ETSI TR 102 311 V1.2.1 (2015-11)

TECHNICAL REPORT
Fixed Radio Systems;
Point-to-point equipment;
Specific aspects of the spatial frequency reuse method

2 ETSI TR 102 311 V1.2.1 (2015-11)

Reference
RTR/ATTM-04029
Keywords
DFRS, digital, DRRS, FWA, MIMO, radio
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3 ETSI TR 102 311 V1.2.1 (2015-11)
Contents
Intellectual Property Rights . 5
Foreword . 5
Modal verbs terminology . 5
Introduction . 5
1 Scope . 6
2 References . 6
2.1 Normative references . 6
2.2 Informative references . 6
3 Definitions, symbols and abbreviations . 7
3.1 Definitions . 7
3.2 Symbols . 8
3.3 Abbreviations . 8
4 Overview . 9
4.1 Capacity improvement of the MIMO system (Spatial Multiplexing) . 9
4.2 Difference between Cross-Polarization and Spatial Frequency Reuse (MIMO) . 11
4.3 Methods to achieve spatial frequency reuse . 13
4.3.1 Spatial configuration . 13
4.3.1.1 MIMO channel with spatial configuration . 13
4.3.1.2 MIMO System Model . 13
4.3.2 Spatial frequency reuse based on rich scattering . 14
4.3.3 Spatial frequency reuse based on link geometry . 15
4.3.3.1 Channel matrix pure line of sight case . 15
4.3.3.2 Maximal orthogonal condition and optimal antenna spacing . 18
4.3.3.3 Spatial diversity gain . 20
4.3.3.4 Working with antenna spacing below the sub-optimal condition . 20
4.3.3.5 Channel matrix considering link propagation . 21
4.3.3.6 Multi-polarized MIMO . 22
4.4 MIMO Performance . 22
4.5 The spatial frequency reuse canceller . 24
4.5.1 Open-Loop MIMO . 24
4.5.2 Closed-Loop MIMO . 25
4.5.3 MIMO receiver cancellation technique comparison . 27
5 Verification by field trial and simulation . 28
5.1 Overview . 28
5.2 5 GHz field trial . 28
5.2.1 MIMO channel measurement experiment - Aims . 28
5.2.2 MIMO channel measurement experiment - Configuration and plan . 29
5.2.3 MIMO channel measurement setup . 29
5.2.3.1 Tx setup . 29
5.2.3.2 RX setup . 29
5.2.3.3 Test results and analysis . 30
5.2.3.3.1 Results . 30
5.2.3.3.2 Analysis . 31
5.2.3.3.3 MIMO channel measurement experiment - Conclusions . 33
5.3 18 GHz field trial . 33
5.3.1 MIMO channel measurement experiment - Aims . 33
5.3.2 MIMO channel measurement experiment - Configuration and plan . 33
5.3.3 MIMO channel measurement setup . 33
5.3.4 Test results and analysis . 34
6 Verification by simulation . 35
6.1 The simulation block diagram . 35
6.2 The simulation results . 37
ETSI
4 ETSI TR 102 311 V1.2.1 (2015-11)
7 Void . 37
8 Practical implementation . 38
8.1 Overview . 38
8.2 Installation Issues . 38
8.3 Availability Calculation . 39
9 Summary . 39
Annex A: List of Topics to be considered in Standardization . 40
A.1 Topic List . 40
Annex B: Antenna Geometry and Composite Antenna RPE's . 41
B.1 Antenna Geometry . 41
B.2 Composite Antenna RPE's . 41
Annex C: MIMO Status in 2014 . 44
History . 45

ETSI
5 ETSI TR 102 311 V1.2.1 (2015-11)
Intellectual Property Rights
IPRs essential or potentially essential to the present document may have been declared to ETSI. The information
pertaining to these essential IPRs, if any, is publicly available for ETSI members and non-members, and can be found
in ETSI SR 000 314: "Intellectual Property Rights (IPRs); Essential, or potentially Essential, IPRs notified to ETSI in
respect of ETSI standards", which is available from the ETSI Secretariat. Latest updates are available on the ETSI Web
server (http://ipr.etsi.org).
Pursuant to the ETSI IPR Policy, no investigation, including IPR searches, has been carried out by ETSI. No guarantee
can be given as to the existence of other IPRs not referenced in ETSI SR 000 314 (or the updates on the ETSI Web
server) which are, or may be, or may become, essential to the present document.
