# Real-Time Communications in Large-Scale Wireless Networks

Authors: Liang Song; Dimitrios Hatzinakos
Journal: International Journal of Digital Multimedia Broadcasting
 (2008)

---

## Abstract

There is an emerging need for realizing real-time quality of service (QoS) over multihop wireless communications in large-scale wireless networks. The applications can include wireless mesh infrastructure for broadband Internet access supporting multimedia services, visual sensor networks for surveillance, and disaster-relief networks. However, a number of challenges still exist as revealed by recent works, where the dataflow QoS performance such as throughput and end-to-end delay can degrade fast with the number of wireless hops. We propose to use large-scale cognitive networking methods
to resolve the wireless multihop challenges. By the cognitive-networking concept, data packets travel along opportunistically
available paths in the network with opportunistically available spectrum in every hop. Reliable end-to-end communications
can be achieved for real-time services, where we show that (1) dataflow throughput can be independent of any number of
wireless hops, (2) end-to-end delay and delay variance increase linearly with the number of wireless hops, and (3) delay variance
decreases to zero with higher network density. These results are supported by analysis, simulations, and experiments.


---

## Body

## 1. Introduction

Large-scale
wireless networks, for example, mobile ad hoc networks, wireless mesh networks,
as well as wireless sensor networks, have been receiving significant attention
in the past few years. Recently, there has been growing interest in realizing
real-time quality of service (QoS) over multihop wireless transmissions in
large-scale wireless networks. For example, the driving commercial applications
include wireless mesh infrastructure for broadband Internet access [1], supporting Voice over
Internet Protocols (VoIP) or Multimedia over IP, and wireless sensor network
with real-time event detection/reporting, especially in video surveillance,
that is, visual sensor networks  [2].Compared to the classical many-to-one (starlike)
networks, such as cellular phone networks and WiFi- (IEEE 802.11) [3] enabled wireless local area
networks (WLANs), a wireless mesh-based infrastructure for broadband access has
the advantage of much lower capital and operational costs and can achieve
higher service coverage. As one example, municipal WiFi mesh networks are
rolling out in a number of major cities, providing wireless web surfing and
email services to general public. Considering the popularity of Internet voice
and video, further developments for supporting VoIP within the wireless mesh
infrastructure are highly demanded. On the other hand, visual sensor networks
appear to be one of the killer applications for wireless sensor networks, since
a lot of major cities have installed public-administrated surveillance cameras
for various purposes. As of now, those cameras are normally attached by cables.
By adopting wireless connections, there will be significant cost reduction in
the installation, which can enable much denser deployment. Moreover, related
applications also include the disaster-relief wireless networks, with ad hoc
formation, where the real-time information delivery can be of life and death
importance.However, many challenges still exist in realizing
real-time QoS over multihop wireless networks. It has been well known that
dataflow throughput, end-to-end delay, and delay jitter can degrade fast when
the number of wireless hops increases [4, 5]. The limitation can be primarily introduced by dynamic
network-resource availabilities including both spectrum bandwidth and wireless
nodes/radios. Specifically, random spectrum availability is based on wireless
fading and interferences prevailing in unlicensed bands (e.g., ISM bands); and
random radio availability is due to dynamic traffic load (congestions) and
other factors such as radio failure. In traditional wireless networking, the
media access control (MAC) layer sets up “logic wired links” over
wireless media, which assume predetermined spectrum availability. On top of it,
the network layer runs ad hoc routing protocols which assume predetermined
radio availability and network topology. It is difficult to have effective QoS
models in the traditional network protocol stack  [6], when both spectrum
bandwidth and radio availabilities cannot be predetermined in large-scale
wireless networks.In order to resolve the wireless multihop limitation,
there have been proposals to install multiple radios in one single wireless
node [4] and design
network routing protocols based on wireless link status, as well as other
combined metrics [5].
Although evidence shows that improvements could be obtained, these approaches
do not address real-time QoS.  Moreover, existing approaches can generally
suffer from the lack of scalability. Typically, the complexity of existing
protocols can grow fast with the number of wireless nodes neighboring each
other (higher network density), since there are a large number of links to be
managed and/or tracked on every node. Other research work that investigates
real-time QoS in wireless networks could be based on inappropriate assumptions
for large-scale wireless networks, such as the assumption on fixed link
bandwidth [7].In this paper, we apply the methods of large-scale
cognitive networking [8]
to resolve the wireless multihop limitation. The concept of cognitive
networking opportunistically utilizes network resources including both spectrum
bandwidth and wireless node/radio availability to realize reliable
communications in large-scale wireless networks. The adopted network
architecture is the Embedded Wireless Interconnect (EWI) [8–11], where wireless linkage is
redefined introducing abstract wireless links. By definition, abstract
wireless links can be arbitrary functional abstractions of mutual cooperations
among proximity wireless nodes, where the categories can include broadcast,
unicast, multicast/anycast, and data aggregation, among others. Therefore, wireless
link modules are designed as the units for realizing different abstract
wireless links at individual wireless nodes. The architecture of EWI is then
developed upon two layers, where the bottom wireless link layer supplies a
library of wireless link modules; and the upper system layer can organize the
modules for achieving effective application programming interface (API).Conforming to the cognitive networking concept, both
the operating spectrum and the participating nodes of an abstract wireless link
is opportunistically decided based on their instantaneous availabilities. By
the unicast module design in the cognitive networking, data packets can take
opportunistically available paths in the network from source to destination,
with opportunistically available spectrum in every hop. In comparison, dynamic
changes in spectrum and radio availability can create bottlenecks on the
routing path of traditional wireless networking, where such bottlenecks are all
resolved by the proposed methods. Therefore, reliable end-to-end communications
can be achieved, by the opportunistic utilization of network resources. The
presented unicast module design is also implemented by cognitive-radio
prototyping [12]. In
the performance analysis, real-time QoS metrics including throughput, expected
end-to-end delay, and delay variance, are studied. The following propositions
are obtained.(i)
All the investigated real-time QoS metrics
improve with larger network scale, and the complexity on individual
nodes remains constant independent of any network scale. It is also shown that
the performance dynamics, as indicated by end-to-end delay variance, can
diminish to zero with higher network density.(ii)
Reliable communications can be achieved over a
large number of wireless hops. In principle, the throughput can be independent
of the source-to-destination distance; while the expected end-to-end delay, and
the delay variance, increase linearly with the source-to-destination distance.(iii)
Considering the resource constraints, such as
energy consumption or network capacity, we identify that radio transmitting
power can be an effective control knob for traffic prioritization in dealing
with the tradeoff between achievable QoS performance and resource consumptions.Therefore, the two major contributions of the paper
are the following: (1) the first design & implementation of real-time
communications for large-scale wireless networks; (2) the QoS performance
analysis of the designed real-time unicast module. In what follows, related
works are surveyed in Section2; the unicast wireless link module design and
implementation are described in Section 3; the performance analysis of
real-time QoS metrics is presented in Section 4; the simulation and experiment
results are reported in Section 5 and 6, respectively; the conclusion is given
in Section 7.


## 2. Related Work

Related works in cognitive networking and the EWI
network architecture have previously appeared in [1, 8–12].  As a pilot architectural reference model, EWI was
first introduced in the application-specific studies in wireless sensor
networks [10, 11]. In [9], recent research works in
the cross-layer design of wireless sensor networks are surveyed, where it is
suggested that EWI can be an unified design architecture. The concept of
large-scale cognitive wireless networks has been presented in [8], where EWI was adopted as the network architecture. In
[1, 12], the EWI is further
utilized to construct a ubiquitous wireless mesh infrastructure for broadband
Internet access.The unicast design can also be related to existing
research works in opportunistic routing [13–17]. In principle,
opportunistic routing schemes deal with the codesign of routing and MAC
protocols. However, previous research works usually deal with single-hop
performance metrics, while the contribution of this paper deals with end-to-end
QoS for real-time communications. Moreover, contributions are made in
large-scale cognitive networking, with a report of experiment results.In [13], the protocol selects the next hop relay node by a
slotted ACK (acknowledge) mechanism. Having successfully received a data
packet, the node calculates a priority level, which is inversely proportional
to the distance between the node and the packet destination. The node with the
highest priority is then selected distributively as the next hop relay node. In
[14, 15], a technique named GeRaF
was proposed, where the node forwarding region is divided into smaller sections
with different priorities, as decided by the forwarding distances. The
performance analysis of GeRaF included the single-hop energy consumption and
latency tradeoff, as well as the multihop count number. The study in [16] investigated the
architectural aspects of opportunistic routing, where the performance of the
component design is analyzed based on single-hop metrics and light-traffic
scenario. In [17], the
authors discussed the opportunistic relay node selection in a two-hop
transmission scenario. The relay-node priority criterion is based on the gain
of source-to-relay channels and relay-to-destination channels.


## 3. Module Design and Implementation

A unicast wireless link is an abstraction of the
proximity wireless nodes cooperation for unicasting. Since unicasting usually
involves the information delivery from source to destination over multiple
hops, the unicast module design decouples the end-to-end network behavior into
proximity wireless nodes cooperation. In the following, some elements of the module
design and implementation are presented. The module state-diagram is then
shown.


### 3.1. Network Address

Network address is related to the context, subject to
a “cost of delivery” criteria. Letd and s denote the network addresses of the
destination node and the source node, respectively. Given the destination d of a data packet at one wireless node n,
a local parameter cn,d is assumed obtainable, which indicates the
approximate or average cost of delivering the packet to the destination from
the node n independent of dynamic changes. In large-scale
wireless networks, the cost of delivery cn,d is usually a function of the distance from one
local node n to the destination d.In location-centric networks (e.g., [10]), where wireless nodes are
aware of their own locations, for example, by global position systems (GPS) or
triangulation estimations, the network address of one node n is solely decided by the node n location coordinates Ln.
Given the destination coordinates Ld of a packet, cn,d=|Ln−Ld| can be readily calculated in geometry, defined
as the specific distance.In data-centric networks (e.g., [18]), the network address can
be decided by the application specific data. The cost of delivery cn,d is the application data gradient, which can be
assumed as a monotonically increasing function of the distance between n and d.In a data-collecting or fusion network, for example,
wireless sensor networks, the sink (data collector) can broadcast a number of
identity advertisement packets, which is thereon flooded in the network, by
broadcasting. Every node can count the average smallest number of hops from the
sink, on receiving the advertisement packets. The count number can be used ascn,d for one node n.
A similar approach appeared in [19] yet in a more general scenario, where the logic
address, that is, a vector of the estimated distance or hop number to a group
of anchors, is maintained for every wireless node. New nodes joining in the
network can estimate their own logic address by acquiring the address of
neighboring nodes.Although other types of address can be applicable, we
use the location address in this paper for analysis, simulations, and
experiments.


