This document discusses multiple-antenna techniques. It begins by explaining why multiple antennas can be used to enhance signal-to-noise ratio through spatial diversity or beamforming gain, and to enhance bit rate through spatial multiplexing. It then covers various multiple-antenna configurations and techniques including single-user and multi-user MIMO, transmit diversity methods like space-time block coding, and receive diversity methods like selection combining, equal gain combining and maximum ratio combining. Beamforming using antenna arrays to synthesize radiation patterns is also discussed.
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HIAST-Ayman Alsawah Lecture on Multiple-Antenna Techniques in Advanced Mobile Systems v10
1. Communication Systems Master PROGRAM
Advanced Mobile Communication
Multiple-Antenna Techniques
2013-2014
Lecture 03-v10
Ayman Alsawah
ayman.alsawah@hiast.edu.sy
Higher Institute of Applied Sciences & Technology
2. Multiple-Antenna (MIMO) in the “Big Picture”
Uo to 5 x 20 MHz, 8x4 MIMO
OFDM, 4x4 MIMO, All-IP
Carrier Aggregation (to 40 MHz), 16/64 QAM, HARQ, MIMO
WCDMA (5 MHz), QPSK/BPSK, Freq. full-reuse, fast power control
8PSK, Adaptive Modulation & Coding
Multiple time-slots/user, packet-switching
Narrow-Band FDMA-TDMA (200 KHz), GMSK
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3. Why Multiple Antennas?
Exploit spatial dimension to:
Enhance received S(I)NR (Spatial diversity/Diversity Gain or Beamforming/Array Gain)
Enhance bit rate (Spatial Multiplexing/Multiplexing Gain)
WiFi AP
IEEE 802.11n (2007)
IEEE 802.11ac (2012)
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4. Multiple-Antenna Configurations
S = Single
M = Multiple
I = Input
O = Output
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5. SU-MIMO versus MU-MIMO
Single-User
MIMO
Multi-User
MIMO
LTE Rel’8 /DL (2008)
Wifi 802.11ac /DL (2013)
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6. Fading problem (Flat fading)
Fading of Rx power causes: - degradation in BER if the Bit Rate is fixed
- limitation in Bit Rate if the BER is fixed
Average Rx pwr
Min required pwr
(Rx sensitivity)
Time
Rx Power (dBm)
Fading margin
Deep fade (target BER violation)
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7. Example of performance over flat fading
(dB)
BPSK
Uncoded
Flat Rayleigh fading
Coherence time ≥ Tb
Coherent detection
(AWGN)
Error probability
Solutions?
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8. 1-Time diversity via Coding & Interleaving
code word bit Error burst
Block fading model
(Approximation)
Non-Interleaved: A B C D E F G H I
Interleaved: A D G B E H C F I
Deinterleaved: A B C D E F G H I
Interleaving depth
t
Rx Pwr
Tc
Deep fade
’
Tc
Example: GSM
• Coded speech packet
interleaved over 8 bursts
• 1 user-assigned burst
every frame of ~5 ms
Packet interleaved
on 40 ms
• @900 MHz, 120 km/h:
fd = 100 Hz
Tc = 10 ms
After deinterleaving, isolated errors
have “more chance” to be corrected
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9. 2- Frequency diversity via Freq. Hopping
Frequencies much
be spaced by more
than the coherence
bandwidth Bc
Example: GSM
• Slow-FH ~200 hop/s
(Optional feature)
• Frame ≈ 4.6 ms
(8 user bursts)
• Typical Urban:
τRMS ≈ 1 μs
Bc = 1/(5τRMS)
Power gain (dB)
900 MHz, 3 Km/h, Rayleigh flat fading
= 200 KHz Time (ms)
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10. 2- Frequency diversity via OFDM
|H(f)|
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11. 3- Spatial diversity via Multiple Antennas
Time
Power gain (dB)
Ant 1
Ant 2
Tx Rx
• For uniform surrounding scatterers:
uncorrelated power gains
if antenna spacing = λ/2
• In practice: spacing λ
Example: GSM900
• 2 Rx antenna @BTS
• λ = 30 cm
• Separation = 2-3 m
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12. 4- Polarization diversity
+45°
Rx
-45°
Rx
Methods for exploiting “Rx Diversity” in
time, frequency, space, polarization, …?
DECT Handset
(1900 MHz)
H
V
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13. 4- Polarization diversity in GSM
Duplexing
Filter
+45° -45°
Main Diversity
From Tx PA To Combiner
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14. Rx Diversity: mathematical model
Flat fading complex baseband model (Narrow-band or per-OFDM-subcarrier)
rk = hk . s + nk , k = 1,…,L.
s = transmitted symbol (M-QAM in general)
with normalized average power E[|s|2] = 1 & symbol period Ts = 1
L = number of diversity branches
hk = baseband complex gain on antenna k, invariant during 1 symbol
{hk} are iid zero-mean complex circular Gaussian random processes
|hk| is Rayleigh distributed with E[|hk|2] = 1 (normalized power gain)
|hk|2 (power gain) is exponentially distributed
{nk} are iid zero-mean complex circular WGN processes with E[|nk|2]=N0
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15. Rx Diversity: SNR & CSI
rk = hk . s + nk , k = 1,…,L.
γk = |hk|2 Instantaneous SNR: . E[|s|2]/E[|nk|2] =|hk|2/N0
Average SNR: γk, ave = E[|hk|2]/N0 = 1/N0 γk, AWGN
Instantaneous Ebno: (Eb /N0)k =|hk|2/(N0 log2 M),
Average Ebno:
M = Modulation order
(Eb /N0)k, ave = 1/(N0 log2 M) (per branch)
Received signal:
Channel State Information:
CSI Rx = subset of {{mag(h1), …, mag(hL)}, {arg(h1), …, arg(hL)}}
CSI Tx = none!