Foreword
This Technical Report (TR) has been produced by ETSI Technical Committee Access, Terminals, Transmission and
Multiplexing (ATTM).
Modal verbs terminology
In the present document "shall", "shall not", "should", "should not", "may", "need not", "will", "will not", "can" and
"cannot" are to be interpreted as described in clause 3.2 of the ETSI Drafting Rules (Verbal forms for the expression of
provisions).
"must" and "must not" are NOT allowed in ETSI deliverables except when used in direct citation.
Introduction
It has been known for a long time that in order to improve theoretically the capacity of a given communication channel
with maintaining the existing power at the transmitter and SNR at the receiver, the best solution is to dismantle the
aggregate single channel into independent orthogonal sub-channels all using the same carrier frequency. To this
theoretical improvement a considerable practical implementation can be added, given that with the distributing of
payload among sub-channels the required order of the modulation scheme can be reduced. One example of exploiting
this payload distribution method can be found in the existing "co-channel dual polarization" mode. With this
implementation the aggregate payload is distributed between the both orthogonal independent sub-channels - the two
perpendicular linear polarization carriers. The present document describes a new approach of orthogonalization , the
spatial frequency re-use. As in the case of polarization, in order to perform the separation at the receiver, a special
module should be incorporated - similar to the cross-polarization Interference Canceller (XPIC) - the Spatial Frequency
Reuse Canceller (SFRC). In general, the SFR method is not limited to only two sub-channels as in the CCDP case, and
systems that use it are able to double, triple or multiple the spectral efficiency without any trade off on the system gain
as it is normally the case with improving the spectral efficiency by going to high order QAM modulation.
The present document includes an updated view of the SFR scheme using Multiple Antenna Techniques (MIMO).
Furthermore, some theoretical aspect reviews, installation issues, results from a new in field trial, considerations about
planning and, in the end, a living list for relevant standards modifications have been added.
Main changes reported in the present document are related to the MIMO system model, performance with non-optimal
antenna spacings, installation issue, new field trial, antenna composite RPE and MIMO deployment status in Europe.
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6 ETSI TR 102 311 V1.2.1 (2015-11)
1 Scope
The present document provides, initially, a theoretical overview of how point-to-point systems that use SFRC could
improve the link capacity and/or system gain, or could focus power in different directions or cover an area. Focus is put
on LOS links.
In general these different results may "compete" with one another and for example an increase of capacity may require
an increase of system gain. Few basic methods for implementing SFR are provided in the present document.
Simulation and field trial results are provided in order to show the discussed techniques and the main improvements for
the SFRC over the "Internal" Co-Channel Interference (ICCI).
Main report subjects:
• Increase the link capacity (by increasing the spectral efficiency).
• Increase the link system gain (by increasing the receiver SNR).
• Methods of implementing SFR (by using MIMO).
• Verification by simulations and trials.
• Improvement parameter definition.
• Planning matters (installation issues and availability calculation).
• Living list for standard modifications.
2 References
2.1 Normative references
References are either specific (identified by date of publication and/or edition number or version number) or
non-specific. For specific references, only the cited version applies. For non-specific references, the latest version of the
reference document (including any amendments) applies.
Referenced documents which are not found to be publicly available in the expected location might be found at
http://docbox.etsi.org/Reference.
NOTE: While any hyperlinks included in this clause were valid at the time of publication, ETSI cannot guarantee
their long term validity.
The following referenced documents are necessary for the application of the present document.
Not applicable.
2.2 Informative references
References are either specific (identified by date of publication and/or edition number or version number) or
non-specific. For specific references, only the cited version applies. For non-specific references, the latest version of the
reference document (including any amendments) applies.
NOTE: While any hyperlinks included in this clause were valid at the time of publication, ETSI cannot guarantee
their long term validity.
The following referenced documents are not necessary for the application of the present document but they assist the
user with regard to a particular subject area.
[i.1] Recommendation ITU-R F.699: "Reference radiation patterns for fixed wireless system antennas
for use in coordination studies and interference assessment in the frequency range from 100 MHz
to about 70 GHz".
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7 ETSI TR 102 311 V1.2.1 (2015-11)
3 Definitions, symbols and abbreviations
3.1 Definitions
For the purposes of the present document, the following terms and definitions apply:
2 H
Eigenvalue ( λ ): Eigenvalues of the matrix H × H are the root of the characteristic equation:
H 2
det( H × H − λ I ) = 0
expectation (E ): weighted average value of a Random Variable over all possible realizations that the Random
H
Variable may assume
NOTE 1: The weight coefficients are the probability value that the Random Variable assumes that value.