### 3.2. Radio Implementation

The terminology of cognitive radio was first suggested
in [20] as an
ideal-omnipotent radio which can take all the parameters into consideration for
user-centric communications. Cognitive radio was later reviewed in [21, 22] as the radio with dynamic
spectrum access. In [8], two propositions are further suggested for the
cognitive radio for large-scale wireless networks.(i)
The radio can opportunistically sense the
spectrum
resource, so that the selected spectrum usage will not be interfering with
other on-going wireless communications.(ii)
The radio can opportunistically poll one or
more other proximity radios onto the selected spectrum, so as to realize
certain types of local cooperations.The above two propositions can extend the concept of
pure cognitive radio to cognitive networks, which implement both dynamic
spectrum access and dynamic radio access. In the network architecture EWI, a
wireless node can initiate an abstract wireless link, that is, certain types of
local cooperations among a number of proximity wireless nodes. Hence, both the
set of wireless nodes and the operating spectrum are opportunistically decided
for an abstract wireless link. Further, the initiated link will not be
interfering with other wireless communications, in accordance with the first
cognitive proposition.In the test-bed development of the paper, we
prototyped an experimental tone-based cognitive radio [8, 12]. Specifically, the radio
can access a group of predetermined data channels, where every data channel is
also associated with two distinctive frequency tones, that is, one sensing tone
and one polling tone. The sensing and polling tones are at distinctive
frequency different from the data channel. The radio hardware is therefore
composed of two transceivers, which are the tone transceiver and the data
transceiver, respectively. On initiating an abstract wireless link, the radio
senses for an available channel, with the vacant data channel and the vacant
sensing/polling tones. It then broadcasts the polling tone associated to the
selected channel, to poll its surrounding nodes. On detecting the rising edge
of the polling tone, the surrounding nodes can decide to join in the initiated
abstract wireless link based on their autonomous availability. On joining in an
abstract wireless link, the radio of the surrounding nodes also broadcasts the
sensing tone. As such, both sensing and polling tones protect wireless link
modules from spectrum interferences. We note that the use of frequency (busy)
tones has also appeared in numerous works of MAC protocols [23, 24]. However, here we have the first implementation over
multiple channels, and such implementation is in the context of large-scale
cognitive wireless networks.The unicast wireless link module is programmed on the
cognitive radio prototype (shown in Figure1). The experiment hardware is a
stack of two radio boards (TELOSB [25]). The radio board is composed of one IEEE 802.15.4
[26] compatible
transceiver, Chipcon CC2420, one TI MSP430 Microcontroller, and the program interface.
The top radio board is utilized as the tone transceiver, while the bottom radio
board is utilized as the data transceiver. The two are wired up by the digital
interface shown in Figure 1. Three independent data channels in the 2.4 GHz
band are allotted to the radio platform, while the associated tones are also in
the band of 2.4 GHz. The unicast module is programmed in the firmware of TI
MSP430.Figure 1
Cognitive radio
prototype.


### 3.3. Packet Relaying Process

Under an initiated wireless link, the packet relaying
process picks one available relay node and sends the data information from the
source or a previous relay node to the new relay node.Four types of packets are used in the packet relaying
process, which are RTS, CTS, DATA, and ACK, respectively. RTS, CTS, and ACK are
control packets, while DATA is the data information unit. Let nodenp denote the relay node at the hop p,
the next hop relay node np+1  is found by the following procedure, which
incurs local wireless nodes cooperation in proximity, that is, a unicast
wireless link.First, the nodenp broadcasts a RTS, including the module type
(unicast), the destination address d,
and the self-address np.
Upon receiving the RTS at one node n,
if the condition cn,d<cnp,d is satisfied, the node n initializes a timer, with the timeout period
as Td(np,n,d). Td(np,n,d) is inversely proportional to cnp,d−cn,d,
which is determined by the specific physical radio technology, for
example,(1)Td(np,n,d)=C0cnp,d−cn,d+SIFS,where C0 is a constant, and n≠d.  SIFS is the smallest (minimal) inter frame space
(delay constant), which is composed of the module processing time and the
transceiver RX/TX switch time. In our current test-bed implementation, Td(np,n,d) is also slotted according to the minimal carrier-sensing
time. Note that the condition cn,d<cnp,d is enforced, so that the cost of delivery to
the destination is always descending which prevents any loop.The noden then backs off and monitors the data channel
for the period Td(np,n,d).
If the data channel is free during that period, the node n replies with a CTS, declaring itself as the
next hop relay node np+1.
Otherwise, the node n quits the unicast module. As such, the node
with the smallest cost cn,d should be elected as the next hop relay node np+1.
After having received the CTS, the node np transmits the DATA packet, and after receiving
the DATA packet, the node np+1 replies an ACK, completing the round of
relaying. In the case that more than one node send out their CTS
simultaneously, the transmissions will collide on some specific bits, for
example, the node address, where the CTS packets are different. Since this
collision can be detected by certain mechanism, such as cyclic redundancy check
(CRC), at np,
the node np can use an appended procedure to differentiate
one node as np+1,
either before or after the DATA transmission.The described mechanism is illustrated in Figure2. In
the last hop, the destination d is always assigned with the minimal delay,
that is, Td(np,d,d)=SIFS.Figure 2
Packet relaying
mechanism.


### 3.4. Module State Diagram

The state diagram of a single unicast module in the
wireless link layer is shown in Figure3, which can give a summary of the
implementation. The definitions of the states and the associated transferring
branches can be self-explainable, in accordance with previous descriptions.Figure 3
Wireless link
layer state diagram.The wireless link layer stays in the IDLE state, when
no module is involved. It can initiate a unicast module, for example, on
receiving the command from the system layer, so as to send certain amount of
information (i.e., contained in one DATA packet) to a specified destination. In
the IDLE state, the wireless link layer also monitors the set of polling tones,
which are associated to the predetermined group of data channels. On detecting
the rising edge of one polling tone, it sends one module request to the system
layer. Upon approval, the wireless link layer listens to the RTS packet on the
data channel, which is associated with the detected polling tone. Otherwise, it
goes back to the IDLE state. Furthermore, after having received one DATA
packet, the unicast module automatically relays it, if the current node is not
the destination.Table1 shows an example set of primitive functions on
the interface between the system layer and the wireless link layer, as related
to the unicast module. The parameter Priority in Table 1 can be used for
specifying the traffic class, which will be explored further in Section 4.5.3.Table 1
Exemplary
primitive functions related to the unicast module.
FunctionDescriptionDirectionSendUnicast(DA, DATA, Priority)Command of sending the unicast DATA to the
destination address DA;From system to wireless linkStatusUnicast(&Status)Return the command status of
sendUnicast (⋯), for example, Success or Fail;From wireless link to systemIndicateUnicast(SA, DATA, Priority)Indicate the received unicast DATA from the
source address SA;From wireless link to systemModuleRequest()Request for listening to the RTS, that is, defined
in the unicast module;From wireless link to systemModuleResponse(&Status)Return the request status of
moduleRequest(), that is, Permitted or Denied;From system to wireless linkGetState(&State)Get the current state.From system to wireless link


### 3.5. Discussion

By opportunistically dealing with network resources
including both spectrum bandwidth and radio availability, data packets take
opportunistically available paths with opportunistically available spectrum in
every hop. Since the unicast module operates opportunistically in proximity
wireless nodes, the end-to-end performance of real-time QoS, can be
statistically assured, adding up the sequential proximity operations. This
discussion can provide an intuitive explanation of the performance analysis
results in Section4.Specifically, random spectrum availability is handled
by the cognitive radio implementation, where a source or relay node tries to
find an available data channel for initiating the unicast wireless link.
Important aspects of random node/radio availability are as follows: the node
deployment, mobility, and traffic congestion. In general, it indicates that the
nodenp,
that is, the pth hop relay, would be uncertain about the
availability of the next hop relay node, before the RTS probing. The RTS/CTS
exchange in the module design opportunistically finds the next hop relay, in a
group of available candidates.In traditional computer networks, dynamic traffic load
is limited by network congestion control. The network layer drops overflowed
packets by queueing management, which is then detected by the transport layer.
Such methods have been known to incur problems in wireless networks [27]. By the real-time unicast module, the paradigm of the
classical “network queueing” could be transferred to “queueing in
network.”  In an individual relay node, a DATA packet is forwarded automatically
without lengthy buffering in one local queue. Sequential DATA packets nominally
take opportunistically decided paths from the source to the destination, which
are buffered in the network, instead of any predetermined nodes.Therefore, it can be intuitive to conceive that the
QoS performance metrics should improve with larger network scale, since the
network density contributes to the diversity (or more radio resource) that can
be opportunistically exploited. This agrees with other theoretical results, for
example, in [28],
where it is stated that summed network transport capacity should increase with
network scale, on the order of Θ(N),
where N is the number of nodes.Moreover, in the proposed method, any node does not
need to consider or know every other possible node as a candidate for the next
hop. In the formation of abstract wireless linkage, the participating nodes are
decided by their autonomous availability. The unicast module design also
assures that there would only be one RTS response in most cases by the
carrier-sensing mechanism. Therefore, the module complexity at individual nodes
remains constant, independent of the network scale.


## 3.1. Network Address

Network address is related to the context, subject to
a “cost of delivery” criteria. Letd and s denote the network addresses of the
destination node and the source node, respectively. Given the destination d of a data packet at one wireless node n,
a local parameter cn,d is assumed obtainable, which indicates the
approximate or average cost of delivering the packet to the destination from
the node n independent of dynamic changes. In large-scale
wireless networks, the cost of delivery cn,d is usually a function of the distance from one
local node n to the destination d.In location-centric networks (e.g., [10]), where wireless nodes are
aware of their own locations, for example, by global position systems (GPS) or
triangulation estimations, the network address of one node n is solely decided by the node n location coordinates Ln.
Given the destination coordinates Ld of a packet, cn,d=|Ln−Ld| can be readily calculated in geometry, defined
as the specific distance.In data-centric networks (e.g., [18]), the network address can
be decided by the application specific data. The cost of delivery cn,d is the application data gradient, which can be
assumed as a monotonically increasing function of the distance between n and d.In a data-collecting or fusion network, for example,
wireless sensor networks, the sink (data collector) can broadcast a number of
identity advertisement packets, which is thereon flooded in the network, by
broadcasting. Every node can count the average smallest number of hops from the
sink, on receiving the advertisement packets. The count number can be used ascn,d for one node n.
A similar approach appeared in [19] yet in a more general scenario, where the logic
address, that is, a vector of the estimated distance or hop number to a group
of anchors, is maintained for every wireless node. New nodes joining in the
network can estimate their own logic address by acquiring the address of
neighboring nodes.Although other types of address can be applicable, we
use the location address in this paper for analysis, simulations, and
experiments.


