Theoretical Aspects of Wireless Sensor and Ad Hoc Networks · communication topologies with...

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Theoretical Aspects of WirelessSensor and Ad Hoc Networks

Part I: Distributed Cooperative Communication Techniques

Mischa Dohler

TECH/IDEA

France Telecom R&D

[email protected]

Hamid Aghvami

CTR

King’s College London

[email protected]

Tutorial Presentation, PIMRC 2006, Helsinki, Finland 1

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– Location of France Telecom R&D –

Figure 1: Grenoble in the Alps - ’Silicon Valley’ of France.

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– Before We Start –

Internet search results on ’wireless distributed relaying communications’:

• 1999: a handful (beginning of my personal research in this subject)

• 2006: 2,280,000 (Google, January 2006)

All of these documents contain some related information; but, even if only 1% of them is

really useful to us, we would have to read and analyse 22,800 links. If we took 5 min for

each, we would be occupied for 1 year! Hence, our questions at the beginning of this tutorial:

• Is it really useful to start working in an area which seems to be so well explored?

• If so, what are the areas which still need exploration?

• Will these systems yield decades of research but barely any commercial products?

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– Tutorial Emphasis –

• Due to the large amount of fundamental and advanced material, we had to cut down on

many important contributions. Apologies if we missed yours!

• Also, you all have a very diverse background ranging from computer scientists to

information theorists. Apologies if some material seems too basic to you; however, ...

• The aim of this tutorial is to give you:

– a sufficient overview of the concept,

– some detailed knowledge on some of the issues,

– some feeling for other issues,

– and some tools which facilitate related analysis.

• Ideally, this tutorial should inspire you and stipulate you to apply your knowledge and

enthusiasm to distributed, cooperative communication systems – be they cellular, ad

hoc or sensor networks.

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– Tutorial Overview –

1. Some Useful Definitions

2. Motivation & Application

3. Background & Milestones

4. Channel Characterisations

5. Shannon Capacity & Outage

6. Physical Layer Algorithms

7. MAC & X-Layer Design

8. The Road Ahead

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PART 1SOME USEFUL DEFINITIONS

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System Characterisation

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– Infrastructure –

Infrastructure (physical or logical):

• infrastructure-based (ie available prior to deployment, eg cellular networks or WLAN),

• infrastructure-less (ie emerges after deployment or unavailable, eg ad hoc networks).

Management of infrastructure:

• centralised (eg cellular network),

• decentralised (eg WLAN mesh network).

Note that:

• you may have a decentralised infrastructure-based system (e.g. decentralised RRM)

• you may have a centralised infrastructure-less system (e.g. clustering)

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– Information Flow (1/2) –From source to destination/target, the information flow can be:

• point-to-point (traditional)

• point-to-multipoint (broadcast)

• multipoint-to-point (multiple access)

• multipoint-to-multipoint (general)

P2P P2MP MP2P MP2MP

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– Information Flow (2/2) –Realisation of flow by means of:

• direct link (no relays between source and target)

• relaying links (relay(s) between source and target)

• relaying stages (clusters where information passes approx. the same time)

direct link relay link relay stages

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– Node Behaviour –The nodes in the network can have the following behaviour:

• egoistic (no help)

• supportive (unidirectional help)

• cooperative (mutual help)

egoistic supportive cooperative

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– Relaying Methods –

There are the following basic relaying methods:

• Amplify and Forward (AF)

– frequency band translation

– amplification of analog signal (different methods)

• Compress and Forward (CF)

– detection (without decoding)

– quantization and compression

• Decode and Forward (DF)

– detection and decoding

– (possible) re-encoding

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– Decode & Forward Methods –

The most tractable DF methods are:

• repetition based (repeat codeword during relaying)

• channel code based (relay parity information)

• space-time code based (construct ST codeword)

repetition

s-MT

r-MT t

channel code

s-MT

r-MT t

same data parity data

ST code

s-MT

r-MT t

ST data

Supportive Case:

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– Degrees of Freedom –

• We observe that a combination of above methods and mechanisms leads to

communication topologies with infinite degrees of freedom.

• We will hence only touch upon:

– AF methods

• And we will concentrate only on:

– cooperative, single-stage, repetition-based DF methods

– cooperative, single-stage, channel coded DF methods

– cooperative, multi-stage, space-time coded DF methods

• Numerous contributions on AF, DF and CF methods for even more general topologies

are publicly available, but are out of the time-frame of this tutorial.

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Shannon Capacity

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– Definition of Capacity –

• Shannon proved that one can design codes facilitating a communication rate R bits/symbol with

arbitrarily small error.

• He also showed that these codes must be infinite (very long), so as to average out the effect of

noise.

• His theory was not concerned with code construction or code complexity, nor with decoding

delay.

• The maximum data rate at which reliable communication is possible is referred to as capacity C

of the channel.

• This capacity is independent of the signal processing used at either end of the channel.

• The capacity (per dimension) of a AWGN channel with power signal constraint S and noise

power N is

C =12

log2

(1 +

S

N

)

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– Capacity & Ergodic Channels –

• A stochastic process is ergodic if the time averages may be used to replace ensemble averages;

or, no sample helps meaningfully to predict values that are very far away in time from that

sample (i.e. the time path of the stochastic process is not sensitive to initial conditions).

• An ergodic channel can support a maximum error-free transmission rate with 100% reliability,

which is referred to as capacity. For a SISO channel it can be expressed as

C = Eλ

{log2

(1 + λ S

N

)}.

λ

Codeword #n

Time t

Instantaneous

Channel Power

[dB]

codeword length T ∞→Codeword #n

Time t

Codeword #m

codeword length T ∞→

Figure 2: Fading behaviour of an ergodic channel.

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– Outage & Non-Ergodic Channels –

• A stochastic process is non-ergodic if it is not ergodic; or, any sample helps meaningfully to

predict values that are very far away in time from that sample (i.e. the time path of the stochastic

process is sensitive to initial conditions).

• A non-ergodic channel cannot support a maximum error-free transmission rate with 100%

reliability; however, it can support any given rate Φ with a certain probability Pout(Φ) which is

referred to as rate outage probability.

λ

Codeword #n

Time t

Instantaneous

Channel Power

[dB]

codeword length T ∞→Codeword #n

Time t

Codeword #m

codeword length T ∞→

Figure 3: Fading behaviour of a non-ergodic channel.

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PART 2MOTIVATION & APPLICATIONS

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System Trade-Offs

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– System Deployment Aims –

End-users, manufacturers, service providers and government perceive the deployment aims

entirely differently.

• Users: The aim is to offer to the user better services for less money everywhere and

anyhow.

• Manufacturers: The aim is to provide technology at the lowest possible research,

development and manufacturing costs.

• Service Providers: The aim is to integrate innovative and commercially tangible

services seamlessly into existing services.

• Government: The aim is to provide reliable services which are important to the security

and health of the citizens (cost is usually no issue).

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– Capacity Demand versus Capacity Supply –

Demand for System Capacity Limits on System Capacity

Density of wireless devices is increasing. Spectrum is not being released fast enough.

Applications require increasing data-rates. Maximum transmission power is limited.

End-user craves for higher data-rates. Complexity of scheduler increases.

• Already, the offered capacity falls short to the required capacity. To make things worse,

the required system capacity is increasing faster than the potentially offered capacity.

• It would hence be desirable to have a communication mechanism in place which is

inherently self-scaling in terms of data-rate demand versus supply.

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– Potential Solutions –

The majority of telecom research is currently combating exactly this discrepancy between

capacity demand and supply. Some approaches are listed below.

• Balance traffic between existing networks, e.g. between WLAN and 3G. The approach

is often referred to as heterogeneous resource management.

• One could also increase the density of the base stations and access points; however,

this is fairly expensive.

• Create a mesh network using relaying terminals, which effectively emulates an increase

of the density of base stations and access points.

• Increase the spectral efficiency of the wireless link (e.g. MIMO).

It has been proposed to conjoin MIMO and relaying technologies.

This tutorial is dedicated to some of the design challenges of such networks.

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– Multiple-Input-Multiple-Output –MIMO: t transmit antennas connected to r receive antennas via a wireless fading channel,

with the following options:

• space-time block coding: no CSI at Tx, diversity gain, robust to interference

• space-time trellis coding: no CSI at Tx, diversity & coding gains, robust to interference

• spatial multiplexing: reliable CSI at Tx, multiplexing gains, susceptible to interference

• beamforming: CSI at Tx, ’power gains’, minimising interference

Information

Source

Transmitter

Space-Time

Processing

Receiver

Space-Time

Processing

Information

Sink

s s

tTransmit

Antennas

rReceive

Antennas

h11

hr,t

H

MIMO

Channel

Figure 4: MIMO transceiver structure.

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– Pros & Cons of MIMO –

Some of the pros and cons of multiple-input-multiple-output (MIMO) systems:

• Advantages:

– offers a high spectral efficiency

– realistic encoding strategies with varying degrees of complexity are known

– research area seems to be infinite

• Disadvantages:

– more channel coefficients have to be estimated (for coherent detection)

– requires the antennas to be sufficiently decorrelated

– implementation into mobile terminals is difficult

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– Relaying –Traditional relaying approach: single link connection from source to sink with the following

characteristics:

• RF: cannot listen & talk at the same time in the same band

• PHY: transparent, regenerative or hybrid relaying mechanisms

• MAC: reservation-based or randomised access schemes

Figure 5: Conventional relaying network.

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– Pros & Cons of Relaying –

Some of the pros and cons of relaying systems:

• Advantages:

– coverage area of BS or AP can be extended

– infrastructure-less networks can be maintained

– aggregate pathloss is lower than for direct link communication

– hence, transmit power is lower and/or data rates higher

• Disadvantages:

– transceiver complexity may increase

– synchr. and access methods are more complex compared to traditional solutions

– more traffic and hence interference is generated; also end-to-end delays are higher

– where is a real application after decades of research ?!

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– Distributed Cooperative Topology –Distributed & cooperative approach: several parallel links from source to sink, where

(parallel) nodes may cooperate among each other, thereby realising MIMO capabilities with

the following requirements:

• capacity: use of distributed over traditional approach should not decrease capacity

• complexity: increase in transceiver complexity should be justifiable

cooperation

Figure 6: Distributed & cooperative relaying network.

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– Pros & Cons of Cooperative Relaying –

Combining both techniques, i.e. MIMO, preferably in a distributed fashion, and relaying

technologies, we have

• Advantages:

– low Tx-power consumption or high data rates due to MIMO

– low Tx-power consumption or high data rates due to relaying

– increased coverage area & no need for infrastructure

– low correlations to facilitate MIMO and hence diversity/multiplexing gains

• Disadvantages:

– interference & end-to-end delays are generally still high(er)

– complexity of network maintenance is increased, e.g. synchronisation

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– First Key Milestones –

• Early innovative contributions on relaying and cooperative relaying, as well as MIMO,

inspired the concept of distributed cooperative relaying a.

• Surprisingly, relaying systems have already been studied for almost four decades!

Some deployment examples are given subsequently.

Relaying

MIMO

Cooperative

Relaying

1968

Meulen

1979

Cover & Gamal

1996

3GPP ODMA

1998

Nix et al

1996

Foshini, Telatar

1998

Alamouti, Tarokh

2001

Dohler

2002

Laneman,

Hunter

2003

Gupta,

Stefanov

2000

Laneman

1998

Sendonaris

et al

aMany more fundamental contributions, of course, emerged subsequently, which are not listed here due to

space constraints. A more detailed state-of-the-art review will be done subsequently.

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Example Deployments

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– UMTS Coverage & Capacity Extension –

An extension to the Opportunity Driven Multiple Access (ODMA) relaying protocol [1] is the

deployment of distributed relaying so as to extend the coverage area and the capacity of a cellular

UMTS FDD system or a hot-spot UMTS TDD system.

Figure 7: Distributed relaying cellular FDD or hot-spot TDD coverage extension.

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– In-Home Broadband Access –

Nokia has proposed to deliver high-speed data to sparse residential areas by means of roof-top

relaying systems [2]. Distributed relaying promises an increase in data-rates and link stability. It is

facilitated by the fairly static communication topology.

InternetBackbone

Figure 8: Distributed relaying rooftop scenario [2].

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– WLAN Coverage & Capacity Extension –

Wireless Local Area Networks (WLANs) have sporadic hot-spot coverage in offices, cafes, train

stations, etc [3]. Distributed relaying potentially increases capacity at WLAN cell edges and closes

coverage holes in sufficiently dense deployment areas.

Figure 9: Coverage extension of high-capacity indoor WLAN towards outdoor users.

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– Vehicle-to-Vehicle Communication –

Future vehicles will allow for platooning (automated steering within a group of cars), in-vehicle

internet access, inter-vehicle communication, etc [4]. The increasing density of vehicles allows the

deployment of distributed relaying vehicle systems which can support above systems with low

probability of outage.

Figure 10: Distributed vehicle-to-vehicle communication scenario.

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– Ad-Hoc Networks –

Ad-hoc networks find applications in civil and military applications, e.g. communication among

firemen in difficult circumstances. Distributed relaying will be shown to increase the link stability (or,

alternatively, decrease the link outage probability) significantly.

Figure 11: Distributed relaying ad-hoc network facilitating communication among firemen.

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– Sensor Networks –

Large scale sensor networks are only recently emerging with a large spectrum of applications [5].

Distributed relaying will be shown to decrease the power consumption per relaying sensor node.

fire-detecting sensor

Figure 12: Distributed relaying sensor network for fire detection in forests.

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– Unmanned Aerial Vehicles –

Hybrid solutions are also foreseen, such as UAVs and sensor networks. In [6], it has been shown

that cooperative UAVs considerably increase the reliability of the transmission of sensor readings.

Transmit Sensor Cluster Receive Sensor Cluster

60 km

UAV Relay Cluster

10

00

m

Figure 13: Distributed and cooperative UAVs acting as relays, which can utilise beamforming, STCs,

multiplexing, etc., to relay sensor readings.

