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EE 5407 Part II: Spatial Based WirelessCommunications

Instructor: Prof. Rui Zhang

E-mail: rzhang@i2r.a-star.edu.sg

Website: http://www.ece.nus.edu.sg/stfpage/elezhang/

Lecture I: Introduction

March 4, 2011

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About The Instructor

• Senior Research Engineer, Institute for Infocomm Research (I2R);

Assistant Professor (joint appointment), ECE Department, NUS

• B. ENG & M. ENG, ECE Department, NUS; Ph.D, EE Department,

Stanford University

• Current Research Interests: (1) Wireless Communication (Multiuser

MIMO, Cognitive Radio, Cooperation Communication, Energy Efficiency

& Energy Harvesting); (2) Convex Optimization for Applications in

Signal Processing & Communication; (3) Information Theory

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Outline

• Overview of Wireless Communications

• Introduction to Multi-Antenna Wireless Communications

• Course Overview

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Overview of Communications Systems

There are seven layers (physical, data link, network, transport, session,

presentation, application) in the Open Systems Interconnection (OSI) model.

The three lower layers are closely related to communication system design.

• Physical Layer: Transmitter⇒Channel⇒Receiver

– Transmitter: channel coding, modulation, pulse shaping, power

control, precoding, ...

– Channel: impairments due to path loss, multipath propagation, time

variation of the channel, interference and noise

– Receiver: equalization, demodulation, channel decoding, ...

• Data-Link Layer:

– Medium Access Control (MAC): Protocols to allow frames to be sent

over the shared media without undue interference to other nodes.

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– Multiple Access Schemes: Physical layer schemes to support multiple

users to communicate with the same base station (access point).

∗ Time division multiple access (TDMA)

∗ Frequency division multiple access (FDMA)

∗ Code division multiple access (CDMA)

∗ Spatial division multiple access (SDMA)

∗ Orthogonal frequency division multiple access (OFDMA)

• Network Layer:

– Routing: Define the route by which the message from the source is

passed to the ultimate destination within the network.

– Quality of Service (QoS) Control: throughput, delay, ...

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Overview of Wireless Communication Systems

• Cellular mobile systems

– Most popular

– To provide wireless connections anytime, anywhere

– Voice dominated; video transmission and high speed internet are also

in high demand

– Mobility requirement

– Range: kilometer to tens of kilometers

– Standardization activities and multiple access schemes

∗ 2G/2.5G: GSM TDMA; IS-95 CDMA

∗ 3G: CDMA-2000, WCDMA, TDS-CDMA

∗ 3.5G: HSDPA, HSUPA

∗ 3.9G (3G Long Term Evolution): OFDMA, IFDMA

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∗ 4G: OFDMA+SDMA (MIMO-OFDM)

– Challenges: capacity, coverage, high data rate

• Wireless local area networks (WLAN, WiFi)

– Providing high speed wireless connections for LAN environment

– Hot spots (airport, hotel, shopping mall), office and home

environment, campus, ...

– Standardization activities

∗ Low rate: IEEE802.11b (2 - 11Mbps, 2.4GHz)

∗ Medium rate: IEEE802.11a (6 - 54Mbps, 5.2GHz), IEEE802.11g (6

- 54Mbps, 2.4GHz); OFDM

∗ High rate: IEEE802.11n (peak rate around 600Mbps, 5.2GHz,

thanks to MIMO technology); MIMO-OFDM

– Range: < 20 m for peak data rate; around 100m for lowest rate

– Challenges: high data rate, coverage

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• Fixed/mobile wireless data services

– Last-mile broadband wireless access technique

– Alternative or complement to cable modem, DSL

– Data-dominated services

– Range: tens of kilometers

– Standardization activities

∗ IEEE802.16: 10 - 60 GHz; Jan 2001

∗ IEEE802.16e (WiMAX): 2 - 11 GHz; Jan 2006; with mobility;

OFDM, SCCP, MIMO.

∗ IEEE802.22 (Wireless regional area networks (WRAN) based on

cognitive radio technology): 54 MHz - 862 MHz (TV channels)

– Challenges: coverage, high data rate

• Wireless personal area networks (WPAN)

– Providing high speed wireless connections for very short distance

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using ultra wideband (UWB) technology

– To replace physical cables, wireless USB, ...

– Home networking

– Peak data rate: 480Mbps

– Standardization activity: IEEE 802.15 working group.