NOTE 2: Subscript "H" refers to the name of the Random Variable, for the reference scope "H" is the Channel
Matrix.
EXAMPLE: Mathematical formulation:
- discrete scalar random variable "X": "X" takes values "x , x …" with probabilities "p , p …"
1 2 1 2
∞
E[]X = x × p
∑ i i
i=1
- continuous scalar random variable "X": "X" takes continuous values and f(x) is the probability
density function
+∞
E[]X = x × f()x ⋅ dx
∫
−∞
- Matrix Random Variable "H":
h h . . h
⎡ ⎤
11 12 1M
⎢ ⎥
h h . . h
21 22 2M
⎢ ⎥
⎢ ⎥
E[]H = E . . . . . =
H NM
⎢ ⎥
... ... ... ... ...
⎢ ⎥
⎢ ⎥
h h . . h
⎣ N1 N 2 NM
⎦
E[]h E[h] . . E[h ]
⎡ ⎤
11 12 1M
⎢ ⎥
E[]h E[h ] . . E[h ]
21 22 2M
⎢ ⎥
⎢ ⎥
= . . . . .
⎢ ⎥
... ... ... ... ...
⎢ ⎥
⎢ ⎥
E[]h E[h ] . . E[h ]
N1 N 2 NM
⎣ ⎦
Hadamard product ( ◦): operation that takes two matrices of the same dimensions, and produces another matrix where
each element "ij" is the product of elements "ij" of the original two matrices
H
Hermitian transpose (·) : N × M matrix "H" with complex entries is the M × N "H*" matrix obtained from "H" by
taking the transpose and then taking the complex conjugate of each matrix entries
NOTE: Also known as Complex Transpose.
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8 ETSI TR 102 311 V1.2.1 (2015-11)
matrix trace (Tr): trace of an N × N square matrix "Q" is defined to be the sum of the elements on the main diagonal
N N
Tr()Q = q + q + .q = q = λ
11 22 NN ∑ ii ∑ i
i=1 i=1
power constraint: constraint applicable to the total transmission power level of the MIMO system (P ) with respect
MIMO
to the transmitted power level by the SISO system (P )
SISO
NOTE: If the MIMO system transmits the same power level of the reference SISO system then the power
constraint holds. Otherwise if P is higher than P , e.g. in case of
MIMO SISO
N × M MIMO P = N × P , the constraint does not hold.
MIMO SISO
singular value (λ): defined as the square root of the Eigenvalues
3.2 Symbols
For the purposes of the present document, the following symbols apply:
α Transmission Power Weight (for Water Filling/Pouring)
A Free Space Loss and Fading Attenuation Effects Matrix
argmin(.) Argument which minimize the brackets content
B Bandwidth
C Capacity [bit/s/Hz]
dB decibel
dBc decibel relative to mean carrier power
dBi decibel relative to an isotropic radiator
dBm decibel relative to 1 milliWatt
dBW decibel relative to 1 Watt
d Optimal Distance between Antennas
opt
E Expectation over variable H
H
H NxM Channel Matrix
I Unitary Matrix
λ Singular Value of Channel Matrix (H)
2 H
λ Eigenvalue of Matrix H·H
M Number of Transmit Antennas
m Modulation Order
N Number of Receive Antennas
N Noise Power Spectral Density
P Transmission Power Level
P Transmission Power Level of MIMO system (total)
MIMO
P Transmission Power Level of SISO system
SISO
ppm parts per million
ρ SNR
S̅ Average Received Power
X Polarization Effects Matrix (XPD)
det Matrix Determinant
Tr Matrix Trace
◦ Hadamard Product
|·| Absolute Value
H
(·) Hermitian Transpose
3.3 Abbreviations
For the purposes of the present document, the following abbreviations apply:
AWGN Added White Gaussian Noise
BER Bit Error Ratio
BLAST Bell Laboratories Layered Space Time
C/N Carrier to Noise
CCDP Co-Channel Dual Polarization
CEPT Comité Européen des Postes et Télécommunications
CS Channel Separation
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9 ETSI TR 102 311 V1.2.1 (2015-11)
CTF Channel Transfer Function
ECC Electronic Communication Committee
FS Fixed Service
ICCI "Internal" Co-Channel Interference
IDU InDoor Unit
ITU-R International Telecommunication Union - Radiocommunication
LOS Line Of Sight
MIMO Multiple Input Multiple Output
ML Maximum-Likelihood
MMSE Minimum Mean Square Error
MP Multi-Path
MSE Mean Square Error
MW MicroWave
nLOS near-Line Of Sight
NLOS Non-Line Of Sight
PP Point-to-Point
PTP Point To Point
QAM Quadrature Amplitude Modulation
RF Radio Frequency
RIC Radio Interface Capacity
RPE Radiation Power Envelope