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Design Challenges

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– Design Drivers (1/2) –

When designing such systems, we are mainly driven by

• cost

• politics

• performance

We are primarily interested in performance, which is heavily influenced by

• tolerable complexity

• prevailing interference

• occurring mobility

• power constraints

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– Design Drivers (2/2) –

not power constrained power constrained

static rooftop scenario sensor scenario

dynamic vehicular scenario WLAN scenario

Power constraints influence mainly RF/PHY/MAC design, where we need

• RF components with low power consumption

• PHY with low-complexity transceivers

• MAC with energy-preserving mechanisms

Mobility and dynamics influence mainly MAC/IP design, where we need

• MAC with adaptive scheduling techniques

• IP data routing with low overhead

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– Design Challenges –

The design of any system is a very complex interplay between technological & supporting

analysis, as well as associated commercial viability.

RF front end

PHY

MAC

IP

Application

Channel Modelling

System Capacity

Supporting AnalaysisTechnological Analysis

Link Capacity

Services

OPEX

Business Case

CAPEX

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– Challenges for Business Case –

Services

• identification of commercially viable services using distributed topology

• seamless integration into existing services

• facilitation of simple billing mechanisms

CAPEX & OPEX

• correct estimation of short- and mid-term CAPEX

• correct estimation of mid- and long-term OPEX

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– Challenges for Supporting Analysis (1/3) –

Channel Modelling

• measurements of channel in distributed scenarios (low Tx & Rx)

• deterministic modelling using e.g. ray tracing tools (specific environments)

• stochastic-empirical modelling, reflecting

– temporal, spectral and spatial dependency of

– pathloss (pathloss coefficient, breakpoint behaviour, etc)

– shadowing (statistics, variance)

– fading (Doppler, PDP; statistics, variance)

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Link Capacity

• closed form capacity expressions for systems with the following properties:

– cooperative, multi-user, MIMO

– broadcast, multiple access or general relaying channel

– Rayleigh fading channel

• extension of the above to generalised fading (statistics, correlation, temporal behaviour)

• extension of the above to the case of imperfect channel state information

• max mutual information for other constraints (non-Gaussian codebooks, delay limits)

• synthesis of topology from the above insights and design guidelines

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System Capacity

• analysis, synthesis and design of optimum Shannonian MAC protocols having

– total and perfect topology information everywhere

– imperfect and partial topology information

– no or very limited topology information

• design of protocols which minimise overhead

• protocols which optimally join traditional and distributed cooperative systems

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– Challenges for Technological Analysis (1/3) –

Radio Front-End

• distributed synchronisation for cooperative communication

• saturation of amplifiers (near-far effect during cooperation)

• filter to minimise power spill-over during relaying

• low noise transparent relaying mechanisms

• efficiency and power consumption

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Physical Layer

• choice of relaying, ie transperant/regenerative/hybrid [very well explored]

• degree of cooperation, ie number and choice of nodes [well explored]

• determination of suitable performance metrics (total power, complexity, etc.)

• tangible cross-layer design (coding, modulation, power control, etc.)

• codes which are robust to synchronisation, channel estimation errors, etc.

• codes which can easily trade diversity gains, coding gains, throughput and complexity

• novel interference cancellation techniques (use of temporal characteristics)

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MAC Layer

• determination of suitable performance metrics (protocol overhead, etc.)

• unifying framework for distributed MACs

• tangible cross-layer design (ACM, power control, persistency factor, packet length,

routing)

• optimum access strategies (CSMA/reservation/hybrids)

• interference mitigation and avoidance protocols

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PART 3BACKGROUND & MILESTONES

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– The Most Generic Topology –Question: What is the capacity and rate outage probability of a wireless network operating over

generic fading channels, where each terminal is in possession of multiple antenna elements, each

terminal wishes to communicate with any other terminal and cooperation is allowed?

Answer: Nobody knows! However, subsequent state-of-the-art review shows that we are getting

closer.

terminals

co

op

era

tio

n

Figure 14: Distributed-MIMO relaying network with arbitrary source(s) and sink(s).

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Brief Overview

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– Relaying Communication Systemsa (1/3) –

• Shannon introduced capacity of one-way channel [30], and later also studied the capacity of a

two-way channel.

• The method of relaying has been introduced in 1971 by van der Meulen in [31], where a

source-destination pair is supported by relay.

• Lower and upper bounds on the capacity of the discrete-memoryless relay channel were

established by van der Meulen and Sato in [31, 32].

• Milestone capacity theorems were established by El Gamal and Cover in [33, 34] for

– physically degraded and reversely degraded discrete memoryless relay channels,

– physically degraded and reversely degraded AWGN relay channels with average power

constraints,

– deterministic relay channels, and

– relay channels with feedback.

aBased on survey and references given in [50, 51, 52].

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– Relaying Communication Systems (2/3) –

• Cover and El Gamal in [34] derived a max-flow min-cut upper bound and a general lower bound

based on combining the generalized block-Markov and side-information coding schemes.

• El Gamal and Aref in [35] established the capacity of the relay channel with one

deterministic component.

• Generalisations to the many-relay channels were established by El Gamal in [36].

• Aref obtained the capacity for a cascade of degraded relay channels in [37].

• Capacity-achieving codes were derived

– by Vanroose and Meulen in [38] for deterministic relay channels, and

– by Ahlswede, Kaspi and Kobayashi in [39, 40] for permuting relay channels with states or

memory.

• In [41], Schein and Gallager investigated achievable rates for AWGN channels with two relays.

• In [42], Gamal and Zahedi obtained the capacity of a class of orthogonal relay channels.

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– Relaying Communication Systems (3/3) –

• In [43], Zahedi et al established upper and lower bounds on the capacity of AWGN channels

with linear relaying functions.

• The capacity of AWGN relay networks with large number of nodes were investigated

in [44]−[47], leading to some novel milestone results.

• Rodoplu and Meng in [48] investigated the saving in transmission energy using relaying, which

is applicable to energy-constrained wireless sensor networks.

• In [49, 50], Gamal and Zahedi obtained bounds on the minimum energy-per-bit using upper and

lower bounds on the capacity of AWGN relay channels.

• In [51], Dohler obtained closed form ergodic capacity expressions for special cases of

distributed cooperative relaying networks.

• Numerous other bounds have been established, by Goldsmith, Tse, Verdu, Gespert,

Ephremides, Boelcskei, El Gamal, Gupta, Aazhang, Host-Madsen, Wornell, Yeh, Zhang,

Vishwanath, Yates, Erkip, ...

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More Detailed Overview

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– Cooperative Relaying Systemsa (1/4) –

• As said before, the method of relaying has been introduced in 1971 by van der Meulen in [31]

and has also been studied by Sato [32]. A first rigorous information theoretical analysis of the

relay channel, however, has been exposed by Cover and Gamal in [34], a more detailed

description to which can be found in his book [53].

• In these contributions, a source MT communicates with a target MT directly and via a relaying

MT. In [34] the maximum achievable communication rate has been derived in dependency of

various communication scenarios, which include the cases with and without feedback to either

source MT or relaying MT, or both. The capacity of such a relaying configuration was shown to

exceed the capacity of a simple direct link.

• It should be noted that the analysis was performed for Gaussian communication channels only;

therefore, neither the wireless fading channel has been considered, nor have the power gains

due to shorter relaying communication distances been explicitly incorporated into the analysis.

aSubsequent exposure of the background is a little bit in more details.

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– Cooperative Relaying Systems (2/4) –

• Only in the middle of the 90s, research in and around the Concept Group Epsilon revived the

idea of utilising relaying to boost the capacity of wireless networks, thereby leading to the

concept of ODMA [1]. The power gains due to the shorter relaying links have been the main

incentive to investigate such systems to reach MTs out of BS coverage. The emphasis of the

study was its applicability to cellular systems, as well as a suitable protocol design; no

theoretical investigations into capacity bounds, etc., have been performed.

• Interesting milestones into the above-mentioned theoretical studies have been the contributions

by Sendonaris, Erkip and Aazhang, which date back to 1998 [54]. In their study, a very simple

but effective user cooperation protocol has been suggested to boost the uplink capacity and

lower the uplink outage probability for a given rate. The designed protocol stipulates a MT to

broadcast its data frame to the BS and to a spatially adjacent MT, which then re-transmits the

frame to the BS. Such a protocol certainly yields a higher degree of diversity because the

channels from both MTs to the BS can be considered uncorrelated.

• The simple cooperative protocol has been extended by the same authors to

more sophisticated schemes, which can be found in the excellent contributions [55] and [56].

Note that in its original formulation [54], no distributed space-time coding has been considered.

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• The contributions by Laneman in 2000 [57] are a conceptual and mathematical extension to [54],

where energy-efficient multiple access protocols are suggested based on decode-and-forward

and amplify-and-forward relaying technologies. It has been shown that significant diversity and

outage gains are achieved by deploying the relaying protocols when compared to the direct link.

Note again, that no distributed space-time coding has been considered.

• The case of distributed space-time coding has been analysed by Laneman in his PhD

dissertation [58]. In his thesis, information theoretical results for distributed SISO channels with

possible feedback have been utilised to design simple communication protocols taking into

account systems with and without temporal diversity, as well as various forms of cooperation. He

has demonstrated that cooperation yields full spatial diversity, which allows drastic transmit

power savings at the same level of outage probability for a given communication rate.

• A vital asset of his thesis is also a discussion on the applicability of the suggested protocols to

cellular and ad-hoc networks. However, [58] does not incorporate an analysis of distributed

cooperative MIMO multi-stage communication systems as discussed subsequently.

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• Gupta and Kumar were the first to statistically analyse the information theoretically offered

throughput for large scale relaying networks [44]. They showed that under somewhat ideal

situations of no interference, hop-by-hop transmission and pre-defined terminal locations,

capacity per MT decreases by 1/√

M with an increasing number of MTs M in a fixed

geographic area. They also showed that if the terminal and traffic distributions are random, then

the capacity per terminal decreases even in the order of 1/√

M log M .

• The analysis in [44] has been extended by the same authors to more general communication

topologies, where the interested reader is referred to the landmark paper [64].

• Furthermore, Grossglauser and Tse have shown that mobility counteracts the decrease in

throughput for an increasing number of users in a fixed area [59]. The protocols suggested

therein benefit from the decreased power for a hop-per-hop transmission for decreasing

transmission distances. It also benefits from the location variability due to mobility, i.e. a packet

is picked up from the source MT by any passing by r-MT and only re-transmitted (and hence

delivered) when passing by the target MT.

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– MIMO Communication Systems –

• Contributions on MIMO systems have flourished ever since the publication of the landmark

papers by Telatar [60] and Foschini & Gans [61] on capacity and Foschini [68], Alamouti [69]

and Tarokh [70, 71] on the construction of suitable space-time transceivers.

• The BLAST system introduced by Foschini in 1996 [68], a transmitter spatially multiplexes signal

streams onto different transmit antennas which are then iteratively extracted at the receiving side

using the fact that the fades from any transmit to any receive antenna are uncorrelated and of

different strength. The BLAST concept has ever since been extended to more sophisticated

systems, a good summary of which can be found in [72].

• Alamouti introduced a very appealing transmit diversity scheme by orthogonally encoding two

complex signal streams from two transmit antennas, thereby achieving a rate one space-time

block code [69].

• His work was then mathematically enhanced by the landmark paper of Tarokh [71], who

essentially exposed various important properties of space-time block codes. In [70], he also

showed how to construct suitable space-time trellis codes which were shown to yield diversity

and coding gain.

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– MIMO Cooperative Relaying Systems (1/2) –

• A system utilising the advantages of both MIMO and relaying has been suggested by M. Dohler

in December 1999 and has hence become one of the main research topics within the Mobile

Virtual Centre of Excellence (M-VCE).

• Numerous studies [62] have led to a set of patents [63], which are backed by about 20 industrial

members, such as Vodafone, Nokia, Philips, Nortel Networks, Samsung, etc.

• The studies encompassed the following (in timely order):

– downlink distributed receive diversity in cellular systems

– downlink distributed MIMO in cellular systems

– uplink distributed MIMO in cellular systems

– introduction of distributed relaying to cellular systems

– extension of the above to WLAN and hot-spot systems

– generalisation to arbitrary distributed relaying topologies

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– MIMO Cooperative Relaying Systems (2/2) –

• A landmark contribution on relaying systems deploying multiple antennas at transmitting and

receiving side has been made by Gupta and Kumar [64]. The network topology exposed therein

is the most generic one can think of, i.e. any MT may communicate with any other MT.

• In [64], an information theoretic scheme for obtaining an achievable communication rate region

in a network of arbitrary size and topology has been derived. The analysis showed that

sophisticated multi-user coding schemes are required to provide the derived capacity gains.

Note also that the exposed theory is fairly intricate, which makes the design of realistic

communication protocols a difficult task.

• Specific distributed space-time coding schemes have also been suggested recently, e.g. by A.

Stefanov and E. Erkip [73]. In this publication, two spatially adjacent MTs cooperate to achieve

a lower frame error rate to one or more destination(s), where a quasi-static fading channel has

been assumed. Distributed space-time trellis codes have been designed which maximise the

performance for the direct link from either of the MTs to the destination and the relaying link.

• Although contributions on the topic of cooperative (MIMO) relaying have begun to emerge, the

amount of work done is scarce in comparison to the vast amount of potential scenarios.

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Latest Developments

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– Currently Active Researchersa –

Capacity:

• van der Meulen, Ephremides, Yeh, Tse, Wornell, El Gamal, Host-Madsen, Sabharwal,

Goldsmith, Franceschetti, Gupta, Kumar, Dohler, Verdu, Nosratinia, Hunter, Kramer, etc.

Performance:

• van der Meulen, Erkip, Tarokh, Zhang, Ephremides, Yeh, Tse, Veeravalli, Wornell, El Gamal,

Mitra, Vishwanath, Boelcskei, Nabar, Hassibi, Willems, Xie, Host-Madsen, Sabharwal, Motani,

Goldsmith,Franceschetti, Gupta, Kumar, Aazhang, Dohler, Verdu, Nosratinia, Hunter, Zhao,

Valenti, Toumpis, Kramer, Hasna, Alouinni, Giannakis, Stefanov, etc.