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16. Rx Diversity: 1-Antenna Selection
Select the highest power
gain branch (max |hk|2)
Suitable for non-coherent
detection where fading
phases are not needed
CSI Rx = {mag(hk)}
Used on LTE UL with 2 antennas
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17. Rx Diversity: 2-Antenna Switching
Switch to the max power
gain antenna when the
current one falls below a
given threshold
Ant. Sw.
threshold
CSI Rx = {mag(hk)}
Simplified hardware at the price of
degraded error performance
compared to “Antenna Selection”
Better solutions?
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18. Rx Diversity: 3-Equal-Gain Combining
rk = hk . s + nk , k = 1,2.
z = r1 exp(-j arg(h1)) + r2 exp(-j arg(h2))
= (|h1| + |h2|) . s + [ n1 exp(-j arg(h1)) + n2 exp(-j arg(h2)) ]
Instant. SNR (= Instant. EbNo for BPSK):
γEGC = (|h1|+|h2|)2 E[|s|2]/E[|n1 exp(-j arg(h1))+n2 exp(-j arg(h2))|2]
= (|h1|+|h2|)2 / (2N0)
BPSK error proba.: Pe, EGC = E[Q((2γEGC)1/2)] (1/N0) -L
Expectation w.r.t. (h1, h2) joint pdf
CSI Rx = {arg(hk)}
EGC is optimum when branches’ SINR’s have similar values
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19. Rx Diversity: 4-Max. Ratio Combining
* + r2 h2
z = r1 h1
*
= (|h1|2 + |h2|2) . s + [ n1 h1
* + n2 h2
* ]
rk = hk . s + nk , k = 1,2.
Instant. SNR (= Instant. EbNo for BPSK):
γMRC = (|h1|2+|h2|2)2 E[|s|2]/E[|n1 h1
* + n2 h2
*|2]
= (|h1|2+|h2|2)2 / [(|h1|2+|h2|2)N0]
= (|h1|2+|h2|2) /N0
= |h1|2/N0 +|h2|2 /N0 (sum of branches’ SNRs)
BPSK error proba.:
CSI Rx = {hk}
Pe, MRC = E[Q((2γMRC)1/2)] (1/N0) -L
MRC is THE optimum combining method, equivalent to a spatial matched filter
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20. BPSK performance over Rayleigh Flat Fading
Bit error probability
Average SNR per branch Eb/N0 (dB)
Other methods for exploiting multiple antennas?
Diversity Gain
Slope increase
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21. Reminder: Antenna Radiation Pattern
Isotropic Antenna Directive Antenna
Uniform radiation intensity
Tx power = PT
= PT /4 (W/strad)
Radiation intensity
= R(, )
Tx power = PT
Gain(, ) = 10 log10 D(, ) is measured in dBi (dB relative to isotropic antenna)
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22. Example: Half-wave dipole antenna
Maximum gain = 2.15 dBi
Vertical Cut
Horizontal Cut
Antenna pattern is Tx/Rx reciprocal
How to synthesize more complex directive patterns?
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23. Array antennas
WiFi AP.
Array antennas allows to control the radiation pattern by suitably arranging
antenna elements and adjusting the amplitude and phase of the signal
received from/fed to each element, we talk about “Beamforming”
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24. Adaptive beamforming
Var. Gains
Var. phases
Applications?
RF beamforming
Tx case
Main beam steering
Remote electrical tilting
Interference reduction
…
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25. App. 1: Radar Beam Steering
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26. App. 2: BS electrical down-tilting
Max Gain = 15 - 20 dBi
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27. App. 3: Switched beam
CSI @ BS:
DL: CSI Tx = direction of user
UL: CSI Rx = direction of user
1
2
3
4
Weights
Codebook
Index
Active beam
selection
Direction of Arrival
(DoA)
Array Gain
= Average SNR enhancement
due to radiation focusing in
the direction of user, w.r.t.
average SNR of single antenna
No diversity gain
Multi-beam is also possible
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28. App. 4: SIR maximization
Desired
user
Interfering
user
Weights
Beam synthesis
Directions of Arrivals
CSI @ BS:
DL: CSI Tx = direction of users
UL: CSI Rx = direction of users
Array Gain
Spatial filtering
or
Zero-Forcing Beamforming
What if baseband complex CSI was available instead of DoA?
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29. Baseband Beamforming – no interference
Baseband model:
On UL:
CSI Tx = none
CSI Rx = full
Without noise: Maximize signal power <=> EGC
With noise: Maximize SNR <=> MRC
Exercise:
Prove that:
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30. Baseband Beamforming – with interference
User 1
User 2
Baseband model:
On UL:
CSI Tx = none
CSI Rx = full
Exercise:
• Find weights that yield: y = S1 (interference from user 2 is cancelled) under
perfect CSI Rx and without noise (Interference Rejection Combining (IRC)).
• What is the feasibility condition of this IRC?
• In the noisy case, give the expression of both y and the SINR.
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31. Space-Division Multiple Access (SDMA)
On UL:
CSI Tx = none
CSI Rx = full
S1
S2
“Baseband Multi-beam”
Multiplexing Gain
UL data rate is doubled:
2 users transmit simultaneously
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32. Array Gain & Diversity Gain
• Array Gain = Average SNR / Single-Branch average SNR
• Diversity Gain = - log10(Δ Average error proba.) / log10(Δ Single-Branch average SNR)
@ Hi SNR
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33. Multiple Tx Antennas (MISO)
Closed-Loop Techniques:
Channel-State Information (CSI) known @ Tx side through Feedback
Tx Diversity: Antenna selection/switching (Feedback = antenna index only)
Precoding (pre-weighting) for in-phase combining @ Rx antenna
Tx RF Beamforming: beam steering, beam switching, multi-beam.
Open-Loop Techniques:
No CSI @ Tx
STBC (Space-Time Block Coding)
SFBC (Space-Frequency Block Coding)
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34. STBC Example: 2x1 Alamouti
CSI Tx = none
CSI Rx = full
Space-Time
Precoding matrix:
No array gain
Diversity gain = 2 (full)
No multiplexing gain (full)
Used in WiFi 802.11n (2008)
S. M. Alamouti, “A simple transmit diversity technique for wireless communications,”
IEEE J. Sel. Areas Comm., vol. 16, pp. 1451–1458, Oct. 1998.
