infinite number ofInfinite number of
Finite complexity
(N ≈ 25) (N ≈ 25)
Lp-norm method (LPNM)
Geometrical model
BEATS/CUBAN Workshop 200418/37
Application of the Generalized Principle of Deterministic Channel Modelling
A Geometrical Model for a MIMO Channel
Dn2
Dn1ABS
1
δBS
A2MS
αMS
δMS
0MS
BSα
nBSφ
AMS1
D2n
BSφmax
Sn
v
y
0BS
D
2ABS
φMS
D
n
1n
x
R
v
α
• The geometrical model is known as the one-ring model for a 2 × 2 channel.
• The local scatterers are laying on a ring around the MS.
• If the number of scatterers N → ∞, then the discrete AOA φMS
n tends to a continuous RV φ MS with
a given distribution p(φ MS), e.g., the uniform distribution, the von Mises distribution, the Laplacian
distribution, etc.
BEATS/CUBAN Workshop 200419/37
The Reference Model
• Channel coefficients: h11(t) = limN→∞
1√N
N∑
n=1anbne
j(2πfnt+θn)
h12(t) = limN→∞
1√N
N∑
n=1a∗nbne
j(2πfnt+θn)
h21(t) = limN→∞
1√N
N∑
n=1anb
∗ne
j(2πfnt+θn)
h22(t) = limN→∞
1√N
N∑
n=1a∗nb
∗ne
j(2πfnt+θn)
where the phases θn are i.i.d. RVs and
an = e jπ(δBS/λ)[cos(αBS)+φBSmax sin(αBS) sin(φMS
n )]
bn = e jπ(δMS/λ) cos(φMSn −αMS)
fn = fmax cos(φMSn − αv)
• Channel matrix: H(t) = [hij(t)] =
(
h11(t) h12(t)
h21(t) h22(t)
)
• Channel capacity: C(t) = log2 det
(
I2 +SBS, total
2NnoiseH(t)HH(t)
)
[bits/s/Hz]
BEATS/CUBAN Workshop 200420/37
Statistical Properties of the Reference Model
• Space-time CCF: ρ11,22(δBS, δMS, τ ) := E{h11(t)h∗22(t + τ )}
= limN→∞
1
N
N∑
n=1
a2n b2
ne−j2πfnτ
=
π∫
−π
a2n(δBS)b
2n(δMS)e
−j2πfnτp(φMS)dφMS
• Time ACF: rh11(τ ) := E{h11(t)h∗11(t + τ )}
=
π∫
−π
e −j2πfmax cos(φMS−αv)τp(φMS) dφMS
Relationships: rh11(τ ) = rh12(τ ) = rh21(τ ) = rh22(τ ) = ρ11,22(0, 0, τ )
• 2D space CCF: ρ(δBS, δMS) := ρ11,22(δBS, δMS, 0)
=
π∫
−π
a2n(δBS)b
2n(δMS)p(φMS)dφMS
BEATS/CUBAN Workshop 200421/37
The Stochastic Simulation Model
• Channel coefficients: h11(t) = 1√N
N∑
n=1anbne
j(2πfnt+θn)
⇒ The phases θn are i.i.d. RVs
• Channel matrix: H(t) =
(
h11(t) h12(t)
h21(t) h22(t)
)
⇒ Stochastic channel matrix
• Channel capacity: C(t) = log2 det
(
I2 +SBS, total
2NnoiseH(t)HH(t)
)
[bits/s/Hz]
⇒ Stochastic process
⇒The analysis of C(t) has to be performed by using statistical aver-
ages, e.g., Cs = E{C(t)}.
BEATS/CUBAN Workshop 200422/37
Statistical Properties of the Stochastic Simulation Model
• Space-time CCF: ρ11,22(δBS, δMS, τ ) := E{h11(t)h∗22(t + τ )}
=1
N
N∑
n=1
a2n(δBS)b
2n(δMS)e
−j2πfnτ
• Time ACF: rh11(τ ) := E{h11(t)h∗11(t + τ )}
=1
N
N∑
n=1
e −j2πfmax cos(φMS
n −αv)τ
Relationships: rh11(τ ) = rh12(τ ) = rh21(τ ) = rh22(τ ) = ρ11,22(0, 0, τ )
• 2D space CCF: ρ(δBS, δMS) := ρ11,22(δBS, δMS, 0)
=1
N
N∑
n=1
a2n(δBS)b
2n(δMS)
=1
N
N∑
n=1
e j2π(δBS/λ)[cos(αBS)+φBS
max sin(αBS) sin(φMS
n )]·e j2π(δMS/λ) cos(φMS
n −αMS)
BEATS/CUBAN Workshop 200423/37
The Deterministic Simulation Model
• Channel coefficients: h11(t) = 1√N
N∑
n=1anbne
j(2πfnt+θn)
⇒ The phases θn are constant quantities
• Channel matrix: H(t) =
(
h11(t) h12(t)
h21(t) h22(t)
)
⇒ Deterministic channel matrix
• Channel capacity: C(t) = log2 det
(
I2 +SBS, total
2NnoiseH(t)HH(t)
)
[bits/s/Hz]
⇒ Deterministic process
⇒The analysis of C(t) has to be performed by using time averages,
e.g., Ct =< C(t) >.