## 3.2. Radio Implementation

The terminology of cognitive radio was first suggested
in [20] as an
ideal-omnipotent radio which can take all the parameters into consideration for
user-centric communications. Cognitive radio was later reviewed in [21, 22] as the radio with dynamic
spectrum access. In [8], two propositions are further suggested for the
cognitive radio for large-scale wireless networks.(i)
The radio can opportunistically sense the
spectrum
resource, so that the selected spectrum usage will not be interfering with
other on-going wireless communications.(ii)
The radio can opportunistically poll one or
more other proximity radios onto the selected spectrum, so as to realize
certain types of local cooperations.The above two propositions can extend the concept of
pure cognitive radio to cognitive networks, which implement both dynamic
spectrum access and dynamic radio access. In the network architecture EWI, a
wireless node can initiate an abstract wireless link, that is, certain types of
local cooperations among a number of proximity wireless nodes. Hence, both the
set of wireless nodes and the operating spectrum are opportunistically decided
for an abstract wireless link. Further, the initiated link will not be
interfering with other wireless communications, in accordance with the first
cognitive proposition.In the test-bed development of the paper, we
prototyped an experimental tone-based cognitive radio [8, 12]. Specifically, the radio
can access a group of predetermined data channels, where every data channel is
also associated with two distinctive frequency tones, that is, one sensing tone
and one polling tone. The sensing and polling tones are at distinctive
frequency different from the data channel. The radio hardware is therefore
composed of two transceivers, which are the tone transceiver and the data
transceiver, respectively. On initiating an abstract wireless link, the radio
senses for an available channel, with the vacant data channel and the vacant
sensing/polling tones. It then broadcasts the polling tone associated to the
selected channel, to poll its surrounding nodes. On detecting the rising edge
of the polling tone, the surrounding nodes can decide to join in the initiated
abstract wireless link based on their autonomous availability. On joining in an
abstract wireless link, the radio of the surrounding nodes also broadcasts the
sensing tone. As such, both sensing and polling tones protect wireless link
modules from spectrum interferences. We note that the use of frequency (busy)
tones has also appeared in numerous works of MAC protocols [23, 24]. However, here we have the first implementation over
multiple channels, and such implementation is in the context of large-scale
cognitive wireless networks.The unicast wireless link module is programmed on the
cognitive radio prototype (shown in Figure1). The experiment hardware is a
stack of two radio boards (TELOSB [25]). The radio board is composed of one IEEE 802.15.4
[26] compatible
transceiver, Chipcon CC2420, one TI MSP430 Microcontroller, and the program interface.
The top radio board is utilized as the tone transceiver, while the bottom radio
board is utilized as the data transceiver. The two are wired up by the digital
interface shown in Figure 1. Three independent data channels in the 2.4 GHz
band are allotted to the radio platform, while the associated tones are also in
the band of 2.4 GHz. The unicast module is programmed in the firmware of TI
MSP430.Figure 1
Cognitive radio
prototype.


## 3.3. Packet Relaying Process

Under an initiated wireless link, the packet relaying
process picks one available relay node and sends the data information from the
source or a previous relay node to the new relay node.Four types of packets are used in the packet relaying
process, which are RTS, CTS, DATA, and ACK, respectively. RTS, CTS, and ACK are
control packets, while DATA is the data information unit. Let nodenp denote the relay node at the hop p,
the next hop relay node np+1  is found by the following procedure, which
incurs local wireless nodes cooperation in proximity, that is, a unicast
wireless link.First, the nodenp broadcasts a RTS, including the module type
(unicast), the destination address d,
and the self-address np.
Upon receiving the RTS at one node n,
if the condition cn,d<cnp,d is satisfied, the node n initializes a timer, with the timeout period
as Td(np,n,d). Td(np,n,d) is inversely proportional to cnp,d−cn,d,
which is determined by the specific physical radio technology, for
example,(1)Td(np,n,d)=C0cnp,d−cn,d+SIFS,where C0 is a constant, and n≠d.  SIFS is the smallest (minimal) inter frame space
(delay constant), which is composed of the module processing time and the
transceiver RX/TX switch time. In our current test-bed implementation, Td(np,n,d) is also slotted according to the minimal carrier-sensing
time. Note that the condition cn,d<cnp,d is enforced, so that the cost of delivery to
the destination is always descending which prevents any loop.The noden then backs off and monitors the data channel
for the period Td(np,n,d).
If the data channel is free during that period, the node n replies with a CTS, declaring itself as the
next hop relay node np+1.
Otherwise, the node n quits the unicast module. As such, the node
with the smallest cost cn,d should be elected as the next hop relay node np+1.
After having received the CTS, the node np transmits the DATA packet, and after receiving
the DATA packet, the node np+1 replies an ACK, completing the round of
relaying. In the case that more than one node send out their CTS
simultaneously, the transmissions will collide on some specific bits, for
example, the node address, where the CTS packets are different. Since this
collision can be detected by certain mechanism, such as cyclic redundancy check
(CRC), at np,
the node np can use an appended procedure to differentiate
one node as np+1,
either before or after the DATA transmission.The described mechanism is illustrated in Figure2. In
the last hop, the destination d is always assigned with the minimal delay,
that is, Td(np,d,d)=SIFS.Figure 2
Packet relaying
mechanism.


## 3.4. Module State Diagram

The state diagram of a single unicast module in the
wireless link layer is shown in Figure3, which can give a summary of the
implementation. The definitions of the states and the associated transferring
branches can be self-explainable, in accordance with previous descriptions.Figure 3
Wireless link
layer state diagram.The wireless link layer stays in the IDLE state, when
no module is involved. It can initiate a unicast module, for example, on
receiving the command from the system layer, so as to send certain amount of
information (i.e., contained in one DATA packet) to a specified destination. In
the IDLE state, the wireless link layer also monitors the set of polling tones,
which are associated to the predetermined group of data channels. On detecting
the rising edge of one polling tone, it sends one module request to the system
layer. Upon approval, the wireless link layer listens to the RTS packet on the
data channel, which is associated with the detected polling tone. Otherwise, it
goes back to the IDLE state. Furthermore, after having received one DATA
packet, the unicast module automatically relays it, if the current node is not
the destination.Table1 shows an example set of primitive functions on
the interface between the system layer and the wireless link layer, as related
to the unicast module. The parameter Priority in Table 1 can be used for
specifying the traffic class, which will be explored further in Section 4.5.3.Table 1
Exemplary
primitive functions related to the unicast module.
FunctionDescriptionDirectionSendUnicast(DA, DATA, Priority)Command of sending the unicast DATA to the
destination address DA;From system to wireless linkStatusUnicast(&Status)Return the command status of
sendUnicast (⋯), for example, Success or Fail;From wireless link to systemIndicateUnicast(SA, DATA, Priority)Indicate the received unicast DATA from the
source address SA;From wireless link to systemModuleRequest()Request for listening to the RTS, that is, defined
in the unicast module;From wireless link to systemModuleResponse(&Status)Return the request status of
moduleRequest(), that is, Permitted or Denied;From system to wireless linkGetState(&State)Get the current state.From system to wireless link


## 3.5. Discussion

By opportunistically dealing with network resources
including both spectrum bandwidth and radio availability, data packets take
opportunistically available paths with opportunistically available spectrum in
every hop. Since the unicast module operates opportunistically in proximity
wireless nodes, the end-to-end performance of real-time QoS, can be
statistically assured, adding up the sequential proximity operations. This
discussion can provide an intuitive explanation of the performance analysis
results in Section4.Specifically, random spectrum availability is handled
by the cognitive radio implementation, where a source or relay node tries to
find an available data channel for initiating the unicast wireless link.
Important aspects of random node/radio availability are as follows: the node
deployment, mobility, and traffic congestion. In general, it indicates that the
nodenp,
that is, the pth hop relay, would be uncertain about the
availability of the next hop relay node, before the RTS probing. The RTS/CTS
exchange in the module design opportunistically finds the next hop relay, in a
group of available candidates.In traditional computer networks, dynamic traffic load
is limited by network congestion control. The network layer drops overflowed
packets by queueing management, which is then detected by the transport layer.
Such methods have been known to incur problems in wireless networks [27]. By the real-time unicast module, the paradigm of the
classical “network queueing” could be transferred to “queueing in
network.”  In an individual relay node, a DATA packet is forwarded automatically
without lengthy buffering in one local queue. Sequential DATA packets nominally
take opportunistically decided paths from the source to the destination, which
are buffered in the network, instead of any predetermined nodes.Therefore, it can be intuitive to conceive that the
QoS performance metrics should improve with larger network scale, since the
network density contributes to the diversity (or more radio resource) that can
be opportunistically exploited. This agrees with other theoretical results, for
example, in [28],
where it is stated that summed network transport capacity should increase with
network scale, on the order of Θ(N),
where N is the number of nodes.Moreover, in the proposed method, any node does not
need to consider or know every other possible node as a candidate for the next
hop. In the formation of abstract wireless linkage, the participating nodes are
decided by their autonomous availability. The unicast module design also
assures that there would only be one RTS response in most cases by the
carrier-sensing mechanism. Therefore, the module complexity at individual nodes
remains constant, independent of the network scale.


## 4. Performance Analysis of Real-Time QoS

The performance analysis mathematically quantifies the
major propositions in the paper. The results can also provide useful network
planning guidance for deployments.


### 4.1. Objectives and Approaches

In supporting real-time QoS, the metrics of
throughput, expected end-to-end delay, and delay variance, are studied for the
unicast wireless link module. Two types of resource consumptions are
considered, which are network capacity and network energy consumption.
Therefore, we centrally explore the following three questions. (1) How do the
QoS metrics change with network scale? (2) How do the QoS metrics change with
the source-to-destination distance? (3) How to control the resource allocation,
so as to achieve the QoS requirements?Given the sources and the destination d of a unicast dataflow, let l=|Ls−Ld| denote the source-to-destination distance.
Analytical results are obtained under the asymptotic condition of long-range
unicasting, l→∞,
where the justification can be that long-range unicasting presents the
worst-case scenario of the network performance under practical interests. On
the other hand, concise analytical formulation of the QoS metrics can be
obtained under this long-range asymptotic condition, which can provide
analytical insights to previous questions.


### 4.2. Analytical Models

In the performance analysis, models about node
distribution, wireless channel, power consumption, bandwidth availability, and
the IDLE probability are adopted.


#### 4.2.1. Node Distribution Model

The node distribution is modeled as a two-dimensional
(2D) Poisson process [29], with the node density λ.
That is, given an area A of the size |A| in the field, the number of nodes in the area
follows Poisson distribution with the parameter λ|A|.
The Poisson modeling can be typical for random node distribution and/or random
mobility.


#### 4.2.2. Wireless Channel Model

Given an arbitrary transmitting noden,
and a receiving node m,
the successful transmission probability, in general, is a function of the
transmitting power Pt,
the radio data rate R,
and the distance ζ=|Lm−Ln|.
We denote this function as f(Pt,R,ζ).For example, if small-scale Rayleigh fading [30] is assumed, the channel
model can be given by(2)f(Pt,R,ζ)=Prob(Pt⋅G⋅ξN0⋅R⋅ζα≥B)=e−(N0⋅R⋅ζα⋅B)/(Pt⋅G).In (2), G is a propagation-loss constant; N0 is the receiver-noise power spectrum density; α is the path loss component in wireless channel
[30]; B is a threshold constant representing the
receiver sensitivity; and ξ is a unit-mean exponential random variable.
This model will also be utilized to obtain the numerical results in Section 5.


#### 4.2.3. Power Consumption Model

Referring to the state diagram in Figure3, the node
power consumption at the IDLE state is denoted by PI,
that is, the low-power monitoring of the polling tones; the power consumption
at the states of  “Send DATA”, “Send RTS”,  “Send CTS”, and
“Send ACK”, is modeled by(3)PS+(1+β)⋅Pt,where PS is the transmitter circuits power consumption; β is a constant decided by the RF power
amplifier efficiency  [31];
and Pt is the transmitting power as defined
perviously. The node power consumption in other states or time is modeled by a
constant PR,
which denotes the receiving (or idle listening) power consumption.