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35. 2x1 Alamouti Precoding & Decoding
Tx Side:
Rx Side:
Decoding: (power constraint ignored here)
Exercise: Find instantaneous & average decoded SNR
H (orthogonal matrix)
(inverse ~ transpose & conjugate)
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36. SFBC Example: 2x1 Alamouti
In OFDM-MIMO systems like LTE, time
slots can be replaced with subcarriers
when implementing Alamouti
Used in UMTS & LTE
STBC & SFBC can be generalized to more than 2 Tx antennas
See also Alamouti 2x2
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37. MIMO Flat Fading Baseband Model
Precoder
Decoder
Data in out
Generate
CSI Tx
Generate
Precoder
T Antennas R Antennas
hRT
n1
n2
nR
x1
x2
xT
y1
y2
yR
hR1
h1T
h11
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38. MIMO Signal Model
Channel matrix:
Rayleigh iid model:
AWGN Noise vector: n
(R x T)
Received vector: y H x n
RX1 RXT TX1 RX1
(full rank)
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39. MIMO Spatial Multiplexing
Spatial Multiplexing is a Closed-Loop (Full CSI Tx & Rx) MIMO
technique for increasing data rate (i.e. obtaining a multiplexing gain)
- Channel matrix is considered deterministic (known to the receiver) and can
be decomposed using SVD = Singular-Value Decomposition:
where:
RXT RXR RXT TXT
• U & V are unitary (orthogonal) square matrices (i.e. UUH = IR, VVH = IT)
• is a diagonal matrix whose main diagonal is formed of
min{T, R} strictly positive real values:
R>T R=T R<T
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40. MIMO: simple & great idea!
Received vector: y x n H UV
Let’s send instead of (data pre-processing): x x V~ x
y x n x n H ~ UV V U
y~
Now multiply the received vector by (post-processing): H U
y x n x n y UH ~ UHU UH ~
y x n~
min{T, R} parallel Gaussian channels
n n H U ~ n U
has the same distribution as since is unitary
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41. x x V~y H ~ U y
~
~
~
~
T R
x
V
H=UVH UH ~
• Case T<R: T data symbols are sent on parallel
T received values + (R-T) zeros to be ignored
n1
n2
nR
~
• Case T≥R: R data symbols + (T-R) dummy zeros are sent on parallel
R received values
In all cases: data rate is increased by min{T, R} “Multiplexing Gain”
(For the same error performance than SISO and without extra spectrum)
y
x1
x2
xT
y1
y2
yR
Feedback = V
LTE & WiMax (up to 8x4 on DL)
WiFi .11n (4 streams)
WiFi .11ac (8 streams)
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1949 Claude Shannon and Robert Pierce develop basic ideas of CDMA
1956 RAKE receiver patented
1970s Several CDMA developments for military systems (e. g. GPS)
One main advantage of spatial diversity relative to time and frequency diversity is that no additional bandwidth or power is needed in order to take advantage of spatial diversity. The cost of each additional antenna, its RF chain, and the associated signal processing required to modulate or demodulate multiple spatial streams may not be negligible, but this trade-off is often very attractive for a small number of antennas.
An IEEE 802.11ac Wi-Fi device can contain between one and eight antennas.
Uplink Transmission Modes
LTE does not use multi-antenna transmission in the uplink direction, this will be available only from Release 10 onwards as part of the LTE-Advanced specification work. It is possible, however, to use multi-user MIMO (or virtual MIMO) in the uplink direction. This means that an eNodeB allocates users orthogonal references symbols and allocates them in the same resource space and then processes the transmission from two users like a MIMO transmission in order to separate the two independent data streams. In this case the uplink data rate of an individual UE is unchanged.
Uplink Transmission Modes
LTE does not use multi-antenna transmission in the uplink direction, this will be available only from Release 10 onwards as part of the LTE-Advanced specification work. It is possible, however, to use multi-user MIMO (or virtual MIMO) in the uplink direction. This means that an eNodeB allocates users orthogonal references symbols and allocates them in the same resource space and then processes the transmission from two users like a MIMO transmission in order to separate the two independent data streams. In this case the uplink data rate of an individual UE is unchanged.
Fading margin can attain 9 dB on UL & 19 dB on DL in GSM
Diversity in economy (portfolio)
Coherent detection = phase rotation is compensated for.
I think that in the uncoded case, the correlation of fading does not affect the performance (The only assumption here is that the coherence time is at least equal to symbol time)
Codes designed for AWGN channels can exhibit worse performance in fading than an uncoded system.
Slowly fading channels require large interleavers, which in turn can lead to large delays.
Coding and interleaving is a form of diversity, and performance of coding and interleaving is often characterized by the diversity order associated with the resulting probability of error. This diversity order is typically a function of the minimum Hamming distance of the code. Thus, designs for coding and interleaving on fading channels must focus on maximizing the diversity order of the code, rather than on metrics like Euclidean distance which are used as a performance criterion in AWGN channels.
Coding and interleaving is a suboptimal coding technique, since the correlation of the fading which affects subsequent bits contains information about the channel which could be used in a true maximum-likelihood decoding scheme. By essentially throwing away this information, the inherent capacity of the channel is decreased [5]. Despite this capacity loss, interleaving codes designed for AWGN is a common coding technique for fading channels, since the complexity required to do maximum-likelihood decoding on correlated coded symbols is prohibitive.
Interleaving causes delay, but, neither the code rate nor the minimum Hamming distance are changed . The latter means that the error detection and error correction capabilities of the linear block code B(n, k, d) with respect to independent errors are not improved by the interleaving step. However, error bursts consisting of burst neighbouring errors within the received word can now be corrected. If the linear block code B(n, k, d) is capable of correcting up to e errors, the interleaved code is capable of correcting error bursts up to length e x t with interleaving depth t .
Time diversity by FEC only:
The application of Forward Error Correction (FEC) coding yields time diversity if the channel varies significantly during one code word or coded frame. In this case, the decoder performs a kind of averaging over good and bad channel states.