Medium Access Control:

• Gkelias, Dohler, Shea, Wong, etc.

aApologies if we missed your contribution.

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PART 4CHANNEL CHARACTERISATION

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– Preliminary Note –

• Channel models are utmost vital in the designing process of wireless systems, because

it influences power budget dimensioning, transceiver design, performance behaviour,

etc.

• There are, however, only a few relaying channel measurements/models available and no

explicit models, which cater for the distributed cooperative communication channel.

• We hence need to adapt known channel measurements and models to the distributed

cooperative case, until explicit models will become available.

• We proceed with the following topics:

– general channel characterisation

– point-to-point channel models (single hop)

– 2-hop amplify & forward relaying channel

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Space-Time-FrequencyCharacteristics

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– General Characteristics (1/5) –

Base Station : BSMobile Station : MS

Line-of-Sight: LOSnon-LOS: nLOS

MS#1

(LOS)

BS

MS#1

(nLOS)

3. Scattering

1. Free-SpacePropagation

2. Reflection

4. Diffraction

MS#2

(LOS)

MS#2

(nLOS)

Figure 15: Channel scenario for LOS/nLOS traditional and cooperative links.

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Re

ceiv

ed

Po

we

r [d

B]

Distance [m]

-20dB/dec (Free-Space)

-n*10dB/dec (Clutter )

Shadowing Mean

Shadowing

Fading (measured)

Figure 16: Received power versus distance due to pathloss, shadowing and fading.

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Pathloss:

• Characteristics: deterministic due to free-space propagation, n = 2,

measurable > 1000 · λ

• Disadvantage: power loss which requires more Tx power with increasing distance

• Advantage: spatially limits generated interference

Shadowing:

• Characteristics: random due to obstacles, lognormal, mean absorbed in pathloss

(hence n = 2, . . . , 6), variance 2dB-18dB, measurable > 40 · λ

• Disadvantage: random power loss which requires link-budget margin

• Advantage: further limits spatially generated interference; capture effect at MAC

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(Small-Scale) Fading:

• Characteristics: random due to phasor additions, central/non-central complex Gaussian

or other, measurable at ≈ λ/2

• Disadvantage: random power loss which requires link-budget margin; often, rapid

changes in channel which needs to be catered for

• Advantage: creates temporal, spectral and spatial signatures (picked up by proper code)

Fourier Transform → useful tool for visualising fading

• channel time variation → doppler spectrum

• multipath component (MPC) delays → frequency spectrum

• spatial fading → angular spectrum

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Fading Cases:

• time domain: slow/fast fading (large/small coherence time)

• frequency domain: non-selective/selective fading (large/small coherence bandwidth)

• spatial domain: non-selective/selective fading (large/small coherence distance)

8 possible fading cases: (4 in time & frequency, spatial domain treated later)

• slow & frequency-flat

• fast & frequency-flat

• slow & frequency-selective

• fast & frequency-selective

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– Spatial Fading Representation –

• MIMO channel is described by H, where hk,l is channel from k−th Tx to l−th Rx antenna

H =

⎛⎜⎜⎜⎜⎜⎝

h11 h12 · · · h1,t

h21 h22 · · · h2,t

......

. . ....

hr,1 hr,2 · · · hr,t

⎞⎟⎟⎟⎟⎟⎠

• model is useful for analysis but difficult to visualise

InformationSource

Space-TimeEncoder

Space-TimeDecoder

InformationSink

s s

t

Transmit

Antennas

r

Receive

Antennas

h11

hr,t

H

MIMO

Channel

Figure 17: Multiple-Input-Multiple-Output transceiver and channel.

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– Angular Fading Representation (1/3) –

• Transformation

HΩ = U∗r · H · Ut

with unitary matrix U{r,t} with entries

1√{r, t}e(−j2πkl/{r,t}), {k, l} = 0, . . . , {t − 1, r − 1}

gives information over spatial domain Ω, i.e.

HΩ =

⎛⎜⎜⎜⎜⎜⎝

hΩ11 hΩ

12 · · · hΩ1,t

hΩ21 hΩ

22 · · · hΩ2,t

......

. . ....

hΩr,1 hΩ

r,2 · · · hΩr,t

⎞⎟⎟⎟⎟⎟⎠ ,

where non-zero entries of this angular matrix correspond to resolved MPCs.

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– Angular Fading Representation (2/3) –

t

Transmit Antennas

r

Receive Antennas

resolved clusters in angular domain

Figure 18: MIMO channel resolved in the angular domain.

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– Angular Fading Representation (3/3) –Degree-of-Freedom (Rank):

• minimum number of non-zero rows and non-zero columns in HΩ

• depends on amount of clutter in channel & antenna separation

• determines the data multiplexing capabilities of the channel

Diversity Gain:

• number of non-zero entries in HΩ

• depends on connectivity of channel & antenna separation

• determines the reliability of the channel

Power Gain:

• strongest eigenvalue of HΩ (w.r.t. weaker eigenvalues; condition number max λi/ min λi)

• determines the beamforming capabilities

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– Spatially Distributed Fading –

Distributed topology is submerged into rich clutter environment, resulting in:

• full-rank channel → maximum degrees-of-freedom (high data throughput)

• fully connected channel → maximum diversity gain (high reliability)

• well conditioned channel → little beamforming gain (limited range)

BS

NLOS, from cellular:

same pathloss

same shadowing

different fading

NLOS, distributed:

different pathloss

different shadowing

different fading

LOS, distributed:

different pathloss

same shadowing

different fading

Figure 19: Example distributed pathloss, shadowing and fading realisations.

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Point-to-Point Models

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– Important Channel Parameters –

• pathloss coefficient

• shadowing variance and shadowing correlation distance

• fading statistics for each multipath component (MPC) and correlation properties

• power delay profile (PDP) with RMS delay spread

Power

P

Delay τ

Instantaneous contributions

of MPCs to PDP

Instantaneous

PDP

Mean

Delay

RMS Delay

Spread

Averaged

PDP

P1

P2

P3

Tap#1

Tap#2

Tap#3

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– Channel Behaviour Trendsa (1/3) –

Pathloss

• traditional links (high BS/AP, low MTs): n = 2 (LOS), n = 2, . . . , 4 (nLOS)

• cooperative links (low cooperating MTs): n = 2 (LOS), n = 4, . . . , 6 (nLOS)

Shadowing Variance

• traditional links (high BS/AP, low MTs): 2, . . . , 6dB (LOS), 6, . . . , 18dB (nLOS)

• cooperative links (low cooperating MTs): 0, . . . , 2dB (LOS), 2, . . . , 6dB (nLOS)

Shadowing Coherence Distance

• traditional links (high BS/AP, low MTs): tens of meters (LOS), >100m (nLOS)

• cooperative links (low cooperating MTs): negligible (LOS), some meters (nLOS)

aAll trends are (slightly) frequency dependent; these values are only indications based on [7]−[19].

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– Channel Behaviour Trends (2/3) –

First MPC Fading Statistics (other MPCs are Rayleigh distributed)

• traditional links (high BS/AP, low MTs): Ricean K = 2, . . . , 10 (LOS), Rayleigh (nLOS)

• cooperative links (low cooperating MTs): Ricean K > 10 (LOS), Rayleigh (nLOS)

Power Delay Profile

• traditional links (high BS/AP, low MTs): negative-exponential, clustered

• cooperative links (low cooperating MTs): negative-exponential

RMS Delay Spread

• traditional links (high BS/AP, low MTs): depends on cell size, τRMS = 50ns, . . . , 4μs

• cooperative links (low cooperating MTs): τRMS = 10ns, . . . , 40ns

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– Channel Behaviour Trends (3/3) –

-20dB/dec (Free-Space)

-n*10dB/dec (Clutter )

Shadowing Mean

Shadowing

Fading (measured)

Narrowband & Non-Cooperative Wideband & Non-Cooperative

reduced Fading

Narrowband & Cooperative

reduced Shadowing Mean

reduced

Shadowing Variance

Wideband & Cooperative

reduced Shadowing Mean

reduced Fading

reduced

Shadowing Variance

Figure 20: Wideband receiver reduce fading margin; cooperative communication can counteract

shadowing (and fading).

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– Pathloss and Channel Models –

Cellular & Fixed Broadband (traditional link)

• Pathloss: Okumura-Hata, Walfish-Ikegami, COST231, Dual-Slope Model

• Channel Model: COST207, 3GPP A&B, Stanford University Interim Channels SUI1-6

Indoors & WLAN (traditional & cooperative link)

• Pathloss: COST231, COST259-Multiwall Model

• Channel Model: ETSI-BRAN, IEEE

(Bluetooth,) Zigbee & UWB (cooperative link)

• Pathloss: IEEE 802.15.3a CH1-CH4, IEEE 802.15.4a

• Channel Model: IEEE 802.15.3a CH1-CH4, IEEE 802.15.4a, (UWB book)

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AF Relaying Channel

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– Relaying: AF versus DF –

What the channel concerns, there are two fundamental relaying techniques:

• receive, decode, re-encode and forward - Decode & Forward (DF)

• receive, amplify and forward - Amplify & Forward (AF)

Decode & Forward:

• capable of achieving maximum rate, but complex to implement

• channels between relays are decoupled (hence prior models apply)

Amplify & Forward:

• capacity sub-optimum, but simpler to implement

• channels between relays are dependent, thereby changing all statistics

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– Two-Hop AF Relay Channel (1/2) –

• Exposed results related to the AF relay channel have been compiled from [20]−[26].

• We assume AF relaying from BS → relay MT (r-MT) → target MT (t-MT).

• The received signal at the t-MT, r2, can be expressed as (omitting the time index)

r2 = A · h1 · h2 · s + A · h2 · n1 + n2 (1)

where

– A is amplification factor

– h1 is channel between BS & r-MT and h2 between r-MT & t-MT

– both channels are modelled as ZMCG with power σ21 and σ2

2 , respectively

– n1,2 are the respective AWGN noise terms with equal power σ2n

– P1 and P2 is transmission power of BS and r-MT, respectively

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– Two-Hop AF Relay Channel (2/2) –

• The fixed gain relay amplification factor A has been proposed by [27]

A =

√P2

P1 · σ21 + σ2

n

, (2)

which requires only statistical knowledge of the first-hop channel.

• The variable gain relay amplification factor A has been proposed by [28]

A =

√P2

P1 · |h1|2 + σ2n

, (3)

which requires instantaneous knowledge of the first-hop channel.

• More application-dependent factors have been proposed, but due to simplicity we will

concentrate now on the fixed gain approach with A ≡ 1 [20].

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– Statistical Properties (1/4) –

• The probability density function (pdf) of the double-Gaussian channel envelope

α = |h| = h1 · h2, which influences the received signal power, can be derived as

fα(α) =4α

σ21 · σ2

2

K0

(2

√α2

σ21 · σ2

2

), (4)

where K0(x) is the zeroth order modified Bessel function of the second kind.

• The temporal auto-correlation function of h(t) is given as

Rhh(τ) = 1/2 · σ21 · σ2

2 · J0(2πf1τ) · J0(2πf2τ) · J0(2πf3τ), (5)

where f1 = v1/λ1, f2 = v1/λ2, f3 = v2/λ2 are Doppler shifts induced by MTs, λ

is the wavelength, v is the velocity, τ is the time-lag, and J0(x) is zeroth-order Bessel

function of the first kind.

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

6

7

8

9

10

Amplitude α

Pro

babi

lity

Den

sity

Fun

ctio

n

2−Hop AF Relay ChannelsSingle−Hop Rayleigh Channel

σ12=0dB

σ22=0dB

σ12=−10dB

σ22=0dB

σ12=−20dB

σ22=0dB

Figure 21: Observations: behaviour is symmetric; weakness of one channel can be compensated by

strength of other; the weaker both channels (σ21σ2

2 ), the lower the mean; hence, gain control is vital.

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Time−Lag τ [s]

Aut

o−C

orre

latio

n F

unct

ion

2−Hop AF Relay ChannelsSingle−Hop Rayleigh Channel

v1=v

2=0.01m/s

v1=0.1m/s

v1=v

2=0.1m/s

v1=v

2=1m/s

Figure 22: Observations: 2-hop relay channel decorrelates faster than single-hop channel, which is

good for code design but bad for channel estimation purposes.

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• The doppler spreads of cellular, MT-to-MT and 2-hop relay channel are respectively

given as

Bd =

√f21

2, Bd =

√f22 + f2

3

2, Bd =

√f22 +

f23

2(6)

which, assuming f1 = f2 = f3, means that relay channel has 70% and 25% larger

spread than cellular and MT-to-MT channels, respectively.

• Given fixed gain amplification, the instantaneous Signal-to-Noise Ratio (SNR) is

γ =γ1 · γ2

γ2 + γ1 + 1(7)

where γi = Pi|hi|2/σ2n and γi = Piσ

2i /σ

2n

• Similarly, the Level Crossing Rate, Frequency of Outage and Average Outage Duration

can be derived.92

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Open Issues

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– Open Issues –

As far as we are aware of, these are still open or only partially solved problems:

• Real-time distributed channel measurements & modelling, which capture

– shadowing correlation length for more general cooperative scenarios,

– distributed temporal shadowing behaviour,

– distributed temporal fading behaviour,

– interference pollution in cooperative bands.

• Closed-form mathematical description of AF relaying channel

– in terms of statistics and temporal behaviour,

– for different choice of amplification,

– for more general channels (Nakagami, Lognormal, composite),

– for generic number of relaying stages.

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PART 5SHANNON CAPACITY & OUTAGE

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– A Little Glimpse [64] –

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• Obtaining the capacity of a wireless system is vital in understanding the achievable

rates and their reliability.

• There are more than 100 highly complex contributions available today, which requires us

to concentrate on a very few of them.