∗ Multiband OFDM with bandwidth about 500 MHz

∗ Impulse radio based DS-CDMA with bandwidth about 2GHz

– Range: < 10 m

– Challenges: coverage

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Impairments for Wireless Transmissions

• Path loss ⇒ low received signal-to-noise ratio (SNR) ⇒ low rate, short

distance

• Shadowing and Fading ⇒ received SNR fluctuation ⇒ increased BER

• Multi-path ⇒ inter-symbol interference (ISI) ⇒ low received

signal-to-interference-plus-noise ratio (SINR) ⇒ increased BER

• Co-channel interference (occurs when two or more users operate over the

same frequency band at the same time) ⇒ low received SINR ⇒

increased BER, low capacity

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General Challenges For Wireless Communications

Given the fact that transmission resources such as power and bandwidth are

limited, the challenges are

• How to increase the channel capacity (data rate) without increasing the

bandwidth and transmission power?

• For a given transmission rate, how to extend the coverage without

increasing the transmission power?

• How to increase the system capacity with multiple users?

Answer: Exploiting spatial dimension using multiple antennas

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Potential Gains Achieved By Antenna Arrays

• Array gain: the increase of average SNR at the receiver that arises from

the coherent combining effect of multiple antennas at the receiver or

transmitter or both.

• Diversity gain: the increase of transmission reliability by compensating

for channel fading via exploiting spatial channel diversity.

• Spatial multiplexing gain: the increase of data rate by communicating

multiple data streams from multiple transmit antennas to multiple

receive antennas (without power or bandwidth increase).

• Interference mitigation gain: the increase of received SINR by

nulling/suppressing the co-channel interference via antenna-array

beamforming.

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Multi-Antenna Channel Model

• Single-User (Point-to-Point) Transmission:

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Signal Model: MIMO Case

• Consider the narrow-band transmission over the flat-fading channel,

which is valid when

– channel coherence bandwidth is much larger than transmission signal

bandwidth

– or channel multi-path delay spread is much smaller than transmission

symbol period

• Consider the block-fading (slow-fading) channel model

– channel is constant during each transmission block (consisting of

many symbols), but may change from one block to another

– valid when channel coherence time is much larger than block duration

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• Discrete-time baseband signal model for each block transmission:

y(n) = Hx(n) + z(n) (1)

– r: number of antennas at the receiver

– t: number of antennas at the transmitter

– n: symbol time index

– y(n) ∈ Cr×1: received signal vector

– H ∈ Cr×t: channel matrix; the element at the ith row and jth

column of H , denoted by hij = [H ]i,j, is the complex channel

coefficient from the jth transmit antenna to ith receive antenna,

i ∈ {1, . . . , r}, j ∈ {1, . . . , t}

– x(n) ∈ Ct×1: transmitted signal vector; it is assumed that x(n) is

circularly symmetric random vector, and has zero mean, E[x(n)] = 0,

and covariance matrix, Sx , E[x(n)xH(n)], where

∗ Sx is Hermitian symmetric, i.e., Sx = SHx

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∗ Sx is positive semi-definite, i.e., for any vector v ∈ Ct×1,

vHSxv ≥ 0. Note that all eigenvalues of Sx are non-negative real

numbers, and the eigenvalue decomposition of Sx can be written by

Sx = UxΛxUHx , where Ux ∈ C

t×t and UxUHx = I, and Λx is a

t × t diagonal matrix with the diagonal elements being the

eigenvalues of Sx

– z(n) ∈ Cr×1: noise vector at the receiver; it is assumed that z(n)’s

are independent over n, and z(n) is circularly symmetric and jointly

Gaussian random vector, referred to as circularly symmetric complex

Gaussian (CSCG), and has zero mean and covariance matrix,

Sz , E[z(n)zH(n)]; for brevity, denote z(n) ∼ CN (0, Sz)

– z(n) is independent of x(n) ∀n

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Circularly Symmetric Distribution

Definition: The random vector x is circularly symmetric if ejφx has the

same probability distribution as x for all real φ.

Theorem: Assume that z is a complex jointly-Gaussian random vector with

zero mean. Then z is circularly symmetric if and only if (iif)

M z , E[zzT ] = 0.

• Let z = [z1, . . . , zN ]T . Note that M z = 0 implies that

– E[(Re(zi))2] = E[(Im(zi))

2],∀i ∈ {1, . . . , N}

– E[Re(zi) × Im(zi)] = 0,∀i ∈ {1, . . . , N}

– E[Re(zi) × Re(zj)] = E[Im(zi) × Im(zj)],∀i, j ∈ {1, . . . , N}, i 6= j

– E[Re(zi) × Im(zj)] = −E[Im(zi) × Re(zj)],∀i, j ∈ {1, . . . , N}, i 6= j

• The distribution or probability density function (PDF) of a zero-mean

CSCG random vector z depends only on Sz.

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MIMO Channel Distribution

• IID (independent and identically distributed) Rayleigh-fading channel:

– H consists of independent CSCG random variables each with zero

mean and variance σ2, i.e., hij ∼ CN (0, σ2),∀i, j.