Definition: Ergodic fading if all fading states are experienced over a codeword (see Coding for Wireless Channels -Biglieri -2005). The figure in this slide (non-interleaved) corresponds to non-ergodic channel. But, with sufficiently long codeword and deep interleaving, we retrieve the ergodicity.
In block fading, we talk about outage capacity (max rate that can be exceeded with a given proba).
In independent fading, we talk about ergodic capacity & AWGN codes can be used.
Note that interleaving fits the no-CSI-Tx case. If CSI-Tx, one can use adaptive modulation & coding.
However, CSI-Rx is always necessary for correct detection in the flat-fading channel.
Hopping frequencies much be spaced by more than the coherence BW
In addition to coherence time and bandwidth, it is sometimes useful to define the coherence distance of a channel in which multiple antennas are used. This is the maximum spatial separation of two antennas over which the channel response can be assumed constant: specifically, we say that the channel is space selective if the separation between antennas is larger than the coherence distance.
The required spacing differs considerably at the mobile and the base station in a macrocell environment.
A narrow angular distribution will produce a slow decrease in the correlation with antenna spacing, which will limit the usefulness of space diversity, whereas environments with significant scatterers widely spread around the antenna will produce good space diversity for modest antenna spacings.
See “Antennas and Propagation for Wireless Communication Systems -2nd - Saunders, Zavala -2007” page393 for an example of space correlation analysis.
Since the incident field on a base station antenna is predominantly vertically polarized, space diversity antennas are typically vertically polarized. Equal average branch power is in this case obvious, but the requirements for low correlation need some further analysis.
The actual voltages at the antenna terminals are additionally affected by the mutual coupling between the antennas, which may be particularly significant for antennas spaced with their main lobes aligned with each other, as would typically be the case with horizontal spacing of vertically polarised antennas. Perhaps counterintuitively, it has been shown by both theory and experiment that this mutual coupling tends to reduce the correlation coefficient, so that acceptable diversity can be obtained with horizontal spacings as small as 0.1 lambda [Fujimoto, 94].
In microcell environments, both the base and mobile antennas are submerged among scatterers, so the angular spread of scatterers is very high. However, there is a high probability of encountering a strong line-of-sight component, so the p.d.f. of the angles may be strongly non-uniform. The usefulness of space diversity will depend on the particular geometry of the scatterers in the cell.
In picocells the angles of arrival will be distributed even more widely in three dimensions, particularly when propagation takes place between floors.
Handset diversity:
Likewise, the use of two similar antennas spaced apart by a small fraction of wavelength is far more effective than might be expected. The mutual coupling between the elements interacts with the spatial field patterns to produce low cross-correlation even with a spacing of only 0.05–0.10 wavelengths.
The spacing required between antenna elements to maintain certain decorrelation depends on mutual coupling and the disposition of scatterers causing the multipath transmission. For instance, in the absence of mutual coupling, spacing of about λ/2 should be sufficient at a mobile terminal that is usually surrounded uniformly by scatterers. On the other hand, spacing of the order of 10 λ or more may be necessary to maintain the same decorrelation value at an elevated base station.
In micro-cell deployments with base-station antennas below roof-top level and indoor deployments, the environment as seen from the base station is more similar to the environment as seen from the mobile terminal. In such scenarios, a smaller base-station antenna distance is typically sufficient to ensure relatively low mutual correlation between the fading experienced by the different antennas.
Azimuth spread: Algans et. al [11] present a c.d.f. of a estimated from TSUNAMI II measurement data. The median values are between 5؛ and 8؛ for an urban environment.
Concept of diversity port
The polarization of a wave radiated by an antenna in a specified direction at a point in the far field is defined as “the
polarizationof the (locally) plane wave which is used to represent the radiated wave at that point. At any point in the far field of an antenna the radiated wave can be represented by a plane wave whose electric-field strength is the same as that of the wave and whose direction of propagation is in the radial direction from the antenna. As the radial distance approaches infinity, the radius of curvature of the radiated wave’s phase front also approaches infinity and thus in any specified direction the wave appears locally as a plane wave.”
In a highly scattering environment, the signal is received in almost all polarizations irrespective of the transmitter polarization. Although the decorrelation between the signals received in two orthogonally polarized states is not as good as in well-separated spatially diverse antennas, the loss in diversity improvement at the 1% probability level was shown to be less than 1 dB at 842 MHz
Both reflection and diffraction processes are polarisation sensitive and can produce a rotation of the polarisation of the scattered wave compared to the incident wave. The compound effect of multiple instances of these processes in the propagation path depolarises a vertically polarised transmission, producing a significant horizontally polarised component at the receiver. This allows polarisation diversity when two collocated but differently polarised antennas are used as the branches of a diversity receiver. Collocation is attractive to reduce the aesthetic impact of base station antennas and to allow a very compact solution in the handheld case. Base station polarisation diversity also helps to reduce the polarisation mismatch which may be produced by hand-held users who tend to hold their hand-held with an average
angle of around 45 to the vertical, although this is mainly significant in line-of-sight cases.
Combining Methods:
• Maximum Ratio Combining (MRC):
Maximum ratio combining achieves the maximum signal to noise ratio at the receiver’s output by weighting each received replica yj [k] by the corresponding complex conjugate channel coefficient h∗j [k] and successive summation versus
j. Therefore, this method requires the knowledge of amplitudes and phases of all involved channels, and requires a scanning and tracking for all components. Due to this knowledge, MRC is not restricted to PSK but is also applicable for
multiamplitude signals like QAM. However, it is sensitive to channel estimation errors.
• Equal Gain Combining (EGC):
With equal gain combining, only the phase rotations for each yj [k] are compensated, the magnitudes remain unchanged. This method only requires the phases of all channel coefficients, not the magnitudes. However, due to missing knowledge of the channels’ magnitudes, this technique is not suited for ASK and QAM modulation and it performs worse than MRC.
• Square Law Combining:
If the channel is highly time varying and its phase cannot be estimated accurately, square law combining of orthogonally modulated signals is an appropriate method to exploit diversity. Here, the squared magnitudes of the received signals are simply added, resulting in a noncoherent receiver. This technique can only be applied for orthogonal signaling schemes (Kammeyer 2004; Proakis 2001).