• For this reason, we will concentrate on the following topics:

– achievable rates & outages through cooperation

– cooperative, single-stage, channel coded DF schemes

– cooperative, single-stage, space-time (block) coded DF schemes

– cooperative, multi-stage, space-time coded DF schemes

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Rates & OutagesThrough Cooperation

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– System Model [55] –

For below simple system (and later generalisations), we would like to know what is

• the maximum achievable network rate (ergodic channel), or

• the network’s outage behaviour (non-ergodic channel).

s-MT#1

s-MT#2

t-MT#0

Encoder s-MT#1

Encoder

s-MT#2

W1

Y1

Y2

W2

X1

K10

K20

K12

K21

X2

Z2

Z1

Z0 Y0

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– Mathematical Formulation –The mathematical formulation of the cooperative communication model is:

Y0 = K10 · X1 + K20 · X2 + Z0 (8)

Y1 = K21 · X2 + Z1 (9)

Y2 = K12 · X1 + Z2 (10)

where

• Y0, Y1, Y2 are the received signal at the target mobile terminal (t-MT), first source MT

(s-MT#1) and second source MT (s-MT#2), respectively;

• X(1,2) is the signal transmitted by s-MT (1,2);

• Kij are the respective Rayleigh fading coefficients with variance ξ2ij and are assumed

to be frequency-flat and ergodic;

• Z0, Z1, Z2 are the respective AWGN components with total spectral density N0.

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– Transmitters & Receivers (1/2) –

• Three cases concerning channel knowledge at the Tx are considered in [55]:

– user i knows nothing about Ki0,

– user i knows knows only the phase of Ki0,

– user i knows knows amplitude and phase of Ki0.

• The user’s transmitters use the classical superposition coding (super-imposed

codebooks of large block length).

• The receivers utilise suitable decoders, such as:

– successive decoder,

– sliding-window decoder,

– backward decoder.

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– Transmitters & Receivers (2/2) –

• Without violating causality, s-MT#1 structures its information W1 such that:

– information W10 is sent at rate R10 directly to BS with fractional power P10,

– information W12 to be sent at rate R12 to the BS via #2 with fractional power P12,

– cooperative information U1 is sent directly to BS with fractional power PU1.

• The encoder then constructs signal X1 = X10 + X12 + U1 to be sent with power

P1 = P10 + P12 + PU1.

• s-MT#2 proceeds similarly as s-MT#1.

• It is imperative that power and rate allocations are such that all codebooks can be

perfectly decoded.

• For a given power constraint, it is hence the aim to determine the maximum feasible rate

in such a network.

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– Achievable Rates (1/4) –Theorem [55]: An achievable rate region for the system given in (8)−(10) is the closure of the

convex hull of all rate pairs (R1, R2) such that R1 = R10 + R12 and R2 = R20 + R21, with

R12 < E

{C

(K2

12P12

K212P10 + N0

)}(11)

R21 < E

{C

(K2

21P21

K221P20 + N0

)}(12)

R10 < E

{C

(K2

10P10

N0

)}(13)

R20 < E

{C

(K2

20P20

N0

)}(14)

R10 + R20 < E

{C

(K2

10P10 + K220P20

N0

)}(15)

R10 + R20 + R12 + R21 < E

{C

(K2

10P10 + K220P20 + 2K10K20

√PU1PU2

N0

)}(16)

where C(x) = 12 log2(1 + x) is the capacity of an AWGN channel and E{·} denotes the

expectation with respect to the fading realisations Kij .103

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– Achievable Rates (2/4) –

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Rate R2

Rat

e R

1

no cooperation

cooperation

ideal

Figure 23: Symmetric rate region for no cooperation, ideal cooperation with error-free inter-user

channel, and realistic cooperation with good inter-user channel (E{K12} = .95); N0 = 1, P1 =P2 = 2, E{K10} = E{K20} = .63 [55].

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Rate R2

Rat

e R

1 ideal cooperation

cooperation

no cooperation

Figure 24: Asymmetric rate region for no cooperation, ideal cooperation with error-free inter-user

channel, and realistic cooperation with medium inter-user channel (E{K12} = .71); N0 = 1,

P1 = P2 = 2, E{K10} = .95 and E{K20} = .30 [55].

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• Ideal cooperation is for a noiseless inter-user channel and serves as an upper bound of

cooperation. No cooperation (ignoring Y1 and Y2) yields the typical multiple access

channel. In the cooperative case, as the inter-user channel degrades, performance

approaches that of no cooperation.

• Points of interest are the

– equal rate point (R1 = R2),

– maximum rate sum point (max(R1 + R2)),

– degraded relay rate points (R1 = 0, R2 �= 0 and R1 �= 0, R2 = 0).

• [55] showed that in the design region of interest “increase in sum capacity ≈ increase in

coverage area”.

• [55] also demonstrated that repetition-based coding using CDMA spreading sequences

performs well within the rate regions.

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– Rate Outage Probability –

• Of biggest importance is how fast the outage probability Pr[I < R] = Pout drops off

in non-ergodic (slow-fading) channel realisations for increasing SNR, i.e.

Pout ∝ SNR−Δ for SNR → ∞, where Δ is the degree of diversity or diversity order.

• The diversity order can usually be obtained analytically by using

Δ = limSNR→∞

− log2(Pout(SNR))log2(SNR)

. (17)

• Given m cooperating users, the following can be summarised from [55, 28, 74, 58]:

– no cooperation yields Δ = 1,

– DF yields Δ = m,

– AF yields Δ = m.

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– Diversity-Multiplexing Tradeoff (1/2) –

• We observe that the diversity order (and hence the outage probability) is a function of

the rate R, where an increasing R leads to a decreasing Δ.

• We parameterise the performance on the pair (Δ, Rnorm), where Rnorm = R/Rmax,

which portrays the diversity (reliability) versus multiplexing (throughput) tradeoff.

• Some tradeoff relationships were derived in [74]:

– no cooperation: Δ = 1 − Rnorm,

– repetition DF cooperation: Δ = m(1 − mRnorm),

– coded DF cooperation: too long; see subsequent figure,

– space-time cooperation: m(1− 2Rnorm) ≤ Δ ≤ m(1− (m− 1)/m · 2Rnorm).

• The diversity-multiplexing tradeoff is depicted in subsequent figure for various schemes.

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– Diversity-Multiplexing Tradeoff (2/2) –

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

Multiplexing Rate Rnorm

Deg

ree

of D

iver

sity

Δ

coded cooperation

space−time upper bound

space−time lower boundrepetition cooperation

no cooperation

m

m = 5

1/m 1/2 m/2/(m−1)

Figure 25: Diversity order versus rate multiplexing capabilities for various relaying schemes.

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Channel CodedDF Schemes

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– System Model [75, 76] (1/2) –

The characteristics of below coded cooperative scheme are:

• each user tries to transmit (punctured) incremental redundancy to its partner;

• overall code might be block or convolutional code or hybrid;

• no feedback is required, because decisions are based on CRC;

s-MT#1

s-MT#2

t-MT#0

own bitsCRC

Decoder

RCPC

N1 user 1 bits N2 user 2 bits

N1 user 2 bits N2 user 1 bits

Frame 1 Frame 2

Frame 1 Frame 2

punctured N1 bitsto Tx

partner'sbits

RCPC

N2 bits

N2 bits

no

yes

CRC

check

111

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�

– System Model (2/2) –The system operates as follows:

• Rate R code of each user has length N1 + N2; we define α = N1/(N1 + N2).

• N1 valid punctured code bits are transmitted to t-MT & partner.

• If partner decodes N1 successfully (CRC check), then remaining N2 parity bits are sent

by partner to t-MT; otherwise the partner’s own N2 parity bits are sent.

• 4 cases are possible, which the t-MT is either informed of or decides blindly (CRC):

#1

#2

#2's parity

#1's parity

x x

#1's parity

#2's parity

x

#1's parity

#1's parity

x

#2's parity

#2's parity

112

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�

– Outage Probability (1/4) –

• For an instantaneous SNR γ, the ’capacity’ of the link is given as C(γ) = log2(1 + γ)bits/s/Hz.

• The channel is in outage, if the ’capacity’ falls below a threshold R; the corresponding

outage event is C(γ) < R or γ < 2R − 1.

• The outage probability is hence

Pout = Pr(γ < 2R − 1) =∫ 2R−1

0pγ(γ)d γ, (18)

where pγ(γ) denotes the pdf of the SNR.

• For a Rayleigh fading process with mean power Γ, γ is negative-exponentially

distributed and the outage probability is

Pout = 1 − exp(−(2R − 1)/Γ

). (19)

113

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Case 1 (Θ = 1) :

• Both partners decode correctly, which for the inter-user channel means that

C12(γ12) = log2(1 + γ12) > R/α

C21(γ21) = log2(1 + γ21) > R/α

• The outage event for both users given the cooperative information can be written as

C1t(γ1t, γ2t|Θ = 1) = α log2(1 + γ1t) + (1 − α) log2(1 + γ2t) < R

C2t(γ1t, γ2t|Θ = 1) = α log2(1 + γ2t) + (1 − α) log2(1 + γ1t) < R

Cases 2,3 & 4 (Θ = 2,3,4) :

• These cases are obtained in a similar fashion as above.

114

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• Combining the 4 possible cases, the total outage probability for user 1 can hence be

calculated as [76]

Pout,1 = Pr(γ12 > 2R/α − 1) · Pr(γ21 > 2R/α − 1)

·Pr((1 + γ1t)α(1 + γ2t)1−α < 2R) +

Pr(γ12 < 2R/α − 1) · Pr(γ21 < 2R/α − 1)

·Pr(γ1t < 2R − 1) +

Pr(γ12 > 2R/α − 1) · Pr(γ21 < 2R/α − 1)

·Pr((1 + γ1t)α(1 + γ1t + γ2t)1−α < 2R) +

Pr(γ12 < 2R/α − 1) · Pr(γ21 > 2R/α − 1)

·Pr(γ1t < 2R − 1).

• Closed form expressions for the Rayleigh fading case can be found in [76].

115

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�


−10 −5 0 5 10 15 20 25 3010

−4

10−3

10−2

10−1

100

Mean (Uplink) SNR Γ [dB]

Out

age

Pro

babi

lity

C<

R no cooperation

coded cooperation

Figure 26: Outage versus mean uplink SNR, where inter-user channel is 10dB weaker; α = 0.7,

R = 0.5bits/s/Hz.

116

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Space-Time BlockDF Schemes

117

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– Exact O-MIMO Capacity (1/5) –

Orthogonal space-time block codes (STBCs) is a signal processing scheme which orthogonalises

the MIMO channel, henceforth referred to as O-MIMO. For simplicity, we will refer to the maximum

mutual information achievable with such signal processing as O-MIMO Capacity.

We will consider distributed orthogonal STBCs of arbitrary rate R. Furthermore, the sub-channel

realisation hi,j obey Nakagami fading with fading parameter f . The sub-channels may have

different gains, thereby reflecting a possibly distributed deployment.

Distributed

Space-Time Block Encoder

Distributed

Space-Time Block Decoder

Channel

Encoder

FractionalSTBC

Space-Time

Block Decoder

Channel

Decoder

s

s

h11

hr,t

O-MIMO

Channel

FractionalSTBC

FractionalSTBC

Receiver

Receiver

Receiver

Information

Sink

Information

Source

H

Figure 27: Distributed Space-Time Block Code transceiver model.

118

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– Exact O-MIMO Capacity (2/5) –The capacity (maximum mutual information) for O-MIMO channels can generally be expressed

as [65]

C = R log2

(1 +

1R

‖H‖2

t

S

N

)(20)

‖H‖ denotes the Frobenius norm of H, the square of which is given as

‖H‖2 =t∑

i=1

r∑j=1

|hij |2 = tr(HHH

)(21)

where tr(·) denotes the trace operation. From (21), it is clear that

‖Ht×r‖ = ‖h1×t·r‖ (22)

where h � vectorized(H). To simplify subsequent notation, we define

u � t · r (23a)

γi � E {hih∗i } . (23b)

119

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The capacity (maximum mutual information) for O-MIMO channels over Nakagami fading channels

with unequal sub-channel gains γi∈(1,u) and fading parameters fi∈(1,u) can be expressed as [51]

C = Ru∑

i=1

fi∑j=1

Ki,j

Γ(j)Cj−1

(1R

γi

jt

S

N

)(24)

Ki,j =

(− 1

Rγi

fitSN

)j−fi

(fi − j)!∂fi−j

∂sfi−j

⎡⎢⎢⎣

u∏i′=1,i′ �=i

1(1 − 1

Rγi′fi′ t

SN · s

)fi′

⎤⎥⎥⎦

s=

�

1R

γifit

SN

�−1

(25)

Cζ(a) =1

log(2)

ζ∑μ=0

ζ!(ζ − μ)!

[(−1)ζ−μ−1(1/a)ζ−μe1/aEi(−1/a) (26)

+ζ−μ∑k=1

(k − 1)!(−1/a)ζ−μ−k

]

where Γ(·) is the complete Gamma function and Ei(ζ) is the exponential integral function.

120

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Capacity saturates fast with f and it never exceeds the Gaussian channel:

2 4 6 8 10 12 14 16 18 202

2.5

3

3.5

Nakagami−f Fading Factor

Cap

acity

[bits

/s/H

z]

1 Tx2 Tx Alamouti3 Tx − 3/4−Rate4 Tx − 3/4−Rate3 Tx − 1/2−Rate4 Tx − 1/2−RateGaussian Channel

Figure 28: Capacity versus the Nakagami f fading factor; SNR=10dB, r = 1.

121

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Capacity of distributed STBC scheme exhibits a high stability:

γ1Fractional

STBC

FractionalSTBC

γ2

ChannelEncoder

InformationSource

Space-Time

Block Decoder

Channel

Decoder

InformationSink

(a) Distributed Alamouti scheme with unequal

sub-channel gains due to different pathloss &

shadowing.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.5

1

1.5

2

2.5

3

3.5

4

4.5

γ1

Cap

acity

[bits

/s/H

z]

1 Tx − SISO (γ1)

1 Tx − SISO (γ2=2−γ

1)

2 Tx − Alamouti (γ1 & γ

2=2−γ

1)

(b) Capacity versus the normalised power γ1

in the first link over a Nakagami fading channel;

SNR=10dB, f = 10 and γ2 = 2 − γ1.