RSL Received Strength Level
Rx Receiver
SAW Surface Acoustic Wave
SDG Spatial Diversity Gain
SFR Spatial Frequency Re-use
SFRC Spatial Frequency Reuse Canceller
SISO Single Input Single Output
SNR Signal to Noise Ratio
STD Standard Deviation
SVD Singular Value Decomposition
T Symbol Period
Tx Transmitter
UCA Uniform Circular Array of antenna
ULA Uniform Linear Array of antenna
URA Uniform Rectangular Array of antenna
VBLAST Vertical Bell Laboratories Layered Space Time
XPD Cross-Polarization Discrimination
XPIC Cross-Polarization Interference Canceller
ZF Zero-Forcing
4 Overview
4.1 Capacity improvement of the MIMO system (Spatial
Multiplexing)
For an N × N MIMO systems the "Spatial Multiplexing" refers to the promising Capacity improvement. Basically, "N"
independent orthogonal sub-channels, are provided on the same communication channel (CS), then the SISO maximal
achievable spectral efficiency (C) is multiplied by a factor "N" without adding any power resource (i.e. for the MIMO
system the single transmitter level is P/N). Figure 4.1 shows a Single Input Single Output (SISO) system compared with
a Multiple Input Multiple Output (MIMO) using the same physical resource i.e. the given channel (CS).
This is valid only in some conditions: when the sub-channels are orthogonal or independent which means that the
statistical expectation of the product of samples of the signals taken from any pair of the independent sub-channel is
very low or ideally null.
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10 ETSI TR 102 311 V1.2.1 (2015-11)
For the purpose of such capacity improvement any orthogonalization method is valid, either polar or spatial. In addition
to the theoretical capacity improvement there is also the available practical improvement. In practice the division of the
aggregate payload among the sub-channels facilitates lowering the order of the modulation. For example, aggregate
capacity of 156 Mbit/s over 28 MHz, when divided between two sub-channels, each one of them carrying only
78 Mbit/s over 28 MHz channel. In comparison, a single channel payload implementation requires 128 QAM
constellations, while with the sub-channel approach a 16 QAM per carrier is sufficient. From the equations in figure 4.1
it can be concluded that the theoretical difference between the two approaches is 9 dB, however due to practical
considerations such as linearity and phase noise, the gain improvement is higher, i.e. around 11 dB.

SISO system
single channel
P SNR
Transmitter
Receiver
C   log (SNR)
∝
MIMO system
N orthogonal sub-channels
P/N SNR/N
P/N SNR/N
Receiver
Transmitter
P/N SNR/N
N
P/N SNR/N
C N log (SNR)
∝
Figure 4.1: Comparison between SISO system and MIMO system
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11 ETSI TR 102 311 V1.2.1 (2015-11)
4.2 Difference between Cross-Polarization and Spatial
Frequency Reuse (MIMO)
Unlike from the cross-polarization case, e.g. used in CCDP systems, where the Cross Polarization Discrimination
(XPD) in "normal" conditions limits that the energy of one polarization signal falls back into the other polarization
status, in a spatial frequency reuse system the energy of all sub-channels are at similar levels and all mixed together
creating a lot of mutual interference between sub-channels.
Figure 4.2 compares the receiving sections of a cross-polarization system against spatial frequency reuse system
(2 × 2 MIMO). The meanings of the variables in the figure 4.2 are:
i
• r : received signal component at antenna element i-th (i = 1, 2) generated by the transmitted signal x .
xi i
i
• y : i-th (i = 1, 2) demodulated signal component generated by transmitted signal x and received at antenna
xi i
element i-th (i = 1, 2).
i 1 1 1 2 2 2
• r : the whole received signal at antenna element i-th (i.e. r = r + r and r = r + r ).
x1 x2 x1 x2
i 1 1 1 1 1 1
y : the whole demodulated signal from antenna element i-th (i.e. y = y + y and y = y + y ).