• Selection Combining:
Selection combining represents the simplest combining method because it only selects a subset of all replicas for further processing and neglects all the remaining signals. This reduces the computational costs and may even lead to a better performance than MRC, because channels with very low SNR cannot be accurately estimated and contribute much noise.
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Maximal-Ratio Combining (MRC)
In the absence of interference, MRC is the optimal combining scheme (regardless of fading statistics) but comes at the expense of complexity since MRC requires knowledge of all channel fading parameters. Since knowledge of channel fading amplitudes is needed for MRC, this scheme can be used in conjunction with unequal energy signals, such as M-QAM or any other amplitude/phase modulations. Furthermore, since knowledge of channel phases is also needed for MRC, this scheme is not practical for differentially coherent and noncoherent detection. Indeed, if channel phase estimates are obtained, then the designer might as well go for coherent detection, thus achieving better performance.
Equal Gain Combining (EGC)
Although suboptimal, EGC with coherent detection is often an attractive solution since it does not require estimation of the fading amplitudes and hence results in a reduced complexity relative to the optimum MRC scheme. However, EGC is often limited in practice to coherent modulations with equal energy symbols (M-ary PSK signals). Indeed, for signals with unequal energy symbols such as M-QAM, estimation of the path amplitudes is needed anyway for automatic gain control (AGC) purposes, and thus for these modulations MRC should be used to achieve better performance [3].
In many applications the phase of the received signal cannot be tracked accurately, and it is therefore not possible to perform coherent detection. In such scenarios, communication systems must rely on noncoherent detection techniques
such as envelope or square-law detection of frequency-shift-keying (FSK) signals [6, Ch. 5] or on differentially coherent detection techniques such as differential phase-shift-keying (DPSK) [6, Ch. 7]. As explained above, using MRC is not practical for such types of detection schemes that are rather used in conjunction with post-detection EGC [7, Sect. 12.1, p. 680], [3, Sect. 5.5.6, p. 253].
Selection Combining (SC)
The two former combining techniques (MRC and EGC) require all or some of the CSI (fading amplitude, phase, and delay) from all the received signals. In addition, a separate receiver chain is needed for each diversity branch that adds to the overall receiver complexity. On the other hand, SC-type systems only process one of the diversity branches. Specifically, in its conventional form, the SC combiner chooses the branch with the highest SNR. In addition, since the output of the SC combiner is equal to the signal on only one of the branches, the coherent sum of the individual branch signals is not required. Therefore, the SC scheme can be used in conjunction with differentially coherent and noncoherent modulation techniques since it does not require knowledge of the signal phases on each branch as would be needed to implement MRC or EGC in a coherent system.
Switched Combining
For systems that use uninterrupted transmission, such as frequency-division multiple-access systems, SC in its conventional from may still be impractical since it requires the simultaneous and continuous monitoring of all the diversity branches [3, p. 240]. Hence SC is often implemented in the form of switched or scanning diversity, in which, rather than continually picking the best branch, the receiver selects a particular branch until its SNR drops below a predetermined threshold. When this happens the receiver switches to another branch. There are different variants of switched combining [8], but in its simplest form the switch-and-stay combining (SSC) receiver switches to, and stays with, the other branch regardless of whether the SNR of that branch is above or below the predetermined
threshold [9,10]. SSC diversity is obviously the least complex diversity scheme to implement and can be used in conjunction with coherent modulations
as well as noncoherent and differentially coherent ones.
Two criteria are necessary to obtain a high degree of improvement from a diversity system. First, the fading in individual branches should have low cross-correlation. Second, the mean power available from each branch should be almost
equal. If the correlation is too high, then deep fades in the branches will occur simultaneously. If, by contrast, the branches have low correlation but have very different mean powers, then the signal in a weaker branch may not be useful even though it is less faded (below its mean) than the other branches.
We say that the noise is spatially white (across the antennas).
Does not requires knowledge of fading phases unless coherent detection is performed.
Suitable for Unipolar M-ASK like OOK.
May use other metrics than the SNR (highest absolute power, error rate, etc.),
• Selection Combining:
Selection combining represents the simplest combining method because it only selects a subset of all replicas for further processing and neglects all the remaining signals. This reduces the computational costs and may even lead to a better performance than MRC, because channels with very low SNR cannot be accurately estimated and contribute much noise.
Selection Combining (SC)
The two former combining techniques (MRC and EGC) require all or some of the CSI (fading amplitude, phase, and delay) from all the received signals. In addition, a separate receiver chain is needed for each diversity branch that adds to the overall receiver complexity. On the other hand, SC-type systems only process one of the diversity branches. Specifically, in its conventional form, the SC combiner chooses the branch with the highest SNR. In addition, since the output of the SC combiner is equal to the signal on only one of the branches, the coherent sum of the individual branch signals is not required. Therefore, the SC scheme can be used in conjunction with differentially coherent and noncoherent modulation techniques since it does not require knowledge of the signal phases on each branch as would be needed to implement MRC or EGC in a coherent system.
Decision metric can be RSSI, SINR, CRC check
“Switch and stay”
Switched Combining
For systems that use uninterrupted transmission, such as frequency-division multiple-access systems, SC in its conventional from may still be impractical since it requires the simultaneous and continuous monitoring of all the diversity branches [3, p. 240]. Hence SC is often implemented in the form of switched or scanning diversity, in which, rather than continually picking the best branch, the receiver selects a particular branch until its SNR drops below a predetermined threshold. When this happens the receiver switches to another branch. There are different variants of switched combining [8], but in its simplest form the switch-and-stay combining (SSC) receiver switches to, and stays with, the other branch regardless of whether the SNR of that branch is above or below the predetermined threshold [9,10]. SSC diversity is obviously the least complex diversity scheme to implement and can be used in conjunction with coherent modulations
as well as noncoherent and differentially coherent ones.
EGC = coherent combining, MRC = coherent combining with weighting (matched combining)
Here we are summing useful signal powers
Ergodic error proba.