Figure 29: Topology and performance of distributed Alamouti scheme.

122

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– Exact O-MIMO Outage Probability (1/2) –

• Since for non-ergodic fading channels the channel realisation H is chosen randomly and kept

constant over the codeword transmission, there is a non-zero probability Pout(Φ) that a given

transmission rate Φ cannot be supported by the channel [60].

• Pout(Φ) can generally be expressed as

Pout(Φ) = Pr

(m∑

i=1

log2

(1 +

λi

t

S

N

)< Φ

)(27)

This requires the calculation of an m-fold convolution of the pdf of log2

(1 + λi

tSN

)generated

by the randomness of λi with pdfλi(λi).

• Given a STBC system with t transmit and r receive antennas (O-MIMO) communicating over

Nakagami channels with unequal sub-channel statistics, the outage probability is given as [66]

Pout(Φ) =u∑

i=1

fi∑j=1

Ki,j

Γ(j)γ

(j,

(2Φ/R − 1

)/(1R

γ

fit

S

N

))(28)

where Ki,j is given by (25).

123

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– Exact O-MIMO Outage Probability (2/2) –The outage probability of a distributed STBC scheme also exhibits a high stability:

γ1Fractional

STBC

FractionalSTBC

γ2

ChannelEncoder

InformationSource

Space-Time

Block Decoder

Channel

Decoder

InformationSink

(a) (Distributed) Alamouti scheme with unequal


shadowing.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2

4

6

8

10

12

14

16

18

20

γ1

(Out

age)

Pro

babi

lity

that

onl

y R

ates

< 2

bits

/s/H

z ca

n be

sup

port

ed [%

] 1 Tx − SISO (γ1)


1)


2=2−γ

1)

(b) Outage probability Pout(Φ) versus the

normalised power γ1 in the first link for the dis-

tributed Alamouti scheme at a desired rate of

Φ = 2 bits/s/Hz; SNR=15dB.


124

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Multi-Stage STCDF Schemes

125

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– Choice of (practical) Topology (1/4) –

• The theoretical findings of Cover, Kumar, Gupta, Tse, Laneman, etc. are very interesting,

however, very difficult to deploy and optimise in a practical manner. Already the multiple access,

broadcast and single-hop relaying schemes over Gaussian channels, as analysed by Cover, are

fairly intricate to optimise.

• Cover [53, chapter 14.3] has established the capacity bounds for the multiple access channel

where, using sophisticated multi-user (MU) transceivers, the achievable rates for 2 users are

R1 ≤ 12

log2

(1 +

P1

N

), R2 ≤ 1

2log2

(1 +

P2

N

), R1+R2 ≤ 1

2log2

(1 +

P1 + P2

N

)

• Using orthogonal FDMA, for example, the achievable rates for 2 users are [53]

R1 =W1

2log2

(1 +

P1

NW1

), R2 =

W2

2log2

(1 +

P2

NW2

)

• The MU case (dotted line) and FDMA case (solid line) are depicted in Figure 31. Similar curves

are obtained for the broadcast channel as well as relaying channel.

126

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Loss in rate due to sub-optimum channel access scheme is small:

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

Rate of User #1

Rat

e of

Use

r #2

FDMA/TDMA CapacityCDMA/MU Capacity

C=0.5⋅ log2(1+P

2/N)

C=0.5⋅ log2(1+P

2/(P

1+N))

C=0.5⋅ log2(1+P

1/(P

2+N))

C=0.5⋅ log2(1+P

1/N)

Area, where FDMA.TDMA is inferior toCDMA/Multi−User Detection

Optimum resource sharing, where bandwidth is proportinal to

signal power.

Figure 31: Achievable rates for a multiple access channel with two users.

127

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• It can first be observed that maximum (MU) and practical (FDMA) sum rate, i.e. R1 + R2, is the

same in the point where the users in the FDMA scheme are allocated an optimum bandwidth

equal to their power, i.e. W1 = P1 and W2 = P2.

• If FDMA (or TDMA) is used, then the resource allocation scheme which maximises capacity

hence also ensures that the achieved sum-capacity is equal (or close) to the maximum

achievable capacity.

• Since only FDMA and TDMA schemes are analytically tractable for large relaying networks,

these will be the main subject of the tutorial.

• Besides the basic multiple access schemes, i.e. FDMA and TDMA, we assume a path

reservation protocol where communication from source to sink is not interfered by other links

due to a prior reserved routing path. This routing path is reserved only during the transmission

of a single packet or several packets.

• The main aim of the analysis is hence to design resource allocation rules which maximise the

throughput along a reserved path through the given topology.

128

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We will investigate the capacity, outage probability and error rate performance of a communication

link from a source towards a sink operating over generic fading channels, where relaying and

cooperation is allowed, and each terminal is in possession of multiple antenna elements.

2nd Interference Zone Z-th Interference Zone1st Interference Zone

6th

VAA

5th

VAA

4th

VAA

(V-2)nd

VAA

(V-1)st

VAA

V-th

VAA

targ

et te

rmin

al

3rd

VAA

2nd

VAA

1st

VAA

so

urc

e t

erm

inal

1st

RelayingStage

2nd

RelayingStage

co

op

era

tion

rela

yin

g t

erm

ina

l

Figure 32: Distributed-MIMO multi-stage relaying topology with interference zones.

129

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– Related Definitions –Source, Sink and Relaying Terminals:

Wireless terminals with intention to transmit information from a source towards a sink with

the possible aid of relays.

Virtual Antenna Array (VAA):

Grouping of terminals in spatial proximity which wirelessly cooperate to enhance signal

reception (diversity) and transmission (diversity, space-time coding & multiplexing).

Cooperation:

Procedure which utilises the wireless interface between terminals belonging to the same

Virtual Antenna Array to enhance signal reception.

Relaying Stage:

The wireless interface between two consecutive Virtual Antenna Arrays.

Interference Zone:

Within an interference zone, resources in terms of frame duration, frequency band and

spreading code must not be re-used.130

�

�

�

�

– General Deployment (1/3) –

Source Terminal:

• it broadcasts its data to the remaining terminals in the first VAA,

• it uses given cooperative resources in terms of power, etc.

First Relaying VAA:

• it is formed by q1 spatially adjacent terminals (including the source!),

• each terminal possesses n1,i antenna elements (first subscript relates to first VAA and 1 ≤ i ≤ q1),

• after cooperation, the data is space-time encoded (codebook has t1 =

�q1i=1 n1,i spatial dimensions),

• each terminal transmits only n1,i∈(1,q1) spatial dimensions (so that no codeword is duplicated),

• it uses relaying resources in terms of power, bandwidth, frame duration.

131

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Second Relaying VAA:

• it is formed by q2 spatially adjacent terminals with n2,i antenna elements each,

• some may cooperate, hence forming Q2 clusters (everybody coop.: Q2 = 1, nobody coop.: Q2 = q2),

• j−th cluster contains r2,j receive antennas (1 ≤ j ≤ Q2 ,

�q2i=1 n2,i =

�Q2j=1 r2,j ),

• there are hence Q2 MIMO channels in the first stage (each with t1 Tx antennas and r2,j Rx antennas),

• cooperation uses given cooperative resources,

• after cooperation, the data is space-time encoded (codebook has t2 =

�q2i=1 n2,i spatial dimensions),

• each terminal transmits only n2,i∈(2,q2) spatial dimensions (so that no codeword is duplicated),

• it uses relaying resources in terms of power, bandwidth, frame duration.

132

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v−th Relaying VAA:

• it is formed by qv spatially adjacent terminals with nv,i antenna elements each,

• cooperation, space-time encoding and resource utilisation is congruent to above.

V −th Relaying VAA:

• it is formed by qV adjacent terminals with nV,i antenna elements each (including the target!),

• all terminals cooperate (non-cooperative terminals have no influence on data flow),

• there is hence one MIMO channel (with tV −1 Tx antennas and

�qVi=1 nV,i Rx antennas),

Target Terminal:

• after cooperation, data is space-time decoded and passed to information sink .

133

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�

– Aim of PHY/MAC Analysis –Find optimum fractional resources to be assigned to each mobile terminal

so as to maximise the end-to-end data throughput for a specifiedcommunication scenario, where the resource considered are

frame duration, frequency band and power.

Frame Duration:

• In time-division multiple access (TDMA), each relaying stage is assigned a given frame

duration which may or may not overlap with other stage’s frames.

Frequency Band:

• In frequency-division multiple access (FDMA), each relaying stage is assigned a given

frequency band which may or may not overlap with other stage’s frequency bands.

Power/Energy:

• Each terminal in the relaying stage is assigned a given power (energy). The energy

required to deliver a packet from source to sink ought to be independent of the topology.

134

�

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�

�

– FMDA-Based Relaying –

• α(f)v is the fractional bandwidth allocated to the v−th relaying stage operating in FDMA,

• for fairness of comparison, we have∑V −1

v=1 α(f)v = 1.

1st VAA

Orthogonal

FDMA-based

Relaying

1st Stage

t

f

t t

f

t

f

W

W#1

W#2

W#3

W#4

T

Non-Orthogonal

FDMA-based

Relaying

t

f

t t

f

t

f

W

W#1

W#2

T

Interference

2nd VAA 3rd VAA 4th VAA 5th VAA

2nd Stage 3rd Stage 4th Stage

Figure 33: Orthogonal (no interference) and non-orthogonal (interference) relaying methods.

135

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�

�

�

– TMDA-Based Relaying –

• α(t)v is the fractional frame duration allocated to the v−th stage operating in TDMA,

• for fairness of comparison, we have∑V −1

v=1 α(t)v = 1.

Orthogonal

TDMA-based

Relaying

t

f

t t

f

t

f

W

T#

1

T#

2

T#

3

T#

4

T

Non-Orthogonal

TDMA-based

Relaying

t

f

t t

f

t

f

W

T#

1

T#2

T

1st VAA

1st Stage

2nd VAA 3rd VAA 4th VAA 5th VAA

2nd Stage 3rd Stage 4th Stage

Interference

Figure 34: Orthogonal (no interference) and non-orthogonal (interference) relaying methods.

136

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– Power & Energy Allocation –

FDMA-based Relaying TDMA-based Relaying

Ev = β(Ef )v E, Tv = T, Wv = α

(f)v W Ev = β

(Et)v E, Tv = α

(t)v T, Wv = W∑V −1

v=1 β(Ef )v ≡ 1,

∑V −1v=1 α

(f)v ≡ 1

∑V −1v=1 β

(Et)v ≡ 1,

∑V −1v=1 α

(t)v ≡ 1

Sv = β(Sf )v S, Sv = Ev/Tv Sv = β

(St)v S, Sv = Ev/Tv

→ β(Sf )v = β

(Ef )v → β

(St)v = β

(Et)v /α

(Et)v∑V −1

v=1 β(Sf )v ≡ 1,

∑V −1v=1 α

(f)v ≡ 1

∑V −1v=1 α

(t)v β

(St)v ≡ 1,

∑V −1v=1 α

(t)v ≡ 1

Time T

Power S1st Stage 2nd Stage 3rd Stage

E1

E2

E3

S1, S

3

S2

T1

T2

T3

Figure 35: Relationship between power, energy and time.

137

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�

– Equivalence between TDMA & FDMA –

FDMA-based Relaying TDMA-based Relaying

C = α(f)v · W · log2

(1 + β

(Sf )v ·S

α(f)v ·W ·N0

)C = α

(t)v · W · log2

(1 + β(St)

v ·SW ·N0

)= α

(f)v · W · log2

(1 + β

(Ef )v

α(f)v

· SN

)= α

(t)v · W · log2

(1 + β(Et)

v

α(t)v

· SN

)

C is the Shannon capacity, W is the total bandwidth, N is the total noise power captured over W ,

N0 is the noise power spectral density, αv is the fractional bandwidth/frame duration and βv is the

fractional energy allocated to the v−th stage.

Since both access schemes are equivalent, we will henceforth use:

C = αv · W · log2

(1 +

βv

αv· SN

)(29)

V−1∑v=1

βv ≡ 1 &V−1∑v=1

αv ≡ 1 (30)

138

�

�

�

�

– Maximum Ergodic Throughput (1/3) –

• The aim is to maximise the end-to-end data throughput for the topology shown in Figure 32

assuming an ergodic fading channel.

• Throughput is defined as the information delivered from source towards sink, which requires a

certain duration of communication T and frequency band W .

• Subsequent analysis will refer to the normalised (spectral) throughput Θ in [bits/s/Hz].

• An ergodic channel offers a normalised capacity C in [bits/s/Hz] with 100% reliability, which

allows relating capacity and throughput via Θ = C .

• Maximising the throughput Θ is hence equivalent to maximising the capacity C .

• If a certain capacity was to be provided from source to sink, all channels involved must

guarantee error-free transmission.

The end-to-end capacity C is hence dictatedby the capacity of the weakest link.

139

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�


• Each topology has K = V − 1 distributed relaying stages.

• The v−th stage has Qv+1 MIMO channels with tv transmit antennas and rv+1,j∈(1,Qv+1)

receive antennas (for the example below: Qv+1 = 2, tv = 5, rv+1,1 = 3 and rv+1,2 = 3).

(v+1)-st Tier VAAv-th Tier VAA

nv,1

nv,2

nv,3

nv+1,1

nv+1,2

nv+1,3

MIMO #1: (nv,1

+nv,2

+nv,3

) x (nv+1,1

+nv+1,2

)

MIMO #2: (nv,1

+nv,2

+nv,3

) x (nv+1,3

)

Figure 36: Established MIMO channels from the vth to the (v + 1)st relaying VAA.