BEATS/CUBAN Workshop 200424/37
Statistical Properties of the Deterministic Simulation Model
• Space-time CCF: ρ11,22(δBS, δMS, τ ) := < h11(t)h∗22(t + τ ) >
=1
N
N∑
n=1
a2n(δBS)b
2n(δMS)e
−j2πfnτ
• Time ACF: rh11(τ ) := < h11(t)h∗11(t + τ ) >
=1
N
N∑
n=1
e −j2πfmax cos(φMS
n −αv)τ
Relationships: rh11(τ ) = rh12(τ ) = rh21(τ ) = rh22(τ ) = ρ11,22(0, 0, τ )
• 2D space CCF: ρ(δBS, δMS) := ρ11,22(δBS, δMS, 0)
=1
N
N∑
n=1
a2n(δBS)b
2n(δMS)
=1
N
N∑
n=1
e j2π(δBS/λ)[cos(αBS)+φBS
max sin(αBS) sin(φMS
n )]·e j2π(δMS/λ) cos(φMS
n −αMS)
BEATS/CUBAN Workshop 200425/37
Parameter Computation Method
Parameters: The model parameters to be determined are the discrete AOAs φMSn (n = 1, 2, . . . , N).
Aim: Determine the model parameters φMSn such that
ρ11,22(δBS, δMS, τ ) ≈ ρ11,22(δBS, δMS, τ ) .
Solution: Lp-norm method
E(p)1 :=
{
1τmax
τmax∫
0
|rh11(τ ) − rh11(τ )|pdτ
}1/p
E(p)2 :=
{
1δBSmax δMS
max
δBSmax∫
0
δMSmax∫
0
|ρ(δBS, δMS) − ρ(δBS, δMS)|pdδMS dδBS
}1/p
Two alternatives: (i) Joint optimization: E(p) = w1E(p)1 + w2E
(p)2
w1, w2: weighting factors
(ii) Using two independent sets {φ′MSn } and {φMS
n }in rh11(τ ) and ρ(δBS, δMS), respectively.
⇒ Orthogonalization of the optimization problem.
BEATS/CUBAN Workshop 200426/37
Structure of the Simulation Model
+
. . .
. . .
. . .
. . . . . .
. . .
. . .
. . .
. . .. . .
. . .
. . .
. . .
+
. . .
. . .
1/√
N
1/√
N
1/√
N
s2(t)
r1(t) r2(t)
bN∗b∗
2b∗1bNb2b1
a1 a2 aN
s1(t)
a∗N
a∗2
a∗1
ej(2πfN t + θN )
ej(2πf2t + θ2)
ej(2πf1t + θ1)
BEATS/CUBAN Workshop 200427/37
Performance Evaluation
• Comparison of the time ACFs rh11(τ ) (reference model) and rh11(τ ) (simulation model)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−0.5
0
0.5
1
Time separation, τ (s)
Tim
e au
toco
rrel
atio
n fu
nctio
n
Reference modelSimulation modelSimulation
τmax
Reference model: Based on the one-ring model with uniformly distributed AOAs φMS.
Simulation model: Designed by using the Lp-norm method (N = 25 , p = 2, τmax = 0.08 s, fmax = 91 Hz).
BEATS/CUBAN Workshop 200428/37
Reference model Simulation model
2-D space CCF ρ(δBS, δMS) 2-D space CCF ρ(δBS, δMS)
0
5
10
15
20
25
30
0
0.5
1
1.5
2
2.5
3
−0.5
0
0.5
1
2−D
spa
ce c
ross
−co
rrel
atio
n fu
nctio
n
0
5
10
15
20
25
30
0
0.5
1
1.5
2
2.5
3
−0.5
0
0.5
1
2−D
spa
ce c
ross
−co
rrel
atio
n fu
nctio
n
δMS/λ δBS/λ δMS/λ δBS/λ
Reference model: Based on the one-ring model with uniformly distributed AOAs φMS.
Simulation model: Designed by using the Lp-norm method with N = 25
(p = 2, δBSmax = 30λ, δMS
max = 3λ, αBS = αMS = 90◦, φBSmax = 2◦).