#### 4.2.4. Bandwidth Availability and the IDLE Probability

When initiating a unicast module, we assume that the
node can always find an available channel by the cognitive radio without
significant delay. The IDLE probability is the probability that a given node is
in the IDLE state (shown in Figure3), and can be engaged in a unicast wireless
link being initiated by other nodes around it. We assume that there is a fixed
(or lower bounded) IDLE probability “ρ”,  in the analysis.With limited network capacity and arbitrary traffic
load, these two assumptions need to be ensured by an appropriate call admission
control (CAC) mechanism. On the other hand, given analogous experiences of the
popular video streaming on peer-to-peer overlay networks, it could also be
appropriate to assume no CAC mechanism, while the traffic volume demanding can
always fall below the planned (or unplanned) network capacity. In large-scale
wireless networks, the capacity could be of relatively cheap resources, given abundant
wireless nodes and the use of unlicensed band, while the traffic load is not
necessarily related to the number of wireless nodes. These considerations give
the optimization formulations under different types of resource consumptions in
Section4.5.


#### 4.2.5. Other Parameters and Notations

The packet lengths (bit) of RTS, CTS, DATA, and ACK
are denoted byLR, LC, LD,
and LA,
respectively. TS denotes the time delay in the “channel
sensing” state in Figure 3, and TB denotes the time delay in the “Backoff  Td” state. We also use the notations E(⋅) and σ2(⋅) to denote the mean and the variance of a
random variable.


### 4.3. Iterative Performance Analysis

“Iterative performance” can be similar to
“single-hop performance.” However, with the notation of “iterative
performance,”  we also consider the scenario where the next hop relay node
is not found in the transferring branch from “Send RTS” to “channel
sensing” of Figure3. The reason resides in the random node availability,
for example, no potential relay candidate is in the IDLE states. Due to this
difference, the terminology “iteration” instead of “hop” is used in
the following analysis, and “iterative delay” indicates the time delay of
an iteration, whereas “iterative energy consumption” indicates the
network energy consumption in one iteration.Particularly, consider that there are totallyI iterations from the source s to the destination d.
Let {ni∣1≤i≤I} denote the revelent set of nodes, which
initiates the unicast wireless link. Obviously, there is n1=s,
and nI sends the DATA packet directly to the
destination d.
The iteration number I is therefore a random variable.


#### 4.3.1. Iterative Delay

Letτi denote the iterative delay at an iteration i. (Other possible models are also discussed in
Appendix C, which contribute to the same end-to-end performance analysis
results.) If the DATA transmission is
completed in the iteration, τi can be calculated by the formula   (LR+LC+LD+LA)/R+TS+TB.
Otherwise, if the DATA transmission is uncompleted since no relay is found, τi can be given by  LR/R+TS+TB.
Obviously, for the last iteration (i=I), the DATA transmission is completed.Wheni<I,
the probability of uncompleted DATA transmission depends on the relay
candidates availability on the forwarding plane. Due to the Poisson node
distribution model with the density λ,
and the node IDLE probability ρ,
the distribution of relay candidates conforms to an inhomogeneous Poisson
process with the density function λ⋅ρ⋅f(Pt,R,ζ) on the forwarding plane, where ζ indicates the distance to the node ni.
Therefore, the “uncompleted” probability is decided by the
“equal-zero” probability of a Poisson random variable with the mean λ⋅ρ⋅Ω,
which is given by e−λρΩ. Ω is always positive, and is given by the
integration of the channel model f(⋅,⋅,⋅) on the forwarding plane:(4)Ω=∫0∞∫−∞∞f(Pt,R,x2+y2)dxdy.According to the above analysis,{τi∣1≤i<I} can be modeled as a set of random variables
with identical distributions, where the expectation E(τi) is(5)E(τi)=LRR+TS+TB+LC+LD+LAR⋅(1−e−λρΩ).


#### 4.3.2. Iterative Energy Consumption

Letϵi denote the iterative energy consumption at an
iteration   i. (Other possible models are also discussed in
Appendix C, which contribute to the same end-to-end performance analysis
results.)
If the DATA  transmission is not completed in the iteration, the
energy consumption of the node ni is (TS+TB)⋅PR+LR/R⋅[PS+(1+β)Pt],
according to the described models. The energy consumption of one relay
candidate is given by TS⋅PI+LR/R⋅PR.
The number of the relay candidates around ni,
which receive the RTS, is a Poisson random variable, with the mean value λ⋅ρ⋅Ω.
Here Ω can be still given by (4), but is integrated
on the backward plane, that is, ∫−∞0∫−∞∞f(Pt,R,x2+y2)dxdy,
instead of the forwarding plane. Therefore, the expected iterative energy
consumption under uncompleted DATA transmission is the summation: (TS+TB)⋅PR+LR/R⋅[PS+(1+β)Pt]+λ⋅ρ⋅Ω⋅(TS⋅PI+LR/R⋅PR).If the DATA transmission is completed in the
iteration, the energy consumption of the nodeni  is (TS+TB)⋅PR+(LR+LD)/R⋅[PS+(1+β)Pt]+(LC+LA)/R⋅PR.
The energy consumption of one relay candidate, which is not elected as the next
node ni+1,
is still TS⋅PI+LR/R⋅PR.
The number of the relay candidates is a Poisson random variable with the mean
value 2λ⋅ρ⋅Ω,
including both the forward and the backward planes. On the node ni+1,
the additional energy consumption is LD/R⋅PR+(LC+LA)/R⋅[PS+(1+β)Pt].
Therefore, the expected iterative network energy consumption under completed
DATA transmission is (TS+TB+(LC+LD+LA)/R)⋅PR+(LR+LC+LD+LA)/R⋅[PS+(1+β)Pt]+2λ⋅ρ⋅Ω⋅(TS⋅PI+LR/R⋅PR).Since the DATA transmission is always completed in the
last iteration,ϵI is directly obtained from the previous
discussion. When i<I,
similar to the previous analysis of τi,
the probability of uncompleted DATA transmission is decided by e−λρΩ.
Therefore, {ϵi∣1≤i<I} can be modeled as a set of random variables
with identical distributions, where the expectation E(ϵi) is(6)E(ϵi)=(TS+TB)⋅PR+LRR⋅[PS+(1+β)Pt]+λ⋅ρ⋅Ω⋅(TS⋅PI+LRR⋅PR)+(1−e−λρΩ)⋅{LC+LD+LAR⋅[PR+PS+(1+β)Pt]+λ⋅ρ⋅Ω⋅(TS⋅PI+LRR⋅PR)}.


#### 4.3.3. Number of Iterations

Given all the parameters, the total iteration numberI is a random variable decided by the
source-to-destination distance l.
It is shown in Appendix A that the mean value E(I) and the variance σ2(I) are(7)E(I)=lE(Λ)+o(l),(8)σ2(I)=l⋅σ2(Λ)E(Λ)3+o(l),respectively.In the above, the random variableΛ generally indicates the forwarding distance of
one single iteration. Λ is defined with the pdf (probability density
function) pΛ(x):(9)pΛ(x)={λρ⋅e−λρ∫x∞g(u)du⋅g(x),x>0,e−λρΩ⋅δ(0),x=0,0,x<0,where(10)g(u)=∫−∞∞f(Pt,R,u2+v2)dv.Proved in AppendixB, we point out that the
expectation E(Λ) is an increasing function of the node density λ,
but is upper bounded, as decided by the channel model f(⋅,⋅,⋅).
Furthermore, the variance σ2(Λ) decreases to zero with higher λ.
Given (7) and (8), both E(I) and σ2(I) can decrease with higher node density λ.
These relations can also be intuitively understood, which will be exploited for
interpreting the end-to-end performance analysis results next.


### 4.4. End-to-End Performance Analysis

Analytical results are presented for the maximal
throughputΦ,
the expected end-to-end delay ϒ,
the end-to-end delay variance Θ,
and the expected network energy consumption per DATA packet Ξ,
of a dataflow from the source s to the destination d,
under the long-range asymptotic condition l→∞.
The discussion shows how these metrics change with the source-to-destination
distance l,
as well as the network density λ.


#### 4.4.1. Throughput

The maximal throughputΦ is decided by how many DATA packets can be
sent out from the source s to the destination d in a period of time, subject to the condition
that this time period is much larger than the packet traveling time. According
to previous analysis in Section 4.3.1, the probability of the completed DATA
transmission in an iteration is 1−e−λρΩ.
Therefore, the expected number of iterations initiated by s for one DATA packet is  1/(1−e−λρΩ),
and the associated time expectation is (LR/R+TS+TB)/(1−e−λρΩ)+(LC+LD+LA)/R.Given the DATA packet lengthLD,
the maximal throughput is thus obtained as(11)Φ=LD⋅R(LR+(TS+TB)⋅R)/(1−e−λρΩ)+LC+LD+LA.It is shown that the maximal throughputΦ can be independent of the
source-to-destination distance l.
It also increases monotonically with the node density λ,
approaching the limit decided by the radio data rate R and the overhead ratio.


#### 4.4.2. Expected End-to-End Delay

The end-to-end delay is given by∑i=1Iτi.
The expected end-to-end delay ϒ is(12)ϒ=(a)E(∑i=1Iτi)=(b)[E(I)−1]⋅E(τ1)+τI=(c)l⋅LR+(TS+TB)⋅R+(LC+LD+LA)⋅(1−e−λρΩ)R⋅E(Λ)+o(l),where (a) is given by the
definition; (b) is due to the fact that {τi∣1≤i<I} are of identical probability distribution
[32]; and (c) is
obtained directly from (5) and (7).Therefore, the expected end-to-end delayϒ increases linearly with the
source-to-destination distance l.
It also decreases with the node density λ,
approaching a bounded limit.


#### 4.4.3. Delay Variance

LetIc denote the number of the iterations with
completed DATA transmission, that is, the number of wireless hops, and let Iu denote the number of the iterations with
uncompleted DATA transmission. Ic and Iu are independent random variables, and I=Ic+Iu.
The delay variance Θ is calculated by the
following:(13)Θ=(a)σ2(∑i=1Iτi)=(b)σ2(Ic)⋅(LR+LC+LD+LAR+TS+TB)2⁢+σ2(Iu)⋅(LRR+TS+TB)2=(c)σ2(Ic)⋅[(LC+LD+LAR)2+2⋅(TS+TB+LRR)⋅LC+LD+LAR]+σ2(I)⋅(LRR+TS+TB)2=(d)l⋅σ2(Λ)E(Λ)3⋅{(1−e−λρΩ)2⋅[(LC+LD+LAR)2+2⋅(TS+TB+LRR)⋅LC+LD+LAR]+(LRR+TS+TB)2}−l⋅e−λρΩ⋅1−e−λρΩE(Λ)⋅[(LC+LD+LAR)2+2⋅(TS+TB+LRR)⋅LC+LD+LAR]+o(l),where (a) is given by the
definition; (b) is due to the analysis in Section 4.3.1, that is, the iterative delay under completed and uncompleted
transmissions respectively; (c) is due to the fact that σ2(I)=σ2(Ic)+σ2(Iu);
(d) is obtained from the result of σ2(I) in (8), as well as the σ2(Ic) derived in (A.4) of Appendix A.Therefore, the end-to-end delay varianceΘ increases linearly with the
source-to-destination distance l. Θ also diminishes to zero with the network
density λ,
since the component σ2(Λ) also decreases to zero with higher λ.