•
x1 x2 x1 x2
Thus two cases arise:
1) Cross-Polarization System
In this system two antennas, one for each polarization status (e.g. horizontal and vertical) are present.
In an ideal case without any cause of depolarization, e.g. the antenna XPD is high enough and no rain or other
atmospheric phenomena are active, at V-polarized antenna (i = 1) the received signal power level of the
V-polarized transmitted signal (r ) is much higher than the received signal power level of the H-polarized
x1
transmitted signal (r ). The same stands with inversed behaviour between the polarization status signals for
x2
the second antenna (i = 2).
XPIC algorithm cancels the self-interference of the unwanted polarization signal, for example H for the first
antenna and V for the second one.
2) Spatial Frequency Reuse (MIMO) System
Even in this system two antennas, or more, are present but they may use the same polarization (in the example
the vertical one).
1 1 2 2
In this case the received signal components, the couple (r , r ) for antenna 1 and (r , r ) for antenna 2,
x1 x2 x1 x2
at each antenna have similar power level and the received signal components are not orthogonal to each other.
Thus the difference in the phase of the signals, due to different sub-channel paths (space diversity), generated
1 2
by MIMO antenna arrangement forms a kind of "orthogonality" or diversity between y and y .
An SFRC algorithm can facilitate the separation of the mixed input signals for data detection and, as well, the
cancellation of the generated self-interference preventing any degradation on the received threshold.
NOTE: Orthogonality between two signals can be defined as a zero expectation of their sampled product over the
symbol period T.
Spatial Frequency Reuse and Cross-Polarization may be exploited together in order to increase the number of
independent sub-channels (Multi-Polarized MIMO).
ETSI
12 ETSI TR 102 311 V1.2.1 (2015-11)

Figure 4.2: Cross-polarization versus spatial frequency reuse
ETSI
13 ETSI TR 102 311 V1.2.1 (2015-11)
4.3 Methods to achieve spatial frequency reuse
4.3.1 Spatial configuration
4.3.1.1 MIMO channel with spatial configuration
Figure 4.3.1.1 describes a typical communication channel with spatial configuration which also stands for spatial
frequency reuse applications. In the example three antennas are considered either in transmission and receiver sides,
thus it can be defined as a 3 × 3 MIMO system.
The dotted lines in figure 4.3.1.1 represent the sub-channels between each couple of transmit and receive antennas.
Mathematically the coefficients "h " (i, j = 1…3) denote the Channel Transfer Function (CTF) and all together the
ij
coefficients form a Channel Matrix" H". The received signal at each antenna port is a linear combination of the
transmitted signals (see clause 4.2 and figure 4.2).
X1 h11 y1
h12
h21
TX
RX
y2
X2
h22
TERMINAL
TERMINAL
h31
h32
y3
X3
h33
Figure 4.3.1.1: 3 × 3 MIMO channel with spatial configuration
4.3.1.2 MIMO System Model
In figure 4.3.1.2 it is depicted a MIMO System Model block diagram. The meaning of the symbols follows:
X = TX symbol vector
x = j-th input signal at j-th transmit antenna
j
R = received signal vector
r = i-th received signal at i-th receive antenna
i
Y = RX estimated symbol vector
y = i-th output signal at i-th receive antenna
i
H = Channel Matrix
h = Channel Transfer Function coefficient from antenna 'j' (TX) to antenna 'i' (RX)
ij
N = Noise signal vector
n = i-th noise signal at i-th receive antenna
i
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14 ETSI TR 102 311 V1.2.1 (2015-11)
n
x r y
1 1 1
TX (MOD) RX (DEM)
1 1
H (Channel Matrix)
⎡ h h . . h ⎤
11 12 1M
n
j
⎢ ⎥
h h . . h
21 22 2M
⎢ ⎥
x r y
i j i
TX (MOD) ⎢ ⎥ RX (DEM)
i . . . . . j
⎢ ⎥
... ... ... ... ...
⎢ ⎥
⎢ ⎥
h h . . h
⎣ N1 N 2 NM ⎦
n
N
x r y
M N N
TX (MOD) RX (DEM)
M N
Figure 4.3.1.2: MIMO System Model
In general, the channel coefficients can be represented as a complex value:
jβij(f)
h = α (f) e
ij ij
where:
" α (f)" is the attenuation characteristic of the (i, j) sub-channel (as a function of the frequency)
ij
" β (f)" is the phase characteristic of the (i, j) sub-channel (as a function of the frequency)
ij
Under above defined assumptions (I = M × N pseudo-identity matrix):
Y = H × X + I × N y = Σ (h x ) + n with j = 1…M
i j ij j i
NOTE 1: I is a M x N pseudo-identity matrix.