140

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�


• At each stage, we cluster such that the capacity of all clusters (MIMO channels) is as equal as

possible.

• For the analysis, we discard all but the weakest MIMO channel because the stronger MIMO

channels will then definitely be error-free.

• (If all sub-channel gains are equal, then the weakest MIMO channel is dictated by the cluster

with the smallest number of antennas.)

• For the analysis, the v−th relaying stage is hence represented by one MIMO channel with tv

transmit and rv � minj∈(1,Qv+1){rv+1,j} receive antennas.

• The aim of the analysis is to maximise the minimum capacity C , i.e.

C = supα,β

{min

{C1(α1, β1, λ1, γ1), . . . , CK(αK , βK , λK , γK)

}}(31)

over the fractional sets α � (α1, . . . , αK) and β � (β1, . . . , βK) in dependency of the

channel statistics λ � (λ1, . . . , λK) and average channel gains γ � (γ1, . . . , γK).

141

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�

– MIMO Relaying without Resource Reuse (1/4) –

• With the parameter constraints given by (30), increasing one capacity inevitably requires

decreasing the other capacities.

• The minimum is maximised if all capacities are equated and then maximised.

• The capacity of the v−th stage is given as Cv = αv · Eλv

{mv log2

(1 + λv

γv

tv

βv

αv

SN

)}.

• In [51], the end-to-end throughput-maximising optimised fractional power and optimised

fractional bandwidth (frame duration) have been obtained as

αv =

∏w �=v Eλw

{mv log2

(1 + λwρw

γw

tw

SN

)}∑K

k=1

∏w �=k Eλw

{mv log2

(1 + λwρw

γw

tw

SN

)} (32)

βv = ρv · αv (33)

with

ρv ≈ K ·∏

w �=v3√

γw · Λ2(tw, rw)∑Kk=1

∏w �=k

3√

γw · Λ2(tw, rw)(34)

142

�

�

�

�


• In [51], the end-to-end throughput-maximising optimised fractional power with equal fractional

bandwidth (frame duration) have been obtained as

αv =1K

(35)

βv =

∏w �=v γw · Λ2(tw, rw)∑K

k=1

∏w �=k γw · Λ2(tw, rw)

(36)

• For the purpose of comparison, the case of no optimisation is also considered, for which the

resource allocation strategies are

αv =1K

(37)

βv =1K

(38)

143

��

��

InputChannel Gains from each

Relaying Stageγ

1, ..., γ

Κ

InputNumber of A ntenna

Elements at each Stage

t1, r

1, …, t

K, r

K

CalculateMIMO Gains at each Stage

Λ1, ..., Λ

Κ

CalculateAuxiliary Coeff icients

ρ1, ..., ρ

Κ

CalculateFractional Bandwidths

α1, ..., α

Κ

SortFractional Resources

α1< ... < α

Κ, β

1< ... < β

Κ

CalculateFractional Powers

β1, ..., β

Κ

OutputFractional B andwidth

Allocations

OutputFractional Power

Allocations

α1,..., α

Κ−1, α

Κ=1− α

1−...− α

Κ−1 β1,..., βΚ−1, βΚ=1− β1−...− βΚ−1

144

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�


0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

SNR at First Relaying Stage [dB]

End

−to

−E

nd C

apac

ity C

[bits

/s/H

z]

Optimum End−to−End CapacityOptimised Bandwidth and Optimised PowerEqual Bandwidth and Optimised PowerEqual Bandwidth and Equal Power

t1 = 1, r

1 = 1

t2 = 1, r

2 = 1

t3 = 1, r

3 = 1

p = [0, 5, 10]

p = [0, 0, 0]

p = [0, −5, −10]

(a) Achieved end-to-end capacity of various

fractional resource allocation strategies for a 3-

stage network.

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

SNR at First Relaying Stage [dB]

End

−to

−E

nd C

apac

ity C

[bits

/s/H

z]

Optimum End−to−End CapacityOptimised Bandwidth and Optimised PowerEqual Bandwidth and Optimised PowerEqual Bandwidth and Equal Power

t1 = 1, r

1 = 2

t2 = 2, r

2 = 3

t3 = 3, r

3 = 2

p = [0, 5, 10]

p = [0, 0, 0]

p = [0, −5, −10]

(b) Achieved end-to-end capacity of various

fractional resource allocation strategies for a 3-

stage network.

Figure 37: Performance of fractional resource allocation algorithms for different 3-stage topologies;

here p � [10 log10(γ1/γ1), 10 log10(γ2/γ1), 10 log10(γ3/γ1)]

145

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Open Issues

146

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– Open Issues –

In the field of capacity, there are endless unsolved problems. However, we believe that these

are some interesting open issues:

• Analysis of rate & outage behaviour of

– synchronisation-robust cooperative systems,

– cooperative systems with imperfections (channel, feedback, correlation, etc.),

– cooperative systems in shadowing channels.

• Using capacitive insights to

– optimise the choice (and placement) of cooperative nodes,

– optimise the cooperative communication protocol.

147

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PART 6PHY LAYER ALGORITHMS

148

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• Analysing the PHY layer performance of a wireless system is vital in understanding,

optimising and synthesising system parameters.

• There are several hundred highly complex contributions available today, which requires

us to concentrate on a very few of them.

• For this reason, we proceed with the following topics:

– cooperative, single & multi-stage, space-time block coded DF schemes;

– some case studies for cellular & sensor networks;

– cooperative spectrum sensing.

• These are contributions which we found very interesting but have no time to dwell on:

– Sendonaris et al : CDMA-based cooperative transceiver analysis & design [56];

– Stefanov et al : design & optimisation of inter-user and direct space-time codes [73];

– Giannakis et al : closed-form error rates for AF cooperative schemes [77];149

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Space-Time BlockDF Schemes

150

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– System Model –

• Transmitter:

– number of transmit antennas: t

– transmitted space-time block codeword: x ∈ Ct×1

– transmit power constraint: tr(E{xxH

}) ≤ S

• Channel:

– channel from transmitter i ∈ (1, t) to receiver j ∈ (1, r): hi,j

– fading realisations of hi,j : frequency-flat & uncorrelated

– grouping of sub-channel gains hi,j : H

• Receiver:

– received signal: y = Hx + n

– r−dimensional noise vector n has variance N per entry

• Cooperative Link:

– assumed to be error-free (!)

151

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– Exact STBC Error Probabilities (1/4) –

• We will consider distributed cooperative STBCs of arbitrary rate R.

• Furthermore, the sub-channel realisation hi,j obey Nakagami fading with fading parameter f ;

the sub-channels may have different gains, thereby reflecting a possibly distributed deployment.

• We define u � t · r, γi � E {hih∗i } and assume

∑ui=1 γi = u.

Distributed

Space-Time Block Encoder

Distributed

Space-Time Block Decoder

FractionalSTBC

Space-Time

Block DecoderError

Detector

s s

h11

hr,t

O-MIMO

Channel

FractionalSTBC

FractionalSTBC

Receiver

Receiver

Receiver

Information

Source

H

s

Figure 38: Distributed Space-Time Block Code transceiver system.

152

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Let’s define

PPSK(α, u, M) � 1(1 + α)u

[1

2√

π

Γ(u + 1/2)Γ(u + 1) 2F1

(u, 1/2; u + 1; (1 + α)−1

)(39)

+√

1 − gPSK

πF1

(1/2, u, 1/2 − u; 3/2;

1 − gPSK

1 + α, 1 − gPSK

)]

PQAM(α, u, M) � 1(1 + α)u

2q√π

Γ(u + 1/2)Γ(u + 1) 2F1

(u, 1/2; u + 1; (1 + α)−1

)(40)

− 1(1 + 2α)u

2q2

π(2u + 1)F1

(1, u, 1; u + 3/2;

1 + α

1 + 2α, 1/2

)

where Γ(x) is the complete Gamma function, 2F1(a, b; c; x) is the Gauss hypergeometric function

with 2 parameters of type 1 and 1 parameter of type 2 [78] (§9.14.1)), and F1(a, b, b′; c; x, y) is the

Appell hypergeometric function of two variables [78] (§9.180.1). Furthermore, α is a parameter, M

is the modulation order, gPSK � sin2(π/M), gQAM � 3/2/(M − 1), q � 1 − 1/√

M .

153

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• Based on the analysis of [79] & [51], the symbol error rate (SER) of M-QAM and M-PSK STBC

systems operating over a Nakagami fading channel with different sub-channel gains γ i∈(1,u)

and different fading factors fi∈(1,u) can be derived in closed form as

Ps(e) =u∑

i=1

fi∑j=1

Ki,j · PPSK/QAM

(1R

γi

fit

S

N, j, M

)(41)

where

Ki,j =1

(fi − j)!(− 1

Rγi

fitSN

)fi−j

∂fi−j

∂sfi−j

⎡⎢⎣ u∏

i′=1,

i′ �=i

1(1 − 1

Rγi′fi′ t

SN · s

)fi′

⎤⎥⎦

s=

�

1R

γifit

SN

�−1

.

• For memoryless fading channels, the bit error rate (BER) and frame error rate (FER) for frames

of D symbols are respectively well approximated by

Pb(e) ≈ Ps(e)log2(M)

and Pf (e) ≈ 1 − (1 − Ps(e)

)D(42)

154

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Error rate performance of distributed STBC scheme exhibits a high stability:

γ1Fractional

STBC

FractionalSTBC

γ2

ChannelEncoder

InformationSource

Space-Time

Block Decoder

Channel

Decoder

InformationSink

(a) Distributed Alamouti scheme with unequal


shadowing.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 210

−6

10−5

10−4

10−3

10−2

10−1

100

γ1

SE

R

1 Tx − SISO (γ1)


1)


2=2−γ

1)

(b) SER versus the normalised power γ1 in the

first link for a distributed Alamouti system oper-

ating at 2 bits/s/Hz; SNR=30dB.


155

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Multi-Stage STBCDF Schemes

156

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– Maximum Throughput –

The aim is to maximise the end-to-end data throughput for the below topology assuming various

relaying methodologies with transceivers of finite complexity:

6th

VAA

5th

VAA

4th

VAA

(V-2)nd

VAA

(V-1)st

VAA

V-th

VAA

targ

et te

rmin

al

3rd

VAA

2nd

VAA

1st

VAA

so

urc

e t

erm

ina

l

1st

Relaying

Stage

2nd

Relaying

Stage

co

op

era

tion

rela

yin

g t

erm

inal

Figure 40: Distributed-MIMO multi-stage relaying topology.

157

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�

– Maximum Throughput for End-to-End Transmission (1/3) –

• We first derive fractional resource allocation rules assuming that a decision on the correctness

of the received signal is done at the t-MT.

• This should not be confused with transparent relaying, where the information is simply amplified

and forwarded. It is also in contrast to a stage-by-stage detection, where a decision on the

correctness of the received signal is done at each stage.

• We will deal first with the case of full at each relaying stage; such a scenario provides a great

simplification to analysis, since the errors in consecutive stages become independent.

• Then we will deal with the generic relaying process with partial cooperation (clustering), where

one r-MT may have a more reliable estimate than another r-MT in the same relaying VAA,

leading to error-dependencies between the stages.

• Subsequently, the problem of maximising the end-to-end throughput is shown to be equivalent to

the problem of minimising the end-to-end BER.

158

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• It is assumed here that the source MT (s-MT) transmits B bits per frame to the target MT (t-MT)

via K relaying stages. The normalised end-to-end throughput can be expressed as

Θ = minv∈(1,K)

{α′

vRv log2(Mv)} · (1 − Pf,e2e(e)

)(43)

where α′v , Rv and Mv are the fractional frame duration, STBC rate and modulation index of the

vth stage respectively, and Pf,e2e(e) is the end-to-end FER.

• Eq. (43) has to be understood as follows. If there were no losses between a directly communicating s-MT

and t-MT, then all of the B bits reach the receiver; the throughput normalised by the total number of sent

bits hence amounts to 1. The use of a modulation scheme with index M and a STBC with rate R during a

fractional frame duration α′ to accomplish such link results in a throughput, normalised by the utilised time

and frequency, as 1 · α′ · R · log2(M) [bits/s/Hz]. It is then diminished by the loss caused by the

end-to-end FER Pf,e2e(e). For a communication system with K relaying stages, the weakest link in the

chain determines the throughput, hence minv∈(1,K)

�

α′vRv log2(Mv)

�

. It is thus the aim to derive

optimum resource allocation strategies, which maximise the end-to-end throughput.

159

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• First, the modulation indices Mv∈(1,K) are fixed and the limiting case where SNR→ ∞ is

considered. This allows α′v to be found from (43) by equating α′

vRv log2(Mv) for all v:

α′v =

∏Kw=1,w �=v Rw · log2(Mw)∑K

k=1

∏Kw=1,w �=k Rw · log2(Mw)

(44)

• Second, it can easily be shown that Θ ∝ −Pb,e2e(e), i.e. one has to minimise the end-to-end

bit error rate by optimally assigning fractional transmission power to each relaying stage. The

BER at each stage is related with the occurring SER via (42), where for low error rates one

symbol error causes one bit error.

• Third, the optimum modulation order Mv∈(1,K) has to be determined in dependency of the

previously derived fractional resource allocations. This is easily done by permuting all possible

modulation orders at each stage such as to maximise the end-to-end throughput. Since the

number of modulation orders will be limited, such optimisation is feasible without consuming too

much computational power.

160

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– Full Cooperation (1/4) –

• We assume full cooperation with equal-power Rayleigh fading channels.

• Assuming independent errors among the stages, the end-to-end BER can be approximated as

Pb,e2e(e) ≈K∑

v=1

PPSK/QAM

(γv · β′

v · S/N/tv/Rv, uv, Mv

)log2

(Mv

) (45)

where the sub-index v relates to the v-th relaying stage.