#### 4.4.4. Network Energy Consumption

The expected
network energy consumption for one DATA packetΞ is(14)Ξ=(a)E(∑i=1Iϵi)=(b)[E(I)−1]⋅E(ϵ1)+ϵI=(c)l⋅E(ϵ1)E(Λ)+o(l),where (a) and (b) are given by
the definition and the fact that {ϵi∣1≤i<I} are of identical probability distributions
[32]; (c) is obtained
directly from (7), and the component ϵ1 can be replaced by the result in (6).
Therefore, Ξ also increases linearly with the
source-to-destination distance l.


### 4.5. Optimizations under QoS Constraints

Consider that the dataflow has certain QoS
requirements on throughput, expected end-to-end delay, and delay variance, for
example,Φ≥Φth, ϒ≤ϒth,
and Θ≤Θth.
Here, Φth, ϒth,
and Θth are the threshold constants representing those
QoS constraints, respectively. The optimizations aim to minimize the resource
consumption, subject to these QoS constraints.Two types of resource consumptions, including network
energy consumption and network capacity, are considered here, which lead to
different optimization formulations. As pointed out in Section4.2.4, these two formulations can be representing different networking
scenarios. In capacity limited networks, every node can have cabled power
supply. The number of nodes is therefore limited by engineering costs, and the
possible use of long-range radio also limits the available bandwidth. On the
other hand, in energy limited networks, the nodes can be powered by energy
scavenging, for example, solar cells. Therefore, the number of wireless nodes
can be large, which can also use short-range radio with vast unlicensed
bandwidth. These contribute to large network capacity. Other works with similar
considerations have been discussed in [33].


#### 4.5.1. Capacity Limited Networks

The objective of the optimization is to minimize the
transmitting powerPt,
so as to limit the occupied geographic area of an unicast link. In accordance
with the results in [28], this approach can save the use of wireless network
capacity. Therefore, the optimization formulation is(15)minPtsubjectto:Φ≥Φth;ϒ≤ϒth;Θ≤Θth.


#### 4.5.2. Energy Limited Networks

The objective of the optimization is to minimize the
expected network energy consumption per DATA packetΞ:(16)minΞsubjectto:Φ≥Φth;ϒ≤ϒth;Θ≤Θth.


#### 4.5.3. Solutions and Traffic Priority

In order to
solve the optimizations in (15) and (16), the transmitting power Pt can be an ideal control knob (optimization
variable), for the resource allocation. Both (15) and (16) can be found as
convex optimization problems over Pt,
where efficient solutions are guaranteed [34].Specifically, as shown in (11), Φ monotonically increases with Pt,
since Ω (defined in (4)) monotonically increases with Pt,
provided by any realistic channel model f(⋅,⋅,⋅).
As shown in (12), ϒ monotonically decreases with Pt,
since E(Λ) monotonically increases with Pt (proved in Appendix B).  Θ also monotonically decreases with Pt in (13), since σ2(Λ) monotonically decreases with Pt (proved in Appendix B). Moreover, as shown in
(14), Ξ can be verified as a convex function of Pt,
where both E(ϵ1) and E(Λ) monotonically increase with Pt.
Due to the described monotonicity, the convexity of the optimizations in (15)
and (16) can then be obtained, over the control knob Pt.Therefore, we suggest that the transmitting powerPt can provide an effective control knob for the
tradeoff  between the resource consumptions and the real-time QoS requirements.
In fact, different levels of Pt can be configured for different classes of
traffics, for example, voice, video (streaming), or data, which then decide the
unicasting “priority”.Further investigation may also include the radio data
rateR,
so as to generate the problem of joint power and rate control. Unfortunately,
the convexity over R cannot be obtained for a general channel
propagation model f(⋅,⋅,⋅).
Future studies may address the problem on some specific models.


### 4.6. Summary

In summary, the analytical results indicate that all
the investigated real-time QoS metrics can improve with larger network scale.
In particular, the maximal throughputΦ increases with the network density λ to a predetermined bound, while the expected
end-to-end delay ϒ decreases with λ,
approaching a predetermined bound, as decided by other related parameters. On
the other hand, the delay variance Θ falls to zero with higher network density λ,
which indicates that the network performance can be made arbitrarily stable,
simply by dropping more nodes in the network. For supporting long-range
communications over a relatively large number of wireless hops, the analytical
results show that the maximal throughput Φ can be independent of the
source-to-destination distance, while both the expected delay ϒ and the delay variance Θ increase linearly with the
source-to-destination distance. Furthermore, it is identified that the radio
transmitting power Pt can be an ideal control knob for the tradeoff
between the real-time QoS requirements and the resource consumptions, for
example, energy consumption or network capacity.We consider that all these propositions could be
intuitively conceivable for large-scale wireless networks. Since the analytical
results are obtained under the long-range asymptotic conditionl→∞,
they may present the worst-case scenario analysis for practical considerations.
In the next section, the simulation results are also provided, showing how
these metrics converge.


## 4.1. Objectives and Approaches

In supporting real-time QoS, the metrics of
throughput, expected end-to-end delay, and delay variance, are studied for the
unicast wireless link module. Two types of resource consumptions are
considered, which are network capacity and network energy consumption.
Therefore, we centrally explore the following three questions. (1) How do the
QoS metrics change with network scale? (2) How do the QoS metrics change with
the source-to-destination distance? (3) How to control the resource allocation,
so as to achieve the QoS requirements?Given the sources and the destination d of a unicast dataflow, let l=|Ls−Ld| denote the source-to-destination distance.
Analytical results are obtained under the asymptotic condition of long-range
unicasting, l→∞,
where the justification can be that long-range unicasting presents the
worst-case scenario of the network performance under practical interests. On
the other hand, concise analytical formulation of the QoS metrics can be
obtained under this long-range asymptotic condition, which can provide
analytical insights to previous questions.


## 4.2. Analytical Models

In the performance analysis, models about node
distribution, wireless channel, power consumption, bandwidth availability, and
the IDLE probability are adopted.


### 4.2.1. Node Distribution Model

The node distribution is modeled as a two-dimensional
(2D) Poisson process [29], with the node density λ.
That is, given an area A of the size |A| in the field, the number of nodes in the area
follows Poisson distribution with the parameter λ|A|.
The Poisson modeling can be typical for random node distribution and/or random
mobility.


### 4.2.2. Wireless Channel Model

Given an arbitrary transmitting noden,
and a receiving node m,
the successful transmission probability, in general, is a function of the
transmitting power Pt,
the radio data rate R,
and the distance ζ=|Lm−Ln|.
We denote this function as f(Pt,R,ζ).For example, if small-scale Rayleigh fading [30] is assumed, the channel
model can be given by(2)f(Pt,R,ζ)=Prob(Pt⋅G⋅ξN0⋅R⋅ζα≥B)=e−(N0⋅R⋅ζα⋅B)/(Pt⋅G).In (2), G is a propagation-loss constant; N0 is the receiver-noise power spectrum density; α is the path loss component in wireless channel
[30]; B is a threshold constant representing the
receiver sensitivity; and ξ is a unit-mean exponential random variable.
This model will also be utilized to obtain the numerical results in Section 5.


### 4.2.3. Power Consumption Model

Referring to the state diagram in Figure3, the node
power consumption at the IDLE state is denoted by PI,
that is, the low-power monitoring of the polling tones; the power consumption
at the states of  “Send DATA”, “Send RTS”,  “Send CTS”, and
“Send ACK”, is modeled by(3)PS+(1+β)⋅Pt,where PS is the transmitter circuits power consumption; β is a constant decided by the RF power
amplifier efficiency  [31];
and Pt is the transmitting power as defined
perviously. The node power consumption in other states or time is modeled by a
constant PR,
which denotes the receiving (or idle listening) power consumption.


### 4.2.4. Bandwidth Availability and the IDLE Probability

When initiating a unicast module, we assume that the
node can always find an available channel by the cognitive radio without
significant delay. The IDLE probability is the probability that a given node is
in the IDLE state (shown in Figure3), and can be engaged in a unicast wireless
link being initiated by other nodes around it. We assume that there is a fixed
(or lower bounded) IDLE probability “ρ”,  in the analysis.With limited network capacity and arbitrary traffic
load, these two assumptions need to be ensured by an appropriate call admission
control (CAC) mechanism. On the other hand, given analogous experiences of the
popular video streaming on peer-to-peer overlay networks, it could also be
appropriate to assume no CAC mechanism, while the traffic volume demanding can
always fall below the planned (or unplanned) network capacity. In large-scale
wireless networks, the capacity could be of relatively cheap resources, given abundant
wireless nodes and the use of unlicensed band, while the traffic load is not
necessarily related to the number of wireless nodes. These considerations give
the optimization formulations under different types of resource consumptions in
Section4.5.


### 4.2.5. Other Parameters and Notations

The packet lengths (bit) of RTS, CTS, DATA, and ACK
are denoted byLR, LC, LD,
and LA,
respectively. TS denotes the time delay in the “channel
sensing” state in Figure 3, and TB denotes the time delay in the “Backoff  Td” state. We also use the notations E(⋅) and σ2(⋅) to denote the mean and the variance of a
random variable.


## 4.2.1. Node Distribution Model

The node distribution is modeled as a two-dimensional
(2D) Poisson process [29], with the node density λ.
That is, given an area A of the size |A| in the field, the number of nodes in the area
follows Poisson distribution with the parameter λ|A|.
The Poisson modeling can be typical for random node distribution and/or random
mobility.


## 4.2.2. Wireless Channel Model

Given an arbitrary transmitting noden,
and a receiving node m,
the successful transmission probability, in general, is a function of the
transmitting power Pt,
the radio data rate R,
and the distance ζ=|Lm−Ln|.
We denote this function as f(Pt,R,ζ).For example, if small-scale Rayleigh fading [30] is assumed, the channel
model can be given by(2)f(Pt,R,ζ)=Prob(Pt⋅G⋅ξN0⋅R⋅ζα≥B)=e−(N0⋅R⋅ζα⋅B)/(Pt⋅G).In (2), G is a propagation-loss constant; N0 is the receiver-noise power spectrum density; α is the path loss component in wireless channel
[30]; B is a threshold constant representing the
receiver sensitivity; and ξ is a unit-mean exponential random variable.
This model will also be utilized to obtain the numerical results in Section 5.


## 4.2.3. Power Consumption Model

Referring to the state diagram in Figure3, the node
power consumption at the IDLE state is denoted by PI,
that is, the low-power monitoring of the polling tones; the power consumption
at the states of  “Send DATA”, “Send RTS”,  “Send CTS”, and
“Send ACK”, is modeled by(3)PS+(1+β)⋅Pt,where PS is the transmitter circuits power consumption; β is a constant decided by the RF power
amplifier efficiency  [31];
and Pt is the transmitting power as defined
perviously. The node power consumption in other states or time is modeled by a
constant PR,
which denotes the receiving (or idle listening) power consumption.


## 4.2.4. Bandwidth Availability and the IDLE Probability

When initiating a unicast module, we assume that the
node can always find an available channel by the cognitive radio without
significant delay. The IDLE probability is the probability that a given node is
in the IDLE state (shown in Figure3), and can be engaged in a unicast wireless
link being initiated by other nodes around it. We assume that there is a fixed
(or lower bounded) IDLE probability “ρ”,  in the analysis.With limited network capacity and arbitrary traffic
load, these two assumptions need to be ensured by an appropriate call admission
control (CAC) mechanism. On the other hand, given analogous experiences of the
popular video streaming on peer-to-peer overlay networks, it could also be
appropriate to assume no CAC mechanism, while the traffic volume demanding can
always fall below the planned (or unplanned) network capacity. In large-scale
wireless networks, the capacity could be of relatively cheap resources, given abundant
wireless nodes and the use of unlicensed band, while the traffic load is not
necessarily related to the number of wireless nodes. These considerations give
the optimization formulations under different types of resource consumptions in
Section4.5.


