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EE401: Advanced Communication Theory
Professor A. ManikasChair of Communications and Array Processing
Imperial College London
Multi-Antenna Wireless Communications
Part-A: An Introductory Overview
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Table of Contents1 Introduction
SISO Wireless Channel Tx & RxGeneric Rx ArchitectureWireless Systems ClassificationSIMO, MISO and MIMO: Non-Parametric ModelsSIMO, MISO and MIMO: Parametric ApproachIntroductionDifferential Geometry - IntroductionAntenna Array Space ResponseAntenna Array Patterns and Channel Capacity
Motivation ExamplesSIMO Wireless Reception and TrackingMAI CancellationCochannel Interference Cancellation with MotionSpace-only and Spatiotemporal Gain Patterns (SIMO)Spatiotemporal Capacity
Examples of Real Array SystemsA 2GHz Antenna Array of 48 ElementsOwens Valley Radio Observatory ArrayThe New Mexico Very Large Array of 27 ElementsA Large Circular ArrayAntenna Arrays for Modern Wireless Systems
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Introduction SISO Wireless Channel Tx & Rx
SISO Wireless Channel Tx & RxA wireless system can be partitioned into 3 main parts:
1 Tx (a "source " that sends/transmits some information using wavepropagation)
2 Wireless Channel (the physical propagation paths )3 Rx ( a "sink " that receives the transmitted waves)
and the objective in general isI to increase the communication speed (which is known as channelcapacity)without sacrificing the quality of service (for a given energy +bandwidth)
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Introduction Generic Rx Architecture
Generic Rx Architecture
The quality of the receiver (Rx) is a function of the quality of theestimated channel parametersNote that the receiver is continuously designed (based on theseestimates) from time frame to time frame.
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Introduction Wireless Systems Classification
Wireless Systems Classification
There are many classifications. For instance:1 according to the bandwidth/carrier: narrowband or wideband2 according to the spreading capabilities: conventional or spreadspectrum
3 according to the number of carriers: single carrier or multicarrier4 according to the "generation": 1G, 2G, 3G , 3G+5 according to the "access": TDMA,FDMA , CDMA ,
The overall aims:I speed = ↑,I but maintaining reliability (quality of service) & spectral effi ciency(EUE,BUE)
The current speed is expected to increase by the utilisation of thenew technology of multiple antennas (MIMO) and this gives rise to anew classification which super-sets all the above.
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Introduction Wireless Systems Classification
New Wireless Systems ClassificationThis new classification is according to the number of antennasused in both Tx and Rx
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Introduction Wireless Systems Classification
New Wireless Systems ClassificationThis new classification is also according to the number of antennasand the space-only or spatiotemporal signal processing used in bothTx and Rx (this is the main focus of this topic)
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Introduction Wireless Systems Classification
My TerminologyTerminology-1 (More Representative)1 SISO: Scalar-Input-Scalar-Output Channel
2 SIVO: Scalar-Input-Vector-Output Channel
3 VISO: Vector-Input-Scalar-Output Channel
4 VIVO: Vector-Input-Vector-Output ChannelAlternative TerminologyTerminology-2 (Initial)1 SESE: from Single-Element (SE) Tx to Single-Element (SE) Rx
2 SEME: from Single-Element (SE) Tx to Multiple-Element (ME) Rx
3 MESE: from Multiple-Element (ME) Tx to Single-Element (SE) Rx
4 MEME: from Multiple-Element (ME) Tx to Multiple-Element (ME) Rx
Terminology-3 (More Popular)1 SISO: Single-Input-Single-Output
2 SIMO: Single-Input-Multiple-Output
3 MISO: Multiple-Input-Single-Output
4 MIMO: Multiple-Input-Multiple-Output
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Introduction Wireless Systems Classification
Mobile Evolution - Motivation
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Introduction Wireless Systems Classification
Mobile Evolution - Motivation (cont.)
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Introduction SIMO, MISO and MIMO: Non-Parametric Models
SIMO Wireless Systems (non-parametric)
Single-Input Multiple-Output (SIMO)
Remember: SISO - one complex number β per path
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Introduction SIMO, MISO and MIMO: Non-Parametric Models
MISO Wireless Systems (non-parametric)
Multiple-Input Single-Output (MISO)
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Introduction SIMO, MISO and MIMO: Non-Parametric Models
MIMO Wireless Systems (non-parametric)
Multiple-Input Multiple-Output (MIMO)β1,1 β1,2 ... β1,N (Tx)β2,1 β2,2 ... β2,N (Tx)...
.... . .
...βN (Rx),1 βN (Rx),2 ... βN (Rx),N (Tx)
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Introduction SIMO, MISO and MIMO: Parametric Approach
Parametric ApproachesIntroduction
The above modelling will result into a statistical approach (used inWiener’s estimation theory and Shannon’s communication theory).e.g. many MIMO books, papers and tutorials: non parametric
Although this approach is suitable for single antenna systems (i.e.SISO), it does not properly fit multiple antennas since it
I ignores the Cartesian coordinates and orientations of Tx and Rx (i.e.ignoring the geometry/location of the multiple antennas),
I ignores the directions of the signals,
I ignores propagation models (planewaves or spherical waves),
I etc.
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Introduction SIMO, MISO and MIMO: Parametric Approach
Revisiting Multiple-Input Multiple-Output (MIMO)
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Introduction SIMO, MISO and MIMO: Parametric Approach
Summary Table of SISO, MISO, SIMO and MIMO
Non-Parametric Parametric(Array Processing)
SISO: β
SIMO:
βTx ,1βTx ,2...
βTx ,N (Rx)
= βa(Rx)
MISO:
β1,Rxβ2,Rx....