• Since optimisation is too intricate with the closed forms for the M-QAM and M-PSK error rates,

we need to upper-bound them which leads to

Pb,e2e(e) ≤K∑

v=1

Av (1 + Bvβ′v)−uv (46)

where the constants Av and Bv are given as [51]

Av =

⎧⎨⎩

Mv−1Mv log2(Mv) for M-PSK

2qv

log2(Mv) for M-QAMBv =

⎧⎨⎩

gPSK,v

Rv

γv

tv

SN for M-PSK

gQAM,v

Rv

γv

tv

SN for M-QAM

161

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�



fractional frame duration have been obtained as (see [51])

α′v =


k=1


(47)

β′v =

[K∑

w=1

α′w

(u−1

v A−1v Buv

v

u−1w A−1

w Buww

) 1umax+1

]−1

(48)

where umax = max(u1, . . . , uK).

• The allocation strategies for the case of resource reuse and/or Nakagami fading channels with

arbitrary fading statistics are derived in a similar fashion.

162

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Allocation algorithms yield near-optimum end-to-end BER:

0 5 10 15 20 25 30 35 40

10−4

10−3

10−2

10−1

100

End

−to

−E

nd B

ER

SNR [dB]

Optimum (numerical)Near−Optimum (algorithm)Non−Optimised

t1 = 1, r

1 = 2, M

1 = 4

t2 = 2, r

2 = 2, M

2 = 4

p = [0, 10]

t1 = 1, r

1 = 1, M

1 = 4

t2 = 1, r

2 = 1, M

2 = 4

p = [0, 10]

t1 = 1, r

1 = 1, M

1 = 4

t2 = 1, r

2 = 1, M

2 = 4

p = [0, 0]

t1 = 2, r

1 = 2, M

1 = 256

t2 = 2, r

2 = 1, M

2 = 64

p = [0, 10]

(a) Comparison between optimum and near-

optimum, as well as non-optimised end-to-end

BER for a two-stage relaying network.

0 5 10 15 20 25 30 35 40

10−4

10−3

10−2

10−1

100

End

−to

−E

nd B

ER

SNR [dB]


t1 = 2, r

1 = 2, M

1 = 16

t2 = 2, r

2 = 1, M

2 = 64

t3 = 1, r

3 = 2, M

3 = 256

p = [0, 5, 10]

t1,2,3

= 1r1,2,3

= 1M

1,2,3 = 4

p = [0, 5, 10]

t1 = 1, r

1 = 2, M

1 = 4

t2 = 2, r

2 = 2, M

2 = 4

t3 = 2, r

3 = 2, M

3 = 4

p = [0, 5, 10]

(b) Comparison between optimum and near-


BER for a three-stage relaying network.

Figure 41: Performance of various 2- & 3-stage relaying topologies.

163

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– Full Cooperation (4/4) –Savings of up-to 5dB or 0.5bits/s/Hz can be achieved with optimisation:

0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

End

−to

−E

nd T

hrou

ghpu

t [bi

ts/s

/Hz]

SNR [dB]


t1 = 2, r

1 = 4

t1 = 4, r

2 = 4

R1 = 1, R

2 = 3/4

t1 = 2, r

1 = 2

t1 = 2, r

2 = 2

R1 = 1, R

2 = 1

t1 = 1, r

1 = 1

t1 = 1, r

2 = 1

R1 = 1, R

2 = 1

B = 100 p = [0, 10] M

1 = 4, M

2 = 4

(a) Comparison between optimum and near-


throughput for various configurations of a two-

stage relaying network.

0 5 10 15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

3.5

4

End

−to

−E

nd T

hrou

ghpu

t [bi

ts/s

/Hz]

SNR [dB]

Near−Optimum with Optimised Modulation IndexNo Optimisation

p = [0, 10] t1 = 2, r

1 = 2

t2 = 2, r

2 = 2

M1,2

= 256

M1,2

= 64

M1,2

= 16

M1,2

= 4

M1,2

= 2

(b) Numerically optimised modulation index

where M1,2 = (2, 4, 16, 64, 256) to yield

near-optimum end-to-end throughput, com-

pared to non-optimised systems.

Figure 42: End-to-end throughput for 2-stage relaying topologies.

164

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�

– Partial Cooperation (1/7) –

• We assume partial cooperation (clustering) with unequal-power Rayleigh fading channels.

• To obtain the exact end-to-end BER is not trivial, as an error occurring in one cluster may or may

not be corrected by a parallel cluster.

• This creates dependencies between the error events at each stage in dependency of:

– the modulation scheme used,

– the prevailing channel statistics,

– the average channel attenuations,

– as well as the deployed STBC.

• The fairly complex interdependencies call for suitable simplifications, where we will weigh the

strength of a channel with a given error probability against the strength of the other channels.

• Subsequent explanations relate to Figure 43.

165

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�


3rd TierVAA2nd Tier

VAA

1st Tier

VAA

So

urc

e M

T

4th Tier

VAA

Targ

et M

T

(1,1)

(1,2)

(2,1)

(2,2)

(2,3)

(2,4)

(3,1)

(3,2)

P1,1

P1,2

P2,1

P2,2

P3,1

Figure 43: 3-stage distributed O-MIMO communication system without cooperation.

166

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• We assume that the system operates at low error rates which causes only one error event at a

time in the entire network.

• Let us assume that an error occurs in link (1,1); however, (1,2) is error free. Then the probability

that the error propagates further is related to the strengths of channels (2,1) and (2,3).

• It is intuitive and hence conjectured here that the probability that such error propagates is

proportional to the strength of the STBC branch it departs from, here (2,1) for one of two MISO

channels, and (2,2) for the other one.

• Therefore, the probability that an error which occurred in link (1,1) with probability P1,1

propagates through the O-MISO channel spanned by (2,1) and (2,3) is approximated as

P1,1 · γ2,1/(γ2,1 + γ2,3), where the strength of the erroneous channel (2,1) is normalised by

the total strength of both sub-channels.

• To capture the probability that such an error propagates until the t-MT, all possible paths in the

network have to be found and the original probability of error weighed with the ratios between

the respective path gains.

167

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• Taking the previously said into account and assuming that at high SNRs only one such error will

occur at any link, the end-to-end BER for the network depicted in Figure 43 can be expressed as

Pb,e2e(e) ≈[P1,1(e)

(γ2,1

γ2,1 + γ2,3

γ3,1

γ3,1 + γ3,2+

γ2,2

γ2,2 + γ2,4

γ3,2

γ3,1 + γ3,2

)+

P1,2(e)(

γ2,4

γ2,2 + γ2,4

γ3,2

γ3,1 + γ3,2+

γ2,3

γ2,1 + γ2,3

γ3,1

γ3,1 + γ3,2

)]+[

P2,1(e)(

γ3,1

γ3,1 + γ3,2

)+ P2,2(e)

(γ3,2

γ3,1 + γ3,2

)]+[P3,1(e)

]

• This can be simplified to

Pb,e2e(e) ≈[ξ1,1P1,1(e) + ξ1,2P1,2(e)

]+[

ξ2,1P2,1(e) + ξ2,2P2,2(e)]

+[ξ3,1P3,1(e)

]

where ξv,i is the probability that an error occurring in link (v, i) will propagate to the t-MT.

168

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• This is easily generalised to networks of any size and any form of partial cooperation.

• To this end, remember that there are Qv∈(1,K) cooperative clusters at the vth stage, each of

which will yield an error probability of Pv∈(1,K),i∈(1,Qv).

• The end-to-end BER is hence approximated as

Pb,e2e(e) ≈K∑

v=1

Qv∑i=1

ξv,iPv,i(e) (49)

where the probabilities ξv,i are easily found from the specific network topology.

• The BERs Pv,i(e) can be found from the previously derived SERs with an appropriate number

of transmit and receive antennas per cluster, as well as prevailing channel conditions.

• The proposed approximation holds with high precision, as demonstrated by means of the

following performance graphs.

169

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�


0 5 10 15 20 25 30 35 40 45 50

10−4

10−3

10−2

10−1

100

End

−to

−E

nd B

ER

SNR [dB]

Exact (numerical)Approximate (analysis)

γ1,1

= 4, γ1,2

= 1γ2,1

= 1, γ2,2

= 4

γ1,1

= 0.1, γ1,2

= 0.05γ2,1

= 10, γ2,2

= 20

(a) Numerically obtained and derived end-to-

end BER versus the SNR in the first link for a

two-stage network without cooperation.

0 5 10 15 20 25 30 35 40 45 50

10−4

10−3

10−2

10−1

100

End

−to

−E

nd B

ER

SNR [dB]

Exact (numerical)Approximate (analysis)

γ1,1

= 1.9, γ1,2

= 0.1γ2,1

= 0.1, γ2,2

= 1.0γ2,3

= 1.0, γ2,4

= 1.9γ3.1

= 1.9, γ3,2

= 0.1

γ1,1

= 1.6, γ1,2

= 0.4γ2,1

= 0.4, γ2,2

= 1.0γ2,3

= 1.0, γ2,4

= 1.6γ3.1

= 1.6, γ3,2

= 0.4

γ1,1

= 21, γ1,2

= 22γ2,1

= 13, γ2,2

= 14γ2,3

= 15, γ2,4

= 16γ3.1

= 7, γ3,2

= 8

(b) Numerically obtained and derived end-to-

end BER versus the SNR in the first link for a

three-stage network without cooperation.

Figure 44: End-to-end BER of various 2- & 3-stage relaying topologies.

170

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fractional frame duration have been obtained as

α′v =


k=1


(50)

β′v =

⎡⎢⎢⎢⎢⎢⎢⎣

K∑w=1

α′w

√√√√√√√√√√

Qv∑i=1

∑j∈i

ξ−1v,i K

−1v,i,jA

−1v Bv,i,j

Qw∑i=1

∑j∈i

ξ−1w,iK

−1w,i,jA

−1w Bw,i,j

⎤⎥⎥⎥⎥⎥⎥⎦

−1

(51)

where the notation j ∈ i represents the j th sub-channel belonging to the ith cluster, Further-more, Kv,i,j =

∏j′∈i,j′ �=j

γv,j

γv,j−γv,j′and

Av =

{Mv−1

Mv log2(Mv) for M-PSK2qv

log2(Mv) for M-QAMBv,i,j =

{ gPSK,v

Rv

γv,j∈i

tv

SN for M-PSK

gQAM,v

Rv

γv,j∈i

tv

SN for M-QAM

171

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Case Studies

172

�

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�

– Case Study I (1/3) –

• We consider a TDMA-based relaying system, which allocates to each r-MT a fractional

transmission power of βv∈(1,K)/αv∈(1,K).

• The SNR in the v-th relaying stage is easily derived as

SNRv =βv

αv·(

d0

dv

)n

· S

N(52)

where d0 is the distance between s-MT and t-MT, dv is the distance spanning the v-th relaying

stage, n is the pathloss coefficient, and S/N is the SNR experienced at the t-MT if direct

communication took place.

• From (52), we can see that the SNR gain is mainly dictated by the ratio between the respective

distances and the pathloss coefficient.

173

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Relaying outperforms direct communication in low SNR (or low SINR) region:

0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

End

−to

−E

nd T

hrou

ghpu

t [bi

ts/s

/Hz]

SNR of Direct Link [dB]

Direct CommunicationTwo−Hop Relaying

n = 4

n = 3

n = 2

B = 100 t0,1,2

= r0,1,2

= 1M

0,1,2 = 4

d1,2

= 0.5 d0

(a) End-to-end throughput for a direct commu-

nication link and two-stage relaying links with

varying pathloss coefficient.

0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

End

−to

−E

nd T

hrou

ghpu

t [bi

ts/s

/Hz]



B = 100 n = 4 t0 = r

0 = 1

M0 = 4

d1,2

= 0.5 d0

t1 = 1, r

1 = 2, M

1 = 4

t2 = 2, r

2 = 1, M

2 = 16

t1 = 1, r

1 = 2, M

1 = 4

t2 = 2, r

2 = 1, M

2 = 64

t1 = 1, r

1 = 2, M

1 = 4

t2 = 2, r

2 = 1, M

2 = 4

t1 = 1, r

1 = 1, M

1 = 4

t2 = 1, r

2 = 1, M

2 = 4

(b) End-to-end throughput for a direct commu-

nication link and two-stage relaying links with a

varying relaying scenario.

Figure 45: End-to-end throughput of various 2-stage relaying topologies.

174

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Relaying yields higher relative gains over direct communication at low SNRs (or low SINRs):

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

End

−to

−E

nd T

hrou

ghpu

t [bi

ts/s

/Hz]

First Hop Distance / Total Distance [%]


SNR = 20dB

SNR = 10dB

B = 100 n = 4 t0 = 1, r

0 = 1, M

0 = 4

t1 = 1, r

1 = 2, M

1 = 4

t2 = 2, r

2 = 1, M

2 = 16

(a) End-to-end throughput versus distance of

first direct link normalised by the total distance

at different direct link SNRs.

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

End

−to

−E

nd T

hrou

ghpu

t [bi

ts/s

/Hz]

First Hop Distance / Total Distance [%]


SNR = 20dB

SNR = 10dB

B = 100 n = 4 t0 = 1, r

0 = 1, M

0 = 16

t1 = 1, r

1 = 2, M

1 = 16

t2 = 2, r

2 = 1, M

2 = 4

(b) End-to-end throughput versus distance of

first direct link normalised by the total distance

at different direct link SNRs.

Figure 46: End-to-end throughput versus distances between terminals.

175

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�

– Case Study II (1/2) –

• Now, the MTs are placed randomly in the shaded area of size a× b which are placed at distance

c from each other, thereby realising a two-stage distributed-MIMO communication system.

• Relaying is accomplished by means of one or two cooperating r-MTs. It is assumed that the two

cooperating r-MTs are spatially close together, thereby experiencing approximately the same

pathloss from the s-MT and towards the t-MT.

• All simulations use a packet length of B = 100 and a pathloss coefficient of n = 4; the

dimensions of the shaded areas are (fairly arbitrary) set to a = b = 50 with a mutual distance

of c = 100. The terminal placement within these areas obey a uniform distribution.