## 4.2.5. Other Parameters and Notations

The packet lengths (bit) of RTS, CTS, DATA, and ACK
are denoted byLR, LC, LD,
and LA,
respectively. TS denotes the time delay in the “channel
sensing” state in Figure 3, and TB denotes the time delay in the “Backoff  Td” state. We also use the notations E(⋅) and σ2(⋅) to denote the mean and the variance of a
random variable.


## 4.3. Iterative Performance Analysis

“Iterative performance” can be similar to
“single-hop performance.” However, with the notation of “iterative
performance,”  we also consider the scenario where the next hop relay node
is not found in the transferring branch from “Send RTS” to “channel
sensing” of Figure3. The reason resides in the random node availability,
for example, no potential relay candidate is in the IDLE states. Due to this
difference, the terminology “iteration” instead of “hop” is used in
the following analysis, and “iterative delay” indicates the time delay of
an iteration, whereas “iterative energy consumption” indicates the
network energy consumption in one iteration.Particularly, consider that there are totallyI iterations from the source s to the destination d.
Let {ni∣1≤i≤I} denote the revelent set of nodes, which
initiates the unicast wireless link. Obviously, there is n1=s,
and nI sends the DATA packet directly to the
destination d.
The iteration number I is therefore a random variable.


### 4.3.1. Iterative Delay

Letτi denote the iterative delay at an iteration i. (Other possible models are also discussed in
Appendix C, which contribute to the same end-to-end performance analysis
results.) If the DATA transmission is
completed in the iteration, τi can be calculated by the formula   (LR+LC+LD+LA)/R+TS+TB.
Otherwise, if the DATA transmission is uncompleted since no relay is found, τi can be given by  LR/R+TS+TB.
Obviously, for the last iteration (i=I), the DATA transmission is completed.Wheni<I,
the probability of uncompleted DATA transmission depends on the relay
candidates availability on the forwarding plane. Due to the Poisson node
distribution model with the density λ,
and the node IDLE probability ρ,
the distribution of relay candidates conforms to an inhomogeneous Poisson
process with the density function λ⋅ρ⋅f(Pt,R,ζ) on the forwarding plane, where ζ indicates the distance to the node ni.
Therefore, the “uncompleted” probability is decided by the
“equal-zero” probability of a Poisson random variable with the mean λ⋅ρ⋅Ω,
which is given by e−λρΩ. Ω is always positive, and is given by the
integration of the channel model f(⋅,⋅,⋅) on the forwarding plane:(4)Ω=∫0∞∫−∞∞f(Pt,R,x2+y2)dxdy.According to the above analysis,{τi∣1≤i<I} can be modeled as a set of random variables
with identical distributions, where the expectation E(τi) is(5)E(τi)=LRR+TS+TB+LC+LD+LAR⋅(1−e−λρΩ).


### 4.3.2. Iterative Energy Consumption

Letϵi denote the iterative energy consumption at an
iteration   i. (Other possible models are also discussed in
Appendix C, which contribute to the same end-to-end performance analysis
results.)
If the DATA  transmission is not completed in the iteration, the
energy consumption of the node ni is (TS+TB)⋅PR+LR/R⋅[PS+(1+β)Pt],
according to the described models. The energy consumption of one relay
candidate is given by TS⋅PI+LR/R⋅PR.
The number of the relay candidates around ni,
which receive the RTS, is a Poisson random variable, with the mean value λ⋅ρ⋅Ω.
Here Ω can be still given by (4), but is integrated
on the backward plane, that is, ∫−∞0∫−∞∞f(Pt,R,x2+y2)dxdy,
instead of the forwarding plane. Therefore, the expected iterative energy
consumption under uncompleted DATA transmission is the summation: (TS+TB)⋅PR+LR/R⋅[PS+(1+β)Pt]+λ⋅ρ⋅Ω⋅(TS⋅PI+LR/R⋅PR).If the DATA transmission is completed in the
iteration, the energy consumption of the nodeni  is (TS+TB)⋅PR+(LR+LD)/R⋅[PS+(1+β)Pt]+(LC+LA)/R⋅PR.
The energy consumption of one relay candidate, which is not elected as the next
node ni+1,
is still TS⋅PI+LR/R⋅PR.
The number of the relay candidates is a Poisson random variable with the mean
value 2λ⋅ρ⋅Ω,
including both the forward and the backward planes. On the node ni+1,
the additional energy consumption is LD/R⋅PR+(LC+LA)/R⋅[PS+(1+β)Pt].
Therefore, the expected iterative network energy consumption under completed
DATA transmission is (TS+TB+(LC+LD+LA)/R)⋅PR+(LR+LC+LD+LA)/R⋅[PS+(1+β)Pt]+2λ⋅ρ⋅Ω⋅(TS⋅PI+LR/R⋅PR).Since the DATA transmission is always completed in the
last iteration,ϵI is directly obtained from the previous
discussion. When i<I,
similar to the previous analysis of τi,
the probability of uncompleted DATA transmission is decided by e−λρΩ.
Therefore, {ϵi∣1≤i<I} can be modeled as a set of random variables
with identical distributions, where the expectation E(ϵi) is(6)E(ϵi)=(TS+TB)⋅PR+LRR⋅[PS+(1+β)Pt]+λ⋅ρ⋅Ω⋅(TS⋅PI+LRR⋅PR)+(1−e−λρΩ)⋅{LC+LD+LAR⋅[PR+PS+(1+β)Pt]+λ⋅ρ⋅Ω⋅(TS⋅PI+LRR⋅PR)}.


### 4.3.3. Number of Iterations

Given all the parameters, the total iteration numberI is a random variable decided by the
source-to-destination distance l.
It is shown in Appendix A that the mean value E(I) and the variance σ2(I) are(7)E(I)=lE(Λ)+o(l),(8)σ2(I)=l⋅σ2(Λ)E(Λ)3+o(l),respectively.In the above, the random variableΛ generally indicates the forwarding distance of
one single iteration. Λ is defined with the pdf (probability density
function) pΛ(x):(9)pΛ(x)={λρ⋅e−λρ∫x∞g(u)du⋅g(x),x>0,e−λρΩ⋅δ(0),x=0,0,x<0,where(10)g(u)=∫−∞∞f(Pt,R,u2+v2)dv.Proved in AppendixB, we point out that the
expectation E(Λ) is an increasing function of the node density λ,
but is upper bounded, as decided by the channel model f(⋅,⋅,⋅).
Furthermore, the variance σ2(Λ) decreases to zero with higher λ.
Given (7) and (8), both E(I) and σ2(I) can decrease with higher node density λ.
These relations can also be intuitively understood, which will be exploited for
interpreting the end-to-end performance analysis results next.


## 4.3.1. Iterative Delay

Letτi denote the iterative delay at an iteration i. (Other possible models are also discussed in
Appendix C, which contribute to the same end-to-end performance analysis
results.) If the DATA transmission is
completed in the iteration, τi can be calculated by the formula   (LR+LC+LD+LA)/R+TS+TB.
Otherwise, if the DATA transmission is uncompleted since no relay is found, τi can be given by  LR/R+TS+TB.
Obviously, for the last iteration (i=I), the DATA transmission is completed.Wheni<I,
the probability of uncompleted DATA transmission depends on the relay
candidates availability on the forwarding plane. Due to the Poisson node
distribution model with the density λ,
and the node IDLE probability ρ,
the distribution of relay candidates conforms to an inhomogeneous Poisson
process with the density function λ⋅ρ⋅f(Pt,R,ζ) on the forwarding plane, where ζ indicates the distance to the node ni.
Therefore, the “uncompleted” probability is decided by the
“equal-zero” probability of a Poisson random variable with the mean λ⋅ρ⋅Ω,
which is given by e−λρΩ. Ω is always positive, and is given by the
integration of the channel model f(⋅,⋅,⋅) on the forwarding plane:(4)Ω=∫0∞∫−∞∞f(Pt,R,x2+y2)dxdy.According to the above analysis,{τi∣1≤i<I} can be modeled as a set of random variables
with identical distributions, where the expectation E(τi) is(5)E(τi)=LRR+TS+TB+LC+LD+LAR⋅(1−e−λρΩ).


## 4.3.2. Iterative Energy Consumption

Letϵi denote the iterative energy consumption at an
iteration   i. (Other possible models are also discussed in
Appendix C, which contribute to the same end-to-end performance analysis
results.)
If the DATA  transmission is not completed in the iteration, the
energy consumption of the node ni is (TS+TB)⋅PR+LR/R⋅[PS+(1+β)Pt],
according to the described models. The energy consumption of one relay
candidate is given by TS⋅PI+LR/R⋅PR.
The number of the relay candidates around ni,
which receive the RTS, is a Poisson random variable, with the mean value λ⋅ρ⋅Ω.
Here Ω can be still given by (4), but is integrated
on the backward plane, that is, ∫−∞0∫−∞∞f(Pt,R,x2+y2)dxdy,
instead of the forwarding plane. Therefore, the expected iterative energy
consumption under uncompleted DATA transmission is the summation: (TS+TB)⋅PR+LR/R⋅[PS+(1+β)Pt]+λ⋅ρ⋅Ω⋅(TS⋅PI+LR/R⋅PR).If the DATA transmission is completed in the
iteration, the energy consumption of the nodeni  is (TS+TB)⋅PR+(LR+LD)/R⋅[PS+(1+β)Pt]+(LC+LA)/R⋅PR.
The energy consumption of one relay candidate, which is not elected as the next
node ni+1,
is still TS⋅PI+LR/R⋅PR.
The number of the relay candidates is a Poisson random variable with the mean
value 2λ⋅ρ⋅Ω,
including both the forward and the backward planes. On the node ni+1,
the additional energy consumption is LD/R⋅PR+(LC+LA)/R⋅[PS+(1+β)Pt].
Therefore, the expected iterative network energy consumption under completed
DATA transmission is (TS+TB+(LC+LD+LA)/R)⋅PR+(LR+LC+LD+LA)/R⋅[PS+(1+β)Pt]+2λ⋅ρ⋅Ω⋅(TS⋅PI+LR/R⋅PR).Since the DATA transmission is always completed in the
last iteration,ϵI is directly obtained from the previous
discussion. When i<I,
similar to the previous analysis of τi,
the probability of uncompleted DATA transmission is decided by e−λρΩ.
Therefore, {ϵi∣1≤i<I} can be modeled as a set of random variables
with identical distributions, where the expectation E(ϵi) is(6)E(ϵi)=(TS+TB)⋅PR+LRR⋅[PS+(1+β)Pt]+λ⋅ρ⋅Ω⋅(TS⋅PI+LRR⋅PR)+(1−e−λρΩ)⋅{LC+LD+LAR⋅[PR+PS+(1+β)Pt]+λ⋅ρ⋅Ω⋅(TS⋅PI+LRR⋅PR)}.