Distribution of squared sum of 2 Rayleigh
Note: The array gain (average combined SNR to single-branch average SNR) depends on the correlation of h1 & h2, which will not be the case in MRC.
Suitable for M-PSK
We can devide z by (|h1|+|h2|) to recover the decision regions if they were known, this does not change the SNR.
• Equal Gain Combining (EGC):
One way to improve on this is to add the signals from all the branches. If this were done directly on the complex signals,
however, the random real and imaginary components would combine incoherently, resulting in the same fading statistics at the combiner output (although a greater total power). To provide any true diversity, the signals must be co-phased so that they add coherently; the noise on each branch is independent and randomly phased, hence it adds only incoherently.
With equal gain combining, only the phase rotations for each yj [k] are compensated, the magnitudes remain unchanged. This method only requires the phases of all channel coefficients, not the magnitudes. However, due to missing knowledge of the channels’ magnitudes, this technique is not suited for ASK and QAM modulation and it performs worse than MRC.
Equal Gain Combining (EGC)
Although suboptimal, EGC with coherent detection is often an attractive solution since it does not require estimation of the fading amplitudes and hence results in a reduced complexity relative to the optimum MRC scheme. However, EGC is often limited in practice to coherent modulations with equal energy symbols (M-ary PSK signals). Indeed, for signals with unequal energy symbols such as M-QAM, estimation of the path amplitudes is needed anyway for automatic gain control (AGC) purposes, and thus for these modulations MRC should be used to achieve better performance [3].
In many applications the phase of the received signal cannot be tracked accurately, and it is therefore not possible to perform coherent detection. In such scenarios, communication systems must rely on noncoherent detection techniques
such as envelope or square-law detection of frequency-shift-keying (FSK) signals [6, Ch. 5] or on differentially coherent detection techniques such as differential phase-shift-keying (DPSK) [6, Ch. 7]. As explained above, using MRC is not practical for such types of detection schemes that are rather used in conjunction with post-detection EGC [7, Sect. 12.1, p. 680], [3, Sect. 5.5.6, p. 253].
EGC = coherent combining, MRC = coherent combining with weighting (matched combining)
About 1 dB better than EGC (Goldsmith)
Here we are summing SNR’s (In general average SNR’s are diff)
Ergodic error proba.
Sum of L squared iid rayleigh is Chi-square with L degrees of freedom.
SEE “Oestges, Clercxs -MIMO Wireless Communications” p.13: MRC array gain = diversity gain = nb of antennas
Note: The array gain (average combined SNR to single-branch average SNR) DOES NOT depend on the correlation of h1 & h2, which was not the case in EGC. BUT, diversity gain will depend on the correlation since it affects the distribution of SNR and so the average error proba.
Attention: 4-MRC becomes better than AWGN for low SNR because with average SNR per branch = AWGN SISO SNR, the performance of 4-MRC outperforms that of SISO AWGN. Anyway, the difference in error proba is insignificant.
IMPORTANT: see “Oestges, Clercxs -MIMO Wireless Communications” page 8
Same ref proves that selection combining captures the same diversity gain than MRC (same slope for HI SNR) but less array gain (horizontal shift to left or SNR gain)
Same ref: calculation of error proba for selection and MRC
H=Azimuth pattern
V=Vertical pattern
Array gain does not depend on the degree of correlation between the branches
Diversity gain is maximal for independent branches and decreases as the correlation between branches increases (is this true for RF beamforming or for BB beamforming only?)
Beamforming is possible in the current generation of IEEE 802.11n products, but many of them did not take advantage of it. With IEEE 802.11ac, beamforming is a standard feature, and all products that implement it will be interoperable and thereby able to operate at maximum range and coverage for the IEEE 802.11ac network.
For example, an 8-antenna AP might be able to use 4x4 MIMO to two physically separated stations at once.
Stare versus steer
We can replace the DoA with the best RSSI on the reverse link using reciprocity (.11n)
Beam-forming can be based either on high or low fading correlation between the antennas
Go back to slide 17 and explain how array gain shows up as SNR shift
The major drawback of the method lies in its reduced array and diversity gains in non line-of-sight scenarios (in LOS scenarios, array gain = Nt but there is no diversity to be exploited).
Even if the channels are completely correlated, as might happen in a line-of-sight system, the received SNR increases linearly with the number of receive antennas, owing to the array gain.
MIMO is included in the IEEE 802.11n standard for wireless local area networks (WLANs). Space–time coding and spatial multiplexing are both supported. The current precoding proposals use an open-loop method. The reciprocity principle implies that the best beam on receive must be the best beam for transmit. The access point uses pre-formed beams for receive and transmit and records the beam(s) with the best signal strength on receive for each user, then uses the same beam(s) during transmit.
“Zero forcing beamforming”, null-steering
The interfering user may be in the same cell or in another cell (decrease reuse distance)
All RF beamforming techniques are reciprocal (Tx/Rx)
Spatial Filtering for Interference Reduction
If a base station in a cellular system uses an adaptive array to direct its radiation pattern towards the mobile with which it is communicating (Figure 18.5), then several benefits are produced:
- The transmit power for a given signal quality can be reduced in both uplink and downlink directions, or the cell radius can be increased, thereby reducing the number of base stations required to cover a given area.
- As the mobile transmit power is reduced, its battery life can be extended.
- The channel delay spread is reduced because off-axis scatterers are no longer illuminated.
- Depending on the direction of the mobile, the probability of base stations causing interference to co-channel mobiles in surrounding cells is reduced.
- Similarly, the probability of mobiles causing interference to co-channel base stations is reduced.
MRC is an appropriate antenna-combining strategy when the received signal is mainly impaired by noise. However, in many cases of mobile communication the received signal is mainly impaired by interference from other transmitters within
the system, rather than by noise. In a situation with a relatively large number of interfering signals of approximately equal strength, maximum-ratio combining is typically still a good choice as, in this case, the overall interference will appear relatively ‘ noise-like ’ with no specific direction-of-arrival. However, in situations where there is a single dominating interferer (or, in the general case, a limited number of dominating interferers), improved performance can be achieved if, instead of selecting the antenna weights to maximize the received signal-to-noise ratio after antenna combining (MRC), the antenna weights are selected so that the interferer is suppressed. In terms of receiver-side beamforming this corresponds to a receiver beam with high attenuation in the direction of the interferer, rather than focusing the receiver beam in the direction of the target signal. Applying receive-antenna combining with a target to suppress specific interferers is often referred to as Interference Rejection Combining (IRC)
Matched beamforming/ Eigenbeamfoming?