3rd Tier VAA2nd Tier VAA1st Tier VAA

So

urc

e M

T

Ta

rge

t MT

c = 100

a = 50

b =

50

Figure 47: 2-stage distributed O-MIMO communication system with two cooperating r-MTs.

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– Case Study II (2/2) –

0 5 10 15 20 25 30 35 400

1

2

3

4

5

6

7

End

−to

−E

nd T

hrou

ghpu

t [bi

ts/s

/Hz]


Two−Hop Relaying (Optimised Power and Frame Duration)Two−Hop Relaying (Optimised Frame Duration)Two−Hop Relaying (Non−Optimised)Direct Communication

B = 100 n = 4 t0 = 1, r

0 = 1

t1 = 1, r

1 = 2

t2 = 2, r

2 = 1

M1 = M

2 = 256

M1 = M

2 = 64

M1 = M

2 = 16

M1 = M

2 = 4

(a) End-to-end throughput for a scenario as de-

picted in Figure 47 with two r-MTs and one an-

tenna in s-MT and t-MT.

0 5 10 15 20 25 30 35 400

1

2

3

4

5

6

7

End

−to

−E

nd T

hrou

ghpu

t [bi

ts/s

/Hz]


Two−Hop Relaying (Optimised Power and Frame Duration)Two−Hop Relaying (Optimised Frame Duration)Two−Hop Relaying (Non−Optimised)Direct Communication

B = 100 n = 4 t0 = 1, r

0 = 1

t1 = 1, r

1 = 2

t2 = 2, r

2 = 1

σ2ς = 12dB

M1 = M

2 = 256

M1 = M

2 = 64

M1 = M

2 = 16

M1 = M

2 = 4

(b) End-to-end throughput for a scenario with

shadowing as depicted in Figure 47 with two

r-MTs and one antenna in s-MT and t-MT.

Figure 48: End-to-end throughput for various topologies.

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CooperativeSpectrum Sensing

�

�

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�

– System Model –

• A distributed cooperative set of n nodes wishes to determine if a given frequency band is

occupied.

• To this end, each node utilises an energy detector as per below figure.

• After each decision on occupancy, each node broadcasts its 1-bit decision to the remaining

n − 1 nodes.

• The band is assumed to be occupied if at least one node decides it to be occupied.

• For the analysis, Rayleigh fading towards sensing nodes is assumed, as well as error-free

cooperation.

x(t) Bandpass Filter Square Device Integrator Y Threshold Device H0/H1

Figure 1: Block diagram of energy detector.

�

�

�

�

– Detection Probabilitiesa –

• Hypotheses:

– H0: unoccupied, x(t) = n(t), Y ∼ C − χ22m (m = T · W )

– H1: occupied, x(t) = h · s(t) + n(t), Y ∼ NC − χ22m (NC = 2 · SNR)

• Probabilities with threshold λ (single node):

– false alarm: Pf = P{Y > λ|H0} = Γ(m, λ/2)/Γ(m))

– detection: Pd = P{Y > λ|H1} =Γ(m−1,λ/2)

Γ(m−1) + e−λ

2(1+m·γ)

(1 + 1

mγ

)m−1

×[1 − Γ(m−1, λmγ

2(1+mγ) )

Γ(m−1)

]

• Probabilities (cooperative detection):

– false alarm: Qf = 1 − (1 − Pf )n

– detection: Qd = 1 − (1 − Pd)n

aFollowing the analysis outlined by A. Ghasemi and E.S. Sousa.

�

�

�

�

– Spectrum Detection –

1 2 3 4 5 6 7 8 9 100.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of Users n

Pro

babi

lity

of D

etec

tion

Figure 2: Probability of correct detection versus number of cooperative nodes; λ = 5, m = 1, γ =0dB.

�

�

�

�

– Minimum Required SNR –

1 2 3 4 5 6 7 8 9 102

4

6

8

10

12

14

Number of Users n

Req

uire

d M

inim

um S

NR

[dB

]

Figure 3: Minimum required detection SNR versus number of cooperative nodes; Qd = 0.9, Qf =0.1.

�

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Open Issues

178

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– Open Issues –

Again, there are endless unsolved problems. However, we believe that these are some

interesting open issues:

• Analysis and optimisation of

– robust synchronisation schemes,

– differentially modulated cooperative (space-time) schemes,

– random beamforming with sensor nodes.

• Advanced topics, such as

– design of (sub-)optimum multi-user cooperative transceivers,

– capacity-approaching distributed channel and space-time code design.

179

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PART 7MAC & X-Layer Design

180

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• The MAC layer is central to the throughput and delay of a wireless system.

• There are dozens contributions available today, which is why we only concentrate on

some basic MAC and cross-layer design issues.

• We proceed with the following topic:

– throughput of PHY-optimised CSMA/CA based MACs.

• These are contributions which we found very interesting but have no time to dwell on:

– El Fawal et al : tradeoff analysis of PHY-aware UWB MAC [80];

– Larsson: selection diversity including fading and capture effects [81];

– Shea et al : design and study of cooperative-diversity slotted ALOHA [82];

181

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– MAC in Short –

• The Medium Access Control (MAC) is responsible for scheduling data of users contesting for the

same medium in a suitable way. For a MAC protocol, the figures of interest are data throughput

and delay.

• Optimum MAC mechanisms for centralised and decentralised wired and wireless systems are

very different! We will focus on decentralised wireless relaying MAC protocols which have

successfully been deployed in mobile ad-hoc networks (MANETs).

• Due to the absence of central control and synchronization in MANETs, Carrier Sense multiple

Access with Collision Avoidance (CSMA/CA) is a highly efficient random access scheme that is

widely used in wireless communication systems, such as wireless LAN.

• The most widespread deployed wireless protocol is the IEEE 802.11b MAC that has gained an

increased commercial popularity in recent years. The IEEE 802.11b MAC layer is implemented

using a Distributed Coordination Function (DCF) based on the CSMA/CA scheme.

182

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– MAC is Centre of Gravity! –

The MAC decides upon:

• transmit power levels → error rates, interference behaviour

• frame lengths → throughput, interference behaviour

• scheduling timings → delay, interference behaviour

• IP packet ’buffering’ → QoS

CSMA-type MAC

(conventional)

Reservation-type MAC

(distr. & coop.)

Control Signalling

Data Traffic

synchr/hop reserv/etc. not useful

bursty data ‘regularized’ data

Hybrid

MAC

?

?

183

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�

�

CSMA-TypePHY/MAC OPTIMIZATION

184

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�

�

– Approach for CSMA-type MAC (1/3) –

We are interested in a general mathematical framework which quantifies:

• throughput (for bursty data)

• delay (for signalling and bursty data)

in dependency of

• node density, distribution & traffic

• transmission & interference radii

• pathloss/shadowing/fading models

which allows us to

• characterise performance of CSMA/4W-HS/SW-ARQ/etc protocols

• synthesise an optimum MAC

185

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�

�


Figure 49: Multi-hop CSMA/CA scenario with two different transmit power levels (coverage areas).

186

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�


1. A preliminary analysis yields

• true number of competing users

• average number of users being source, destination, or blocked

• probability of a user transmitting, receiving, or being blocked.

2. This is utilised in the throughput analysis to obtain

• the generated average useful & overhead relaying traffic

• the average useful user & network data throughput

3. This is also utilised in the delay analysis to obtain

• the time a useful & relaying packet has to wait before transmission

• the average delay for useful user & network data

187

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�

Excerpt from Analysis: Competing Users (1/2)During the transmission from user T to user R:

• Users in area A cannot receive but they can transmit (no. NT , prob. of tr. PT )

• Users in area C cannot transmit but they can receive (no. NR, prob. of re. PR)

• Users in area B can neither receive nor transmit (no. NB , prob. of bl. PB )

A CB

RT

Figure 50: Areas of coverage for the transmission T to R.

188

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�

�

Excerpt from Analysis: Competing Users (2/2)The average numbers of users in the respective areas can be obtained as

NT = πdR2t − NB (53)

NR = πdR2t − NB (54)

NB = 2dR2t

⎧⎨⎩cos−1

(x

2Rt

)−(

x

2Rt

)√1 −

(x

2Rt

)2⎫⎬⎭ (55)

where x = 128Rt/45π is the average distance between the transmitter and the receiver,

Rt is the transmission range and d the nodes density.

The respective probabilities of transmission, reception & blockage can be derived as

PT = (1 − PT )2NA(1 − 2PT )NB (56)

PR = PT (57)

PB = 1 − 2PT (58)

189

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�

�

– CSMA-type PHY/MAC Trade-Off –

low modulation index (BPSK) high modulation index (64QAM)

→ low error rate (low prob. of loss) → high error rate (high prob. of loss)

→ long packets (high prob. of collision) → short packets (low prob. of collision)

Can we capture this trade-off analytically?

190

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�

�

�

– CSMA-type PHY/MAC Optimisation (1/5) –

’1’: normalised packet length D: delay period

a: slot duration (=log2(M)/Nb) T : transmission period

p: persistency factor B: busy period

Pf : frame error probability I : idle period

D(1)

D(2)

D(1)

IT(1)

T(1)

T(2)

B(1)

B(2)

Busy Period Idle Period

a1 Sub-delayTransmission

Period

Figure 51: Time sequence of events for basic p−persistent CSMA/CA.

191

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�

�


The useful end-to-end network throughput can be derived as

S =1N

U

B + I(59)

where

• N is the average number of hops from source to destination;

• U is the average useful transmission time;

• B is the average busy time;

• I is the average idle time;

192

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�

�


• We can derive the average idle period I to be

I =a

1 − (1 − g)Mt(60)

• We can derive the average busy period B to be

B = E[D(1)] + (J − 1)E[D(2)] + J (1 + a) (61)

where the average number of busy sub-periods is given as

J =N

(1 − g)(1+1/a)(Mt−1)(62)

and

E[D(j)] =

⎧⎨⎩ d(1) j = 1

d(1 + 1/a) j = 2, 3, ...(63)

where

193

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�

�


d(X) =a

N − (1 − g)X(Mt−1)(64)

·∞∑

k=1

{N(1 − p)k − p

[(1 − p)k − (1 − g)k

p − g

]}

·{

(1 − p)k − p(1 − g)X

[(1 − p)k − (1 − g)k

p − g

]}Mt−1

− a(1 − g)X(Mt−1)

N − (1 − g)X(Mt−1)

∞∑k=1

[p(1 − g)k − g(1 − p)k

p − g

]Mt

• Similarly, we can derive the average useful period U to be

E[U (j)] =

⎧⎨⎩ u(1) j = 1

u(1 + 1/a) j = 2, 3, ...(65)

where

194

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�

�


u(X) =p · (1 − Pf )

N − (1 − g)X(Mt−1)

∞∑k=0

{(1 − p)k+1 (66)

−p(1 − g)X

[(1 − p)k+1 − (1 − g)k+1

p − g

]}Mt−2

·{(1 − g)k(1 − p)k[N(1 − g)X − 1]

+Mt

{(1 − p)k − (1 − g)X

[p(1 − p)k − g(1 − g)k

p − g

]}

·{

N(1 − p)k+1 − p

[(1 − p)k+1 − (1 − g)k+1

p − g

]}}

−Mtgp(1 − g)X(Mt−1)

N − (1 − g)X(Mt−1)

∞∑k=1

[p(1 − g)k+1 − g(1 − p)k+1

p − g

]Mt−1

·[(1 − g)k − (1 − p)k

p − g

]

195

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�

�

�

– CSMA-type PHY/MAC Performance (1/2) –

The absolute spectral throughput changes as well as the optimum modulation scheme and optimum

number of relaying hops:

no relaying (20m)

1-hop relaying (10m)

2-hop relaying (6.7m)

(a) Transmission Ranges

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

Transmission Range [m]

Sys

tem

Spe

ctra

l Effi

cien

cy [b

its/s

/Hz]

256−QAM

64−QAM

16−QAM

QPSK

BPSK

SNR = 30dB

(b) 2Tx, 2Rx, SNR=30dB

Figure 52: Spectral throughout; normalised transmission length ’20’ means no relaying, ’10’ one hop,

’6.7’ two hops, ’5’ three hops, etc.

196

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�

– CSMA-type PHY/MAC Performance (2/2) –

The absolute spectral throughput changes as well as the optimum modulation scheme and optimum

number of relaying hops:

no relaying (20m)

1-hop relaying (10m)

2-hop relaying (6.7m)

(a) Transmission Ranges

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

1.2

1.4

Transmission Range [m]

Sys

tem

Spe

ctra

l Effi

cien

cy [b

its/s

/Hz]

64−QAM

16−QAM 256−QAM

QPSK

BPSK

SNR=20dB

(b) 2Tx, 2Rx, SNR=20dB

Figure 53: Spectral throughout; normalised transmission length ’20’ means no relaying, ’10’ one hop,

’6.7’ two hops, ’5’ three hops, etc.

197

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�

Open Issues

198

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�

�

– Open Issues –

The design and analysis of suitable cooperative MAC protocols is still in its infancy. We

believe that these are some interesting open issues:

• For existing MAC protocols, analysis of

– throughput & delay for finite user populations,

– throughput & delay for realistic queuing models,

– throughput & delay for cooperative systems,

• Design of optimum MAC incorporating

– x-layer optimised PHY and network layer design,

– cooperative links in an explicit way.

199

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PART 8CONCLUSIONS & ROAD AHEAD

200

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�

– Some Thoughts –

• Capacity and algorithmic PHY layer designs are fairly well explored; despite numerous

unsolved problems, novel contributions are likely to be incremental.

• RF, MAC and cross-layer design are areas which are still in its infancy; there is hence a

lot of room for innovative contributions.

• What we need today in these type of networks are entirely novel approaches for system

analysis, such as

– approaches known from physics (macroscopic wave propagation),

– approaches known from biology (emergent behaviour), etc.

• Commercial sensor and ad hoc network products are needed if cooperative systems do

not want to fall for the same fate as traditional ad hoc networks, which have been

researched for several decades without any tangible product on the civil market today.

201

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REFERENCES

202

REFERENCES�

�

�

�

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