## 4.3.3. Number of Iterations

Given all the parameters, the total iteration numberI is a random variable decided by the
source-to-destination distance l.
It is shown in Appendix A that the mean value E(I) and the variance σ2(I) are(7)E(I)=lE(Λ)+o(l),(8)σ2(I)=l⋅σ2(Λ)E(Λ)3+o(l),respectively.In the above, the random variableΛ generally indicates the forwarding distance of
one single iteration. Λ is defined with the pdf (probability density
function) pΛ(x):(9)pΛ(x)={λρ⋅e−λρ∫x∞g(u)du⋅g(x),x>0,e−λρΩ⋅δ(0),x=0,0,x<0,where(10)g(u)=∫−∞∞f(Pt,R,u2+v2)dv.Proved in AppendixB, we point out that the
expectation E(Λ) is an increasing function of the node density λ,
but is upper bounded, as decided by the channel model f(⋅,⋅,⋅).
Furthermore, the variance σ2(Λ) decreases to zero with higher λ.
Given (7) and (8), both E(I) and σ2(I) can decrease with higher node density λ.
These relations can also be intuitively understood, which will be exploited for
interpreting the end-to-end performance analysis results next.


## 4.4. End-to-End Performance Analysis

Analytical results are presented for the maximal
throughputΦ,
the expected end-to-end delay ϒ,
the end-to-end delay variance Θ,
and the expected network energy consumption per DATA packet Ξ,
of a dataflow from the source s to the destination d,
under the long-range asymptotic condition l→∞.
The discussion shows how these metrics change with the source-to-destination
distance l,
as well as the network density λ.


### 4.4.1. Throughput

The maximal throughputΦ is decided by how many DATA packets can be
sent out from the source s to the destination d in a period of time, subject to the condition
that this time period is much larger than the packet traveling time. According
to previous analysis in Section 4.3.1, the probability of the completed DATA
transmission in an iteration is 1−e−λρΩ.
Therefore, the expected number of iterations initiated by s for one DATA packet is  1/(1−e−λρΩ),
and the associated time expectation is (LR/R+TS+TB)/(1−e−λρΩ)+(LC+LD+LA)/R.Given the DATA packet lengthLD,
the maximal throughput is thus obtained as(11)Φ=LD⋅R(LR+(TS+TB)⋅R)/(1−e−λρΩ)+LC+LD+LA.It is shown that the maximal throughputΦ can be independent of the
source-to-destination distance l.
It also increases monotonically with the node density λ,
approaching the limit decided by the radio data rate R and the overhead ratio.


### 4.4.2. Expected End-to-End Delay

The end-to-end delay is given by∑i=1Iτi.
The expected end-to-end delay ϒ is(12)ϒ=(a)E(∑i=1Iτi)=(b)[E(I)−1]⋅E(τ1)+τI=(c)l⋅LR+(TS+TB)⋅R+(LC+LD+LA)⋅(1−e−λρΩ)R⋅E(Λ)+o(l),where (a) is given by the
definition; (b) is due to the fact that {τi∣1≤i<I} are of identical probability distribution
[32]; and (c) is
obtained directly from (5) and (7).Therefore, the expected end-to-end delayϒ increases linearly with the
source-to-destination distance l.
It also decreases with the node density λ,
approaching a bounded limit.


### 4.4.3. Delay Variance

LetIc denote the number of the iterations with
completed DATA transmission, that is, the number of wireless hops, and let Iu denote the number of the iterations with
uncompleted DATA transmission. Ic and Iu are independent random variables, and I=Ic+Iu.
The delay variance Θ is calculated by the
following:(13)Θ=(a)σ2(∑i=1Iτi)=(b)σ2(Ic)⋅(LR+LC+LD+LAR+TS+TB)2⁢+σ2(Iu)⋅(LRR+TS+TB)2=(c)σ2(Ic)⋅[(LC+LD+LAR)2+2⋅(TS+TB+LRR)⋅LC+LD+LAR]+σ2(I)⋅(LRR+TS+TB)2=(d)l⋅σ2(Λ)E(Λ)3⋅{(1−e−λρΩ)2⋅[(LC+LD+LAR)2+2⋅(TS+TB+LRR)⋅LC+LD+LAR]+(LRR+TS+TB)2}−l⋅e−λρΩ⋅1−e−λρΩE(Λ)⋅[(LC+LD+LAR)2+2⋅(TS+TB+LRR)⋅LC+LD+LAR]+o(l),where (a) is given by the
definition; (b) is due to the analysis in Section 4.3.1, that is, the iterative delay under completed and uncompleted
transmissions respectively; (c) is due to the fact that σ2(I)=σ2(Ic)+σ2(Iu);
(d) is obtained from the result of σ2(I) in (8), as well as the σ2(Ic) derived in (A.4) of Appendix A.Therefore, the end-to-end delay varianceΘ increases linearly with the
source-to-destination distance l. Θ also diminishes to zero with the network
density λ,
since the component σ2(Λ) also decreases to zero with higher λ.


### 4.4.4. Network Energy Consumption

The expected
network energy consumption for one DATA packetΞ is(14)Ξ=(a)E(∑i=1Iϵi)=(b)[E(I)−1]⋅E(ϵ1)+ϵI=(c)l⋅E(ϵ1)E(Λ)+o(l),where (a) and (b) are given by
the definition and the fact that {ϵi∣1≤i<I} are of identical probability distributions
[32]; (c) is obtained
directly from (7), and the component ϵ1 can be replaced by the result in (6).
Therefore, Ξ also increases linearly with the
source-to-destination distance l.


## 4.4.1. Throughput

The maximal throughputΦ is decided by how many DATA packets can be
sent out from the source s to the destination d in a period of time, subject to the condition
that this time period is much larger than the packet traveling time. According
to previous analysis in Section 4.3.1, the probability of the completed DATA
transmission in an iteration is 1−e−λρΩ.
Therefore, the expected number of iterations initiated by s for one DATA packet is  1/(1−e−λρΩ),
and the associated time expectation is (LR/R+TS+TB)/(1−e−λρΩ)+(LC+LD+LA)/R.Given the DATA packet lengthLD,
the maximal throughput is thus obtained as(11)Φ=LD⋅R(LR+(TS+TB)⋅R)/(1−e−λρΩ)+LC+LD+LA.It is shown that the maximal throughputΦ can be independent of the
source-to-destination distance l.
It also increases monotonically with the node density λ,
approaching the limit decided by the radio data rate R and the overhead ratio.


## 4.4.2. Expected End-to-End Delay

The end-to-end delay is given by∑i=1Iτi.
The expected end-to-end delay ϒ is(12)ϒ=(a)E(∑i=1Iτi)=(b)[E(I)−1]⋅E(τ1)+τI=(c)l⋅LR+(TS+TB)⋅R+(LC+LD+LA)⋅(1−e−λρΩ)R⋅E(Λ)+o(l),where (a) is given by the
definition; (b) is due to the fact that {τi∣1≤i<I} are of identical probability distribution
[32]; and (c) is
obtained directly from (5) and (7).Therefore, the expected end-to-end delayϒ increases linearly with the
source-to-destination distance l.
It also decreases with the node density λ,
approaching a bounded limit.


## 4.4.3. Delay Variance

LetIc denote the number of the iterations with
completed DATA transmission, that is, the number of wireless hops, and let Iu denote the number of the iterations with
uncompleted DATA transmission. Ic and Iu are independent random variables, and I=Ic+Iu.
The delay variance Θ is calculated by the
following:(13)Θ=(a)σ2(∑i=1Iτi)=(b)σ2(Ic)⋅(LR+LC+LD+LAR+TS+TB)2⁢+σ2(Iu)⋅(LRR+TS+TB)2=(c)σ2(Ic)⋅[(LC+LD+LAR)2+2⋅(TS+TB+LRR)⋅LC+LD+LAR]+σ2(I)⋅(LRR+TS+TB)2=(d)l⋅σ2(Λ)E(Λ)3⋅{(1−e−λρΩ)2⋅[(LC+LD+LAR)2+2⋅(TS+TB+LRR)⋅LC+LD+LAR]+(LRR+TS+TB)2}−l⋅e−λρΩ⋅1−e−λρΩE(Λ)⋅[(LC+LD+LAR)2+2⋅(TS+TB+LRR)⋅LC+LD+LAR]+o(l),where (a) is given by the
definition; (b) is due to the analysis in Section 4.3.1, that is, the iterative delay under completed and uncompleted
transmissions respectively; (c) is due to the fact that σ2(I)=σ2(Ic)+σ2(Iu);
(d) is obtained from the result of σ2(I) in (8), as well as the σ2(Ic) derived in (A.4) of Appendix A.Therefore, the end-to-end delay varianceΘ increases linearly with the
source-to-destination distance l. Θ also diminishes to zero with the network
density λ,
since the component σ2(Λ) also decreases to zero with higher λ.


## 4.4.4. Network Energy Consumption

The expected
network energy consumption for one DATA packetΞ is(14)Ξ=(a)E(∑i=1Iϵi)=(b)[E(I)−1]⋅E(ϵ1)+ϵI=(c)l⋅E(ϵ1)E(Λ)+o(l),where (a) and (b) are given by
the definition and the fact that {ϵi∣1≤i<I} are of identical probability distributions
[32]; (c) is obtained
directly from (7), and the component ϵ1 can be replaced by the result in (6).
Therefore, Ξ also increases linearly with the
source-to-destination distance l.


## 4.5. Optimizations under QoS Constraints

Consider that the dataflow has certain QoS
requirements on throughput, expected end-to-end delay, and delay variance, for
example,Φ≥Φth, ϒ≤ϒth,
and Θ≤Θth.
Here, Φth, ϒth,
and Θth are the threshold constants representing those
QoS constraints, respectively. The optimizations aim to minimize the resource
consumption, subject to these QoS constraints.Two types of resource consumptions, including network
energy consumption and network capacity, are considered here, which lead to
different optimization formulations. As pointed out in Section4.2.4, these two formulations can be representing different networking
scenarios. In capacity limited networks, every node can have cabled power
supply. The number of nodes is therefore limited by engineering costs, and the
possible use of long-range radio also limits the available bandwidth. On the
other hand, in energy limited networks, the nodes can be powered by energy
scavenging, for example, solar cells. Therefore, the number of wireless nodes
can be large, which can also use short-range radio with vast unlicensed
bandwidth. These contribute to large network capacity. Other works with similar
considerations have been discussed in [33].


### 4.5.1. Capacity Limited Networks

The objective of the optimization is to minimize the
transmitting powerPt,
so as to limit the occupied geographic area of an unicast link. In accordance
with the results in [28], this approach can save the use of wireless network
capacity. Therefore, the optimization formulation is(15)minPtsubjectto:Φ≥Φth;ϒ≤ϒth;Θ≤Θth.


### 4.5.2. Energy Limited Networks

The objective of the optimization is to minimize the
expected network energy consumption per DATA packetΞ:(16)minΞsubjectto:Φ≥Φth;ϒ≤ϒth;Θ≤Θth.