BEATS/CUBAN Workshop 200429/37
IV. Simulation of MIMO Channels
• Channel capacity: C(t) := log2 det
(
I2 +SBS, total
2NnoiseH(t)HH(t)
)
[bits/s/Hz]
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
1
2
3
4
5
6
7
8
9
10
11
Time, t (s)
Sim
ulat
ed c
hann
el c
apac
ity, (
bits
/s/H
z)
CapacityMean Capacity
Parameters: N = 25, MBS = MMS = 2, δBS = δMS = λ/2, SNR = 17 dB
BEATS/CUBAN Workshop 200430/37
Scattering Scenario
Geometrical one-ring model:
scatterersCluster of
δBS
y
xδMS
αvφBSmax
v
≈ 2√κ
Parameters:
MBS = MMS = 2
δBS = δMS = λ/2
φBSmax = 2◦
αv = φMS0 = 180◦
fmax = 91 Hz
Reference model: assuming the von Mises distribution for the AOA φMS :
p(φMS) =1
2πI0(κ)e κ cos(φMS−φMS
0 )
κ = 0 : p(φMS) = 1/(2π) (isotropic scattering)
κ → ∞ : p(φMS) → δ(φMS − φMS0 ) (extremely nonisotropic scattering)
Simulation model: designed by using the LPNM with N = 25.
BEATS/CUBAN Workshop 200431/37
PDF of the Channel Capacity C(t)
0 2 4 6 8 100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
PD
F o
f the
cap
acity
C(t
)
Level, r
κ = 0κ = 10κ = 100
o
Observations: • κ influences the PDF pC(r) of the capacity C(t)
• If κ ↑; angular spread of the AOA φMS ↓; Var{C(t)} ↑
BEATS/CUBAN Workshop 200432/37
Normalized LCR of the Channel Capacity C(t)
0 2 4 6 8 100
0.2
0.4
0.6
0.8
1
1.2
1.4
Level, r
NC
(r)/
f max
κ = 0κ = 3κ = 5κ = 10κ = 100
o
Observations: • κ has a strong influence on the LCR NC(r) of the capacity C(t)
• If κ ↑; angular spread of the AOA φMS ↓; NC(r) ↓
BEATS/CUBAN Workshop 200433/37
Normalized ADF of the Channel Capacity C(t)
0 2 4 6 8 100
50
100
150
200
250
300
350
400
450
500
Level, r
TC
(r)⋅
f max
κ = 0κ = 10κ = 100
o
Observations: • κ has a strong influence on the ADF TC(r) of the capacity C(t)
• If κ ↑; angular spread of the AOA φMS ↓; TC(r) ↑.
BEATS/CUBAN Workshop 200434/37
The Effect of κ on the BER Performance
4 5 6 7 8 9 1010
−4
10−3
10−2
10−1
100
Eb/N
0 (dB)
Bit
erro
r ra
te
κ = 0
κ = 20
κ = 30
κ = 40
Coding system: 4-D 16QAM linear 32-state space-time trellis code with 2 transmit and 2 receive
antennas (δBS = 30λ and δMS = 3λ).
Observations: • κ ↑; angular spread ↓; BER ↑• If κ decreases from 40 to 0, then a gain of ca. 1.5 dB can be achieved at a BER
of 2 · 10−3.
BEATS/CUBAN Workshop 200435/37
The Effect of the Antenna Spacing on the BER Performance
4 5 6 7 8 9 1010
−4
10−3
10−2
10−1
100
Eb/N
0 (dB)
Bit
erro
r ra
te
δBS
/λ = 1/2, δMS
/λ = 1/2δ
BS/λ = 1 , δ
MS/λ = 1
δBS
/λ = 30 , δMS
/λ = 3δ
BS/λ = 30 , δ
MS/λ = 1/2
δBS
/λ = 1/2, δMS
/λ = 3δ
BS/λ = 3 , δ
MS/λ = 1
Coding system: 4-D 16QAM linear 32-state space-time trellis code with 2 transmit and 2 receive
antennas.
Observations: • δBS, δMS ↑; spatial correlation ↓; BER ↓• A large spacing among the antennas at the BS provides a better performance
than a large antenna spacing at the MS.
BEATS/CUBAN Workshop 200436/37
VI. Conclusion
a The principle of deterministic channel modelling has been generalized.
a The generalized concept has been applied on the geometrical one-ring scattering model.
a It has been shown how the parameters of the simulation model can be determined by using the
Lp-norm method (LPNM).
a The designed deterministic MIMO channel simulator with N = 25 scatterers has nearly the
same statistics as the underlying stochastic reference model with N = ∞ scatterers.
a The new MIMO space-time channel simulator is very useful in the investigation of the PDF,
LCR, and ADF of the channel capacity C(t) from time-domain simulations.
a Finally, it has been demonstrated that the system performance decreases if the spatial correlation
increases.
BEATS/CUBAN Workshop 200437/37