– Corresponds to rich-scattering environments at both transmitter and

receiver sides

– In this case, we can write hij = αijejθij , where θij = ∠hij is uniformly

distributed over [0, 2π); and αij = |hij| is Rayleigh distributed with

PDF:

fα(x) =2x

σ2e−

x2

σ2 (2)

– Then βij = α2

ij is exponentially distributed with PDF:

fβ(y) =1

σ2e−

y

σ2 (3)

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– For notational brevity, denote H ∼ Hw

• MIMO channel with transmit/receive antenna correlations:

– If the antennas are correlated at the transmitter side, but not at the

receiver side, the MIMO channel can be modeled by

H = HwR1/2

t (4)

where Rt ∈ Ct×t is the covariance matrix describing the transmit

antenna correlations.

– Similarly, the MIMO channel with the correlated receive antennas

and uncorrelated transmit antennas can be modeled by

H = R1/2

r Hw (5)

where Rr ∈ Cr×r is the covariance matrix describing the receive

antenna correlations.

– Generally, in the presence of both transmit and receive antenna

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correlations, the MIMO channel can be modeled by

H = R1/2

r HwR1/2

t . (6)

– The IID channel matrix Hw is a full-rank matrix with probability 1,

i.e., the rank of Hw satisfies Rank(Hw) = min(t, r). In the presence

of transmit and receive antenna correlations,

Rank(H) ≤ min(Rank(Rr), Rank(Rt)), with probability 1.

• There are many other MIMO channel models: Rician fading (with LOS

component), Degenerate channels (e.g., pin-hole channel), ...

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Frequency Selective Fading MIMO Channel

• Consider broadband transmission over frequency selective fading channel

– applicable when signal bandwidth (inverse of symbol duration) is

comparable with channel coherence bandwidth (inverse of multi-path

delay spread), and thus two or more signal propagation paths are

resolvable at the receiver

• Consider the slow-fading/block-fading channel model

• Discrete-time baseband signal model for each block transmission:

y(n) =L−1∑

l=0

H lx(n − l) + z(n) (7)

– L ≥ 1: number of resolvable multi-paths

– H l ∈ Cr×t: channel matrix for the lth path, l ∈ {0, . . . , L − 1}

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Multiuser MIMO System Model

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Spatial Division Multiple Access (SDMA)

• Two or more users each with multiple transmit and/or receive antennas

communicate over the same frequency band and at the same time slot

(e.g., in cellular systems)

– maximizes system capacity

– creates co-channel interference: spatial interference mitigation is

needed (a very active area of research)

• MAC (SIMO, MIMO): models the uplink (UL) transmission of a single

cell; independent transmit processing and joint receive processing

• BC (MISO, MIMO): models the downlink (DL) transmission of a single

cell; joint transmit processing and independent receive processing

• IC (MISO, SIMO, MIMO): models the UL/DL transmission of two or

more cells; independent transmit/receive processing

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Course Overview

• Introduction (Lecture I)

– Overview of multi-antenna wireless communications

– MIMO channel and signal models

• Receive Beamforming (Lecture II)

– SIMO channel

– Receive beamforming techniques: selection combining, equal-gain

combining, maximal-ratio combining

– Diversity order, array gain

• Transmit Beamforming & Transmit Diversity (Lecture III)

– MISO channel

– Transmit beamforming with (w/) Channel State Information at

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Transmitter (CSIT)

– Transmit diversity without (w/o) CSIT: Alamouti code

– MIMO channel:

∗ Joint transmit beamforming and receive beamforming w/ CSIT

∗ Joint transmit diversity and receive beamforming w/o CSIT

• MIMO Systems (Lecture IV)

– Overview of single-antenna/SISO AWGN (additive white Gaussian

noise) and fading channel capacities

– MIMO AWGN channel: capacity, transceiver design for spatial

multiplexing (CSIT-known vs. CSIT-unknown), MIMO detection

– MIMO fading channel: ergodic capacity, outage capacity

• MIMO-OFDM (Lecture V)

– OFDM for SISO frequency selective fading channel

– OFDM for MIMO frequency selective fading channel: MIMO-OFDM

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Course Logistics

• In total, six lectures

• Two continuous assessments (CAs):

– each counts 10% in final grade

– Due date for CA I: March 30, 2011 (in class, firm)

– Due data for CA II: April 13, 2011 (in class, firm)

• Final exam (counts 30% in final grade)

• No tutorials

• Bonus marks:

– Detected typo: 0.5 mark each

– Detected technical error: 1 mark each

– Total marks capped by 5 (out of 100 in final grade)

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Reference Books

• A. J. Goldsmith, Wireless Communications, Cambridge University Press,

2005.

• D. Tse and P. Viswanath, Fundamentals of Wireless Communication,

Cambridge University Press, 2005.

• A. Paulraj, R. Nabar, and D. Gore, Introduction to space-time wireless

communications, Cambridge University Press, 2003.

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