NOTE 2: The model is depicted only in one direction but in real situation the link may be bi-directional.
In RX side the core of the MIMO Decoding Algorithm is the estimation of the channel matrix and the computation of
-1 -1
the inverse matrix "H " (i.e. H·H = I). The above defined assumption results in:
-1 -1 -1 -1
Y = H × R = H × ( H × X + I × N ) = I × X + H × N y = x + Σ (h n )
i i j ij i
-1
In order to obtain "H ", the coefficients of the channel matrix, "H" are necessary. In other words, an estimation of the
channel parameters, " α (f)" and " β (f)", is required. This operation is usually named "Channel Estimation".
ij ij
4.3.2 Spatial frequency reuse based on rich scattering
This method of achieving orthogonality is valid when the link path has considerable amount of multipath scattering
caused by reflections and diffractions on obstacles. This scenario is common in the lower frequency, usually below
6 GHz, where often application scenarios do not present direct line of sight connections. Figure 4.3.2 describes such a
link. The multipath scattering provides statistical independent paths for the signals which reach the receiver with
different amplitude, phase and delay attributes.
ETSI
X
(TX symbol vector)
MIMO Decoding Algoritm
(SFRC)
Y
(RX estimated symbol vector)
15 ETSI TR 102 311 V1.2.1 (2015-11)

y1
X1
TX
RX
X2
y2
TERMINAL
TERMINAL
y3
X33
Figure 4.3.2: Spatial system scattering based
Mathematically in this system with sufficient diversity the elements of the channel matrix (H) become independent and
identically distributed (i.i.d.) circular complex Gaussian terms. When H elements approaching this condition H
becomes "high rank" and "more" orthogonal, and its singular values spread drops.
Such a system has the advantage that it has not great dependency on the antenna geometry, in contrast to the case
described in next clause, as lower spacing between the antennas in the array is sufficient to get diversity between
sub-channels (in the order of 5 or 10 times the wavelength).
However there is great disadvantage with these systems as they are based on scattering due to nLOS/NLOS
propagation, large propagation attenuation should be taken into account when planning the system link budget. This is a
fact that, with the variability of the channel conditions, causes the capacity to be statistical variable.
This scheme is addressable more by WiFi™ and access radio systems where usually there may be no line of sight signal
components.
NOTE 1: If the line of sight component exists, it increases the dependency between sub-channels, reducing the rank
of the matrix, and reduces the orthogonality between sub-channel paths.
NOTE 2: Wifi™ is an example of a suitable product available commercially. This information is given for the
convenience of users of the present document and does not constitute an endorsement by ETSI of this
product.
4.3.3 Spatial frequency reuse based on link geometry
4.3.3.1 Channel matrix pure line of sight case
Consider a MIMO system with N transmit antennas and M receive antennas. Figure 4.3.3.1a describes the case of
M = N = 2 antennas at TX and RX sides where the antenna arrays are formed by parallel and equally spaced elements.
The path length difference between adjacent receive antennas ( ΔR) is:
d
2 2
ΔR = R + d − R ≅ []m
2R
Where R is the link hop distance and d is the inter antenna element distance and the last approximation stands when
R >> d.
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16 ETSI TR 102 311 V1.2.1 (2015-11)

R
R
ΔR
Figure 4.3.3.1.a: Differential path range in carrier propagation
The correspondent phase difference between two different paths is:
2π π d
ϕ = ΔR ≅ ×
λ λ R
[rad]
where λ = c / f is the wavelength of the used carrier.
Thus for the 2 × 2 MIMO as in figure 4.3.3.1.b the channel matrix becomes:
jφ
⎡ ⎤
1 e
[]H =
⎢ ⎥
jφ
e 1
⎣ ⎦
ETSI
d
17 ETSI TR 102 311 V1.2.1 (2015-11)
TX RX
h = 1
φ
jφ
h = e
Max Orthogonal Cond.
jφ
h = e
2 2
φ
h22= 1
Max Orthogonal Cond.
φ
=
φ
π-φ
Arbitrary Path Phase
rotation
Difference
φ =
φ
π/2
π/2
=
Max Orthogonal Cond.