Is it an array gain or a diversity gain?!
SEE “Oestges, Clercxs -MIMO Wireless Communications” p.13: MRC array gain = diversity gain = nb of antennas
This requires that the number of elements is at least equal to the number of mobiles in order to solve the resulting system of simultaneous equations. In practical cases, the optimum weights would have to be estimated in the presence of noise, so an interferer is not removed completely. Instead, the weights are chosen to maximize the signal-to-interference-plus-noise ratio (SINR).
Thus, similar to the case of linear equalization, a better approach is to select the antenna weight vector to minimize the mean square error also known as the Minimum Mean Square Error (MMSE) combining.
SEE “Oestges, Clercxs -MIMO Wireless Communications” page 14
Is it an array gain or a diversity gain?!
This requires that the number of elements is at least equal to the number of mobiles in order to solve the resulting system of simultaneous equations. In practical cases, the optimum weights would have to be estimated in the presence of noise, so an interferer is not removed completely. Instead, the weights are chosen to maximize the signal-to-interference-plus-noise ratio (SINR).
Thus, similar to the case of linear equalization, a better approach is to select the antenna weight vector to minimize the mean square error also known as the Minimum Mean Square Error (MMSE) combining.
For point-to-point communications, this is termed space division multiplexing (SDM), and in multiuser scenarios, it is called space division multiple access (SDMA).
The scattering nature of the propagation channel will cause the signals received from the mobile to be broadened in arrival angle, making them overlap even if the mobiles have some angular separation. Thus the capacity of an SDMA system is limited by the capabilities of the adaptive array and by the characteristics of the channel.
Implementation of SDMA requires major changes to the base station and is difficult to implement with systems for which SDMA was not originally foreseen.
Think about turbo SDMA: s1 is estimated then its contribution is suppressed from the received signal before estimating s2. Then, s1 be better estimated using the last estimation of s2.
For N*M antennas:
Max array gain = M*N (role of correlation? Angle spread, LOS, antenna spacing)
Max diversity gain = M*N (uncorrelated) (see “MIMO Wireless Communications -2007” p.101)
Max multiplexing gain = Min(M,N)
CSIT through FB (FDD) or reciprocity (TDD)
ATTENTION: to divide power by 2, divide amplitude by sqrt(2).
In LTE, transmit-diversity techniques CDD and Antenna selection are called Transmission mode 2.
MRT = Matched filter precoder?
Quantized precoders
T. K. Yo, "Maximum Ratio Transmission," IEEE Trans. Commun., Vol. 47, No. 10, Oct. 1999, pp. 1458 . 1461.
The reciprocity principle is applicable for the “over the air” (i.e. antenna to antenna) segment of the forward and reverse links. In practical systems, however, signal processing is performed at the baseband, i.e., the channel is estimated at the receiver baseband section after the signal has passed through the receive RF chain. The transmit signal uses a different RF chain, which has a different transfer function from that of the receive chain. Therefore, the reciprocity principle can only be applied after the transmit (or receive) RF chain is equalized to make the two chains identical. This equalization requires a calibration process, wherein the difference between the two chains is identified. Calibration is expensive and has made open-loop methods less attractive in practice.
UMTS (Rel-5?)
In the case of closed-loop transmit diversity the base station uses two antennas to transmit the user
information. The use of these two antennas is based on the feedback from the terminal, transmitted in
the FBI bits in the uplink DPCCH. The closed-loop transmit diversity itself has two modes of operation.
In mode 1, the terminal feedback commands control the phase adjustments that are expected to maximize
the power received by the terminal. The base station thus maintains the phase with antenna 1
and then adjusts the phase of antenna 2 based on the sliding averaging over two consecutive feedback
commands. Thus, with this method, four different phase settings are applied to antenna 2.
In mode 2, the amplitude is adjusted in addition to the phase adjustment. The same signaling rate
is used, but now the command is spread over 4 bits in four uplink DPCCH slots, with a single bit for
amplitude and 3 bits for phase adjustment. This gives a total of eight different phases and two different
amplitude combinations, i.e. 16 combinations for signal transmission from the base station. The amplitude
values have been defined to be 0.2 and 0.8, while the phase values are naturally distributed evenly
for the antenna phase offsets, from −135◦ to +180◦ phase offset. In this mode the last three slots of the
frame contain only phase information, while amplitude information is taken from the previous four slots.
This allows the command period to go even with 15 slots as with mode 1, where the average at the frame
boundary is slightly modified by averaging the commands from slot 13 and slot 0 to avoid discontinuities
in the adjustment process.
The closed-loop method may be applied only on the DCHs or with an HS-DSCH together with a DCH.
The open-loop method may be used on both the common and dedicated channels. As part of the feature
clean-up, 3GPP decided to remove mode 2 from Release 5 onwards, as that had not been implemented
in the networks deployed so far.
Note that the lines (or columns) of the matrix are orthogonal [S1 S2][-S2* S1*]h = -S1S2+S1S2=0
Each line can be seen as a codeword
Alamouti a special case of OSTBC, it is the only square complex full rate STBC (see Complex Orthogonal Space-Time processing in wireless communication -2006 – page 36)
Certain STBCs (e.g. the Alamouti code) can achieve the ergodic capacity of a channel with no CSIT
No multiplexing gain but this is a full-rate since min(Nt,Nr)=1
Coherence time must be >2Ts (Quasi-Static channel)
Encoding delay = 2 Ts
Path gains are known at the mobile (typically this is accomplished at some sacrifice in rate by inserting pilot tones into the data frame for channel estimation)
Encoder & decoder are linear
T.I. “Space–time block coded transmit antenna diversity for WCDMA,” Texas Instruments SMG2 document 581/98, submitted October 1998.