### 4.5.3. Solutions and Traffic Priority

In order to
solve the optimizations in (15) and (16), the transmitting power Pt can be an ideal control knob (optimization
variable), for the resource allocation. Both (15) and (16) can be found as
convex optimization problems over Pt,
where efficient solutions are guaranteed [34].Specifically, as shown in (11), Φ monotonically increases with Pt,
since Ω (defined in (4)) monotonically increases with Pt,
provided by any realistic channel model f(⋅,⋅,⋅).
As shown in (12), ϒ monotonically decreases with Pt,
since E(Λ) monotonically increases with Pt (proved in Appendix B).  Θ also monotonically decreases with Pt in (13), since σ2(Λ) monotonically decreases with Pt (proved in Appendix B). Moreover, as shown in
(14), Ξ can be verified as a convex function of Pt,
where both E(ϵ1) and E(Λ) monotonically increase with Pt.
Due to the described monotonicity, the convexity of the optimizations in (15)
and (16) can then be obtained, over the control knob Pt.Therefore, we suggest that the transmitting powerPt can provide an effective control knob for the
tradeoff  between the resource consumptions and the real-time QoS requirements.
In fact, different levels of Pt can be configured for different classes of
traffics, for example, voice, video (streaming), or data, which then decide the
unicasting “priority”.Further investigation may also include the radio data
rateR,
so as to generate the problem of joint power and rate control. Unfortunately,
the convexity over R cannot be obtained for a general channel
propagation model f(⋅,⋅,⋅).
Future studies may address the problem on some specific models.


## 4.5.1. Capacity Limited Networks

The objective of the optimization is to minimize the
transmitting powerPt,
so as to limit the occupied geographic area of an unicast link. In accordance
with the results in [28], this approach can save the use of wireless network
capacity. Therefore, the optimization formulation is(15)minPtsubjectto:Φ≥Φth;ϒ≤ϒth;Θ≤Θth.


## 4.5.2. Energy Limited Networks

The objective of the optimization is to minimize the
expected network energy consumption per DATA packetΞ:(16)minΞsubjectto:Φ≥Φth;ϒ≤ϒth;Θ≤Θth.


## 4.5.3. Solutions and Traffic Priority

In order to
solve the optimizations in (15) and (16), the transmitting power Pt can be an ideal control knob (optimization
variable), for the resource allocation. Both (15) and (16) can be found as
convex optimization problems over Pt,
where efficient solutions are guaranteed [34].Specifically, as shown in (11), Φ monotonically increases with Pt,
since Ω (defined in (4)) monotonically increases with Pt,
provided by any realistic channel model f(⋅,⋅,⋅).
As shown in (12), ϒ monotonically decreases with Pt,
since E(Λ) monotonically increases with Pt (proved in Appendix B).  Θ also monotonically decreases with Pt in (13), since σ2(Λ) monotonically decreases with Pt (proved in Appendix B). Moreover, as shown in
(14), Ξ can be verified as a convex function of Pt,
where both E(ϵ1) and E(Λ) monotonically increase with Pt.
Due to the described monotonicity, the convexity of the optimizations in (15)
and (16) can then be obtained, over the control knob Pt.Therefore, we suggest that the transmitting powerPt can provide an effective control knob for the
tradeoff  between the resource consumptions and the real-time QoS requirements.
In fact, different levels of Pt can be configured for different classes of
traffics, for example, voice, video (streaming), or data, which then decide the
unicasting “priority”.Further investigation may also include the radio data
rateR,
so as to generate the problem of joint power and rate control. Unfortunately,
the convexity over R cannot be obtained for a general channel
propagation model f(⋅,⋅,⋅).
Future studies may address the problem on some specific models.


## 4.6. Summary

In summary, the analytical results indicate that all
the investigated real-time QoS metrics can improve with larger network scale.
In particular, the maximal throughputΦ increases with the network density λ to a predetermined bound, while the expected
end-to-end delay ϒ decreases with λ,
approaching a predetermined bound, as decided by other related parameters. On
the other hand, the delay variance Θ falls to zero with higher network density λ,
which indicates that the network performance can be made arbitrarily stable,
simply by dropping more nodes in the network. For supporting long-range
communications over a relatively large number of wireless hops, the analytical
results show that the maximal throughput Φ can be independent of the
source-to-destination distance, while both the expected delay ϒ and the delay variance Θ increase linearly with the
source-to-destination distance. Furthermore, it is identified that the radio
transmitting power Pt can be an ideal control knob for the tradeoff
between the real-time QoS requirements and the resource consumptions, for
example, energy consumption or network capacity.We consider that all these propositions could be
intuitively conceivable for large-scale wireless networks. Since the analytical
results are obtained under the long-range asymptotic conditionl→∞,
they may present the worst-case scenario analysis for practical considerations.
In the next section, the simulation results are also provided, showing how
these metrics converge.


## 5. Simulation Results

Some fixed parameters in the simulations are listed in
Table2. In particular, the radio transmission parameters are conforming to
the developed test-bed, while others, for example, power consumption and
channel model parameters, are typical for indoor short-range radios. For
example, under these parameters, the radio range is about 10–15 meters, when the transmitting power Pt is 1mW.Table 2
Parameters in
the simulations.
ParameterValueUnitρ0.2N/AR250 Kbits/secLR120bitLC, LA96bitLD1024bitTS250μsecTB750μsecPS, PR1mWPI100μWβ3N/AG−40dBN0−150dBm/HzB10dBα4N/AGiven the source and the destination nodes, separated
by the distancel,
random Poisson points are generated, for every iteration. The generation of the
Poisson points conforms to the density λ⋅ρ on the 2D plane, which represent the available
wireless nodes. 1000 DATA packets are then “sent out”
consecutively from the source to the destination, according to the described
real-time unicast module. The end-to-end delay instance of every DATA packet is
then recorded, from which the simulated end-to-end delay expectation and the
simulated delay variance are estimated by standard statistical methods. The
simulated throughput is also obtained, by dividing the data bulk size 1000⋅LD with the time consumption of sending out the 1000 DATA packets at the source. In the following
figures, we also compare the simulation results to the analytical results
side-by-side, where the lower-order terms, for example, o(l) or o(l),
are neglected in plotting the analytical results.Figures4, 5, and 6 show how the QoS metrics change
with the source-to-destination distance l,
where the node density λ is fixed at 0.1/m2.
Then Figures 7, 8, and 9 show how the QoS metrics change with the network
density λ,
where the source-to-destination l is fixed at 160m.
The number of wireless hops in the simulations can be up to 20. All the
obtained simulation results match well with the analytical results, as well as
the main propositions given in Section 4.6. Especially, Figures 4,
5, and 6 show that close-matching also exists in short-range unicasting,
although the analytical results were obtained under long-range asymptotic
approximation.Figure 4
Throughput
versus source-to-destination distancel (λ=0.1/m2).Figure 5
Expected delay
versus source-to-destination distancel (λ=0.1/m2).Figure 6
Delay variance
versus source-to-destination distancel (λ=0.1/m2).Figure 7
Throughput
versus network densityλ (l=160m).Figure 8
Expected delay
versus network densityλ (l=160m).Figure 9
Delay variance
versus network densityλ (l=160m).Moreover, Figure10 shows how the expected network
energy consumption per DATA packet changes with the transmitting power Pt,
which is observed as a convex function. It is also observed in Figure 10 that
the expected network energy consumption increases linearly with l,
and it decreases with λ in the simulation. These simulation results
conform to previous performance analysis.Figure 10
Network energy
consumption versus transmitting powerPt.


## 6. Experiment Results

In the test-bed (Figure11), the source and the
destination nodes are connected to a laptop computer for the purpose of
collecting experiment records. The wireless nodes are based on the cognitive
radio prototype (Figure 1), with a stack of two radio boards. The cognitive
radio can opportunistically access 3 data channels in 2.4 GHz band, as described in
Section 3.2, where each channel has an
air-interface data rate 250kbps as defined in IEEE 802.15.4 [26].Figure 11
A snapshot of
the test-bed.The real-time unicast module is implemented in the
cognitive radio prototype, with preconfigured address. The packet length
parameters, that is,LR, LC, LD, LA,
are about the same as those listed in Table 2. The node transmitting power is
however fixed at −15dBm.
The experiment results on throughput, end-to-end delay expectation, and delay
variance, are obtained by the following methods. (1) Throughput is calculated
at the source, where the laptop computer forwards 1000 DATA packets to the source node. Since the
source node accepts a new DATA packet from the computer only after the previous
one has been sent out, the computer can count the total time expenditure in
sending the 1000 DATA packets. The measured throughput is
obtained by dividing the bulk size with the time expenditure. (2) On receiving
a DATA packet, the destination also forwards the DATA packet to the laptop
computer, where the end-to-end delay instance of every DATA packet is
calculated at the computer by the difference between the packet departure and
arrival time. The measured end-to-end delay expectation and the delay variance
are then obtained by standard statistical methods. Since the operating system
running at the laptop computer (Windows XP Professional Edition) is by no means
real-time, we tried to minimize the computer running threads in the
experiments.The experiments were conducted in a standard office
environment, where external interferences in the utilized 2.4 GHz band can be
intensive, for example, from adjacent WLAN hot spots. Two sets of experiments
are illustrated in Figure12. In Set-I, the nodes are placed in a straight
line, such that the four configurations correspond approximately to one-hop to
four-hop communications. For example, in the second configuration of Set-I, the
node placement is such that the chance of direct transmission from s to d is small. In Set-II, more relay nodes are
added to every hop being illustrated in Figure 12. The purpose of the two-set
experiments is to compare how the designed unicast module can improve the
test-bed QoS performance. In fact, Set-I experiments can be comparable to
traditional wireless networking where a routing path is predetermined with best
available spectrum in every hop. However, in Set-II experiments, data is
forwarded from s to d opportunistically without any predetermined
path.Figure 12
Illustration of
the two sets of experiments.Figures13, 14, and 15 show the measurement results of
the two-set experiments on throughput, expected end-to-end delay, and delay
variance, respectively. Evidently, the results of Set-II are strictly better
than those of Set-I, beyond the first configuration. In Figure 13, the
throughput of Set-I is reduced by more than 50% from the first to the second configuration,
that is, from one-hop to two-hop, due to the impact of half-duplex radios. A
comparable reduction of throughput is not observed in Set-II. In general, the
throughput of Set-II changes smoothly with different configurations (number of
wireless hops), where the limited reduction can be due to the limited number of
nodes. In Figures 14 and 15, it is further observed that the expected
end-to-end delay and the delay variance increase linearly with the number of
hops (configuration index) in Set-II experiments; whereas they tend to increase
much faster in Set-I experiments.Figure 13
Measurement
results on the throughput.Figure 14
Measurement
results on the expected end-to-end packet delay.Figure 15
Measurement
results on the packet delay variance.


## 7. Conclusions

In the paper, we have implemented a real-time unicast
module in the context of large-scale cognitive wireless networking. By
opportunistically using both spectrum bandwidth and wireless nodes/radio
availability, the most significant result is that the network performance can
improve with larger network scale. Specifically, it is shown that the
performance dynamics, that is, indicated by dataflow end-to-end delay variance,
can fall to zero with higher network density. Furthermore, additional results
show that dataflow throughput can be independent of the number of wireless hops
or the source-to-destination distance, whereas end-to-end delay expectation and
delay variance increase linearly. The obtained analytical, simulation, and
experiment results support these propositions. It is also identified that node
transmitting power can be an effective control knob, for the tradeoff between
the real-time QoS performance metrics and resource consumptions. We suggest
that the presented research could contribute to the development of diverse
commercial and scientific applications with large-scale wireless networking.



---

*Source: 586067-2008-12-22.xml*