βN (Tx),Rx
= βa(Tx)
MIMO:
β1,1 β1,2 ... β1,N (Tx)β2,1 β2,2 ... β2,N (Tx)... ... ... ...
βN (Rx),1 βN (Rx),2 ... βN (Rx),N (Tx)
= βa(Rx)a(Tx)H
⇔ βa(virtual)
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Introduction SIMO, MISO and MIMO: Parametric Approach
The Structure of the Array Response VectorFrom now on in this presentation the vector a will represent allmultiple antenna wireless systems, i.e.
a ,
a(Rx) SIMOa(Tx) MISOa(virtual) = a(Tx) ⊗ a(Rx) MIMO
The vector a is known as
I Array Manifold Vector orI Array Response Vector (alternative symbol S)
The vector a has a profound mathematical structure and is afunction of a number of parameters such as Directions, carrier,etc
a(θ, φ,Fc , c, r1, r2, r3, . . . , rN )
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Introduction SIMO, MISO and MIMO: Parametric Approach
Note
we can also add more wireless parameters from the Tx and Rx.
For instance
a(θ, φ,Fc , c, r x , r y , r z ,pseudorandom sequ, delay, polarisation parameters,No.of subcarriers/carriers, bandwidth, Doppler frequency).
Various forms of a have different dimensions but always a profoundmathematical structureThis leads to Differential Geometry which complements the statisticalsignal processing and Shannon’s communication theory in arrayprocessing problems and wireless systems.
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Introduction SIMO, MISO and MIMO: Parametric Approach
Differential GeometryDifferential geometry is a branch of mathematics that is concernedwith the application of differential calculus for the investigation of theproperties of geometric curves , surfaces and other objects knownas ‘manifolds ’.
Manifolds have a deep and profound mathematical structure andhave been an area of intense pure mathematical analysis.
p 7→mathematical object
In Physics, Albert Einstein (Nobel 1921) used differential geometry toexpress his general theory of relativity
I where the universe is a smooth manifold equipped withpseudo-Riemannian metric (described the curvature of space-time).
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Introduction SIMO, MISO and MIMO: Parametric Approach
Fundamental Questions
Diff. Geom. helps answering somefundamental questions such as:
Q1 Is it possible to express a wirelesssystem as a space curve or a surface(or a manifold - in general)?
Q2 Is it possible to analyse a wirelesssystem by analysing a curve or asurface?
Q3 Is it possible to design a wirelesssystem by designing a curve or asurface?
Q4 What do we stand to gain byexpressing wireless systems asmathematical objects such as curvesor surfaces?
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Introduction SIMO, MISO and MIMO: Parametric Approach
Antenna Array Space ResponseSIMO Example: Rx-Array Diversity
Array systems (smart antennas) and techniques can be seen as themost sophisticated and advanced space diversity systems/techniques.(This type of systems/techniques will be considered in this course.)
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Introduction SIMO, MISO and MIMO: Parametric Approach
Single Antenna (N=1): Space Response
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Introduction SIMO, MISO and MIMO: Parametric Approach
Two Antennas (N=2): Space Response
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Introduction SIMO, MISO and MIMO: Parametric Approach
Three Antennas (N=3): Space Response
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Introduction SIMO, MISO and MIMO: Parametric Approach
Four Antennas (N=4): Space Response
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Introduction SIMO, MISO and MIMO: Parametric Approach
Five Antennas (N=5): Space Response
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Introduction SIMO, MISO and MIMO: Parametric Approach
Space-Only Example: Uniform Linear Array (ULA)
Intersensor spacing=λ/2;
N = number of antennas (located on the x-axis).
Channel Capacity (AWGN):
C = B log2(1+N × SNIRin) (1)
B −→ ∞⇒ C −→ N × 1.44 PsN0 +Nj ↓
(2)
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Introduction SIMO, MISO and MIMO: Parametric Approach
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Introduction SIMO, MISO and MIMO: Parametric Approach
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Introduction Motivation Examples
SIMO Wireless Reception and Tracking (ULA, N=5)
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Introduction Motivation Examples
Multiple Access Interference Cancellation (ULA, N=5)
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Introduction Motivation Examples
Co-Channel Interference Cancellation with Motion (ULA,N=5)
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Introduction Motivation Examples
Example: Space-only & Spatiotemporal Gain Patterns
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Introduction Motivation Examples
Spatio-Temporal Example: PN-code of period 31; Uniform LinearArray (ULA) with intersensor spacing=λ/2; N = number of antennas
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Introduction Motivation Examples
SISO capacity :
C = B log2(1+ SNIRout ) bits/sec (3)
MIMO Capacity :
C = B log2
(det(Rxx )
det(Rnn)
)bits/sec (4)
If bandwidth B −→ ∞ then C =?
SISO : limB→∞
C = 1.44Ps
N0 +NJ(5)
space-only SIMO : limB→∞
C = N × 1.44 PsN0 +NJ ↓
0
(6)
spatiotemporal-SIMO : limB→∞
C = N ×NSP × 1.44Ps
N0 +NJ ↓0
(7)
where N denotes the number of array elements (antennas)
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Introduction Motivation Examples
Space and Spatiotemporal Capacity Curves
N = 5 antennas
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Introduction Examples of Real Array Systems
A 2GHz Antenna Array of 48 Elements
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Introduction Examples of Real Array Systems
Owens Valley Radio Observatory Array
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Introduction Examples of Real Array Systems
The New Mexico Very Large Array of 27 Elements
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Introduction Examples of Real Array Systems
A Large Circular Array
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Introduction Examples of Real Array Systems
Antenna Arrays for Modern Wireless Systems
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Introduction Examples of Real Array Systems
Antenna Arrays for Modern Wireless Systems (cont.)
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