π/2
rotation
π/2 π/2
=
Figure 4.3.3.1.b: Vector Visualization
Instead for a 4 × 4 MIMO system H becomes:
jφ j 4φ j9φ
⎡ 1 e e e ⎤
⎢ ⎥
jφ jφ j4φ
e 1 e e
⎢ ⎥
[]H =
j 4φ − jφ jφ
⎢ ⎥
e e 1 e
⎢ ⎥
j9φ j4φ jφ
e e e 1
⎢ ⎥
⎣ ⎦
ETSI
18 ETSI TR 102 311 V1.2.1 (2015-11)
And more in general for an N × N MIMO system:
jφ j4φ j()N −1 φ
⎡ ⎤
1 e e . e
⎢ ⎥
jφ jφ j()N −2 φ
e 1 e . e
⎢ ⎥
j 4φ jφ j()N −3 φ
⎢ ⎥
[]H =
e e 1 . e
⎢ ⎥
... ... ... ... ....
⎢ ⎥
⎢ j()N −1 φ ⎥
e 1
⎣ ⎦
4.3.3.2 Maximal orthogonal condition and optimal antenna spacing
In the channel matrix the columns correspond to the sub-channels from transmit antenna to all receive antenna, thus the
mutual correlation calculated between the channel matrix columns correspond to the degree of "orthogonality" between
the MIMO sub-channels. It is proofed by theory that the correlation is proportional to the quantity "sin(N·φ)" for an
N × N MIMO system.
The sub-channels are independent if the result of the correlations between the sub-channels is null. This condition is
equivalent to the statements:
φ = ± π / N + 2k π , k is any natural number
These special points can be regarded as "the maximal orthogonal condition".
The "maximal orthogonal condition" can be depicted in the figure 4.3.3.2.a and 4.3.3.2.b as the point where the singular
values of the 2 × 2 and 4 × 4 MIMO take the same value in function of the phase difference between the paths ( φ). In
practical situation the lower solution of φ for the maximal orthogonal condition is in the actual interest.
The singular values are equal, and the
capacity maximum,
when: 0.9
Δ = λ/4 or φ = 90°.
0.8
Max Ortogonal Condition
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 20 40 60 80 100 120 140 160 180
Relative angles [Degrees]
Figure 4.3.3.2.a: Orthogonal condition points 2 × 2 MIMO (normalized channel energy)
ETSI
Singular Values Of Channel Matrix

19 ETSI TR 102 311 V1.2.1 (2015-11)

The singular values are equal,
and the capacity maximum,
when:
0,9
Δ = λ/8 or φ = 45°.
The corresponding antenna
0,8
spacing is then:
0,7
= rλ/4.
s
0,6
For f = 28 GHz,
r = 5 km,
s = 3,6 m.
0,5
0,4
0,3
0,2
0,1
Phase difference (°)
Figure 4.3.3.2.b: Orthogonal condition points 4 × 4 MIMO (normalized channel matrix)
It is of practical interest of finding the antenna spacing d for the maximal orthogonal condition as function of the link
opt
hop distance (R), radio wavelength (λ) and the number of antennas (N):
λ × R
d =
opt
N
m m
[][ ]
m = = m
[] []
no _ dim ension
[]
Above formula stands in case of the antenna separation is the same at both sides of the link and when the number of
transmit antennas and receive antennas are the same (M = N).
More general formulation for optimal antenna spacing's at both link sides is:
λ × R
d ⋅ d =
1 2
min()N, M
m m
[][]
m ⋅ m = = m
[][] []
no _ dim ension
[]
Where d and d are the antenna spacing values respectively at link edge 1 and link edge 2.
1 2
In figure 4.3.3.2.c the required antenna spacings dependence on link frequency and hop distance for the case of dual
antenna array (2 × 2) are depicted for the 18 GHz, 23 GHz, 26 GHz, 28 GHz and 38 GHz frequency bands.
ETSI
20 ETSI TR 102 311 V1.2.1 (2015-11)
Optimal Antenna Spacing for 2x2 MIMO Optimal Antenna Spacing for 2x2 MIMO
9.5 5.5
9.0
8.5
5.0
8.0
] ]
7.5
4.5
m m
[ [
7.0
n n
o o
i i
6.5
t t
a a4.0
r r
6.0
a a
p p
e e
5.5
S S
3.5
a a
5.0
n n
n n
e e
4.5 18 GHz
t t
n n
3.0
A4.0 A
23 GHz
28 GHz
3.5
26 GHz
2.5
3.0
38 GHz
2.5
2.0 2.0
1 1.522.533.5 44.555.566.577.588.599.5 10 11.522.533.544.55
Link Range [m] Link Range [m]
Thousands Thousands
Figure 4.3.3.2.c: Antenna spacing for maximal orthogonal case
4.3.3.3 Spatial diversity gain
In general MIMO system can achieve both separation of independent input signals, that share the same frequency, and
Spatial Diversity Gain (SDG) to the receiver over Single Input Single Output system (SISO), this gain is inherent to the
system due to the antenna plurality.