Space–time coding (STC) schemes defined by Tarokh et al. [74] and Alamouti [5], which introduce temporal and spatial correlation into the signals transmitted from different antennas without increasing the total transmitted power or the transmission bandwidth. There is, in fact, a diversity gain that results from multiple paths between the base-station and the user terminal, and a coding gain that results from how symbols are correlated across transmit antennas. Significant performance improvements are possible with only two antennas at the base-station and one or two antennas at the user terminal, and with simple receiver structures. The second antenna at the user terminal can be used to further increase system capacity through interference suppression.
Space–time block codes
STBCs are usually designed to capture the diversity in the spatial channel, assuming no CSIT. Diversity determines the slope of the error probability versus the SNR and is related to the number of spatial links that are not fully correlated.
A full-diversity code achieves the maximum diversity order of MTMR available in the channel. Not all STBCs offer full-diversity, however. High diversity is useful in a fading link since it reduces the so-called fade margin, which is needed to meet a required link reliability.
An STBC can also be characterized by its spatial rate, which is the average number of distinct symbols sent per symbol time-period. Rate-one STBCs average one symbol per symbol-period, independent of the number of transmit antennas. Orthogonal STBCs have a rate of 1 or less. An STBC with a rate greater than 1 is called a high-rate code; the highest rate can be minMTMR. Spatial multiplexing can be viewed as a special STBC with a full spatial rate but no transmit diversity. A higher STBC rate does not imply reduced diversity; many new codes have high rates and full-diversity.
Space-time block codes (STBC) are assumed to work under rich scattering channel conditions. In contrast, line-of-sight
conditions are typically more suited to beamforming methods, where apriori knowledge of the channel is required at the
transmitter.
Note that the determinant of precoding matrix is |h1|2+|h2|2 >0, it is an orthogonal matrix
The decoding matrix is the inverse (1/delta factor ignored) which is its hermitian matrix (conjugate transpose)!
The decoding is a projection, space-time matched filtering
H is orthogonal: HHh=HhH=(|h1|2+|h2|2)I=(channel power gain) I
We obtain a virtual 2x2 channel that can be decoded without interference so that parallel detection (ZF, ML, MMSE) can be used instead of joint detection.
In LTE orthogonal space frequency block codes (OSTBC) are used that allow simple receiver structures
⇒Symbol by symbol detection rather than vector detection.
The main attractive feature of STBC is the quaternionic structure (see Appendix 4.1 for more discussions on quaternions) of the spatio-temporal channel matrix. This allows us to eliminate inter-antenna interference using a low-complexity linear combiner (which is a spatio-temporal matched filter and is also the maximum-likelihood detector in this case). Then, joint equalization and decoding for each antenna stream proceeds using any of well-known algorithms for the single-antenna case which can be implemented either in the time or frequency domains.
Alamouti discovered a very simple transmitter diversity technique for two Tx antennas, which provides a full diversity order, has no loss of capacity (if the number of Rx antennas is equal to one), and possesses a simple and fast maximum likelihood (ML) decoding. Instead of being joined, the transmitted signals are decoded separately at decoders due to the orthogonality between the columns (and rows) of the code.
The Alamouti STBC has been extended to the case of more than two transmit antennas using the theory of orthogonal designs. There it was shown that, in general, full rate orthogonal designs exist for all real constellations for two, four, and eight transmit antennas only, while for all complex constellations they exist only for two transmit antennas (the Alamouti scheme). However, for particular constellations, it might be possible to construct full-rate orthogonal designs for larger numbers of transmit antennas. Moreover, if a rate loss is acceptable, then orthogonal designs exist for an arbitrary number of transmit antennas.
It has been shown that an orthogonal full-rate design, offering full diversity for any arbitrary complex symbol constellation, is limited to the case of two transmit antennas.
Based on signal constellations, the authors classified STBCs into two classes, namely, STBCs for real signals and STBCs for complex signals. Real STBCs can be used in the case of Pulse Amplitude Modulation (PAM) while complex STBCs are used for Phase Shift Keying (PSK) or Quadrature Amplitude Modulation (QAM) constellations. Both of them may, or may not, include linear processing (LP) at transmitters.
Real STBCs have been well examined. There is a systematic method to construct real STBCs with the maximum rate Rmax = 1 for up to 8 Tx antennas based on Huwitz-Radon theory. The background on the Huwitz-Radon theory can be found in [Ganesan and Stoica, 2000], [Geramita and Seberry, 1979]. These codes also provide a maximum Signal-to-Noise Ratio (SNR) at receivers [Ganesan and Stoica, 2001]
EA-STBC=Extended Alamouti STBC
Stacked Alamouti scheme?
LTE mode 2?: Transmit diversity. Transmit diversity with two or four antenna ports using space-frequency block
coding, a similar approach to the open loop WCDMA transmit diversity described in Chapter 6.
The space-frequency scheme used by LTE in this case is equivalent to the Alamouti space-time coding with the
difference that the frequency dimension is used instead of the time dimension In other words, the scheme invloves 2 neighbouring subcarriers (instead of 2 consecutive symbol-times).
2 Tx Alamouti is the only full-rate STBC capable of full diversity (2) for any complex constellation
For more than 2 Tx antennas, we can construct full-rate but sacrificing diversity gain
My summary: Coding rate-diversity gain trade-off
Full-rate Extended Alamouti comes at the price of reduced diversity gain since only quasi-orthogonal equivalent channel matrices are possible
Higher dimension Orthogonal matrices are possible (so diversity order increases with the nb of Tx antennas) but at the price of reduced rate (multiplexing gain < 1) (example: 3 symbols in 4 time slots)
If we limit symbols to real constellations (M-ASK), some full-rate higher dimension orthogonal matrices are possible.
Zero vector here is 1x(TR)
Eigen values of covariance matrix HHh
802.11ac includes support for up to eight spatial streams, versus four in 802.11n. As in 802.11n, spatial multiplexing of multiple streams of data over the same frequencies takes advantage of the extra degrees of freedom provided by the independent spatial paths to effectively multiply channel capacity.