The SDG value can easily be computed from the singular values λ of H. In the maximal orthogonal condition each
singular value will be equal to SQRT(N) and the SDG value is equal to 10 × log (N).
4.3.3.4 Working with antenna spacing below the sub-optimal condition
Figure 4.3.3.4.a illustrates the singular values/SDGs of the two spatial channels in 23 GHz of 5 km hop distance for a
2 × 2 MIMO system. From figure 4.3.3.4.a it can be viewed that moving from optimal antenna spacing may cause only
degradation in performance. As an example it can be seen from the diagram that 5,7 m is the antenna spacing that
correspond to the maximal orthogonal condition SDG = 10 × log (2) (SDG = 10 × log (2) = 3 dB). If the antenna
10 10
spacing will be reduced to 4,7 m one of the spatial channel will drop to 0 dB (same gain as a SISO reference system).
Lowering the antenna spacing to 3,7 m degrades the weaker spatial channel by 3 dB compared to the SISO channel.
ETSI
21 ETSI TR 102 311 V1.2.1 (2015-11)

nt = 2 nr = 2 gamma = 0 f = 23 GHz h = 15 m D = 5 000 m Orient: VV dmax = 5,7 m
-3 dB gain
over SISO
3 dB gain
at d
opt
No gain
over SISO
d = 5,7 m
opt
d [m]
Figure 4.3.3.4.a: 2 × 2 MIMO spatial gain
For comparison in figure 4.3.3.4.b the singular values for 2 × 2 MIMO are reported in the case of considering the whole
power level for the MIMO the same of the SISO one (sum power constraint), in the left, and without power constraint
(doubling the SISO power level), in the right.
In case of the power constraint stands even in the optimal antenna spacing condition there is no SDG over the SISO
case.
+3 dB
(SDG)
Figure 4.3.3.4.b: 2 × 2 MIMO spatial gain with and without sum power constraint
4.3.3.5 Channel matrix considering link propagation
In real link also propagation effects need to be considered. This is important in order to determinate the MIMO link
performance, as it will be seen in term of Capacity in clause 4.4.
ETSI
Absolute spatial gain [dB]
22 ETSI TR 102 311 V1.2.1 (2015-11)
In practise even the path loss attenuation and any fading attenuation effects need to be accounted for any MIMO sub-
channel. It is important to note that even in perfect propagation conditions, each sub-channel experiments different
attenuation values due to difference in path distance. Such asymmetry behaviour is increased in working conditions due
to even small activity in propagation fading, tolerance in transmission power level and receiver noise figure, antenna
gains and geometric link misalignments.
The channel matrix H can be modified in a new matrix Hf as in the following:
H = A o H
f
where:
A = Free Space Loss and Fading Attenuation Effects Matrix (each elements represent the attenuation of the
single sub-channel)
|·| = Matrix Single Element Absolute Value
◦ = Hadamard Product
4.3.3.6 Multi-polarized MIMO
In a MIMO system also the two different polarizations, horizontal and vertical ones, may be used in order to create
diversity. Furthermore, Multi-polarized MIMO can help to increase the number of sub-channels without increasing the
total number of antenna by using dual polarized antenna. This is also important to save physical space for antenna array
installation (e.g. 4 × 4 MIMO requires the installation of four antennas while a 2 × 2 Multi-Polarized MIMO requires
just two dual-polarized antennas).
As in the previous clause, the channel matrix H can be modified in a new matrix Hx which take into account the
polarization effects:
H = X o H
x
Where:
X = Polarization Effect Matrix (the elements are related to the XPD between the transmission and receive
antenna couple)
4.4 MIMO Performance
In order to show MIMO Capacity improvement it is necessary to recall SISO Capacity limit. It is the famous Shannon-
Hartley Theorem which states that the Capacity is:
CSISO = log()1+ ρ  []bit/s/Hz
Where:
S
ρ =
N ⋅ B
= SNR
S̅ = Averaged received Power [W]
N = Noise Power Spectral Density [W
...